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SAT

The SAT is one of the exams many high school students take so that scouting colleges can see which students may or may not fit in with the rest of their student body.  The test scores range on a scale from 600 to a 2400, which is equivalent to a 36 on the ACT.  It is a test that many colleges require their applicant to have taken, unless the Act has been taken.  Some colleges will accept the ACT as a substitute, but many colleges in the east prefer to see SAT scores.

What is the SAT?

The SAT is a test that was developed and is administered by the College Board, which a non-profit organization in the United States.  The SAT was originally introduced as the Scholastic Aptitude Test, but the name was later changed to the Scholastic Assessment Test.  Today, ironically enough, it does not stand for anything; it is an empty acronym.  The current test that is used today was introduced in 2005, when there was a written portion that was added to the exam.  The added writing now makes the test a 3 hour and 45 minute ordeal, and it costs about $50 to take the test in the United States.

It is an exam that shows the test-takers ability to apply skills that he or she has learned in a classroom setting.  Most students take the test more than once in hopes of improving their skills, because the average student will get a higher score the second time because he or she will now know what to expect. 

Some colleges, such as Harvard and Yale, require their applicants to take subject tests.  Subject tests are tests that further test you on specific subjects so that colleges can help with course placement and advise you about what courses you select to take.  There are over 20 different subjects you can choose from, and the section is just added to your test. 

What does the SAT consist of?

The SAT consists of three 800 point sections: Mathematics, Critical Reading, and Writing.  Each section is scored from 200-800 points, so you get 600 points simply for showing up and trying, although you may want to study and shoot for a better score than a 600.  The average SAT score is about 1500, but many schools have a low acceptance rate, so it is good to make sure you get in plenty of studying.

Of the three separate sections, the Writing section is the one that most people struggle with.  According to satscores.us, there was a study done in 2008 that showed that the average scores for the three different sections were as follows:

Mathematics:  515
Critical Reading:  502
Writing:  494

Each of the three major sections, Mathematics, Critical Reading, and Writing, are divided into three parts, with 10 sub-sections.  There is also an additional experimental section that is an additional 25 minutes; this section can be in any one of the three different sections.  This experimental section is not counted toward your own score.  It is simply to help normalize questions for future administrations of the SAT.  Here is some more in-depth information about each of the separate major sections:

Mathematics [3]

  • It is commonly known as the “Quantitative Section” or “Calculation Section.”  It consists of three different scored sections.  It is broken down, timewise, into two 25 minute sections and one 20 minute section
  • One of the 25 minute sections is all multiple choice, and it consists of 20 questions
  • The other one of the 25 minute sections has 10 write-on questions and 8 multiple choice questions.  The 10 write-on questions don’t have a penalty for guessing, because there aren’t any limits to the guessing
  • The 20 minute section consists of 16 questions, and they are all multiple choice

Critical Reading [4]

  • The Critical Reading section is also made up of two 25 minute sections and a 20 minute section
  • There are questions that range from finishing passages to questions about sentence structure and lengthy passages
  • The majority of the Critical Reading section is made up of passages that students read and then there are several questions that will follow.  The time restraints keep the students from being able to reread passages, which allows colleges to see what students can deduce from information that they have likely only been able to read once
  • Generally, during the Critical Reading section, questions at the beginning of the section are easier and questions at the end of it are harder

Writing [5]

  • Many people think that it is simply an essay, but the Writing section of the SAT also includes a few multiple choice questions
  • This is the newest section in the SAT; it was introduced in 2005
  • Most of the multiple choice questions are questions about grammar and sentence structure; the questions ask you to identify errors
  • All essay portions are responses to prompts that are given to the students.  There is no required structure given

SAT Test Preparation Tips and Strategies

Take it more than once!  This is, by far, what will improve your score the most.  Many students go into the test “cold turkey,” without having studied at all.  It is easiest to get a feel for the exam when you have taken it before.  After having taken it once, take practice tests and study with other people that need to take the test.  There are many SAT practice manuals that have tests that are very similar to the actual exam.

Also, be sure you familiarize yourself with all of the materials that you are allowed to use on the exam.  For instance, many sections in the Mathematics section allow you to use a calculator.  Be sure to familiarize yourself with the calculator that you plan to use on the exam so that you can do problems quickly.  The more you practice, the quicker you will be able to do the problems.  Because the SAT is a timed test, it is very important to be able to think quickly.

About the SAT Exam

Below is some useful information about the SAT exam; SAT test dates, SAT fees, and the SAT test content, format, and length.

2011 SAT Test Dates

Test Date Tests Offered Regular Registration Closes Late Registration Closes SAT Fees/Late Reg
October 1, 2011 [6] SAT and Subject Tests September 9, 2011 September 21, 2011 $49/Late $75
November 5, 2011 [6] SAT and Subject Tests October 7, 2011 October 21, 2011 $49/Late $75
December 3, 2011 [6] SAT and Subject Tests November 8, 2011 November 20, 2011 $49/Late $75

 

2012 SAT Test Dates

Test Date Tests Offered Regular Registration Closes Late Registration Closes SAT Fees/Late Reg
January 28, 2012 [7] SAT and Subject Tests December 30, 2011 January 13, 2012 $49/Late $75
March 10, 2012 [7] SAT and Subject Tests February 10, 2012 February 24, 2012 $49/Late $75
May 5, 2012 [7] SAT and Subject Tests April 6, 2012 April 20, 2012 $49/Late $75
June 2, 2012 [7] SAT and Subject Tests May 8, 2012 May 22, 2012 $49/Late $75

 

SAT Calculator Policy, Programs and Tips

The SAT is a time honored tradition that just about every high school student must experience before moving on in their educational career. The math portion of the test is a source of much anxiety and frustration for many people, especially if the science does not come naturally to them. Fortunately, the powers-that-be allow students to use an SAT calculator on that portion of the exam.

SAT Calculator Policy

The following are calculators allowed on SAT exams:

  • Four Function Calculators
  • Graphing Calculators
  • Scientific Calculators

The following calculators are banned from the exam:

  • Calculators with QWERTY keyboards
  • Laptops, Tablets, or Electron Writing Pads
  • Pocket Organizers
  • Calculators with paper tape
  • Any calculator that requires a power outlet
  • Any calculator that makes noise

SAT Calculator Programs

Most scientific and graphing calculators allow you to program formulas into the unit so that you don’t have to continuously type them in again and again. This will both save you time and reduce the chances of making a mistake when entering formulas. Your calculator’s documentation should outline exactly how to enter and save these types of programs.

Here are a few common formulas you may want to program into your unit:

  • Quadratic Equation Solver
  • Area of a Triangle using 3 sides
  • Distance between 2 points
  • Midpoint
  • Sum of “X” consecutive integers
  • Sphere
  • Cone
  • Area of an Equilateral Triangle using Altitude

SAT Calculator Tips

Everyone who has asked if you can use a calculator on the SAT needs to remember a few things. Just because a SAT calculator is allowed on the exam does not mean you can rely on it. Using the calculator can waste precious time if you don’t know how to use it properly. Below are a few tips you may want to follow to get the best use out of your SAT calculator:

  • Bring extra batteries! You will not be able to use the SAT calculator programs that you spent time entering into your unit if you run out of batteries! The SAT calculator policy states that you cannot use a calculator that requires an electrical plug, so make sure you bring extra batteries with you to the exam.
  • Use the calculator sparingly. The SAT exam is designed in such a way that you do not need a calculator for any of the math questions. Try to only use your SAT calculator on questions you get stuck on.
  • Know how it works! You should take the time before hand to know everything about your calculator. Make sure you are an expert on how to use all of your programs and all of the on-board functions of your particular unit.

If you have ever asked “Can you use a calculator on the SAT,” the answer is YES! By following the simple tips in this article you will be able to use your SAT calculator to its maximum potential. Don’t get stuck on the day of the SAT without knowing how your calculator works. Be proactive!

 

SAT Scores Weight in College Admissions

There are a lot of ways that colleges decide who gets to walk through their doors to become a student, but one of the most important is the SAT score. These standardized tests are designed to be the barometer of academic potential, and the top institutions of higher learning demand a sizable SAT score for admission.

While of course colleges will take other factors into account in their admissions decisions, the role of the SAT score is still very important, and a poor SAT score will ruin many an application, especially in the more prestigious colleges.

It can be very difficult for colleges to make objective comparisons about extra curricular activities and other abstract qualities in prospective students. While extra curricular activities are important in the college admissions process, the SAT score gives colleges a concrete number to compare prospective students by. This means that SAT test scores are perhaps given more weight in admissions than standardized test scores would be in a more perfect world where colleges can more easily compare their prospective students.

It’s also important to remember that colleges will make their students average SAT scores public knowledge. It would be very hard for a college like Harvard or Yale to remain known as an “elite” Ivy League institution if people were made aware that they would accept students with mediocre SAT scores.

These two factors mean that many colleges are almost forced to give a lot of weight to SAT scores in their decisions, even if the admissions team personally feel (as many do) that SAT scores aren’t particularly important, or they aren’t a good indicator of academic potential.

However, a good SAT score won’t guarantee admission into any institution, even the ones that put the most emphasis on SAT scores in their admissions policy. You’ll have problems getting into the best institutions without a good GPA, even if you have a perfect SAT score.

Having a high SAT score and a low GPA can send college admissions people a terrible message. It makes you look intelligent, but lazy. The best colleges are absolutely terrified of taking on lazy students. Your academic potential isn’t just about your intelligence; it’s also about your work ethic.

You should also be aware that many colleges are looking for other qualities in their students. Showing leadership in extra curricular activities is very important, especially in Ivy League schools. An exceptionally strong display of leadership could even overcome a slightly weaker SAT score.

Of course, there are many institutions that have a firm policy of disregarding standardized testing. There are over 800 colleges that don’t even require you to provide your score in your application.  This number is growing each year, and many fairly prestigious colleges are beginning to publically declare their distrust of standardized testing in this manner.

Even though SAT scores remain an important way for colleges to determine your academic potential, having a low SAT score isn’t the end of the world, and having a high one doesn’t mean you can write your own ticket. There are many other factors at play.

SAT Test Format and Content

Test Length No. of Questions Possible Score Type of Material

Critical Reading [4]

  • 70 Minutes
  • 1x 20-minute section
  • 2x 25-minute sections

49 Passaged-based reading

Tests your reading comprehension. These questions include summarization questions, figurative language questions, vocabulary questions, inference/exended reasoning questions, interpretation questions, and compare and contrast questions.

800 Points Multiple-Choice

19 Sentence completion questions

Tests your vocabulary, semantics, and inference skills.

Math [3]

  • 70 Minutes
  • 1x 20-minute section
  • 2x 25-minute sections

44 Multiple choice

Basic arithmetic, algebra, and geometry.

800 Points Multiple-Choice

10 Student-produced responses

More arithmetic, algebra, and geometry.

Grid-ins

Writing [5] / Essay [8]

  • 60 Minutes
  • 1x 10-minute section
  • 2x 25-minute sections

25 Improving sentences

Tests your ability in grammar, sentence structure, word choice, and conventional written English.

560 Points Multiple-Choice

18 Identifying sentence errors

Tests your ability to spot subject-verb agreement errors, pronoun errors, sentence structure errors, and common misuses of language.

Multiple-Choice

6 Improving paragraphs

Tests your ability to correct subordination of ideas, correct coordination of idea, correct use of transition, unity of paragraphs, coherence of paragraphs.

240 Points Multiple-Choice

1 Essay

The SAT exams begins with a 25 minute essay. You'll be asked to present and support a point of view on a specific issue. This is not meant to be a final, well-refined version, but instead your first draft.

Written essay

 

The Importance of SAT scores

SAT ScoresSAT scores determine the eligibility of a student and would attract the attention of universities and colleges for you to enroll with them to pursue further studies. The perfect SAT score is actually a valuable asset for the students who seek scholarships and financial aid. 
 

Average SAT Score

 
Most of the scholarship and financial aid programs tend to be merit based programs and consider students who have excelled in the SAT and got good SAT score. However, students who did not put in hard labor end up with average SAT score and are not able to join the desired reputed colleges to pursue their studies. SAT scores are indeed important for the student as they determine the future course of their life. Hence, it is of utmost importance to study hard and get good SAT scores.
 

SAT scores provide financial rewards

 
SAT scores that are higher enjoy scholarship and financial benefits. With rising prices in educational studies, students are now trying to queue for the limited financial aid that is available to them. With so many applications to consider the people who decide on the students to get scholarships rely heavily on the SAT scores. With a perfect SAT score, you are likely to stand out of the crowd and be an automatic choice for financial aid. This is one reason why scores are given more importance these days. A good SAT score is achieved by the student who puts in the hard work and has determination, whereas the students who neglects tends to get average SAT score putting himself in a bad situation. However, proper guidance also determines on the achievement of SAT scores.
 

SAT scores credits

 
SAT scores offers invaluable and attractive metric that is considered by people who tend to award the scholarships. SAT scores are rather a standardized system for scoring. The student should also note that not all the scholarship programs are merit based however require good SAT score. The reason is that each of the colleges tends to have their own policy regarding the financial aid. Hence, the students’ are to carefully look at the policy governing the financial aid before applying for the college. The NACAC found that 4 out of 5 schools entirely relied on the perfect SAT score in determining the eligibility of the student and for financial aid. Students with average SAT score do not get a chance to enroll in good colleges. We can safely conclude that one of the most reliable tool still used are the SAT scores.
 

Raising SAT scores

 
SAT scores can be improved with proper guidance and effort. The student by selecting the right institute for getting SAT preparation can achieve good SAT score. The perfect SAT score is the one that gets the financial aid from the colleges, thus saving huge amount of tuition fees. Students with average SAT score do not stand a chance of joining good and reputed colleges. SAT scores are effective in deciding the students’ future course. By doing proper research, students can raise their SAT scores.

The Pros and Cons of SAT Preparation Methods

SAT, or the “SAT Standard Reasoning Test”, is a form of standardized testing used in the United States for college admission.  The colloquialism “SAT” used to stand for Scholastic Aptitude Test; later, it stood for Scholastic Assessment Test; today, the letters do not represent any particular arrangement of words.

For many individuals, gaining admission to college and acquiring a degree remains an important goal, improving self confidence, credibility and job prospects.  The SAT takes nearly 4 hours to complete.  The national fee to take the test ($49) is small, but the stakes which ride upon a high SAT score are high.  Prospective college students make use of different SAT preparation methods, such as online tutors, private tutors, review books and online courses.  This article will discuss the pros and cons of each of the aforementioned methods.

Private SAT Tutors

A private SAT tutor is an accredited individual that assists a college entrant in the preparatory study of material to help them achieve a high SAT score. 

Pros of private SAT tutors:

  • Accreditation.  A tutor that works with students in a designated location, in person, is likely to have the official certification for their position.
  •  “Face-to-face” time with the student, allowing the tutor to shape their teaching style and emphasis in a manner befitting the student's way of learning.
  • The ability to meet and interview individual tutors prior to choosing one  – something which cannot be done as easily with online tutors.

Cons of private SAT tutors:

  • Cost.  The hourly rate of a private tutor may be higher than that of their online counterparts – face-time and personal investment in a student is valuable, and the costs of a location and travel time are factors that can make private tutoring more expensive.
  • Set lesson times.  Unlike online tutoring services, students and private tutors must work within a more rigid schedule; it is not feasible for a tutor to travel to a student's home for one hour one week, and fifteen minutes the next, or to see a student in their own office for different lengths of time according to the student's needs.

Online SAT Tutors

Pros of online SAT tutors:

  • Convenience – to both the tutor and the student – of conversing remotely.  Neither party has to leave their respective office or residence.  This allows the student to remain flexible, engaging in extracurricular affairs. 
  • Online SAT tutors can help the student for shorter or longer periods of time, depending on their needs.  If the student's parents are involved, tutors will often converse with the parents and work with them to improve upon difficulties the student may be experiencing. 
  • In today's economic climate, the overall lower costs of an online tutor makes utilizing one a viable option for many individuals and families.

Cons of online SAT tutors:

  • The potential for a lower quality of teaching (which may vary in accordance with how low or high the fees are).
  •  A lack of “face-to-face” time, and consequently, diminished understanding of the student's weak points which are better recognized in person.
  • A greater potential for false accreditation (the tutor may be competent at their job, but not certified) than would be possible for an “offline” tutor.

SAT Review Books

An SAT review book is – as the name suggests – a volume of study material in book form designed to help students prepare to write the SAT Standard Reasoning Test and gain entrance into college.  This form of SAT preparation is accessible and very different than the last two methods discussed.

Pros of SAT Review Books:

  • Variety.  There are a number of review books from which the student can choose.  They range in price, length (and accordingly, heft and size), focus, style, presentation, online additions and number of workbooks.  This allows the student to choose which book best matches their manner of learning.
  • (Relative) portability.  For those students who learn best from books, this method allows them to study in a location of their choosing.
  • Silence.  Some individuals learn best with stimulation, such as speech; for those who learn  simply by reading, an SAT review book allows for quietly absorbing and assimilating the contents within.
  • Low cost.  Review books may be costly in comparison to other types of publications, but the financial outlay is one-time.

Cons of SAT Review Books:

  •  They demand the student's focus.  While focus is a trait that should be encouraged in students, a book can, should the student feel so compelled, simply be put down; if the student were face-to-face with a private tutor, that choice could not be made.
  • A lack of support from other individuals.  Though some SAT review books offer interactive extras such as DVDs or web-based features, the student must act as their own moral support unless realtime study help is enlisted.
  • Size.  Though, as mentioned above, a review book is relatively portable, emphasis is placed on the word “relatively” for a reason; some SAT review books are over 600 large-sized pages in length, with a weight to match.

Online SAT Courses

Online SAT courses combine aspects of review books and online tutors.  They are done on the student's own time, and on the internet.  An online SAT course is a web-based course that lets students prepare to write an SAT by studying material provided on account-based websites.

Pros of Online SAT Courses:

  • Anytime access.  This sort of accessibility allows students to peruse study material regardless of the constraints of their personal schedule.
  • Convenience.  A student can work their way through an online SAT course at their own pace, free of pressure to achieve understanding before they are ready.
  • Choice.  Students will find many courses to choose from, of varying depth, duration and cost.

Cons of Online SAT Courses

  • Cost.  As with the other SAT preparation methods discussed in this article, there is a fee to take an online course.  However, the cost is a one-time payment and within the realm of affordability for most.
  • No face-to-face with another person.  Since online courses are done on the student's own time, there is no interaction with anyone else; even using an online tutor provides the student with some – albeit, indirect – contact and support.  Online courses are best suited to those who work and learn well independently.
  • A lack of pencil-and-paper.  Because online SAT courses operate exclusively in the realm of screens and keyboards, students do not get practice writing essays by hand and filling in answers with a pencil, as they would during the real-life SAT.
  • A world of distractions.  Using an online tutor, a student may be tempted to “multitask” and browse other websites, but the likelihood of doing so is greatest when an online course – free of any interaction with another person – is used.  In addition, most online SAT courses must be completed within a predefined window of time (weeks or months).  An unfocused student may find this difficult.

There are many ways to study for an SAT.  Every method has its benefits and drawbacks.  The good news is that students can review the pros and cons of each one.  With such diverse choices, every student will find a way to study which best matches their schedule, budget and learning style.

Critical Reading

Reading Based Passage

Reading passages on the SAT are one of the hardest sections for some people because of the wide range of topics. From history to sociology to literature to science, there are many areas of knowledge used. Additionally, complex vocabulary can really make this section difficult for many people.

Reading Based Passages Facts

Here are some basic facts about the reading passages section of the SAT. 
  1. In total there are 48 separate reading based questions. Eight of them will be short reading passages, while the other 40 will be from longer passages. 
  2. The questions are divided into three sections. The first two are 24 or 25 questions with 25 minutes available to answer, while the last 18 or 19 questions must be completed in 20 minutes. 
  3. A double passage combination will be used for test takers to compare and contrast two passages of text. 
  4. Also, there may be individual passages that are not related at all. 
  5. Long passage questions are usually 60 to 90 lines and are connected to as few as six questions or as many as a dozen questions. 
  6. Long double passages may be 70 to 90 lines and contain 9 to 12 questions. 
  7. History, communication, science, economics, psychology, politics, and literature are some of the topics that may be used in passages. 
  8. There will only be one double long passage on the entire SAT. 
  9. There will be many different types of passages and questions used - some are meant to be extra confusing.

Excessive Use of Words

One theory that some have is that many SAT answers will either have too much or not enough information. Test makers will try to specifically pick tricky words that are close to the correct answer to fool the test taker. However, many times they will be very excessive with their use of the wrong answers, which can leave a pattern to see the correct answer easier.

Read for the Main Idea

Reading for the overall main idea - and NOT for every single detail - is the trick to getting a higher score on the longer SAT reading passages. Being able to skim and come away with the general idea will make it easier to get the correct answer in the allotted time available. Reading every detail is not needed in many cases and can slow down a test taker considerably. For example, a particularly confusing sentence may contain details that are not needed to solve the question correctly. However, by slowing down and concentrating on comprehending that idea, test takers can lose time needed to get the correct answer and score points, which is the main point for those who want a higher SAT score. 
 
Recording Ideas in Reading Based Passages
By recording the main idea into a terse and short statement, a test taker can make it easier to zero in on the correct answer choice more quickly. By being able to quickly summarize an entire passage into a few words, the answer is right around the corner in most cases. Some say the questions should be read first while others think the passage itself should be read first. Most of the time, it is better to start with the passage and then move to the questions, trying to get the general idea of the question - which contains the key for the answer.

Be an Active Reader

Being an active reader on the SAT is important as well. Being absent minded during any passage can leave out an important clue to the correct answer. By being an active reader and underlining words and passages, it is easier to grasp the point of the passage and answer the questions correctly. Learning to recognize unusual usages of the English language or even novel uses is important as these are sometimes used to trick test takers.

Pacing Reading Based Passages

The SAT short passages section should be completed in under three minutes - more quickly than the longer passage section. If over five minutes is spent on this section, there is a huge disadvantage on later, longer passages. Working quickly on the first two sections then moving to the more difficult sections is the best way to go.
 
For longer passes, there may be a super long single passage, a double passage, or two short individual passages. Having as much time left over as possible from the earlier section is the key to having enough time to handle any type of larger passage given. Most of the time should be spent on the longer, more difficult passages.
 
SAT Question Sequencing
 
While the easiest questions may come first, the last question will not necessarily be the most difficult question. A lot of the times, the most difficult question will be just after the five minute warning given. This is because students become more nervous with the verbal announcement that time is running out and there is a higher chance to get bogged down on a difficult question. 
 
By finding questions that are easiest and doing those first, it can leave a test taker with more time to answer other sections that may be more difficult. The compare and contrast questions are usually the biggest time killers and should be saved for later if they might cause problems for a test taker. 
 
Overall, having a game plan and knowing which types of questions a test taker is good and not good at can go a long way in improving the overall SAT score, especially on the critical reading section. 

The Double Passage

A double passage is one that will usually use comparison and contrast questions and is typically the hardest passage to score accurately. The best method is to read passage one and then immediately answer any questions that only deal with passage one. Then read passage two and do the same with the questions and answers. Finally, answering the comparison or contrast questions comes last. This can save quite a bit of time on this section.

Building Vocabulary

As mentioned earlier, building a large vocabulary is important for scoring high on this section of the SAT. From using vocabulary flash cards to reading more to studying lists of SAT related words, there are a lot of ways to prepare. Students should utilize as much time as they can for building their vocabulary weeks or months before taking the SAT.

When to Gamble - Guessing

Occasionally, guessing on a critical reading or critical writing question is a good idea. Most of the time if one or more answer choices can be eliminated, it is a good idea to guess. As the answer choices are eliminated the odds go up, of course. By using good judgement and pacing strategies, it is possible to use guessing to gradually increase the overall SAT score. However, skipping difficult questions - and just recognizing them - is also important for many reasons.

Sentence Completion

The critical reading section of the SAT has been trouble for students since the inception of the exam. Some would say it is the most difficult part of the exam when it comes to getting points - and a higher overall SAT score. There are ways for students to prepare themselves, however, to be better equipped to know what to expect - and how to respond - to various questions on the critical reading section of the SAT. 
 
Especially for sentence completions, being ready and prepared is important for getting a high score. The best way to do this is to improve vocabulary skills. This is a lot of work for just a few extra possible points, but it's one of the best strategies for doing well on the critical reading section of the SAT. 
 
There are other things that should be thought about and strategies to implement, but first here are some basic facts about the SAT sentence completion section. 

SAT Sentence Completion Facts

 

  1. In total, there will be nineteen questions split into three separate sections - 8 questions, 5 questions, and 6 questions. 
  2. The first two take place during a 25 minute session, whereas the last takes place in a separate 20 minute session. 
  3. The answer choices are not random and many words will appear over and over again to confuse students. 
  4. Paying attention to the exact sequence of a question is very important. 
  5. There will be single word and double word answer blanks available. 
  6. One quarter of a point is deducted for wrong answers, which means guessing is not a good idea here. 
  7. There are five difficulty levels of questions - one through five difficulty level. 

 

Follow the Sequence

Another aspect of the SAT sentence completion section to think about is the sequence of difficulty of the questions. Being able to recognize the pattern can help a test taker be able to better use the process of elimination to get the correct answers - and a higher overall SAT score.  
 
In general, the easier questions will appear first on the SAT, which means you can know which ones will take you less time to answer correctly. Having said that, the easier questions sometimes contain tricky language meant to trip up a test taker moving through them quickly. 
 
Second guessing can sometimes become a big problem when solving these types of problems on the SAT. With similar words as answer choices, it can be easy for a test taker to second guess themselves and end up with the wrong answer even though they know the correct answer. Never underestimate the effect of stress during taking of the test. 
 
For harder questions, sometimes the easy or obvious answer will be wrong because there are better answer choices available. Even so, sometimes the easy word on the harder questions seems like the right way to go. Students need to take special care during both the easy and hard questions on this section of the SAT.

Positive and Negative

Another technique for eliminating wrong answer choices on the SAT is to look for clues in the question as to what word best fits in the blank(s) provided. 
 
Example Problem
The queen was charitable, magnanimous, and _________________. 
Given the nature of the two first words "charitable" and "magnanimous," we may place a plus sign on top of the words to indicate that they are words that represent a positive.  Therefore, the next word should also be positive. Looking at the answer choices and marking them positive or negative can eliminate some answer choices from the line-up making getting the right answer easier and more probable. 
 
For this to work, it is important to have a very good vocabulary, of course, but it can be a means for many people to make even the hardest sentence completion questions easier on the SAT. 
 

How to Build Vocabulary

In order to build a bigger and larger and more impressive vocabulary, is not about memorizing long lists of words. The best way to build a vocabulary is to read and use the words in real situations so that they stick in the mind. This takes more time, but a very impressive vocabulary can be built up, which will help significantly with SAT scores.
 
Reading for Vocabulary
This is the basic way to increase vocabulary to get a better SAT score. This is, however, only one way that should be employed by students who want a richer vocabulary. 
 
Vocabulary Flash Cards
The other way to help increase a vocabulary is to use flash cards with words on one side and their definition and sample usage on the other side. The words should come from the SAT related word lists. Also, it is a good idea to only do 15 to 25 cards at a time to get the most benefit. 
 
It is important to realize that increasing a vocabulary isn't something that can be done all at once. However, building a vocabulary over time is very possible and can go a long way in helping someone achieve a higher score on the SAT. 

Looking for the Breadcrumbs

Another good idea for test takers is to look for "breadcrumbs" in the SAT sentence completion section. The questions will contain clues and "keywords" that should be highlighted. They should also be deemed positive or negative so that patterns can be more easily seen. The words are the keys to this section of the SAT, which is why a large vocabulary is so important.

Direction Changers

A trick used by SAT test makers is to change the direction of a question using a phrase. For example, a question may start with a negative observation, but using a subordinate clause change it so that the answer will be a positive factor.

Pacing Sentence Completion

Learning proper pacing for the SAT sentence completion section is very important for many reasons. There are nineteen questions, so it is a good idea to make sure enough time is present for all of them to be answered correctly. Knowing what amount of time to spend on each section is also crucial for getting the highest score possible.
 
What are good time measurements? 
The fastest test takers will get through the first eight questions in under two and a half minutes while the next fastest will usually take three and a half to four minutes to complete it. The best thing to do is not let any single question take more than 20 seconds at the very most, while still leaving time to check each answer to ensure accuracy.
 
Avoid Time Traps
An important thing to remember is that test takers will deliberately include time traps on this section of the SAT to get students bogged down on a single question, unable to maximize the number of points they receive. Never sacrifice too much time on any single question.

Keep Your Head in the Game

Keeping morale up during the SAT exam is important. This can be helped with endurance, discipline and preparation. Even the most prepared is bound to be surprised by something on the exam. However, keeping a clear head will not make this a huge problem at all. The ability of students to improvise during a time based test is one of the qualities being tested.
 
Being able to handle any problems or surprises that come up without losing confidence will help with a better overall score on the SAT. One question (or more) may be difficult, but concentrating on what is known and easier can help boost morale and keep a person headed down the road toward the end of the exam and a higher score.

The Final Questions

The last questions on the sentence completion section require a mastery of complex vocabulary skills. The only way to do well is to know a lot of words really well. The last questions are meant to be difficult and they will be. If a test taker can eliminate two or more choices, it may be a good idea to take the gamble for the points. However, it is wise to remember that a quarter point is taken away for each wrong answer while skipped questions neither give or take away points.

Math

Introduction

General Information and Strategies

SAT Math Difficulty

Some students worry about the math section of the SATs, but a high score is easy to achieve when the math section is understood for what it really is - a way to use a "universal language" (math) to find out more about the test taker. 

SATs are not based on your knowledge of math and other subjects. Rather, the SAT is more about how a person takes a test, which can reveal more about a person than a knowledge-based test. While there are a lot of math questions on the SAT, most of the problems are basic. 

Because math is a universal language taught in classrooms everywhere, it is a good way for the makers of the SAT to test various aspects of a person's abilities beyond simple memorization of facts and recital of information. 

The SAT tests how a person follow directions. It can be a good way to tell if people read carefully and actually comprehend the information they take in. The SAT can also show how well a person deals with stress and whether or not they can think with creativity. 

Critical thinking is the cornerstone of the modern education system, and the SAT is actually a carefully constructed way to test how well someone does with this necessary skill. Colleges and universities can use this information to make sure a student is a good fit with their learning institution. 

In actuality, the math portions of the SAT are usually based on 7th to 9th grade math. Even for those that are not good with numbers, it is simplicity itself to get a high math score on the SAT by knowing more about the actual test and testing process. And this is what colleges and universities are looking for in students - the ability to look at a problem and come up with the best answer possible. 

The people who make the tests are required to come up with questions that are "tricky" or "sneaky." They do this to make sure the test accurately finds people who are college material. In fact, students taking this test are expected to fit a certain bell curve. In order to stay employed, they need to make sure they create test questions that "trip up" certain students who do not read carefully and understand the instructions. 

SAT Bell Curve

The Bell Curve is a scale that is seen over and over in different situations. In the case of the SAT, it is graded with a score of 200 to 800 - a perfect score. The makers of the test expect some people to fail miserably, some people to do okay (the middle or top of the bell) and less people to do really well. 

When people who take the test do not fit the bell curve, it is a sign that the test is either too easy or too difficult, something that will not help a college or university attract the right type of students. Because of this, test makers strive to ensure the test results are a bell curve in most instances. 

SAT Bell Curve

The Bell Curve is a great method to reflect people who take the SAT. While some people will invariably fail miserably, there is another small group of individuals who will do really well at the SAT. Therefore, the test is designed so that most people will fall somewhere in the middle - between the 200 and 800 extremes. 

Because of this, questions are weighted differently on the exam to best reflect a bell curve. So, while a person may get 8 out of 9 questions in one section and go from 580 to 590, in another section getting 8 out of 9 questions may cause them to drop from 740 to 710 - a larger difference. 

Knowing this, a person taking the test for the first time should expect to fall more on the left end of the bell curve. However, with practice and experience, it is easy to increase SAT scores quite dramatically. 

What is a Good SAT Score?

A high score on the SAT is important for many different reasons. Scoring a 200 will make it difficult to get in most colleges - even state colleges - while an SAT score of 800 does indeed open more doors and can lead to more opportunities in life. For some a score in the low 500s is enough, but for others striving for perfection is a necessity. 

Either way, studying and preparing for the SAT can increase the chances of a high score quite dramatically. By preparing and learning how to study for the SAT, students can increase their score to accurately reflect their mental abilities. Another aspect to consider is career possibilities. For example, someone wanting to be a novelist or journalist will want to score higher on the English section of the SAT while the math portion may not be as important. 

However, with any career choice that is made, a high SAT course can open doors to many universities that can really expand and improve a person's life. Educational opportunities are treasures to be won. Getting a high score on the SAT through preparation can be a way to increase the odds of having a great college experience. 

 

The Facts

Are There a Lot of  Math Questions on the SAT?

The SAT math section is split into three sections. In total, there will be 54 math questions that are graded. There is one section of multiple choice questions (25 minutes), one section of multiple choice and grid-ins (25 minutes) and a final section of multiple choice that is 20 minutes. 

How SAT Questions are Arranged 

When taking the SAT math test, it is important to know that the questions go from easier questions to the more difficult ones. For example, on the 25 minute multiple choice section, the first 7 or 8 questions will be very easy while the rest will get progressively more difficult. Smart test takers use this knowledge to their advantage when taking the SAT. The second section with grid-ins is a little different, with questions one to three the easiest while the next four will be slightly harder and the last two will be the hardest. The cycle then starts over with 3 easy questions. 

Number of Math Sections on the SAT

When taking the SAT math section, it should be noted that there is always a section that is secret until the day of your test. Whether it is Math, Critical Reading, or a Writing test, you will not know beforehand. Because of this, it is crucial to make sure you study for all sections of the test as if they would definitely be on the test. 

The good news about this extra section is that it will not count toward the final score. When taking practice SAT tests it may be noticed that they are missing this experimental or variable section in the test. Additionally, if someone does really poorly on a section, there is a chance that it will be the variable section that does not count toward the final score. 

Math Concepts Tested With the SAT?

The math used in the SAT is average 7th to 9th grade math. It consists of arithmetic (numbers), algebra (variables), basic geometry (shapes and graphs), statistics (charts and data) and other questions like logic or sequencing questions. This means there is no trigonometry, calculus or advanced geometry on the SAT math test. This is great news for those who are studying for the math SAT because they can concentrate on just those math concepts that will be on the test, which are easier than some of the more advanced math equations out there. Additionally, it is important to remember that on the SAT sometimes it is more about following directions more than getting the right answer. 

Points for SAT Math Questions?

Every correct question is worth 1 full point while incorrect answers are worth ¼ (.25 of a point.) Each wrong answer will bring down your raw score (from 200 to 800) while skipping a question will not increase or decrease your SAT math score. 

Guessing and Pacing

The first thing to realize is that SAT math is not the same as the math you learned in school. They are the same, of course, but people taking the SAT math section need to realize that it is more about the way the questions are asked on the SAT. Here are some things to consider before taking the math section of the SAT. 

SAT Math: What Works for You?

When it comes to solving math problems, there is more than one way to come to the same (correct) answer. The important thing to remember for test takers is that they should use whatever works best for them. For those who haven't yet gotten an 800 on the math section of the SAT, we will have some tips and techniques to help ace the math portion of the SAT. By studying and learning from the advice we give as well as using our practice tests, a person can radically increase their score on the math part of the SAT. 

It should be noted that the techniques we give you may not work well for school assignments where the teacher wants to know if a student understands the whole process of getting to a particular answer. Having said that, when taking the SAT math section, it is all about getting the correct answer no matter how you get there. This is good news for those who know shortcuts that can give them math answers quickly so they can finish the entire test - and ace it as well. 

To achieve the highest score, the trick is to NOT answer all of the questions on the test. Instead, a person should only answer those questions they absolutely know they are going to get correct. This may not always be possible, but by using good judgement, a person should be able to pick out which answers they feel most confident about on a test. 

For example, if there's a question that is extremely difficult, it may be better to skip it rather than take the time to try to figure it out. The time taken to solve the unfamiliar problem could be better spent answering easier questions for a guaranteed full point at the end of the test. Having said that, once you finish the other questions, it makes sense to go back to any questions you skipped if you have the time left. Then again, if you find trouble with a problem and do not understand it completely, it is better to skip it rather than guess and try to answer it. 

Pacing on the SAT Math Section

Another important aspect of taking the SAT math portion that should be considered is pacing. For example, no more than one third of the time given should be taken on the easy questions while a third of the time is used to try to solve the medium and hard questions on the test. 

While these divisions of time are good for some, the exact amount of time spent on each section will vary from student to student. For those who have tested around 600 and do not think they can do much better, it may be possible to skip the hardest questions on the test in order to get the highest score possible. 

Instead of spending time on problems that are not understood, the time is better spent reviewing other answers to make sure they are correct, which can help the overall final score of the SAT math section. If the concept or question is totally understood it is okay to answer the tougher questions, but even those who have tested over 600 should be careful when taking the math portion of the SAT. 

While skipping some difficult questions is a good idea, it is important for a test taker to keep up with how many questions have been skipped. Taking a look at the test paper bubble sheet can give a person a good idea of how many questions have been skipped. When getting to the end of the test, it may sometimes be worth it to go back and try skipped questions again, but knowing whether or not this is a good idea is most important. 

SAT Math Section: Should You Guess on the Test?

This is a question that many people who are about to take the SAT ask. The answer depends on the person taking the test, of course, but there are some general rules that apply. 

  • Elimination - If one or more answer choices can be eliminated for certain, it is usually a good idea to take a guess. The chances are that your score will slowly go up. A pure guess has a one in five chance of resulting in a full point on the test while if you eliminate two answers, the chance of getting the right answer goes up to one in three. 
  • Pacing - For those who adequately pace themselves during the test, taking the time to go back and guess on an answer if some options can be eliminated is easier and may result in a higher overall SAT score. 
  • Really Tough Questions - Some questions may be hard to understand or about concepts that are not known about. In these cases, it is usually a very good idea to skip the question entirely rather than try to guess the answer. 

 

 

Avoiding Mistakes

One of the biggest problems with people taking the SAT math portion is careless mistakes. Even smart students who study sometimes make careless mistakes that cost them points on their overall SAT score. It is important to remember that the SAT is more about testing the way you take tests rather than how much knowledge you have. To do this, the SAT test makers use tricky questions to try to get students to score lower. 

Some common careless mistakes include not ordering operations correctly, assumptions about a number (like whether or not it is a prime number), or even something simple like forgetting a negative sign in front of a final answer. Other common SAT math mistakes include subtracting instead of adding or solving a problem for the wrong variable. Because SAT math questions are random, it can be difficult to notice when you are consistently making careless mistakes. 

It should be noted that the wrong answers are not just random answers. They are usually created to intentionally trip up or confuse people taking the test. In fact, a lot of the wrong answers may seem correct depending on how a person interprets the question being asked. SAT test makers have been doing this for years to great effect. Over the years, they have learned common mistakes that people make and intentionally offer answer choices that are close but not correct. 

The problem with making careless mistakes on the SAT is that a person could be making them and think they are doing well when in actuality they are going to get a low overall score on the SAT math section. Because of this, it is important to read questions carefully and know exactly what they want as an answer. The best advice to overcome this is to be careful when taking the SAT math portion and know the test makers are out to trick you. 

SAT Rules & Tips

Below are some tips and techniques to help prevent careless mistakes when taking the math portion of the SAT.  None of these rules are set in stone, but they make a good foundation for anyone who is serious about getting a higher score on the math section of the SAT. 

  • Read Slowly - Reading the questions slowly and carefully will help make sure the question is understood completely. Sometimes, a single word change can make the entire question different. Because of this, the slower a person reads the more they are able to comprehend what is actually being asked in the question. This increases the chance of a person getting the correct answer to the SAT math question. 
  • Know When to Solve and When to Skip - Knowing whether or not a problem is easily solvable is important for those who want to score high on the SAT math section. For problems that are easy to solve - even if they are complex - a person should jump into the question and solve it. However, if the equation isn't known or the question isn't totally understood, it's probably better to skip it at first. Knowing the difference is important for those who want to get the highest score possible on the SAT math section. 
  • About 10 Seconds - If it takes less than around ten seconds to solve a complex math question on the SAT, chances are the answer is wrong. Easy questions on the SAT are easy and difficult ones are extremely hard. If it does not seem difficult, a person may be answering the question incorrectly. It is also important to remember that test makers intentionally try to make difficult questions seem easy so that students who do not read carefully and comprehend fall for a wrong answer. If it seems too easy and is not supposed to be easy, there is probably some trickery going on and it is recommended to read the remainder of the question. 
  • Read it Again - Questions should be read twice before they are answered. This is because the people who make the SAT test like to give a series of steps then throw a curve ball and ask something entirely different. For those who do not read the entire question carefully, the chances are high that the wrong answer will be chosen. 
  • Write it Down - One important thing that a lot of people forget when taking the math portion of the SAT is to write their work down. Doing this can help you make sure the math is being done correctly. This may seem like a very simple step - and it is - but employing this practice can dramatically increase the chances of getting an answer correct. Additionally, having the problem written down allows a person to go back and double check the work more easily. All of this adds up to help for the SAT math section. 
  • Calculators Help - Because calculators are allowed, a calculator should be used instead of doing math mentally. This can help increase the chances you are going to get the correct answer. While some people may be impressed by those who can crunch large numbers in their mind easily, the fact is that the SAT math test is all about getting the right answer, not showing off "rain man" math skills. This is why having a calculator and using it even for simple arithmetic is important. 
  • Idiots are Wise - While some people with superior math skills may think that using a calculator makes a person less intelligent or mentally adept, the truth is that using the calculator is actually the smarter choice when dealing with the math section of the SAT. There are no witnesses when taking the test so showing off mental math abilities does not make sense at all. Using a calculator may seem like something that is not needed, but when it comes to the SAT math portion, it is a wise choice indeed. 
  • About Guessing - On the multiple choice math sections of the SAT, the general rule is that if one or more answers can be definitely removed as possibilities, it may be a good idea to take a guess depending on the odds. For the easier questions on the beginning of the test this is the case even more. When no options can be eliminated, however, it is a good idea to skip the question rather than try to answer it. 

Why are all these tips important? When taking the SAT it is easy to become confused and make a simple mistake. From stress to nervousness there are a lot of feelings at play when taking the SAT - even for those who seem calm, cool and collected on the outside. Because of this, simple mistakes like adding instead of subtracting or forgetting a negative sign can be easily made even by the most careful people. This is why taking the time to prepare for the SAT math section is so important for those who want to do as best as they can. Remember that sometimes it is not about getting a perfect 800, but each person getting the best possible score that they can. This is what makes the SAT such a useful and frustrating test. 

 

 

Calculators

As was previously mentioned, using a calculator is a key component to getting the highest score possible on the math section of the SAT. Because of its importance when taking the SAT, it is a good idea to become familiar with using it. The easiest way to do this is to use it often for the weeks leading up to the test. The more a calculator is used, the more comfortable and easy to use it will become for a person. For example, the location of the + and * buttons should be noted carefully so that one is not pressed instead of the other, which can offer up quite a different answer, but more importantly a wrong answer which will lower your overall score. 

There are advanced functions like square root, cube root and parentheses that are needed. However, it should be noted that a graphing calculator is not needed, although they are allowed when taking the test. Also important to note is that batteries are usually taken out of a calculator to clear the memory before a test is taken so that there is no cheating when taking the test. 

Another thing that is important to remember when using a calculator for the SAT math section is that hitting the wrong button - a 5 instead of a 6 for instance - is common. Because of this, it is a good idea to enter numbers slowly and double check them. Being familiar with the calculator being used helps make this easier and quicker, which is important when taking a timed test. For those that do use a graphing calculator, it is recommended to not clear the screen but keep old work around so that it can be referred to if needed when double checking work at the end of the test if there is time. 

The last thing to take note of when using a calculator with the math portion of the SAT test is that most only display around 10 digits. However, on the SAT test, most answers are only three or four digits long. When this happens, it is important to read the question carefully to see whether the answer is meant to be rounded up. Additionally, a person should never round up when not specifically instructed to do so in the text of the question. As always, it should be noted that the makers of the SAT math test intentionally try to trick the person taking the test and this is one way in which they routinely do it. 

Using a calculator during the SAT math portion makes it a little easier, but there are also pitfalls that should be avoided. By knowing what they are and working to avoid them, a person can really increase their overall math score on the SAT. From becoming familiar with the calculator to using it slowly and carefully, there are a lot of actions that can be taken to increase the odds of getting a high score on the math section of the SAT. 

 

Special Rules for Grid-Ins

For those not familiar with the grid-in section of the SAT math section, they are questions in which an answer is put into the bubble. These are the rules from the SAT math test so that you can become familiar with them. We are going to add our opinions on them in parentheses.   

Rules for Grid-ins on the SAT Math Section

  • Mark no more than one circle in any column. (This is important to understand and comprehend fully.) 
  • You will only receive credit if the circles are correctly filled in. (Because of this, a person should take their time and make sure the circles are filled in appropriately.) 
  • Answers can be gridded in any position if they are shorter than the columns provided (For example, a person can start their answers in any column provided.)
  • It is not required to write your answer in the boxes provided at the top, but it is suggested. (When something is suggested, it is usually a good idea to follow the advice and that is the case in this situation.)
  • Some problems can have more than one correct answer.  If so, pick only one to grid in. (Knowing the right answer is important, of course, but following directions and only filling in one grid is even more important.)
  • Answers cannot be negative (This is a key clue that should save some people a long time if a negative answer comes up.) 
  • Mixed numbers must be gridded as improper fractions (Understanding fractions - basic math - is important for those taking the SAT. Brushing up on fractions is a good idea for those who never had math as a strong area of knowledge.) 

 

There are other rules about decimals and rounding up or down that should be followed closely as well. The good thing about grid-ins on the SAT math section is that they do not cause a person to lose points for wrong answers. Because of this, grid-ins should always be answered. After doing the work, even if the answer is not 100% definitely correct, it is a good idea to take the chance and guess with a grid-in. 

Here are some other things to take into consideration when taking the math section of the SAT. It should be noted that these are tips the test makers DO NOT want people to know about. 

  • Zero - Marking an answer 0.4 instead of .4 will be considered wrong, which is an important thing to note when answering grid-in questions on the math section of the SAT. 
  • Far Left First - Answers should ALWAYS be started in the far left column. This is not something required by the test, but it forces a person to carry out decimals as far as possible. Additionally, it can help a person stop from putting the 0 in front of a decimal, which would make an answer incorrect and worth no points. 
  • Fractions - When it comes to fractions on the grid-in sections of the SAT math portion, it should be noted that they do NOT need to be reduced. Additionally, decimal or fraction form is acceptable when giving a grid-in answer. Because of this, time spent not reducing a fraction down can be spent answering other questions and increasing the overall score. 
  • It Should Fit - When filling in a grid-in answer, it is vital that the answer fit in the number of spaces provided. Because of this, really large numbers that do not fit in the given amount of spaces cannot be correct. 
  • Use Boxes First - Before bubbling the answers, the boxes should be filled out first. This is because careless mistakes are common when taking the math portion of the SAT. Anything written in the boxes does not count for an answer, so it is a good way to make sure an answer that is bubbled is done so correctly. 

Additional Grid-in Tricks:

Here are some other things to note when taking the grid-ins on the math section of the SAT.

  • No Negatives or Symbols - Negative numbers and math symbols are never used as grid-in answers. Knowing this can help a person know whether or not their answer is even close to being correct. For example, some questions may ask a person to disregard the percentage symbol when writing an answer. So, an answer that is 15% should be written in as 15 and not .15. This is a common mistake that many people make when taking the grid-ins section of the SAT. 
  • Decimals not Fractions - Sometimes a test question will be given that has an answer in fraction form that will not fit into the bubbles. In these cases, the number should be switched to decimal form in order to fit on the grid-in bubbles. This is another way that test makers try to trick people taking the math section of the SAT so the bell curve is followed when people take the test. 

Overall Rule for Grid In Sections 

The most important thing a test taker can do is trust themselves when they do the work required to get an answer and are confident that it is correct. Frequently, people taking the SAT math section will second guess themselves out of nervousness or frustration and end up getting a lower score than they actually could get. Because of this, it is important for a person to trust their gut when answering questions on the math section of the SAT. Additionally, as mentioned, the fact no points are lost with a wrong answer on the grid-ins section means that a person should guess as long as they can make an educated guess about the correct answer. This is the single most important factor about improving a math score on the SAT. 

 

Tips for the Day of the SAT Math Test

Preparing for the actual day of the test is important for those who want to do well on the SAT. One of the biggest factors that most people face when taking the SAT math portion is the actual stress before the test even starts. Learning how to recognize and deal with this pre-test stress is an important part of getting a great score on the SAT math section. The test makers know they have stress working for them which makes their tricky questions even trickier. 

From panic attacks to hormones getting out of whack, there are a lot of ways physical aspects of the body can cause a person to get a lower score than they normally would when taking the SAT under the best of conditions. Because of this, learning how to deal with stress before the test is a great way to increase the overall score. While a lot of stress is because of physical things that are out of the control of most people, there are techniques and tips that can help. Beyond studying and prepping for taking the SAT, we have some additional tips to help students deal with stress. 

Checklist for SAT Math Test 

  • Don't Panic - Staying calm is of utmost importance when taking the SAT. Knowing when to skip a problem instead of starting to sweat over it is important for keeping a person's overall stress level down. Staying calm, cool and collected during the test enables a person to make sure they don't make careless mistakes, which are quite common when dealing with the SAT questions. 
  • Do NOT Cram - Cramming the night before - instead of getting rest and sleep - can do more harm than good. While this may not seem correct, enough studies have been done to show that getting enough rest and not cramming the night before can actually help a person improve their SAT score. Because of this, it is important for a person to get their mind off the test the night before. Whether this means watching movies or playing video games or reading, something should be done to not think about the SAT and the test the next day. Having said that, going to get and getting a good night of sleep is important. 
  • Get Good Sleep - As mentioned, making sure a person gets a full night of uninterrupted sleep is important when taking the SAT. Because the test makers try to trick those taking the test, those who are half-asleep or not well rested will be more prone to making mistakes. While getting enough sleep is important for many reasons, the next tip is also crucial for those who want to do the best they can on the SAT math section. 
  • Get Up Early - If a person wakes up less than an hour before the test and rushes to take it, there is a good chance they will make simple mistakes that could be avoided. A person needs to make sure they give their mind enough time to "wake up" in the morning so that they are at their best when taking the test. This tip goes along with the next one as well - eating right. 
  • Have a Good Meal - Eating a good, healthy meal - and having enough time to eat it and enjoy it - can go a long way in helping make sure a person is calm and able to take the SAT test to the best of their ability. Another good idea is to bring a snack to the test. During a break, a boost can be just what a person needs to be more mentally alert when answering questions that were designed to be confusing. An energy bar can be a great way to get a boost during a break on the test. 
  • Utilize Breaks Given - While some may think that not taking a break is a good idea, there are many ways that taking a break from a test can help a person do better. While breaks may seem like a short amount of time, it can be just what a body and mind needs to energize and prepare for the next section of the test, whatever it might be. Learning how to stay calm and relax during a break is also important. 
  • Prepare the Night Before - From pencils to calculator to what is going to be worn the day of the test to what is going to be had for breakfast, the more a person prepares for a test the night before. By doing this, a person can make sure they have very little to stress out about the day of the test. This can go a long way in helping them prepare mentally for the grueling work ahead. 

Getting a high score on the SAT math section is not easy and takes everything for a person to do well. 

 

 

 

 

 

Basic Math Concepts

SAT Math Used to Trick Test Takers

While the actual level of math utilized in the SAT math section is not that difficult, there are ways that test makers use math to try to trick test takers. This battle between the makers and takers of the test has been going on since SATs first appeared on the scene. By knowing what tricks and traps to look out for a person can dramatically increase their chance of getting a good score on the math section of the SAT.  The first thing to remember is that the easy questions are meant to be easy. So, there will be fewer tricks found in these questions. The best thing to do is not think too much about whether or not the easy question is a trick question or not. Most times, it should be very obvious what answer the question is looking for so that the answer can be given - whether it is a grid-in or a multiple choice answer. Having said that, if a question in the easy section seems difficult, it may be a sign that the question needs to be looked skipped for the time being and come back to with a fresh mind.  TIP: Do NOT forget to skip a line on the answer sheet if you do skip a question. This can throw off all answers that come after, meaning a dramatically lower score on the math portion of the SAT.  Below is an overview of basic math concepts to help when taking the SAT.  SAT Math Vocabulary Review Knowing what specific math related words mean - especially ones that are similar - is very important for understanding math questions and being able to answer them correctly. 
  • Whole Numbers are basic numbers used for counting. For example, 0, 1, 2, 124, 4297...  Whole numbers are:
    • From zero up to infinity (positive)
    • Positive (except for zero, which has some special rules and considerations.)
    • Never a fraction
    • Never contain a decimal
  • -Integers: Just like whole numbers, but also includes negatives.  Some examples are -4, -3, -416, and also 0, 1, 2, etc.  Integers are:
    • Negative or positive up to infinity
    • Only "counting numbers" 
    • Never a fraction
    • Never contain a decimal
TIP: Whenever the word "integer" is used in an easy math question, it is sometimes used as an SAT math trick used to trick test takers. If the question asks for an integer, it is possible to eliminate any multiple choice answers that have a fraction or decimal. This can be a good way to eliminate wrong answers increasing the chance of getting the right answer. 
  • Odd Numbers: Examples are 1, 5, 9, 11, as well as their negatives -1, -5, -9 and so on. Odd numbers are
    • Always positive or negative
    • Only Integers (no decimals or fractions)
    • Not divisible by 2 evenly. 
  • Even Numbers: Examples are 0, 2, 4, 8, and so on into infinity. There are even negative numbers as well. Even numbers are
    • Always positive or negative
    • Only integers (no fractions or decimals)
    • Always evenly divisible by two (2_)
  • Consecutive: When you see this word on the SAT math section, it simply means something - "in a row." For example an SAT question might ask for "three consecutive numbers" (like 7, 8, 9) although they may also ask for more specifics like "four consecutive odd numbers." Because of this, it is important to not assume right away when the word consecutive is seen. Instead, reading the question carefully and understanding what is being asked for will increase the chances of successfully answering the question and getting points for a high math score on the SAT.  It should also be noted that consecutive numbers will be integers. 

TIP: Test takers should remember that "consecutive numbers" will be integers. Having said that, there are cases the integers may be in an odd location (like a fraction), but as long as the question is read carefully, this will be explained and understood.

BONUS TIP: If a question on the SAT math section asks for "four consecutive numbers" and the  question requires algebra to solve, set up the equation to use X as the smallest number.  The next number will be x + 1, then x + 2  and so on for every consecutive number.  If the question asks for consecutive even numbers or consecutive odd numbers, set up x for the smallest number, but then use x + 2 for the second number, x + 4  for the third number, and so on.  Even for consecutive odd numbers, you still use x + 2, x + 4, and so forth. Plug a number in to further see how this works. 

  • Real Numbers: These are all numbers in existence except for imaginary numbers. The explanation is simple, but occasionally test takers will read too much into the question asking for a "real number" and miss the whole point of the question, getting it wrong and lowering the overall SAT math score. 
  • Rational Numbers: These are "any number that can be written as x / y  where x and y are integers." To further explain...
    • A rational number will be a repeating decimal like .99, a terminating decimal like   .324, or a fraction - 2/9 or 43 / 7 
    • In algebra problems, if the question specifies that the variable will be an integer, something like 5/x would be a rational number.
    • Irrational numbers are ones like π or √2  -- numbers that do not end and cannot be written as fractions.
  • Positive Numbers: These are simply numbers that are greater than zero, reaching to infinity. 
  • Negative Numbers: These are numbers that are less than zero - again to infinity in this direction. 
  • Digits: These are the basic numbers 0 through 9.  Digits are like the numbers on a cellphone. A sample question might ask "When a four-digit number is added to a two digit number, the result will always be …" The answer will be one of the digits 0 through 9.  
  • Distinct: Distinct numbers are "separate" or "different" than others. If a question asks, "In a fraction where x and y are both distinct integers, what happens when..." So, the test makers are looking for two separate numbers, not the same one for both x and y. 
TIP: If  'distinct' does NOT appear in a question, it is important to take into the account that both variables will be the same number. The word distinct can help you limit the answers you have available to you for a specific question.
  • Divisible: This means a number can be evenly divided. For example, 49 is divisible by 7 without a remainder. 
  • Divisor: This is the number that will go into the other number.  For example, in the equation "36 ÷ 4" the divisor would be the number 4.  Some refer to this as the number "outside the bridge" when doing long division.  On the other hand, the dividend is the number "under the bridge."                     
  • Sum/Difference/Product/Quotient: These are the answers for math.  The sum is for addition problems, the difference uses subtraction, the product is found with multiplication, and the quotient is found using division. 
TIP: The words multiply and add will most likely not be used. Instead, questions may ask for the product of two numbers or the difference of two numbers, which means the appropriate methods will need to be used. 
  • Special Rules for the number zero (0)
    • Zero is NOT positive OR negative
    • Zero is an even number
    • Zero is a real, rational, integer. 
    • Zero is  a whole number, and a digit
    • Zero is a multiple of every number 
    • Anything multiplied by zero is zero
PEMDAS: Order of Operations The order of operations will be tested directly on the math portion of the SAT, so it is important to know the order to solve most math problems and get the correct answer.  The order of operations is:
  1. Parentheses
  2. Exponents
  3. Multiply
  4. Divide
  5. Add
  6. Subtract
Multiplication and division are on the same level as well as addition and subtraction, so the list looks a little more like this. 
  1. Parentheses
  2. Exponents
  3. Multiply/Divide
  4. Add/Subtract
TIP: Your calculator may have PEMDAS programmed already, so when you enter a numerical problem into the calculator, it will do sort out the answer correctly.  It is important to make sure  the right numbers and equations are entered otherwise the calculator will never give the correct answer. User operator errors are common which is why it is important to study and practice with a calculator.  BONUS CALCULATOR TIP:  It is crucial to ALWAYS use parentheses around fractions and negatives when they are typed into calculator.  This is a good habit to have for math problems of all sorts.

SAT Math Fractions

Fractions are basic math, but brushing up on the rules surrounding using fractions in math equations can help a person reduce some of the stress that fractions sometimes cause. It is important to once again note that those using calculators should always remember to use parentheses around fractions before typing them into the calculator.  Fraction Review and Overview: Basically, a fraction is a number that represents something that has been divided into pieces. For example 1 / 2 means something has two pieces and the number (the fraction) represents one of them (or half.) The denominator is the bottom number and the numerator is the top number. When a fraction also has an integer, it is known as a mixed number - 2 1 / 2.  Improper fractions have numerators that are larger than the denominators. So, instead of 4 and 3 / 5 it would be written as 23 / 5. Switching mixed numbers to improper fractions allows you to add, subtract or even multiply fractions. To turn a mixed integer into an improper fraction, simply divide the numerator by the denominator. The remainder should be put on the top of the original denominator used.  Adding/Subtracting Fractions It is only possible to add and subtract fractions when their denominator is the same. For example, to add 2 / 3 + 5 / 6 you would need to multiply by 2 / 2 to make it 4 / 5. At that point you could add 4 / 6 + 5 / 6 = 9 / 6.  Multiplying/Dividing Fractions In order to multiply fractions, it is simply a matter of multiplying the numerators straight across as well as multiplying the denominators.  6 / 7 x 8 / 9 = 48 / 63 The SAT answer choices will be reduced fractions. Because of this, if the answer does not match the choices, it may be necessary to reduce the fraction.  A reciprocal of a fraction is simply the fraction with the denominator and numerator switched or flipped. For example, the reciprocal of 2 / 7 is 7 / 2.   A negative reciprocal is like a reciprocal fraction, but with the opposite sign. So, for example, the negative reciprocal of - 8 / 13 is + 13 / 8.  For whole numbers, turn them into a fraction first. So, 3 would become 3 / 1 and the reciprocal would be 1 / 3.   In order to divide fractions, it is necessary to flip and multiply.  So, for example, 4 / 9 divided by 8 / 13 would be 4 / 9 x 13 / 8. It is then a simple matter of following multiplication rules for fractions.  TIP: In some cases it may be possible to cross-cancel. This only works for multiplication problems. Comparing Fractions To compare fractions, simply type the fraction into a calculator to get the decimal value of the fraction.  On the SATs, it is almost never a good idea to try to find the lowest common denominator the way you were taught in school. Instead, use the calculator to reduce the chance or errors and mistakes when taking the math section of the SAT.   

Decimals and Place Values

When taking the math portion of the SAT it is important to know place values. It is very common for people to get the wrong answer when answering questions dealing with place values. Memorizing and knowing at a glance which place value is being talked about is important when taking the SAT math portion. Because the test makers intentionally make questions tricky sometimes, it can be easy to be thrown off for those who do not know their place values. Turning a Fraction into a Decimal For turning a fraction into a decimal, it is simply a matter of saying, top to bottom, 6 divided by 8 for 6 / 8 for example. The result will be a decimal equivalent of the fraction. Be sure to type in the right numbers on the calculator.  Turning a Decimal into a Fraction To turn a decimal into a fraction is even easier. The denominator is the place value. So, for example, if 0.025 twenty-five thousandths the fraction would be 25 / 1000.  TIP:On the SAT grid-ins, it is NOT necessary to reduce unless the answer does not fit in the bubbles exactly.  BONUS TIP:  For grid-ins the answer can be a fraction or a decimal - whichever fits. However, on the multiple choice if the answer you get is a fraction and the choices are decimals, switch it. The same for the other way around if you get a decimal answer and the choices are all fractions.  Decimal Fraction Equivalents It should be noted that you may get an answer like .3333333 from your calculator. It is important not to round this number if it is to be used because it may throw off the whole equation if rounded up too much. Instead, make sure the calculator being used can save the whole decimal as the answer to be used later in the equation. 

Primes, Factors and more

When it comes to the math section of the SAT, primes and factors are another basic math area that people fear although they shouldn't. While there may be tricky questions on the SAT, those that understand primes and factors will have no problems answering the questions found on the SAT math section. To help, we are going to have a basic lesson on factors, prime numbers and other areas that may be found on the SAT. Luckily, these are very simple math concepts that, once mastered, are easy to do no matter how the question is phrased.  Prime Numbers A prime number is one that only has two factors - itself and the number one (1). These two numbers are distinct. This means the number 1 is not a prime number. Prime numbers have no numbers that go into them equally without a remainder - besides themselves and the number one.  The first five prime numbers should be memorized. They are - 2,3,5,7, and 11. Many SAT math questions will only deal with these first five prime numbers, although this is not always the case.  It should also be noted that the number 2 is a special prime number because it is the smallest prime number. Additionally, it is the only prime number that is even. It it very common for SAT test makers to intentionally make questions dealing with prime numbers tricky. The best defense against this is to read the questions carefully and completely, paying special attention to the exact information that they want. By eliminating one or more choices, it increases your chances of getting a correct answer - and points for the question.  Difference Between Factors and Multiples Basically, a factor is a number that will go into another number with no remainder. For example, the factors of the number 20 are 1, 20, 2, 10, 4, and 5. It is important to pay special attention to the ordering of factors. One should be first, followed by the number itself. By doing it this way, the chances of forgetting a number and leaving it out are lessened quite dramatically.  TIP: It is important to never forget about the number one (1) and the number in the question. Even prime numbers have these as a factor. Some SAT math questions will try to intentionally trick you. Because of this, it is important to pay close attention to the number of factors a number has - including itself and the number one.  On the other hand, prime factors are prime numbers that can be divided into a number without a remainder. On the SAT math section, chances are high that prime factorization will come up. It is a good idea to read these questions carefully to figure out exactly what information they want. Listing prime numbers and prime factorization are different and will give different answers. The chances are high that the wrong answer will be one of the choices on multiple choice sections.  A multiple is a number that is derived from multiplying two integers together. These are commonly referred to as the multiplication tables. For example, multiples of 4 are 8, 12, 16 and so on.  TIP: Multiples are answers gotten when multiplied by an integer. For example, zero, negatives and the number on its own are all considered multiples. Knowing this, SAT test makers often rely on the fact that test takers get factors and multiples confused. They will intentionally give answers that may seem right even though they are incorrect.  Greatest Common Factor / Lowest Common Multiple  In order to find the GCF (greatest common factor) of two numbers, simply write down the factors of each number and choose the largest one, even if it is one of the two original numbers. This is another area where the test makers really try to confuse test takers. Because of this, practicing finding the GCF is recommended for those who want to increase their math SAT scores.  To find the LCM (lowest common multiple) simply use the prime factorization tree, although there is a difference from finding the GCF. When finding the LCM, it is only necessary to keep one of each number. Next, multiply the common numbers by all the prime factors left. This will eventually lead to the correct answer for LCM questions on the math section of the SAT.

Divisibility Rules

On the math portion of the SAT, it is important to remember the basics about math and divisibility rules. The more that is known, the easier the math section of the SAT will be. To help brush up basic math skills, we are going to take a look at divisibility rules and how they apply to the SAT math section.  If …. /  It is divisible by …
  • A number is even - It is divisible 2
  • The sum of the digits is a multiple of 3 - It is divisible by 3
  • The last two digits are divisible by 4 - - It is divisible by 4
  • A number ends in 5 or 0 - It is divisible by 5
  • The sum is a multiple of 3 and it is an even number - It is divisible by 6
  • The sum of the last three numbers are divisible by 8 - The entire number is divisible by 8
  • The sum of the numbers is a multiple of 9 - The number is divisible by 9
  • The number ends in zero - The number is divisible by 10
  • The number is divisible by both 3 and 4 - The number is divisible by 12
TIP: Learning to use cross-canceling, decimal equivalents, common fractions and other methods are wonderful ways to help on the SAT math section. However, when a short cut it not possible, it is advisable to do the work on a calculator. Sometimes it is tempting to do the math by hand, but on the SAT only one thing matters - the final score. Those who worry about "showing off" by doing math by hand take a bigger chance of getting a lower overall score on the math section of the SAT. This is not a test about having fun or showing off math skills. When doing basic math, it is important to use all the tools available to get the best score.  Remainders and Patterns When using remainders on the SAT, it is important to remember the basics about remainders. When using a calculator, it can sometimes be tricky. Occasionally, the SAT will ask for an answer in the 13 R 2 variety where R is remainder. When doing long division by hand this is easy to achieve, but sometimes calculators can remove a step giving the wrong type of answer.  TIP: When an SAT math question asks for the remainder, they are looking for a whole number that is left over - not a decimal or a fraction. Sometimes, a tricky question will arise that asks what a number used in a division problem was. Knowing techniques to answer these questions will dramatically increase the chances of a higher score on the math portion of the SAT.  BONUS TIP: Another tricky type of question on the SAT gives the remainder and asks for a number originally used in the division problem.  Example Questions:
  • What is the remainder of 14551 when it is divided by 31?
  • What is the 105th letter in the repeating sequence: B, C, D, E, F, G...
  • For the sequence of numbers: 1, -2, 3, -4, 5, -6, 1, -2, 3, -4, 5, -6, … what is the sum of the first 50 numbers in the sequence?
Remainder questions on the SAT became very common after they started allowing calculators for the SAT math section. They are a simple math concept, but they are easily used in creating questions for the math portion of the SAT that are difficult, confusing and very challenging. 

Patterns Example Question

A quilt is being sewn with a repeating pattern of cross, heart, crest, square. If the first square is a star, what shape would appear on the 42nd square? This type of question can be quite intimidating, even for those who know how to solve it correctly. The good news is that there is no need to have to scratch out a list of symbols to come up with the answer. Simple math problems like this are typically remainder problems.  Answer To find the answer of the above question, it is important to break it down to see what it is wanting for the answer. By taking the place number they want (42) and dividing it by the number of symbols (4), the remainder will be the spot in the list of symbols where the counting should stop.  TIP: If the remainder is zero, the end of the pattern has been reached. In this case, simply choose the symbol at the end of the list. This may not appear frequently on the SAT, but when it does it enables a person to quickly come up with the answer and move on to the next question, increasing the overall score on the math section.  BONUS TIP: As you can see, remainder questions are sometimes masked so that test takers get caught up in the question and can't figure out the best way to come to the correct answer quickly and therefore get a better overall score on the SAT math section. By getting help with learning how to recognize what the questions are really after, test takers can radically increase their math score on the SAT.

Math & Arithmetic Word Problems

One of the most dreaded sections of the math portion of the SAT is the arithmetic word problem. Because the makers of the SAT questions know that students have problems with these types of problems, they take great pains to make sure they make the problems as confusing as possible, even though they usually deal with simple arithmetic.  Here is an example of a problem that may be faced on the SAT. Thomas bought seven bags of oranges for $3.89 per bag. She later realized they were on sale for $2.99 a bag so she went to get the difference. If she was given the amount in pennies, how many pennies would she get back from the cashier? There are very basic math concepts present in this word problem, but it can be intimidating for some people because it is written out as a word problem. Test makers intentionally put information that is not needed into the equation to throw off test takers. At its core, this is a basic math question that is actually quite easy to solve. Rather than giving the answer to this one single question, here is a look at some general overall strategies to use for word problems on the SAT math section.  Strategies for Math Word Problems
  • Break it Down - The best advice is to break it down into individual phrases. For commas, periods and the word and, draw a line to separate the sections of the question. At every stop, it is important to make sure that whatever is asked for is given before proceeding to the rest of the question. 
  • Disregard - Occasionally an SAT word problem will include information that is not needed to get an answer. However, there is a good chance that if the information is used the answer will be wrong, bringing down the overall score on the math section of the SAT. Because of this, it is important to read carefully and disregard any information that is not needed.
  • Step by Step - After the question is broke down into its segments and unnecessary information taken out, the next step is to move through the problem section by section to get the final answer, which should be available as a multiple choice answer. If the answer expected is not given, it may be a good idea to skip the question and come back to it if there is time after working through all the other problems. 
  • Check Work - Before putting down the final answer, read the question one more time. While this takes a little time, double checking work on arithmetic word problems is a good idea to make sure no "stupid mistakes" are made. Word problems are intentionally made to be confusing, which is why it is a good idea to take them slowly. 
TIP: When it comes to word problems on the SAT math section, it is crucial to read and understand the question carefully. Even when the answer is found, test takers should read the question again to make sure nothing is missed. This takes a little more time, but a correct answer is worth a full point whereas an incorrect answer is only worth a portion of a point, which brings the total SAT math score down. 

 

Algebra

Variables

 

Basic algebra, which is found on the SAT math section, deals with variables. Basically, these are unknowns in the equation. By following basic algebra rules, it is possible to do quite well on the math portion of the SAT. However, as with other sections on the test, the people who come up with the questions make sure they have good, tricky questions. The questions that are typically asked on the SAT math section are actually really simple and deal with basic math concepts. Sometimes, however, test takers make the questions more confusing then they need to be. This is especially true when it comes to algebra and variables.  In order to solve an algebra equation, it is necessary to isolate the variable on one side of the equation with the known numbers on the other side. Anything done to one side of the equation must be also done to the other. To start, it is necessary to simplify each side of the equation as far as possible. To get rid of a negative, add that number to both sides of the equation. To get rid of a positive number, subtract it from both sides. If a number is being multiplied, it should be divided to get rid of it on one side. Likewise, if it is being divided on the side with the variable, it should be multiplied on both sides. Eventually, the variable will be left on one side with a number on the other side - the answer.  TIP: Do not reduce answers on the test. Instead, change them into decimals or mixed numbers. Frequently, answers given on the SAT will be improper fractions or integers underneath a square root instead of showing the decimal equivalent. Because of this, it is a good idea to not do any math operations unless it is necessary. For example, if the answers are decimal equivalents, there is no need to figure the answer as a fraction, which can save time on the overall test. This can lead to more correct answers and a higher overall SAT math score, which is the goal.  BONUS TIP: Your variable should always be positive. If it is not, multiply both sides by -1 to get a positive number. It is important to do this with all numbers on both sides of the equation. Beyond this, it is important to brush up on basic algebra skills and do some practice problems on  your own. By doing this, you can allow your mind time to remember everything you were taught over the years in school about math and arithmetic.   

Understanding Like Terms

For more complex algebra equations, it might become necessary to combine like terms. These are terms that have the same variable and are raised to the same power. So, for example, So 2x, 12x, and ⅕x are like terms, but 2, 3x, x2, and ½y are not like terms. While this is a simple concept, it quite frequently tricks people taking the SAT math section.  Combining like terms in an equation is actually really simple. To start, choose one side to clean up, then do the other side. After that, it is just a matter of doing the opposite to both sides to get all the variables on one side of the equation and all of the  numbers on the other side of the equation.  TIP: Numbers that come with a variable (like 12x or 13y) can NOT be combined with a regular number. So, for example, 2x and 12x and be combined, but 2 and 12x cannot be combined because they are unlike terms. Usually, questions that appear difficult are actually just testing the test taker's ability to recognize and combine like terms. By getting variables on one side of the equation and the numbers on the other, most problems become a lot simpler than they at first seem.  Solve for the Variable To solve for a variable, simply follow the same directions above. However, in this case a single number will not be given at the end. That is, there may be a variable in the answer, which is fine when not using factoring.  For example:  Solve for x in terms of y. 3y + x = 42 To solve this equation correctly, it is important to get the variable asked for on one side of the equation.  3y + x = 42 -3y         -3y y = 42 - 3y In the example above, there is no further simplified answer (without using factoring.) Because they are not like terms (42 and 3y), they cannot be combined.  TIP: It is important to read the question carefully and ensure that the right variable is being looked at. While it may seem obvious what a question is asking for at times, it is important to remember that test makers are out to trick test takers, so read the questions carefully and solve for the right variable.     

Using Substitution

To solve for two variables in an equation, it is possible to use substitution once more is known about one variable in the equation. This answer would then be used to find the final answer that the SAT math question is asking for on the test. If you need to solve for two variables, you can substitute information you know about one variable to help solve a second equation. Substitution Example 1 Here is a simple example of a substitution problem that may appear on the math section of the SAT. Remember that sometimes equations look more complicated than they are in reality.  If x = 20 and y = 10, what will be the value of 5x (x - y)? To solve this it is simply necessary to substitute the values for x and y to get the number the question wants. So, for this example 5•20(20 - 10) = 1000 Example Problem 2 If no numbers are given but there is more than one equation on the math section of the SAT test, it is a good idea to choose one equation to begin with and solve for the variable in that equation. Then, the next step is to substitute the answer from the first equation into the second equation.  Here is an example:  If 4x = 12 and 7x + 2y = 25, what is y? The first step is to start with the easier equation. For this question, it would be 4x = 12. The answer will be x= 3 at the end. This number should then be plugged into the second equation in the question.  7•3 + 2y =25 21 + 2y = 25 2y = 4 y = 2 There should always be one equation for each variable that needs to be solved in a question. Occasionally the equation will be simple (like 4x = 12) although at other times it can be quite a bit more complicated. In complicated cases, the equation may have a variable in the answer, which is okay. It is simply a matter of taking that and plugging it into the second equation to get the final answer.  This method of solving for two variables in a question is referred to as substitution.  Occasionally, it is possible to use elimination to solve these problem, which we will go into in a later section of this website.  Overall, as with other sections of the SAT math section, it is important to read the question carefully before attempting to get an answer. 

Elimination for Equations

 

Sometimes when answering a question on the SAT math section it is necessary to use elimination to get the final answer. To do this, it is simply a matter of lining up two equations and adding or subtracting them to get rid of one of the variables. At that point, it is necessary to substitute the information into one of the equations to get the answer for the second variable, which is the final answer of the question.  As with other sections of the SAT math portion, questions surrounding elimination are written to be intentionally tricky and confusing for test takers. Because of this, it is important to read the questions carefully and follow them to the letter in order to get the correct answer and a higher overall SAT math score.  Elimination Example 2x + 5z = 18 and 10x - 5z = 30, what is z? First, line up the equations like they were regular numbers.  2x + 5z = 12 + 10x - 5z = 28 After this, add each column.  2x + 5z = 18 + 10x - 5z = 30 12x + 0z = 48 At this point, one variable should be eliminated by getting it to 0 (zero). At this point, it is possible to solve for X.   12x = 48 x = 4 Now that X is known, it should be substituted into one of the other two equations to solve it for the other one.  2x + 5z = 18 2•4 + 5z = 18 8 + 5z = 18 5z = 10 z = 2 So z = 2 and x = 4. TIP: Sometimes, it will be necessary to multiply one or both equations all the way through by using an integer. This is done to create numbers that will eliminate nicely in the equation. 

Simultaneous Equations

Similar to elimination problems - which is used to trick students - simultaneous equations are not solved by solving a single variable first. Instead, a simultaneous equation needs to be solved all at once - the entire expression. The difference between the two is slight, but understanding and being able to recognize the differences is important so that test takers can get the final answer correct and get a higher overall SAT math score.  Simultaneous Equations The key to solving simultaneous equations is to decide whether addition or subtraction will be needed. It is important to note that when subtracting the negative must be distributed throughout the entire equation. This is a simple mistake that can cause a person to get the wrong answer, which will usually be one of the choices available in the multiple choice section. Like elimination problems, simultaneous equations should be multiplied all the way through to get the correct answer at the end.  TIP: There may not be a reason to multiply the equation through with anything other than a simple number like 2,3 or -3. Experimenting by putting one equation on top and then the other, it should be really easy to see which way it is supposed to go as well as getting the final correct answer, which is important for the overall SAT math score.  Simultaneous Equations Tip TIP: When not sure to use elimination, substitution or simultaneous equations to solve a problem on the math section of the SAT, it is crucial to examine the question carefully to see what the test makers are looking for as the answer. When they ask for more than one variable, it is usually easier to solve for that expression rather than figure out what each variable would be separately. This can save time and allow for more questions to be answered, which can dramaticaly increase the SAT math score.  Simultaneous Equation Word Problems For word problems, it is simply a matter of using a variable for unknowns in the question. For example.  Terry is 3 years younger than twice Heather's age. If Heather will be 15 in two years, how old is Terry? The unknown variables in this question are Terry and Heather's age. It is possible to use the variable T and H instead of X and Y to make it easier to remember which is which when solving the problem.  t = x - 2h - 3 If Heather's age is currently H then her age in two years would be H + 2, which means 2 + h = 15. This would make her age 13, which can be used to solve the rest of the equation. As you can see, the real trick is in reading the word problem and being able to translate it into a math equation. This is the part that most people have problems with when doing Simultaneous Equation word problems.  Another Simultaneous Equation Word Problem  If Heidi is 19 months older than her cousin Tim and four years older than her other cousin Kate and the sum of her cousin's age is 20 years old, how old is Heidi? In this question, the problem is to choose which name to use as a variable. While any would work, it is best to use Heidi since that is what the final answer wants. Because 19 months is not a whole year, decimals will need to be used. For example, this case would be 19 / 12 which would be 1.583 years. Now that this information is known, the rest of the answer is simply a matter of using algebra to come up with the final answer. 

Dealing With Inequalities

An inequality question is similar to a regular equation, but there are some differences. Basically, inequalities are solved like other equations, but there is not an equals sign. This means that there can usually be a range of answers that are correct for any particular question.  5a + 3 > 10 5a > 7 a > 7/5
  • Inequality questions have a range of answers. 
  • When multiplying or dividing a negative number, it is important to switch the direction of the sign of the numbers. 
TIP: It is important to watch for limits on both numbers and inequalities. The difference may change the possible correct answers. This is crucial to understand for those who want to get the highest possible score on the SAT math section. Test makers know that students are confused by inequalities and they use this fact to come up with questions that are intentionally confusing for test takers.  BONUS TIP: Sometimes it is possible for more than one answer to seem correct.  In these cases, it is important to choose the best answer for the question. This means using available information to find out which answer satisfies the question completely - more than any of the other answers. As usual, SAT test makers use this to confuse people taking the SAT math section.   

SAT Math Strategy

 

When taking the SAT math section, it is important to have an overall strategy in order to get the highest score possible. While we have gone over some of the fundamental basics of SAT algebra, there are many other things that need to be thought about - and acted upon - in order to get the highest SAT math score possible. More on Variables: In Terms of … Questions Variables are representations of unknowns that could be any number. The variable is used as a placeholder until the value of that variable can be figured out. In cases like 5x + 2 = 12, the variable is a very specific number that is rather easily found. In other cases, the question will ask to get numerous numbers for the final answer.  TIP: When at least one answer given contains a variable, it is possible to skip a lot of unnecessary math to get the final answer. The question will usually have "In terms of..." in the question somewhere which can help test takers recognize questions where this strategy will work. 
  1. Recognize where the strategy can be used
  2. Substitute a number for the variables in the problem
  3. Using numbers, solve the equation to get the answer and place a circle around it for later reference.
A very good tip is to avoid bad numbers when solving this type of question on the SAT math section. 
  • Never use a 0 or 1 for the variable
  • Never use a 2 if there are exponents present
  • Avoid numbers that will cancel each other out
  • Choose different numbers for each variable to prevent them cancelling each other out
  • Use numbers that are easy to work with, even if they are unrealistic numbers
More General SAT Math Strategies Beyond utilizing the "In Terms of..." Strategy, there are other ways to increase the overall score on the SAT math section. We are going to list some of these tips and techniques and explain why they may help on the math portion of the SAT. 
  • Trick Questions - As with other sections of the SAT, it is crucial to be aware of and look for trick questions throughout the exam. The test makers know how stressful the SAT can be and they use this to their advantage when coming up with deliberately confusing questions for the exam. 
  • Simple Math - Remember that the math used in the SAT is all basic math, concepts that should be known. If they are not, refreshing the memory about basic math skills - especially algebra - is a good idea for many reasons. It can give practice for the actual test and help stimulate the mind. 
  • Check Answers - After first arriving at an answer, it is important to check the answer to make sure it is correct. Doing this takes a little time, but a correct answer will be rewarded with a full point while an incorrect answer will only be a fraction of a point, which affects the overall math score on the SAT. 
  • Skip Entirely - For some questions on the algebra section of the SAT, it is advisable to skip it entirely and not go back. This is especially true for students who are easily confused by word problems, simultaneous equations or any other math concept used on the SAT. As a wrong answer will bring the overall score down on the SAT and a skipped one will not, it sometimes makes sense to skip a question and not go back. 
  • Skip and Go Back - In other cases, when a question is skipped because it is taking too long to answer, it makes sense to go back and answer it fully. Knowing when to go back to a question to try to answer it with a fresh mind is an important skill to have for those who want to get the highest SAT math score possible. 
  • Read Carefully - Reading and comprehending each question is vitally important to getting a high score on the SAT math exam. Because test makers intentionally try to trick test takers, it is always a good idea to ask whether or not the question may be intentionally confusing and go over it with a fine toothed comb, reading carefully and more importantly comprehending what the question wants as an answer. 
There are many other things to do to prepare for taking the SAT math exam. From eating a good breakfast to getting enough sleep the night before, there are many physical things that can be done to increase the chances of getting the highest SAT math score possible.   

 

 

Advanced Number Concepts

Negatives

When it comes to advanced numbers and math concepts, most are covered with a basic understanding of algebra. However, when it comes to the SAT math section, it is always a good idea to review and practice, so we will give some tips and techniques to help deal with negative numbers on the math portion of the SAT.  Negatives Negative numbers are the ones to the left of the zero. This is basic information, but again, reviewing is good when it comes to SAT math questions.  Occasionally, a number in a math problem will have two signs. The basic rule is "one of each is minus and two of the same is positive." So, if a number is -(-1) you must "clean it up" to be 1 before doing any further arithmetic. On the other hand, a + (-3) would become a minus three. After simplifying the numbers, simply add or subtract as needed to get the answer.  When adding or subtracting negatives:
  1. Look at the signs to determine whether to add or subtract.
  2. Simplify the number then add or subtract as needed. 
Additionally, two negatives that are multiplied or divided together will become a positive while one of each sign will result in a negative number. If all else fails, being able to use a calculator may slow a person down slightly, but it can help get through simple math quicker and more accurately for some people.  TIP: The calculator is not a magic tool. It will only supply the answer to the question it is given. For example, if a parentheses is not used, the answer will come out wrong because the calculator does not know it is dealing with two negatives that must be turned to a positive.  Another thing to remember about negative numbers is that they are left of the zero, so small numbers are bigger because they are nearer to zero. When comparing negative numbers, change both signs to positive and look for the opposite of what the questions wants.  After that, it is simply a matter of going from place value to place value to compare the numbers.  Number lines on the SAT math section are typically drawn to scale. This means the lines are just like they appear. So, if they are evenly spaced they will appear evenly spaced. For problems that ask about parts, it is simply a matter of adding the number of spaced (not lines) to find the number of parts of the number. 

 

Absolute Value

When it comes to the SAT math section, an absolute value is represented by two bars on both sides of either a number, variable or expression. Examples would be  |-4|, |x + 3|, and |-(x4 - 1)|. The absolute value is simply the distance from the number zero. Once a number leaves the bars so it can be worked with, it becomes positive.  Example  If you are given a negative value for the variable, it may be a trick question. Absolute value expressions do not become positive numbers until they are removed from the bars. Problems that ask for an easy substitution of a number into an absolute value expression are solved by getting rid of any negative answers.  This allows some answer choices to be eliminated. 

Understanding Exponents

An exponent is the number of times something is to be multiplied by itself, so x5 means x has been multiplied by itself five times - x*x*x*x*x. Typically, exponents will be one step behind normal numbers.  Adding and/or Subtracting Same base AND same exponent needed -  x3 + 2x3 Add or subtract each of the coefficients, but nothing to the base number or exponent.  Multiply and/or Divide Same base needed - y3•y4 Multiply any coefficients, add the exponents; divide each of the coefficients, and then finally subtract the exponents to get the answer.  Raising to a power Things being raised to a power, typically with parentheses - (4w3xz2)5) Raise any coefficients to the outside power, and then simply multiply the exponents for the answer.  TIP: Watch the particular placement of parentheses in the question. Anything found inside the parentheses should be raised to the outside power:                                          Because any two negative numbers multiplied together become positive, any negative number raised to an even numbered power will become a positive number: Additionally, a negative number that is raised to an odd-numbered power will become a negative number: When raising fractions to a particular power, it is important to remember that the numerator and denominator can be split to make the problem easier.   

Negative Exponents

Simply put, negative exponents are those that are "flipped." So, if a negative exponent appears in a denominator in a problem, it is simply necessary to move the numerator to make it a positive or negative depending on the question. 

TIP:  When a question has a fraction that appears complicated, it is possible to clean it up by dividing the coefficients then subtracting the exponents. 

Scientific Notation

While the SAT math section does not use scientific notation that much, it is a good idea to know how to use it correctly. Scientific notation is used for really large or small numbers. To more easily display these large numbers, they are shown as the number times 10 to a certain power. For example, instead of writing 5,444,000,000,000 it would be 5.444 x 1012.  It should be noted however that scientific notation always consists of a number in the "ones" place and is followed by a decimal to cover the other places once it is multiplied out. The exponent that is used with the number ten will be determined by the number of spots the decimal place needed to be moved.  TIP: On of the trickiest questions for scientific notation on the SAT math section comes with trying to fix an answer. 

Rationalizing Denominators

When a denominator has a square root it will not appear that way in the answer choice on the SAT math section. Most of the time, numbers with a square root in the denominator will be rationalized so that they have a whole number as the denominator. The process to achieve this is quite simple. 

To remove the square root in a denominator, simply solve the equation. A square root is just a number that is multiplied by itself. 
 
TIP: Do not rationalize denominators until after looking at the answer choices available on the SAT math section. Occasionally the answers wil be given as a square root while other times they may use a decimal equivalent. Do not do any extra work until you know that you will need to do it as this can save you time to be able to answer more questions correctly and increase your overall math score on the SAT. 
 

Square Roots with Variables

SAT test makers will occasionally try to trick test takers by putting variables into square root questions. However, the trick is to solve these just like normal square root problems. The numbers may be a bit more confusing, but the basic rules of math still apply and never change. 

Fractional Exponents

In a fractional exponent, the numerator of the fraction is the exponent and is under the square root symbol. Likewise, the denominator is the root that is being taken. A lot of the time, questions on the SAT math section will include a number to substitute for the variable. If you are given numbers in some cases, it may be necessary to deal with fractional exponents.
 
Frational Exponent Tips
 
When dealing with fractional exponents, it is important to remember that they often contain perfect squares so that everything will work out evenly. However, this is not always the case. While the numbers may seem messier to some, it is just a matter of following simple rules to get the correct answer. 
 

Mean / Median / Mode

When the makers of the SAT math section come up with questions, they usually try to take basic principles of arithmetic and make them seem to be more complicated than they actually are so they can trick test takers into getting the wrong answer. By knowing the basics of math inside and out, it is easier to spot these tricks and know what will be necessary to come up with the correct answer in all situations.  Mean/Median/Mode These terms all refer to averages, but they are slightly different. The common use of "average" is closest to the "mean" of a number. Having said that, knowing the differences between the three is important for taking the SAT math test.  Median This is the absolute middle number when a list of numbers is arranged least to greatest. Median means middle which is a good way to remember it. To find a median, simply arrange the numbers in a list from least to greatest. At that point, eliminate the first and last numbers one after another until you're only left with one number.  Mode When referring to mode, the question will be asking for the "most" or the number which appears the most often. So, in a list of numbers, it is simply necessary to find the one that appears the most number of times.  TIP: A mode should appear more often than any other number. Numbers that repeat are note the mode.   Mean Mean is the average of a list of numbers. So, to get the mean, add all the numbers and divide by the number of numbers. 

Averages

Whenever the word average is seen in a word problem on the SAT, it is important to write down the number of separate equations that will need to be solved. Averaging questions can be tricky by nature, so it is important to read them carefully and make sure the question is understood correctly. 

TIP: Whatever information is given for a question, it is important to read beyond that and know exactly what the test makers are looking for as the correct answer. It may take a little more time, but when dealing with word problems containing averages, it is important to make sure that the entire question is understood correctly. 
 
Weighted Averages
Simply put, weighted averages are those where one or more groups contribute to the outcome more than others. 
Tom goes to work at an average speed of 60 mph.  Assuming he takes the same road and does not stop, if he averages 40 mph on the way home, what is his average speed for the entire trip in miles per hour format?
 
(A) 40
(B) 48
(C) 50
(D) 52
(E) 55
 
The trick is to find the total number of miles driven as well as the total number of hours that it took. Once this information is known, it is simply a matter of averaging the numbers to get  48 mph for the trip.

Ratios / Rates / Proportions

Understanding the difference between ratios, rates and proportions is important for getting a high math score on the SAT. We are going to take a look at some of the basic information that should be known about ratios, rates and proportions when it comes to the math section of the SAT.  Ratios Ratios are used to establish a relationship between two groups of numbers. They can be written down as fractions, as a series of numbers separated by a colon, or written as words.  TIP: On the SAT math section, if a question gives a ratio in a form other than fraction form, it is advisable to set it up as a fraction to make it easier to deal with and get the correct answer.  Other questions may be more complicated and ask for an answer that is derived from ratios. For example, they may give you a ratio of pizza to pasta and ask for the total number of dishes or plates of food.  EXAMPLE The ratio of slices of pie to slices of cake to bowls of ice cream at the party was five to four to seven.  If there were 52 slices of pie at the party, how many other food choices were also available? To solve, it is simply a matter of adding up the ratios to find the total number of pieces in the ratio.  Ratios are not real numbers so they should never be mixed with real numbers in a fraction.  Proportions Proportions on the SAT math section are a different type of ratio problem that may be asked. For proportion questions, they will typically give two ratios that work together. In word problems, it is important to look for pairs of items that get repeated in the question.  Like ratios, proportion problems need to be set up in the right way to make sure the correct answer is received. Numerators should refer to a single thing - the denominator of the other.  TIP: In some cases they may give you information in hours and also minutes. It is important to pick one and translate one to the other. So, 3 hours and 54 minutes would be 180 minutes and 54 minutes.  The most common type of proportions are called direct proportions or direct variation.   Another type of proportion is called an indirect proportion.  They may also be referred to as an inverse proportion, indirect variation or even an inverse variation. These are used in cases where increasing one thing decreases another thing. For example, if one worker can get so much done in four hours, it does not make sense to say getting three people to help would make it take sixteen hours. This is what is known as an indirect proportion.  In SAT math word problems that use indirect proportions it is important to make sure it is indirect and not a direct proportion question. Remember that test makers are trying to trick test takers into getting the wrong answer.  BONUS:  An additional way to think about the difference between direct and indirect variations is to define them as if x/y = a constant like t while indirect if yx = t.  Rate On the SAT math section, a rate is a ratio that deals with time. For example, a car driving 42 mph, a runner doing 2 miles in 15 minutes.

Translations and Word Problems

Translations in Word Problems

On the SAT math section, it will sometimes be required to "translate" English words into math. These types of problems require a person to translate word for word and also from left to right. While this is an easy section, test takers make mistakes by not taking their time to make sure they understand the problem completely. 
 
Examples: 
The sum of four times a number and 4
 
The square root of the quantity 4y + 7
 
The word/phrase Means
of/times/multiplied • (multiply)
decreased by /difference/ less than -
sum/more than +
what/a number x, n, y (a variable)
Percent /100
is/was/has =
for/per ÷
the quantity ( )
squared/times itself 2
     
When doing these questions it is vital to read from left to right and translate each and every word at every step of the problem. If any words are skipped or it is all done at once, there is a huge chance of a wrong answer.
 
"Less Than/Fewer than:"  
While less than means subtract it can be tricky for some because it means the first number in the question will come second in the word problem on the test. 
 
"Minus the product/Times the sum/etc:"  
When a question asks for 5 times 3, it can be written as 5 * 3. However, some questions may ask for four times the sum of a set of numbers. In these cases, it is a matter of multiplying the number by the sum of the next word - using parentheses. 
 
TIP: When confronted with a word problem it is a good idea to sit back and think about what the question is asking by thinking about it in a real sense. Also, reading the question to make sure no information is missed is very crucial when dealing with these types of problems and questions on the SAT math section. 
 
For numbers that are "ugly," test takers should change the numbers until the problem is easier to understand. This seems like common sense - and it is - but many times someone taking the SAT math section will be confused or frustrated by large, complex or confusing numbers. 
 

 

Percents

When dealing with percents on the SAT math section, it is crucial to have a good understanding of them. For simple fractions, a pizza divided into 8 pieces with 4 of them taken away would leave you with a fraction. In this case, you put the 4 over the 8 (which could be further reduced to ½.) 
 
Percents work in a similar way, but instead of dividing a number into the eight slices or another number, it is divided into 100 pieces so that comparable numbers are used. Remembering that fractions are really a number over 100 is helpful when taking the math section of the SAT. 
 
TIP: When answering questions, it will sometimes be necessary to change percents into fractions. While it is commonly taught to change percents into decimals, on the SAT, it is a good idea to change them into fractions to make the answer easier to get to and make sure it is the correct one. 
 
A lot of the percent problems on the SAT are really just translation problems. Percents in translation problems work the same as in other translation problems, so it is simply a matter of moving from word to word and changing it to math. With percents, however, when the word percent is seen, the number goes in front of the word over the number 100. This turns the percent back into a fraction which means there is no need to worry about moving the decimal place and getting the answer wrong. 
 
Percent Increase/Decrease
For Percent Increase/Decrease Problems, you only need to memorize one formula:
 
CHANGE 
------------  X  100 = percent change
ORIGINAL 
 
The change in value should be divided by the original value and multiplied by 100 to give you the percentage of change - positive or negative. 
 
TIP: The numerator is the change in value - not the new value. 
Percent More Than/Less Than:
 
More difficult problems on the SAT math section that deal with percents will be even more complex because of the extra steps necessary to get the final answer - which will be the correct answer. 
 
Thomas spends $702 on general expenses, $204 for all utilities, and $1200 on rent every month.   The total amount for these bills is 42 percent more than he spent 5 years ago.  How much did he spend on necessities 5 years ago?
 
Problems like this are more difficult because it is not possible to simply add what he spends and subtract a percentage from that. There is one amount that is not known - the amount in the past. 
 
The formulas --  x(1 + %) or x( 1 - %) = new amount for more than/less than problems respectively. In these, x represents the original amount.  
 

 

Probability

SAT math questions that have to deal with probability are simply ratio or proportion problems at their core. So, to solve them, it is just a matter of putting the number in question on top and the total number of outcomes on the bottom of the fraction. 
 
A bowl has ten red marbles, 14 blue, 12 orange, and 8 white marbles.  If one marble is pulled from the bowl randomly without looking, what is the probability that it will be an orange marble?
 
Since the question asks for orange, that is the number that goes on top. Next, find the total number of outcomes, which would be the total number of pieces, or 34 so the probability would be 12/34 - which can be further reduced or simplified. 
 
More complex questions will ask for the probability of two or even more events. In order to solve these types of problems, the important thing is to decide if the events are independent or dependent on each other. Independent ones are those in which an outcome does not affect the outcome of the other - ie they are not dependent on each other. 
 

Combinations

Combinations are another sort of problem on the SAT math section that will be frequently encountered. The good news is that they are easy to deal with. 
 
Combinations
 
Like probability, combinations can be independent or dependent. 
 
Five employees are trying out for positions on a 3-person committee.  How many 3-person committees can be formed that are distinct and different?
 
Five employees are shooting for spots on a 3-person committee.  There will be a Manager, an Editor, and a Secretary.  What is the amount of different 3-person committees can be formed with this infomation. 
 
The first question is dependent on the answer of other questions. For the second example question, every position is a different spot. So, if A is manager, there will only be so many possibilities while if B is manager there may or may not be the same number of possibilities. 
 
In unsure about shortcuts for these types of questions on the SAT, it is a good idea to write out the combinations longhand, but be careful when doing so. This is because combinations are usually on the SAT just to waste time of students taking the test. By writing it all out by hand, time is wasted and taken away from other questions on the test, which can lower the overall math score on the SAT. 
 

Advanced Algebra

For advanced algebra on the SAT math section, there are some questions that are a bit more difficult. To help, we have come up with an overall strategy for the math section of the SAT.    Strategy for Algebra    These are some of the most difficult problems on the entire SAT test. Because of this, it is a good idea to not waste time on solving a problem that is unfamiliar or not fully understood. These types of questions can become real time sinks that make it difficult for test takers to get to all of the questions on the test and get the highest math SAT score possible.    For those who have taken the SAT and got below a 600 on the math section, it may be a good idea to skip all of the advanced algebra questions until the very end. On the other hand, for those who have already scored above 600 on the SAT, concentrating on doing better on this section of the exam can make a real difference on the overall score that is received at the end of the test.    Skipping problems makes a person smart - not dumb - because the SAT is all about the score - about getting the highest score possible. A test taker that knows their strengths and weaknesses and uses that information to take the SAT smartly and get the highest score possible. No one will make fun of someone for skipping problems on the SAT.    TIP: Using the fact that a lot of the test is multiple choice is a good strategy to have. Occasionally, it will be possible to eliminate answers that are known to not be correct, which can make difficult advanced algebra questions easier to answer.   

 

Rules for SAT Math

  1. Organization is important. When taking the SAT math section, keeping work neat will help make sure that the final answer is correct and the full point is received for the question. This also helps make it easier to fix mistakes that may be made because of the ability to backtrack and see work that has been done. 
  2. Knowing the value of the number of the answer choice is will also be important for making sure the correct answer is picked. Rereading problems slowly and with comprehension will make sure that the right answer is picked. 
  3. The answer should be true for each and every part of the question. Some of the types of questions that are most difficult have different requirements for the right answer and more than one of the answers on the multiple choice section will appear to be correct while only one will be the actual correct answer. The answer should be true for all the requirements in the question. 
  4. When an answer that works is found, it is a good idea to move on to the next one. This is only the case where there is 100% certainty that the answer selected is the correct and final answer. 
  5. Keep your work neat and organized.  This is the only form of insurance you have, and the only way you can possibly notice if you made an easily fixable careless mistake.
  6. Know what number the answer choice represents.  This goes back to one of our first rules, rereading the bottom of the question before answering.  You want to make sure that you're looking for the correct thing.  If the question states "A hamburger and soda cost $4.75.  If the soda costs $.75 less than the hamburger, how much does the hamburger cost?"  you need to make sure that you're looking for and answering the cost of the hamburger, not the cost of the soda.
  7. Make sure your answer is true for ALL parts of the question.  Some of the questions in which it is most convenient to Use the Answer Choices are long and complicated with many elements to satisfy.  The answer you select must be true for all of them, not just one or two.
  8. Stop when you get an answer that works.  Unlike ITOS, when you Use the Answer Choices, there can only be one right answer.  When you find it, you're done.  Move on.  Don't waste time checking the other guys.  They're wrong.  Is that clear enough?
 
TIP: Being methodical is important on the SAT math section. Jumping around can confuse a person taking the test. This seems like common sense - and it is - but it is paying attention to the small details when taking the SAT math portion that will really affect the final score, which is the goal. Getting a higher math score on the SAT does not need to be difficult when discipline is used to not skip around needlessly making things more confusing when taking the test. 
 

 

Absolute Value Equations and Inequalities

When absolute values are used in equations or inequalities, they can be more difficult. The important thing to remember is that the absolute value means the equation inside the bars | | may be positive or negative. 
 
TIP: To solve any absolute value inequalities or equations, it is necessary to have the absolute value section on one side while everything else is on the other side before the equation is split into two equations. 
 
So if you're given: 5+ 3|y - 6| = 13, you first need to clean that up to get the absolute value part all by itself.  Clean it up as if the absolute value bars were parentheses you wanted to keep:
5 + 2|y - 6| = 13
2 |y - 6| = 8
|y - 6| = 4
 
At this point it is just a matter of splitting it into equations and solving for the two possible value of y in the equation. 
 
Inequalities
Inequalities are a little trickier to deal with. In these cases the same rules are followed (getting the absolute value on one side and everything else on the other side of the equation, then split into two different equations - one negative and one positive.) Because of the inequality rule of dividing or multiplying negatives, it is important to flip the sign. 
 
If |3x -4| + 6 ≤ 10, what are the values of x?
 
The first step is to clean up the equation to get the absolute value by itself on one side. 
 
|3x - 4| + 6 ≤ 10
|3x - 4| ≤ 4
 
The next step is to rewrite the equation minus the absolute value bars then solve for each - positive and negative. 

 

Factoring

Factoring equations in math is sometimes called "pulling out numbers." This means taking out numbers that every term have in common to make the question easier and more simple. This is similar to what is done with reducing fractions. 
 
Factoring will also work with regular equations. So, if two terms have a single factor in common, it is a good idea to factor even. This is the easiest way to solve these types of problems in most cases. Remember that the test makers are consciously trying to trick the test takers so knowing how to get around the trickery is important. 
 
Factoring with Exponents
When factoring with exponents, it is easy to remember the exponent rules. So, when they are set up like a fraction it is a matter of subtracting exponents. 
 

Quadratic Equations

On the SAT math portion, quadratic equations are not difficult to answer correctly. This is because the quadratic formula does not need to be known. In fact, it may occasionally be less helpful when using it because of a simple strategy that can help increase the math score on the SAT. 
 
TIP: Do the opposite to the quadratic equation. If a quadratic equation is on the test, it is simply a matter of factoring it. Likewise, for factored quadratic equations, it is just a matter of expanding it to standard form. Nearly all of the quadratic equation questions on the SAT math section can be solved in this matter - without knowing the quadratic equation. 
 
Factored and Expanded Quadratic Equations
 
Quadratic equations on the SAT math section that are in standard or expanded form appear as ax3 + bx + c, where a ,b and c are all usually numbers and coefficients. Occasionally, the makers of the SAT test will try to trick students with these types of questions. The rules of the other sections apply - reading the question slowly and carefully and knowing exactly what is being asked for in the question. 
 
Some questions will need FOIL to solve:
 
First
Outer
Inner
Last
 
First Outer Inner Last (FOIL)
To use FOIL on the SAT, a person must first multiply the first terms that appear in a pair of parentheses, then the outer terms, the inner terms and finally the last terms - FOIL. :
 
TIP: It is important to always double check work done by using FOIL. When the signs are gotten wrong it can throw off the whole equation giving a wrong answer and lowering the overall SAT math score. Quadratic equations will always have two distinct answers, but occasionally the question will give you limits.  It will usually be easier to solve for the expression asked for in the question rather than for each separate variable. 
 

Complex Fractions

Complex fraction on the SAT math section are like regular fractions, but they may appear more unseemly. The best way to solve these types of questions is usually to cross-multiply to get the answer. Occasionally a quadratic equation will be left, but in these cases it is just a matter of getting everything to one side of the equation so that the other equals zero and solve from there. 

Functions

In this section of the SAT, strange looking questions may confuse those taking the exam without a little bit of knowledge about these types of questions - particularly functions. Some function questions are common while other ones - more difficult - are thankfully rare.
 
Functions
 
Functions can be graphed as a line in some cases, but for algebra a function is just an equation. So, 3y = 2x + 5 would be a function. Functions are different than regular equations in that they will be written as f(x) or h(x). The f(x) will replace the y value after the equation is solved for y originally. 
 
A function is merely a series of steps to perform. The big difference comes in how these questions are written on the SAT math section. While normal equations may be written out, functions (like f(x) for example) will be written slightly different which can be confusing for some people taking the SAT. 
 
Domain and Range
 
The domain of a function refers to what is put into the equation to get the answer. It is the possible X values for the equation. On the other hand, range refers to what is got out of the equation. If the question asks for the domain they want to know "what values of X are definitely possible." 
 
Let's talk about domain and range.  The domain of a function is what you put into the equation in order to get an answer.  Basically, it means the possible x values.  Range is what you get out of the equation, or, your y or f(x) values. So if they're asking for the domain of the question, they're asking "what values of x are possible in this equation?"
 
TIP: Sometimes values can affect domain or range, which can have an effect on the final answer. Absolute values and square roots both are only positive and a zero cannot appear in a denominator. 
 
 
BONUS TIP: It is a good idea to try 0, 1, negatives and fractions in these types of problems because this can test the limits of range.
 
Occasionally a specific domain for the function will not be given. In these cases, it is a good idea to focus on finding the minimum value of the function. 

Weird Functions

Occasionally on the SAT math section, some questions will look bizarre because of weird, diamond or star shaped symbols. When these are seen, they are talking about functions. Treating the symbol as a parentheses in the f(x) equation. 
 
Linked Function Problems
 
Occasionally on the SAT there will be a function, picture or even a graph that is used for more than one question. In these cases it is important to read carefully so that it is known what is wanted for the answer. Most of the time the two questions will use the same definition of a chart or function but be otherwise unrelated. This is done to confuse test takers. 
 
Questions 13 and 14 refer to the following information.
Day Tickets Sold
Monday 124
Tuesday 124
Thursday 131
Friday 335
One question may ask: 
 
What was the average number of tickets sold per day listed on the chart?
 
While another may ask:
 
If tickets cost $44 each, what is the average amount in dolalrs of tickets sold per day for the entire week?
 
The information from the first equation could be used for the second, but it is not always a good idea to do this. The second question asks for the average for the entire week, which will be different than the average per day. This is just one of many different ways that makers of the SAT math section use to trick students taking the test.

Data Analysis

Other questions on the SAT may have graphs that are not related to or linked with functions. In these cases they may have a function with them but most of the time they will be based on just the information that is presented in the question. 
 
TIP: Many data analysis questions test the ability to read the question carefully and notice the particular details. As with other sections of the SAT, it is important to read with comprehension to know what the test makers want for the correct answer. 
 
A scatterplot will show data that deals with variables related to the same events. On the SAT they may ask to use the data presented. In these cases, it is simply a matter of using the information as would happen with other questions with charts. However, in these cases, each value in a column would relate to the same variable. 
 

Formulas

The SAT does not require the memorization of many formulas. Most of them will be on the geometry section. However, there are two that occasionally come up with algebra questions. 
 
Distance Formula
Distance = rate X time
 
It takes Tom 2.5 hours to bike to work at rate of 12 mph.  Assuming that the same route is taken with no stopping, how long will it take him to get home at twice the rate?
 
This is easy to solve once you know that you need two parts to get the final answer. 
 
Population/Interest Formula
Another formula is...
 
I = P * r * r
 
or
 
Interest Earned = Principal * rate * years
 
There are many other formulas out there, of course, but these two are the most common that will be encountered on the SAT math section. 
 

Must/Always Questions

For these types of questions on the SAT it is important to come up with a strategy that is specific. Whether the question straight out asks for this or infers it, solving this type of question is the same. It is important to not just select an answer and move to the next one. It is necessary to disprove the other answer choices as well. The one that cannot be disproved will be the final answer. 
 
TIP:  Be creative and try to break any patterns that may form. For example, if you are given a < b < c < d < e, try 1, 2, 3, 4 and 5 for the numbers then try 1, 2, 344, 3444, and 1,000,000. The point is to disprove options and not to get through the question quickly. Taking time to answer the question correctly will increase the overall math score on the SAT> 
 

SAT Strategy: Solve the Relationship

Another common type of SAT question is a solve the relationship. The best strategy for these is to remember that they are looking for the relationship between two numbers and not a specific answer. For example, what is the ratio of b to a or what could be the sum of three numbers are both questions where relationships are going to be used. In these cases, substituting numbers instead of variables. 
  1. Choose one variable and change it to a number
  2. Using that number next solve for the other variables in the question's equation
  3. With those numbers, finish the math required by the original question
  4. Choose which answer matches what is gotten with the numbers
It is really that simple. The relationship will never change even if the numbers do change. For example, if the ratio of girls to boys in a class is 2:3, it does not matter if there are 100 boys or just 3 boys - the relationship will always be 2:3. 
 

Guess and Check

Some math problems on the SAT will require a person to throw in numbers to see what works, and these are similar to Must/Always and Solve the Relationship problems on the SAT. However, the difference comes in limits that may be imposed by the question so that only some numbers will work. For these types of problems, there is no shortcut to be taken. To solve them it is necessary to try a series of numbers until the correct answer is found.
 
TIP: For these questions they are looking for a test takers ability to stay organized, neat and be patient to get the final answer. By not jumping around when trying different numbers in the equation, it is possible to quickly get the right answer.

Sets and Sequence

Sets and sequences are another section of the SAT exam that many people have difficulties with, although this should not be the case. We are going to look at sets and sequences so that the overall math score on the SAT can be improved.
 
Sets
On the SAT math section, sets deal with union and intersection. The numbers that are in a set will often be called elements - or members of a set. 
  • A union is asked for with the symbol ∪ and refers to all numbers within the sets 
  • An intersection is asked for with the symbol ∩ and refers to only the numbers that are shared by both sets.
TIP: A good way to remember which is which is to think of the union symbol as a wide U and the intersection as a wide n. These types of questions do not show up often on the SAT and when they do they are not that difficult as long as test takers don't get confused by the symbols. 
 
Sequences
Sequences are also pattern problems that can vary from simple to complex geometric sequences. For the simplest type, the test taker is usually asked to follow certain steps to get the next number. Knowing what a term is - a number or expression in the list - preceding (before) and subsequent (following.) 
 
TIP: Follow the rules as they are written and not how they appear. For example, the second term in a particular sequence may be two times the first term, but this may not be how the sequence is being determined in the question. 
 
Arithmetic and Geometric Sequences
More difficult sequence problems will ask a test taker to carry out a sequence for quite a long time. These sound and look simple, but they take a bit of time to do correctly if they are done in the traditional method. There are actually two ways to do these types of questions. 
  1. Follow the directions and write out the sequence until the answer is achieved
  2. Memorize two sequence forumlas
For those not good at memorizing formulas, it is a better idea to skip sequence questions in order to get a higher math score on the SAT. 
 
An arithmetic sequence is one where each subsequent number is a certain number plus or minus the previous number. 
 
If you are not good at memorizing, you may want to skip sequence questions!  It doesn't matter that the math is easy; sequence questions are often there simply to waste your time.  If you can't remember the formula that goes with them, you're most likely better off skipping these questions and only coming back if you have the time to spend.
So here are the formulas:
 
You may also be asked to find the sum of a certain number of terms in an arithmetic sequence.  In that case, you will need both the formula above, to find the term they're asking about, as well as another formula.

Digits

Digit problems on the SAT appear different than normal variable problems because they usually contain capital letters instead of lowercase letters. 
 
   AB
+BA
------
1A7
 
The capital letter represents a digit regardless of the particular place value. A digit is simple any of the numbers from 0 to 9 - the numbers on a telephone pad. With digit problems, the trick is to guess and check. 
 
TIP: Make sure to use all of the information that is provided in the question. Test makers try to intentionally trick test takers with these types of questions. Also, it is important to remember that there is only a certain amount of time. If a problem is taking too long, it is much better to skip it and answer two easier questions to get the points. The SAT is all about getting the highest score possible - not about answering the most difficult questions. 

Logic

On the math section of the SAT logic questions do not appear often, but when they do they will ask for a reasonable conclusion that is based upon a set of facts that is presented. For example, if X then Y. This means it is an if/then that is seeking a logical conclusion or answer. 
 
EXAMPLE:
 
If the following statement is true: "If Tom lives in Alexandria, then Heather lives in Frankton," which of the following statements must also be true?
 
The best way to solve these types of questions is to substitute a state that is familiar. From here, it is just a matter of trying each combination until you find which one is also true - ie the correct answer. In logic questions "some" can mean one or more. This is another way test makers try to trick the test takers on the SAT math section.

Geometry

Because geometry deals with pictures, there are unique rules for geometry that can help imrove the overall math score. Here are some general rules to think about to help improve your math score on the SAT. 
  1. Drawing - When a question describes something, it is a good idea to draw it. The picture does not have to be "art quality," but scratching it out on paper will give the test taker a good idea of what the question wants. Geometry is visual math and should be treated as such. Again, it should be stressed that the drawing does not need to be perfect as long as it helps with the final answer and getting a full point. 
  2. Scale - If an object in a question is drawn to scale or not is very important information to have. Usually, questions are drawn to scale but occasionally they will not be so as to trick the person taking the test. If the question does not state otherwise, the figure will be drawn to scale. When figures are NOT drawn to scale, it is a good idea to only trust facts and actual numbers explicitly given in the question and not rely too much on the picture or graph. 
  3. Fill It All In - On Geometry questions on the SAT there is occasionally a picture with no labels. These sometimes come with questions that seem difficult to solve. They will either give you a general concept that is understood but the solution or how to solve it is not known. Or there may be no comprehension about the question at all. In either case, it is a good idea to re-read the question carefully and slowly, trying to comprehend as much as possible with each and every word. A good way to help is to fill in everything that is known about a picture with a question on the SAT. Most of the time, seeing the information in visual form will help with getting the correct answer. 
  4. Formulas - It is important to memorize as many formulas - all of them preferably - as possible. Not memorizing the formulas is a big mistake that many students make. Even if a cheat sheet is present, knowing the formula takes less time than looking it up. Also, knowing the formula can make it quicker and easier to solve problems because of the way the brain works. 
 
SAT Formulas
Those formulas are listed at the start of every Math section on the SAT.  
  • The number of degrees of arc in a circle is 360.
  • The measure in degrees of a straight angle is 180.
  • The sum of the measure in degrees of the angles of a triangle is 180.
Perimeter vs. Area
Knowing the difference between area and perimeter is important. Perimeter is the total distance around something and is found by adding up all the sides (which isn't possible on a circle, obviously.) The area is the inside of a two dimensional shape - think square, triangle or even an octagon. The area is found by multiplying the length and width or with another formula for more complex shapes. In order to find the side of a square when the perimeter is known, it is simply a matter of dividing the permiter by four. When the area of a square is known the square root can be used to find a particular side. 
 
Volume
There are many volume formulas, but in general - "area of the base times the height" is the most common that will be used on the SAT math section. This is applicable to all shapes - including cylinders. It is an easy way to recall the volume of any figure that may appear on the exam. 
 
Pi π
A calculator with a PI button is needed for the SAT. It is equal to approximately 3.14. Using a calculator to get an accurate answer is recommended when dealing with this number. Make sure not to use an approximation as an answer unless the question specifically asks for it. 

 

Basic Geometry

Because geometry deals with pictures, there are unique rules for geometry that can help imrove the overall math score. Here are some general rules to think about to help improve your math score on the SAT. 
  1. Drawing - When a question describes something, it is a good idea to draw it. The picture does not have to be "art quality," but scratching it out on paper will give the test taker a good idea of what the question wants. Geometry is visual math and should be treated as such. Again, it should be stressed that the drawing does not need to be perfect as long as it helps with the final answer and getting a full point. 
  2. Scale - If an object in a question is drawn to scale or not is very important information to have. Usually, questions are drawn to scale but occasionally they will not be so as to trick the person taking the test. If the question does not state otherwise, the figure will be drawn to scale. When figures are NOT drawn to scale, it is a good idea to only trust facts and actual numbers explicitly given in the question and not rely too much on the picture or graph. 
  3. Fill It All In - On Geometry questions on the SAT there is occasionally a picture with no labels. These sometimes come with questions that seem difficult to solve. They will either give you a general concept that is understood but the solution or how to solve it is not known. Or there may be no comprehension about the question at all. In either case, it is a good idea to re-read the question carefully and slowly, trying to comprehend as much as possible with each and every word. A good way to help is to fill in everything that is known about a picture with a question on the SAT. Most of the time, seeing the information in visual form will help with getting the correct answer. 
  4. Formulas - It is important to memorize as many formulas - all of them preferably - as possible. Not memorizing the formulas is a big mistake that many students make. Even if a cheat sheet is present, knowing the formula takes less time than looking it up. Also, knowing the formula can make it quicker and easier to solve problems because of the way the brain works. 
 
SAT Formulas
Those formulas are listed at the start of every Math section on the SAT.  
  • The number of degrees of arc in a circle is 360.
  • The measure in degrees of a straight angle is 180.
  • The sum of the measure in degrees of the angles of a triangle is 180.
Perimeter vs. Area
Knowing the difference between area and perimeter is important. Perimeter is the total distance around something and is found by adding up all the sides (which isn't possible on a circle, obviously.) The area is the inside of a two dimensional shape - think square, triangle or even an octagon. The area is found by multiplying the length and width or with another formula for more complex shapes. In order to find the side of a square when the perimeter is known, it is simply a matter of dividing the permiter by four. When the area of a square is known the square root can be used to find a particular side. 
 
Volume
There are many volume formulas, but in general - "area of the base times the height" is the most common that will be used on the SAT math section. This is applicable to all shapes - including cylinders. It is an easy way to recall the volume of any figure that may appear on the exam. 
 
Pi π
A calculator with a PI button is needed for the SAT. It is equal to approximately 3.14. Using a calculator to get an accurate answer is recommended when dealing with this number. Make sure not to use an approximation as an answer unless the question specifically asks for it. 

 

Geometry Vocabulary

Here are some terms and definitions that are important for the SAT geometry section. 
 
Point
A point is a location in space that has no dimension, measurement or mass. It is a spot that exists. They are shown by a dot on a line (*) and are labeled with capital letters like A, B, C and so on. 
 
Line Segment
A line segment is simply the space between two different points. Any two points can make a line and there can be more than two points in a single line. 
 
Ray
A ray is simply a line that extends in one direction infinitely in one direction. It is noted on the exam with a one sided arrow. 
 
Plane
Simply put, a plane is three points in space. There may be more than three points on a plane, but only three need to exist for it to be a plane. When two rays (see above) converge, they create an angle with is noted on the exam by a special symbol followed by three points - one from the vertex (where the rays intersect) and the others the two rays moving outward. 
 
Angels
Measured in degrees, angles are noted by the ° symbol on the exam. A straight angle (a straight line) has a measurement of 180° while vertical angles occur when two different lines intersect to form four triangles. 

Triangles

On the SAT, triangles are referred to on the exam by their three different points. Usually this will have the symbol of a triangle in front of the various points. All three angles of a triangle should always add up to 180°. Also, the perimeter of a triangle is found by adding the lengths of the three sides. 
 
Sometimes triangles will have odd numbers for their side lengths, including square roots. It is simply a matter of adding these up and looking for the answer choice that best reflects the weirdness. Reading the question carefully and slowly also helps. 
 
Right Triangle
A right triangle is one where one of the angles is equal to 90°. On a right triangle, the base and the height are the two sides that meet at the 90° angle. These two sides are the legs of the triangle while the opposite is the hypotenuse. The corner of the 90° angle will always point to the hypotenuse. 
 
If two sides of the right triangle are known the third can be found with the Pythagorean Theorem (a2 + b2 = c2) where a is a leg, b is a leg and c is the hypotenuse. An interesting fact is that the hypotenuse will always be the longest of the three sides on a triangle. 
 
Isosceles Triangle
An isosceles triangle is one where two of the sides are equal and it has two equal angles as a result of this. 
 
Equilateral Triangle
An equilateral triangle is one where all of the three sides are equal in length and all three angles are also equal. 
 
Scalene Triangle
Scalene triangles are those where none of the sides or angles equal each other. It is good to note that two sides (any two) must add up to a number greater than the other third side of the triangle. 
 
Special Right Triangles
A triangle known as a 30-60-90 triangle will have one 30° side, one 60° side, and one 90° side. The short side will be the side opposite of the 30° angle. It is a good idea to always go through the shortest side with these triangles because it doesn't take long to find a different side. 
 
TIP: Do not ever use special angles (like 45 ot 90 for example) when using numbers in a question. This can cause repeat answers that will require new angles to be used and can waste time. 
 
Some common sides of right triangles on the SAT math exam are...
  • 3, 4, 5
  • 5, 12, 13
  • 8, 15, 17
  • 7, 24, 25
Similar/Congruent Triangles
 
When all three angles of two different triangles are equal, the two are considered "similar triangles," which means their sides are in proportion. If two triangles have sides that are all in proportion, their angles will also be equal to each other. 
 
For similar triangles, the ratio of the areas is the ratio of their sides squared.  Therefore, two similar triangles with sides in the proportion 3/4 will also both have areas with the proportion 9/16.

Trigonometry

Again, it should be stressed that trigonometry will not be needed on the SAT math section. When it appears that trig is needed, they may be trying to trick the person taking the test. Usually, the Pythagorean Theorem will work for these types of problems. Having said that, there are times when trig may come in handy on the SAT for getting answers more quickly. So, for those familiar with trigonometry should use it if it can help.

Circles

Basic facts about circles that will help on the SAT math section::
  • The number of degrees in a circle is 360°.
  • The area of a circle is πr2.
  • The circumference of a circle is 2πr or πd.
TIP: It is a good idea to not get the formulas for circumference and area confused as it can result in the wrong answer - which will probably be a choice on the test. Circumference is simply another word for perimeter or distance around something. Circles do not have a perimeter - just a circumference which is figured out with a different formula. 
 
Radius
The radius extends from the center of a circle to the edge of the circle. The radii (multiple form of radius) will be equal for circles. 
 
Diameter
The diameter of a circle extends from one end of a circle to the other end - passing through the center. Likewise, a chord extends from one end of the circle to the other without passing through the center. 
 
Tangent
Tangents are lines that intersect a circle in exactly one spot or point. 
 
Arc
An arc is simply the length of the edge of a circle. It is also a fraction or percentage of the circle's total circumference. 
 
Sector
If a circle was sliced into pieces, a sector is one of the pie pieces. It is a fraction of the total area of a circle. When solving these types of questions, it is a good idea to think of the circle like a pie or a pizza. 

 

Quadrilaterals

Quadrilaterals are four sided figures. The interior angles will always add up to 360 degrees. It is simply a matter of adding the lengths of the sides to get the perimeter of any shape. 
 
Parallelogram
Parallelograms have two pairs of parallel sides and opposite angles that are equal each other.
 
Rectangle
Rectangles are parallelograms where all of the angles are right angles, which makes the opposite sides of a triangle equal. 
 
Square
Squares are parallelograms where all of the angles are right angles and all of the sides are the same length. All sides of a square are equal lengths, so if a square is split on the diagonal it will form two isosceles right triangles - known as two 45-45-90 triangles. This will help make it easy to find the length of a side of the length of the diagonal depending on what the SAT question wants as an answer. 

Polygons

A shape with three or more sides is known as a polygon - triangles, hexagons, quadrilaterals, octagons and more are polygons. When asked for the sum of the interior of a polygon there are a couple ways to solve the problem. Knowing each of these and when to use which one is important for getting a high score on the SAT math section. 
 
TIP: When stuck trying to find the length of a side it is not necessary to do the math all of the time. When able to eliminate two or more wrong answers there are ways to be able to quickly get the correct answer by using the edge of the answer sheet as a ruler to measure the length. 
 

Graphing/Coordinate Geometry

Coordinate Plane
Simply put, a coordinate plane is the name of a graph that has both an x-axis and a y­-axis. The points will be laid out in ordered pairs. It will be represented by a set of parentheses with the value of X first and the value of Y second. When plugging in points, it is important to go from side to side and then up and down when plotting the points. 
 
TIP: When answer choices are ordered pairs, it is important to look closely at the answers. Knowing which order the numbers are supposed to be in will help avoid tricky questions with tricky answer choices. 
 
For finding the distance between two different points it is possible to use the distance formula if it is known. Or, a right triangle can be drawn along the lines of the grid, with a2+b2 = c2 used to solve for the distance that is called for in the question. 
 
Midpoint
A midpoint of a line is found with an ordered pair. 
 
Slope
The slope of a line will be the steepness of the angle. The simples way to solve is to use "y  minus y over x minus x." 

Graphing/Coordinate Geometry

Coordinate Plane
Simply put, a coordinate plane is the name of a graph that has both an x-axis and a y­-axis. The points will be laid out in ordered pairs. It will be represented by a set of parentheses with the value of X first and the value of Y second. When plugging in points, it is important to go from side to side and then up and down when plotting the points. 
 
TIP: When answer choices are ordered pairs, it is important to look closely at the answers. Knowing which order the numbers are supposed to be in will help avoid tricky questions with tricky answer choices. 
 
For finding the distance between two different points it is possible to use the distance formula if it is known. Or, a right triangle can be drawn along the lines of the grid, with a2+b2 = c2 used to solve for the distance that is called for in the question. 
 
Midpoint
A midpoint of a line is found with an ordered pair. 
 
Slope
The slope of a line will be the steepness of the angle. The simples way to solve is to use "y  minus y over x minus x." 

Slope-Intercept Formula

The slope-intercept formula is a common slope formula that will be used on the SAT math section.  The formula y = mx + b will be used where b is the 7-intercept - or a point at which the line crosses the axis.  To find the intercepts fast, use 0 for the opposite variable. 

Graphing Functions

The vertical line test is one of the simplest ways a graphing question will be used on the SAT. It is important to know that f(x) means y. When graphing, the f(x) value will be the same as the y value.  
 
Domain and range are also important for graphing question on the SAT. To find the domain on a graph, it is simply a matter of finding the highest X value and the lowest X value. Everything in between (and including) those two values is the domain.

Transformations

On the SAT math section, functions may move on the coordinate plane according to various rules. The base graph of  y = x or y = x2 starts at the origin, or (0,0).  
 
To make the graph: Do this:
flip upside down make it negative (y = -x2)
narrower multiply by an integer (y = 4x2)
wider multiply by a fraction (y = 1/5x2)
move up the graph add to the quadratic (y = x2+ 1)
move to the left add to the variable (y = (x+1)2)
When using a graphing calculator, it is important to not waste time figuring out the transformations that are not needed for the final answer. While transformations are good to know, with a calculator they are usually not needed on the SAT. 
 
There is also an algebraic transformation which uses the f(x) formula from algebra. 
 
Rotation
Rotation simply rotates an object around a certain point. 
 
Reflection
A reflection of an object is what would be seen if it was help up to a mirror to be viewed. The new image will be a mirror image of the original object. Objects that are symmetrical have a line of symmetry that is the line where reflection occurs. Objects that are symmetrical all the way around are said to have a point of symmetry. 

Solid Shapes, Shaded Regions, and Perception

For solid shapes on the SAT, the questions are usually not very difficult at all. Most deal with volume or surface areas, which are quite easy to find.
 
Volume
The interior of a 3-dimensional object is known as the interior. The volume of most solids can be found by simply multiplying the area of the base times the height of the object. The volume of a rectangular solid would be l•w•h while the volume of a cube would be s3, and the volume of a cylinder would be πr2h.
 
Rectangular solids are a type of prism, although there are triangular and hexagonal prisms. A prism is just a solid where the top and bottom are both a shape (like a triangle for example) while the sides are rectangles. Prisms all have the same formula for finding the volume - the height times the area of the base. 
 
Surface Area
Surface area of a solid can be found by simply adding the areas of all the faces of the object. It is important to not forget about the surfaces on the back of the object that cannot be seen on the drawing on the test. 
 
To find the surface area on the SAT of a rectangular solid, it is simply a matter of multiplying the length times the wwidth, the width by the height, and the length times the height  Multiplying each of those answer by 2 (for the back sides) and adding all the numbers together will be the surface area. 
 
For the surface area of a cube, since all the sides are the same it can be found much faster.  Use the formula 6s2 to find the surface area of a square. 
 
For cylinders, finding the surface area can be a little tricky. Fortunately, the surface area of a cylinder is rarely asked for on the SAT. 
 
Cones, Pyramids and Spheres
Spheres, pyramids and cones do now show up on the SAT that often, but when they do they usually deal with volume. 

Shaded Regions

The SAT may have questions about shaded regions. These typically appear more difficult than they actually are to solve. The idea is to look for smaller shapes within the larger shape. It is usually easier to subtract a smaller shape from a larger shape rather than add up a lot of smaller shapes. 

Perception/Spatial Relations

Questions that deal with perception and spatial relations rarely appear on the SAT math section, but it is still a good idea to know how to solve them just in case. Based on the picture given on the test, it is usually a matter of being able to visualize a solution in the mind. IT is a good idea to try to draw the image described in these questions as many different ways as possible.

Writing

With just a bit of practice, one can gain many points in the SAT multiple-choice writing section. The test makers are known to assess the same skills in this portion, giving a prepared test-taker the ultimate advantage. Preparation will decrease the likelihood of being blindsided by a question, meaning that the more one practices, the quicker and more accurate that person will become at answering the questions in this section of the exam. 
 
Knowing what to expect in the writing multiple-choice section means a faster pace, which leads to more questions answered and a higher overall score. This section of the test can be compared to mathematics – some questions may be baffling, but knowing the pattern of things that will be asked helps demystify this portion of the exam. A confident, self-assured spirit will undoubtedly help to propel the test-taker forward through this section, therefore, preparation is key!

SAT Writing Section Facts

SAT Writing Section Facts
  • The multiple-choice segment contains 49 questions which determine about 70% of your score.
  • Three types of questions will be posed: improving sentence errors, identifying sentence errors, and improving paragraph structure.
  • Two sections will be present – one long and one short.
  • In the first portion, there will be 11 improving sentence error questions, 18 identifying sentence error questions and 6 improving paragraph structure questions. This portion must be completed in 25 minutes.
  • In the next portion, there will be 14 improving sentence error questions. These must be completed in 20 minutes.
  • The most commonly asked question that one can expect to receive next is an improving sentence question.
  • Remember: omission of a question does not hurt or help your score.
  • Incorrect answers carry a penalty of .25 points; preventing guessing.
  • Spending about 42.8 seconds on each question will get you through this section, according to the College Board.
 
To prepare, one should study major areas of grammar until patterns of accuracy can be established. After building a foundation, it is important to look closely at each question type to understand how these foundations relate to each question. Though mechanically the skills needed are the same, there are noticeable differences that one should be aware of per question type. Some areas of mechanics can be fine-tuned with a simple look into question type, while others will require deeper study.

Subject-Verb Agreement

Subject-Verb Agreement 
The subject of a sentence must always agree with the verb.  A common mistake in this area would be: He walk. Obviously, the subject in the sentence “He” does not agree with the verb ”walk.” The correct way of stating the sentence would be “He walks.” If only the SATs were this easy! However, the concept behind the question and the example given is essentially the same. SAT test makers usually present this type of question in three different ways:
 
Subject-Verb Split
instead of placing the subject near the verb (as in the first example), SAT test-makers commonly separate the subject from the verb with distracting words, phrases or clauses. “The mother along with her children (is/are) going to the mall.” In this sentence, what would the correct verb be? “IS”. In this sentence, “mother” functions as the subject, “along with her children” is just a phrase used to distract the test-taker. SAT test makers will try to trick students by placing a plural noun just before the verb. To avoid being tricked, simply cover up the distracting clause before the verb, which should point straight to the actual subject of the subject.
 
Correlative Conjunction
Another common trick that is commonly used in this section of the SATs is the correlative conjunction trick. Two of the most common correlative conjunctions are “Neither/Nor” and “Either/Or”. In these examples, the subject that is closest to the verb will determine which verb to use. For example,” Neither the student nor his classmates are enjoying the lesson. “In this sentence, there are two subjects – “student” and “classmates”. However, the subject “classmates” is closest to the verb, thus the verb must be plural. Knowing this tidbit will help when any correlative conjunction is thrown into the question. This type of trick is used very frequently on the SAT test.
 
Inverted Word Order
SAT test makers have yet another trick up their sleeve. The following will be referred to as the inverted word order trick. When a sentence begins with a long-winded phrase, look for clues that will commit the sentence to a certain verb usage before the subject is even stated. In this particular instance, a reader may become confused and lose track of the subject or mistake the subject for an object previously stated. For example, “At the back of the bus are a small seat and a large seat for students. “ In this example, the test-taker may notice only the first subject “small seat” and skim over the second, which makes the example plural. Inverted constructions like these may fool some less careful test takers, allowing for a careless mistake in subject-verb agreement.

Pronouns

Pronouns 
Understanding the usage, reference, and agreement of pronouns will aid in mastering this portion of the SAT Writing section.
Pronoun Usage
 
Pronoun Usage 
Learning the difference between pronouns that are used as subjects and pronouns that are used as objects is imperative to mastering usage. A common example found on the SATs would be sentences questioning the correct usage of linking verbs. Consider this example: It is me who delivers the pizza. While it may sound right to use the pronoun “me” in this sentence, the correct use of a pronoun is actually “I”. What makes this concept so confusing is that misuse of pronouns is rampant in spoken English.  
 
In order to prepare for the SATs, one must become familiar with the common linking verbs, such as “was”, “were”, “is”, “are” and “am”. Mastering the use of these linking verbs will help when misuse of pronouns are present in a test question. Mapping nominative and objective differences for personal pronouns will also aid in mastering this test portion.  
 
Pronoun use in conjunction with prepositional phrases is also a concern. For example: The president gave the award to her and I. In this example, the correct pronoun is actually “me”, because it functions as the object of a preposition. Conversely, in the following example, “The teacher gave him and I a scolding,” the correct usage is actually “him and me” because “him and I functions as indirect objects.” To the untrained ear, these sentences sound correct, but studying correct usage of objective pronouns and nominative pronouns will prevent any mistakes.
 
Pronoun Antecedent Agreeement
Singular indefinite pronouns carry a huge margin of error for the common student or even those of higher educational regard. These pronouns are so rampantly misused that SAT test makers pile on the questions on the topic of their use. Indefinite pronouns such as “anyone,” “someone,” “no one,” “somebody,” “anybody,” etc should serve as a red flag to indicate the question concerns proper indefinite pronoun usage. The following sentence serves as an example: “Did everybody bring their homework?” Even though this sentence may sound correct, the pronouns “his or her” are proper. Since the term “everybody” refers to a group that contains people of both genders, “his” or “her” is the most appropriate combination. This is a common trick of SAT test makers, and students should be aware.
 
Reference Errors
Makers of the SATs are using reference errors more and more frequently in test questions as they are the most subtle and most difficult to register as incorrect. This type of error can be broken down into three types: general, indefinite, and ambiguous. General and indefinite errors are quite similar, but ambiguous stand alone. The following example is a common type of sentence used on the SAT: Noticing the error on his cable bill, the young tenant knew that they made a mistake. In the first part of the sentence “Noticing the error on his cable bill,” the author assumes that in mentioning “cable bill” that “they” would be understood. In fact, the author does not include an antecedent, which leaves the word “they” without the accompaniment of a noun. 
 
An inference may indicate that “they” refers to people who wrote the cable bill, so “they” could be safely replaced with “The Cable Company.” Keeping an eye out for rootless pronouns (they, this, it, that) will be a good aid in this portion of the exam.  
 
An ambiguous pronoun is another form of a reference error. When the reader of a sentence cannot clearly match a pronoun back to an antecedent, then an ambiguous pronoun error has occurred. In this type of error, when the reader tries to trace a pronoun back to an antecedent, he or she will find it could match two different elements. For example: When the clerk turned around to talk with the customer, she told her some bad news. In this sentence, “she” could refer to either the clerk or the customer. To fix this mistake, the author must replace the pronoun “she” with a correct antecedent.
 
Person
Second person pronoun shifts are another common misuse of grammar to be aware of when taking the SAT test. Often, people will start a sentence in the third person, using common pronouns like “he” or “she”, and then in the latter part of the sentence switch into the second person point of view. This is incorrect. When one begins a second in the third person, the sentence must conclude in that same point of view. For example: When one runs a marathon, you have to be physically and mentally prepared. See how the sentence begins with “one” yet ends with “you”? The correct sentence would be: When one runs a marathon, one must be physically and mentally prepared. Pay attention to pronouns in the second person view because they are commonly misused.
 

The Active vs. the Passive Voice

Knowing the difference between the active and passive voice will most certainly aid in completing the SAT test. Recognizing these distinctions will also improve speed through the test and also mastery of the written section. The SAT test maker will never reward the passive voice in a test answer, so when this voice is recognized it can be automatically thrown out. For example:
  • The spices were put in the cabinet by me. (Passive)
  • I put the spices in the cabinet. (Active)
The first sentence can be recognized as passive for the following reasons. The noun “books” is the subject, however, the true actor that is doing the “putting” is contained in the prepositional phrase. If the actor is not the actual subject of the sentence, then the author must use a wordy verb phrase to distinguish who is completing the action. This long-winded type of response is unnecessary and improper. The active voice allows for use of fewer words and a more assertive sentence.
 
A sentence that uses the passive voice can be identified by the following sentence structure: Linking Verb + Action Verb + Prepositional Phrase. When this sequence is spotted, the passive voice is in use. In conclusion, when a test-taker notices a question response that executes the passive voice, that response can be automatically thrown out. The correct response on an SAT exam will always be in the active voice form.

Parallel Structure

Developing sentences with parallel structure is a challenge for some students, and SAT test makers will definitely pick up on these flaws in the written portion. When stating your ideas, be sure that lists and multiple ideas mirror each other. Each element presented in a list should be uniform in structure. For example: The kids enjoyed going to the fair, dancing at the disco, and they liked attending concerts. Now we view each group of words in that statement as its own separate element:
 
Element 1- going to the fair
Element 2- dancing at the disco
Element 3- they liked attending concerts
 
Can you discern which of these elements does not fit with the others? That’s right; Element 3 contains an entire independent clause that the other two elements do not. Fixing this sentence error is simple, just change element 3 to match the other two. Simply drop the phrase “they liked” to make an agreeable parallel structure. The correct sentence should read: The kids enjoyed going to the fair, dancing at the disco, and attending concerts.

Wordiness

The most common error found in the improving sentence error portion of the exam is wordiness. The SAT test makers reward simple, straight-forward, powerful language, and excessive wordiness or ornamentation is considered an error. Savvy test takers must learn to keep an eye out for this type of mistake.
 
A test maker may add just one word too many, and it could be anything from a pronoun to a gerund. Occam’s Razor is a theory that suggests the simplest explanation is the best explanation when choosing among competing theories in science. This theory can also be applied to SAT test taking, and can prove a useful guide when navigating the written portion of the test.
 
Another simple rule of thumb: if you can state the sentence using fewer words, without distorting the meaning, then this is the statement you should choose among the answer choices. This is a helpful notion when choosing between two or even three different choices – the one with the least amount of words is usually the correct one.

Verb Usage

To complete the written section of the SAT, it is crucial for one to understand and be able to execute the six basic tenses of the English language. Questions are commonly posed on the SAT which deal with or contain broken clocks. What is a broken clock? The concept is simple – verbs have a twofold function, to tell time and to express action. SAT test makers often create questions which deal with the misuse of one but not both of the functions of verbs. 
 
For example, one of the verbs in the sentence may fail to express the correct passage of time or may be out of sequence with the other verbs in the sentence. One must pay special attention to the broken clock trick when dealing with verbs in the perfect tense. While there are a total of twelve tenses in the English language, the SATs primarily deal with the six basic ones that are listed below.
 
6 Verb Tenses
  1. Simple Past
  2. Simple Present
  3. Simple Future
  4. Perfect Past
  5. Perfect Present
  6. Perfect Future 
Most students are quite familiar with the simple tenses of verbs, so this guide will delve deeper into the perfect tenses. While questions involving simple tenses of verbs will appear on the SAT, the majorities of students has rated these questions as ‘easy,’ and are statistically answered correctly. If, however, you’d like to score above average on your exam, mastery of the perfect tenses and knowledge of how to spot broken clocks is critical.
 
Perfect Past Tense
The perfect past tense is expressed when one event (event A) takes place before another event (event B) and both can be considered completed actions. The trick here is to recognize that an event B must take place in order to execute this tense correctly. For example: I had stopped my car before I read the no stopping sign. This is a correct usage of the perfect past tense. Event A (parking) takes place before Event B (reading the sign), because of this sequence of events, the perfect past tense is proper. A common mistake in this type of sentence would be to use “had + a verb”, but that is incorrect.
 
Perfect Present Tense
The perfect present tense is much more common and easier to spot. The perfect present tense is used when an action described start in the past and continues into the present. An example of the perfect present tense is as follows:
 
I have been a mother for ten years.
 
In this sentence, the action of being a mother started ten years ago but continues into present day. This is an example of the perfect present tense being used correctly.
 
Perfect Future Tense
The perfect future tense is in a lot of ways like the perfect past tense, but occurs on the opposite end of the time spectrum. In the perfect future tense, Event A occurs before Event B, but they both take place some time in the future. The following sentence is an example of the perfect future tense: By May 2012, I will have graduated high school. In this sentence, we are clued in to the perfect future tense by the words “May 2012” because this date has not yet occurred. Graduating high school has not yet occurred either; therefore the perfect future tense is appropriate in this situation. When taking the SAT, keep an eye to broken time sequences, which may indicate a break in either perfect future tense or perfect past tense.
 

Sentence Structure Errors: Run-on and Fragment Sentences

When writing, it is common to make sentence structure errors. Therefore, the SAT test makers have formulated a number of questions to test one’s ability to spot these errors. Two of the most common sentence errors are run-on sentences and sentence fragments.
 
Run-On Sentences
Run-On Sentences: Run on sentences can be the result of two different errors. If the author of a sentence fails to place a comma between two independent clauses, the result is a run-on sentence. Likewise, if the author of a sentence fails to use punctuation to separate two or more clauses, a run-on sentence has occurred, giving the reader no opportunity for normal spoken flow.
 
Example for Type A: Faulty Punctuation
Faulty punctuation is a common element that SAT test makers choose to test. Read the following sentence. Mary Jo used watercolor on many of her paintings, she believed it brought her pictures to life. In this sentence, there is a definite fracture. A comma should not be used between the words “paintings” and “she”, a semi-colon or a period would be most appropriate. However, the sentence could also be fixed by adding a conjunction to the sentence. The following list indicates five ways that this sentenced can be corrected.  
  • paintings; she (semi-colon correction)
  • paintings.  She (period correction)
  • paintings, for she (conjunction correction)
  • watercolor since she believed …(subordinate clause correction)
  • watercolor, believing it brought … (phrase correction)
While there are five ways to correct the one sentence, an SAT test maker will not ask you to choose which one is the best. In dealing with run-on sentence errors, the test question will likely include only one correct answer choice. While it is true that some corrections to a run-on sentence are better than others, there are no strict rules concerning these opinions in the English language.
 
Example Type B: No Punctuation
Another common test question on the SATs involves spotting or correcting sentences that contain no punctuation. For example: Walt Whitman was a great American poet he wrote a book of poetry entitled Leaves of Grass. In the preceding sentence, there are two clauses which the author fails to separate with any sort of punctuation. This, as in the previous examples, is also a run-on sentence. The same types of corrections can be used to fix this type of sentence error.  
  • poet; he (semi-colon correction)
  • poet.  He (period correction)
  • poet, and he (conjunction correction)
  • poet who wrote a …(subordinate clause correction)
  • poet, composing a book of …(phrase correction)
Fragment Sentences
Sentence fragments are another common sentence error tested regularly on the SATs. In total, there are six different types of sentence fragments, but for the purpose of test preparation it is best to narrow it down to the most common three. The definition of a fragment sentence is a sequence of words that is missing a subject, predicate, or both.
 
Phrase Fragment
A phrase fragment is when a series of phrases placed together in a sentence give the appearance of a complete thought. This type of fragment is illustrated in the following sentence.
 
During the concert, covering ears because of proximity to the speakers.  
 
In this example, the sentence begins with a phrase, and ends with two other phrases. Phrases do not contain subjects and often do not contain verbs either. The example presented does not have a subject or a verb, thus it is a phrase fragment. Try not to mistake “concert” for the subject and “covering” as the verb. These words lack context, and so do not make a complete sentence.
 
Verb Fragment
A verbal is a word that looks like a verb but doesn’t act as one. A verb fragment is caused by a verbal and is one of the most common types of sentence fragments. A common verbal is the word “dreaded”, as in “I dreaded the next stop.” These types of issues have been known to show up on the SAT exam, creating verb fragments. Questions regarding verb fragments may show up in both improving sentence errors and identifying sentence errors question types. The following is a verb fragment. The students waiting patiently for their teacher. This sentence has a subject “students”, and it also has a pseudo-verb “waiting”, but the way that the sentence is structured makes “waiting” act as an adjective. A simple change from “waiting” to “wait” improves this sentence structure. Commonly on the SAT, a line will be found underneath the verbal. This is an indication that it is the grammar error and should clue one in to the correct choice.  
 
Complex-Compound Fragment
Questions involving complex-compound fragments are becoming more and more prevalent on the SAT exams. It is a more complicated error than phrase or verb fragments, and thus more difficult to detect. These types of errors may be found in both improving and identifying sentence error questions. A complex-compound sentence is basically half of a complex sentence and half of a compound sentence mashed together. Take the example:  
 
Since I had difficulty following the teacher's orders, but the principal made my infraction much clearer to understand. The problem in this sentence lies within the subordinating conjunction “since”. “Since” creates a dependent clause, ending at the world “language.” Before the comma, this sentence is considered complex. If this were a correct, complete sentence, one would find an independent clause beginning after the world “language.” Instead of an independent clause, what is actually present is a conjunction. In this sentence, it seems as if two halves of a thought have merely been pushed together. To correct this sentence error, be on the lookout for a choice that discards either the first word of the sentence, or the conjunction. The underlined portion should be either the first word, or the start of the second half.
 
The preceding is by no means a complete guide to every possibility on the written portion of the SAT. However, these points should account for the majority of questions. By following this guide and understanding the points set forth, one can expect mastery over the majority of sentence error questions on the exam. Spending too much time studying less common or more sophisticated areas of grammar that may be presented on the SAT exam will cause one to invest more time for a smaller point gain.
 

 

Improving Sentence Errors

Improving Sentence Errors: There will be 25 improving sentence errors questions on the SAT exam. The question is commonly disguised as a lengthy sentence with a portion or entire sentence underlined. To complete the question, one must rearrange the underlined portion to conform to traditional grammar standards. Answer choices will likely contain more grammar mistakes that must be omitted quickly in order to keep a fast pace. Remember to omit choices in the passive voice or choices that appear wordy. The correct answer is most likely clear and very straightforward. .
 
Tips for Improving Sentence Errors
General tips for approaching improving sentence error questions are as follows:
  • Try to recognize statements that stand out as odd, even if the specific grammar error within the statement is unbeknownst to you, try to discount the statement and focus on the other choices.
  • The choices may help to isolate what is wrong in the sentence. For example, if the first two answer choices deal with singular verbs and the next three deal with plural verbs, then the question is likely assessing subject-verb agreement. Isolating the subject of the sentence will then allow two or three choices to be quickly omitted, hopefully revealing the correct choice.
  • After narrowing answer choices, discount those that are too wordy. Unnecessary words are a quick signal that there is a better answer somewhere else. This is a tried and true trick that the SAT test makers use year after year, test after test. Becoming aware of this pattern will allow you to maximize your time as well as your score. 
  • Do not become overly frustrated if the error is not apparent straight away. Logic and the process of elimination will be helpful tools in eliminating wrong answers. Remember the patterns that have been discussed in this guide. Narrow the choices down to two or three, and choose the most straightforward, concise answer.
  • Practice makes perfect! Recognizing the patterns of the SAT test is a foolproof pattern to pacing through the test. Read the question and try to isolate anything that seems odd, eliminating that choice. Always look for the most clean, concise statement as your answer choice.
  • Wordiness and common misuse of language should be large indicators for elimination. Discarding these options should narrow the focus on the correct answer choice.
  • Typically, there will be 2-3 questions in each set where there is no problem with the statement.
Be cautious and look for sentence structure errors that appear in the question. Many times an error can be fixed with the simple addition of a period or a verb to complete a sentence fragment. 
 

Identifying Sentence Errors

On the SAT writing section it may be required of test takers to identify sentence errors. This is a little easier than fixing sentence errors because they just have to be spotted. Students should take the entire time given to answer each question. There is a "no error," choice that needs to be thought about carefully before it is checked on the exam. It is thrown in the answer choices to increase the odds of getting the question wrong. 
  • Do not worry about wordiness in this section. This part of the exam will be all about the mechanics of writing not style. 
  • Look for subject-verb agreements errors, sentence structure errors and other common misuses of language. 
  • When a very is underlined, it is a good idea to ask whether the verb tells the right time and whether it agrees with the subject of the sentence in the question. 
  • When a pronoun is underlines, there will be four possible errors to notice - case, agreement, person and reference. The idea is to quickly figure out if a pronoun used it correct or not. 
  • Studying a glossary of English usage is a good idea as some questions with usage errors will occur on the exam. For example, the difference between lay and lie. 
  • When a conjunction is underlined, asking whether there is a fragment is a good idea. Conjunctions are often misused. 
  • There will be around three or four "no error" questions total. If more than this is gotten, there may be a problem with some of them. 
  • The easy questions will be in the beginning with more difficult errors later in the exam. 
  • Keep track of how many "no error" answers come up. 

Improving Paragraphs

Improving paragraphs on the SAT is the smallest part of the exam. It consists of six questions. Here are some things to think about closely. 
  • Correct subordination of ideas
  • Correct coordination of ideas
  • Correct use of transition
  • Unity of the paragraphs
  • Coherence of the test paragraphs.
 
Here are some helpful tips and suggestions for this section of the SAT:
  • Most of the time, there will be just one or two questions that will ask a test taker to combine ideas. The skill here is to know how to subordinate an idea or coordinate an idea. It is important to be aware of cause and effect ideas as this causes common mistakes. 
  • There is a possibility that the test question will ask a test taker to contemplate how an idea might fit into an existing paragraph. It is important to understand whether they are asking for a contrasting sentence or not. 
  • For transitions, it is a good idea to look for ones that accentuate the development of an idea in the paragraph. With contrasts, SAT test makers like to trick test takers by seeing if they are paying attention to the exact momentum of the flow of the paragraph on the question. 
 

Pacing

For the pacing and time section of the SAT, there are 34 questions that need to be completed in 25 minutes for the first section. It is a good idea to go quickly when trying to identify sentence areas. Here are some ideas and tips to help with pacing on the SAT. 
  • Quickness will come with a knowledge of grammar. To gain speed it is important to know grammar inside and out. Knowing it well will help a test taker more quickly identify errors without having to think about it - like multiplication tables in math. 
  • It is very important to know when to move on to the next question and to not waste time on questions because there is a time limit. Taking too much time can negatively reflect on your overall SAT score in a bad way. Every question is worth the same amount of points on the SAT, so it makes sense to answer as many that you know the answer to quickly and get the most points. 
  • When crunched for time on the SAT, do the identifying sentence error section first to leave more time for improving sentence error questions. It is generally not a good idea to do the improving paragraph section first because it can be a time killer with a lot of reading and going from question to question. 
  • One other way to improve the overall time it takes to get through this section is to cancel the first answer choice as soon as something is thought to be wrong or weird about the question. 
 

Conclusion

Here are some other thoughts on the writing section of the SAT exam. 
  • Pay attention to the word "being" in the sentence error section, because it has a very high use in high school writing and many answer choices that contain the word are wrong. 
  • When stuck between two questions, choose the simpler of the two questions and move on. Don't spend too much time on any one question because all the questions are worth the same amount of points.
  • Do not omit any questions unless a difference between them cannot be made out. It is sometimes a good idea to guess when one or more incorrect answers can be ruled out. 
  • Do not get stuck on any single question on the exam. It is important to keep moving to get through as many questions as possible. 
  • When the passive voice is used in an answer, it is usually the wrong answer choice. 
  • It is important for test takers to keep their head in the game when taking the SAT and get enough rest and food (energy) before the test.  
 

Essay

Writing well is a skill that must be learned with practice. Essays can be broken down into parts that are more understandable. Often, test takers make a false assumption that it is necessary to be born with a gift of writing. For academic writing, however, this is not the case. It is also not the case for taking the SAT essay exam. By knowing the traits of essays that win big points with the person grading the exam it is easier to come up with a writing strategy that will work wonders on the SAT.
  • The multiple-choice questions on the SAT will influence  70% of the score, which leaves 30% of the score determined by the essay.
  • Test takers are given 25 minutes to read the essay prompt and finish a completed essay.
  • The top score possible with one reader is 6 and 12 with two readers. 
  • Two readers score the SAT essay in order to make it more fair. 
  • A few mistakes MAY NOT necessarily equal a lower score on the essay section. 
  • The first section of the SAT will be the essay. 
  • Writing prompts usually come from a quote or two that builds a question that asks students to think about and evaluate any claims and come up with a point of view, arguing using various evidence to support the essay. 
 

Quick Strategies

Here are some quick strategies to employ on the essay section of the SAT. 
  • Read the rubric for the characteristics of each score on the SAT. It is important to read example essays carefully to see what score they get and why. 
  • It is vital to think about pacing on the SAT essay section. With only twenty five minutes available, it is important to think of a game plan or strategy and then implement it quickly and efficiently. 
  • Leaving enough time for editing at the end is also important to get the highest score possible on the essay. 
TIP: Help for essays.
 
The Position:___________________________________
Supporting Facts #1?____________________________
Supporting Facts #2?____________________________
Supporting Facts #3?____________________________

Presentation

The presentation of an essay is important because points are gotten for good presentation. There are no rules for good penmanship, but there is no time for sloppiness when taking the SAT essay section. Using crossed-out words, arrows and other markings on the essay will sometimes end up in the subtraction of points off the total score. 
 
By showing care for ideas and having a game plan, it is easier to present the essay better which can lead to a much higher score. Making it easier for those who grade SAT essays can help improve the chances of a higher score, so presentation is important for many different reasons. 

Audience

When writing an SAT essay, it is very important to think about the audience. This is especially true when writing for an audience that is from academia. The people who read and grade the essays want to be able to clearly read the essays. The more hurdles they find with grammar, organization or even penmanship, the higher the chances they will give a lower score. 
 
Most writers struggle with forming clear ideas and expressing them with words. Graders of the SAT essays look for these types of writers and can even enjoy giving them a perfect 6 after reading a lot of other inferior essays. This is why presentation and thinking about the audience is so important for getting the highest score possible. By knowing what the test grader wants to see on the essay, it is easier to construct something that will make them happy to give a high score - even a full 6.

Key Ingredients of a Strong Essay on the SAT

One of the most important things to remember when writing a strong essay for the SAT is that the graders are going to be looking at whether a particular point of view is developed or not. This is the basis of a thesis statement - taking a stance on a subject one way or another. The opening paragraph of an essay should include this as the backbone of the rest of the essay. By establishing a very clear position on a matter, it will be easier to "fill in the blanks" and finish the essay. 
 
WRONG:  The Cleveland Browns play for Cleveland, Ohio.
RIGHT: The Cleveland Browns are the best team in the NFL.
 
While the second may be hard to prove with facts, it takes a definitive stand on the matter and is not merely reciting a fact. The more generalizations that are used in the opening paragraph, the harder it will be to have a complete and cohesive essay. 
 
The more specific a thesis statement, the easier it will be to construct the rest of the essay in a way that you receive the most points possible. The descriptive and emotional the thesis can be made - while sticking to reality - the better essay that will follow the introductory paragraph. 
 
● Start with a clear position on a particular matter.
● Build support for the position in remaining paragraphs.
 
Fact: Abraham Lincoln was a US President during the civil war. 
Argument: Abraham Lincoln played a pivotal role in the North winning the US Civil War. 
 
Speaking only in generalizations and not making a specific argument will force the person grading the essay to give you a three - even if you use the most poetic prose possible. The reason is that a statement of fact is not a thesis statement and not what the SAT essay is asking a test taker to write. 
 
By using exact facts and explaining how they support a claim (or argument), it is possible to easily construct a strong essay quickly that backs up the thesis statement and comes together in a cohesive whole - something that will allow a test grader to give full points. 

All Paragraphs and Sentences for the Greater Good

Unwanted paragraphs or even sentences in an essay are not good. This is why it is important to think about "all paragraphs and sentences for the greater good of the essay." Because the audience of the essay is someone who wants to grade it quickly and accurately without any problems or distractions, it makes sense to focus on unity and coherence. 
 
Every topic sentence should set parameters and boundaries for the discussion. Each and every sentence should develop the initial idea. When a sentence strays off topic, the momentum of the discussion is lost which can lead to a lower score. Not being able to comprehend an idea in the essay easily is bad for the grader. 
 
Thinking the essay through before writing anything down is a good idea so that a structure can be formed and stuck to throughout the essay. This can help avoid getting off topic and lowering the score on the essay. More examples are not necessarily a good thing. Choosing the very best examples is a much better idea.
 
A well written paragraph will show both coherence and unity because all sentences support the main topic sentence. Also, the sentences follow in an order that is logical and that helps enhance the topic. 

Provide Concrete Examples / Avoid Generalizations

Avoiding generalizations in the essay and providing concrete examples of ideas is a very good thing to do in order to get a higher score. Sometimes students repeat the same idea over and over rather than adding depth and layers to the essay. 
 
Using concrete examples from literature, history, current events, or even personal experiences can all add flavor to an essay. Providing specific examples from real life can add depth to an essay which makes it easier for graders to give it a high score. 

Use Clincher Sentences to Conclude Ideas / Avoid a Full Conclusion

Using clincher sentences to conclude ideas can help to avoid full conclusions. Long endings are usually better for academic papers where there is not a 25 minute time limit. With only twenty five minutes available for the SAT essay, it is wise to use that time to construct a very good thesis that states the stand then back it up with concrete examples and ideas that support the thesis.  A clincher sentence at the end can then wrap it all up and give more strength to the thesis statement. 
 
The final sentence is actually very important, especially in a shorter essay like the one found on the SAT exam. By packing a powerful punch at the end, it can really make the rest of the essay stand out - even if there wasn't anything spectacular about it. Rather than trying to make every sentence a home run, it is a good idea to concentrate on coming up with a very good clincher sentence that wraps everything up nicely. A clincher sentence should always support and help out the thesis statement or position taken. 

Length: The Measure of Success

The length of an SAT essay has an effect on the score given. On average, essays with scores of 5 or 6 are usually 350 to 450 words in length - about three or four paragraphs. Essays with only 100 to 200 words usually get a score of 1 or 2. Going too far - beyond 500 words for example - just makes it more difficult for the grader to get through it quickly. Remembering to write for the audience, it is a good idea to shoot for 350 to 400 words on the SAT essay. In this amount of words, it is important to make sure every word packs a strong punch. 

Not the Luck of the Draw / Thinking About Universal Examples

Universal examples are important on the essay section of the SAT. Ideas for essays are to come from "reading, studies, experience, or observations."  When using personal experience, however, it is important to only use those experiences that are major and support the underlying point of the entire essay. Using colorful language is a good idea, but you want to make sure it is easy to read and not too colorful. 

Conclusion

Here are some final thoughts and considerations about the SAT essay section. 
  • At least two examples (large) or three examples (small) should be used for the 350 to 450 word essay. 
  • The introduction should never begin with answering the question - ie "I totally agree with the quote..." 
  • Useless words should be avoided at all costs. In my opinion is one phrase that should be avoided, as well as I think that and I feel that. 
  • Don't panic! Keeping cool, calm and collected during the essay section on the SAT is a good way to make sure a 5 or 6 is received rather than a 2 or 3. 
 

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Each of the following questions has a word or group of words missing. Four alternative words are given; you have to find the best answer choice to make the sentence make complete sense

Math

Writing

Vocabulary and Words Lists

Preparing for the SATs can be a difficult experience. Memorizing SAT vocabulary words from a word list can be one of the easiest ways to raise your SAT score. Critical Reading sentence completion questions test your ability to understand the context in which a word is used. Learning the definition of more SAT words will help boost your Critical Reading score.  We have developed multiple sets of SAT word lists, including one list of the 100 most common SAT vocabulary words. By memorizing these words that are frequently on the test, you will have better odds of knowing the vocabulary words that will be on the SAT test. The 100 most common SAT word list is a great starting point, but if you have time, you should definitely read the other lists as well.

 

100 Most Common SAT Vocabulary Words List

The following list of the 100 most common SAT vocabulary words was made by counting how many times a SAT word was the focus of an SAT test question between 1995 and 2002. These SAT test question types include Analogies, Sentence Completions, and Vocabulary-in-Context items. 

Word or Word Group Definition
abandoned v: to give oneself up to (e.g., evil); to cast off or reject
accusation (accuse) n: an indictment, a charge of an offense; the act of accusing
ambiguity (ambiguous) n: hesitation, doubt; an uncertainty; an instance of double meaning
analyze (analyst) v: to examine critically in order to bring out key elements or structure; to ascertain the elements of something
antagonize (-ism, -istic, -ist) v: to struggle against
apology (apologize, apologetic) n: an acknowledgment of fault or failure
architect (architecture) n: a designer of any complex structure or plan
astute adj: shrewd, crafty
blueprint n: a plan or program of action
boundary n: something that marks the limit or dividing line, or that limit itself
canvas n: a type of cloth used in sails, tents, to paint onv: to solicit support or votes
comic (comedy, comedian) adj: causing or intended to cause laughter
compassion (-ate) n: sympathy, pity
compete (competition, competitive) v: to strive for an objective
complex (complexity) n: a group of related elementsadj: formed by combination; intricate or not easily analyzed
comprehensive adj: large in scope; all-inclusive
compromise n: a joint agreement between two partiesv: to come to terms by mutual concessions
condemn (condemnation) v: to declare to be wrong or evil
conflict n: a battle, a fightv: to fight or to battle
confusion (confused) n: the state of being perplexed
consensus n: agreement or unity of opinion
contemporary adj: occurring at the same time
contempt (contemptuous) n: the act of despising someone or something
convention (conventional) n: an agreement; a norm or generally accepted rule, practice, or behavior; an assembly of people
conversation n: a spoken interchange; a talk
corrective (correct, correction) n: something that counteracts harm; something that restores health or proper behavior
critic (critical, criticism, criticize) n: one who judges the truth or value of any matter
debate (debatable) n: strife or contention in argumentv: to argue, discuss, quarrel over
deceit (deceitful, deceive) n: misrepresentation or concealment of the truth; an instance of such behavior
defend v: to protect or uphold
defined (definable, definition) adj: having a specified outline or form
demand n: a request, especially if urgentv: to ask for or require
deride v: to laugh mockingly at; to scorn
desert v: to abandon
destroy (destruction) v: to ruin or put out of existence
determined adj: resolved upon; resolute
digress (digression) v: to deviate from or to stray; to depart from the main point in argument
discredit n: a lack of reputation; a loss or lack of confidence or trustv: to injure the reputation of; to disbelieve
disease n: illness
disregard v: to pay no attention to
distort (distortion) v: to twist; to misrepresent
document v: to prove by evidence
dominate (dominance, dominant) v: to master; to prevail
doubt (doubtful) n: uncertaintyv: to hesitate to believe; to be uncertain
elect (election, electorate) v: to choosen: chosen, selected
emotion n: a state of mind; a strong feeling
endurance (endure) n: the ability to last or hold out
enhance v: to raise the level of
evaporate (evaporation) v: to convert into gas; to disappear
exclude (exclusive) v: to keep out; to deny entry to
expand (expansion) v: to spread out; to give full expression to
generosity (generous) adj: magnanimity; liberality in giving
hedonism (hedonist, hedonistic) n: the love of pleasure as the chief goal of life
hypocrisy (hypocrite, hypocritical) n: the practice of falsely professing a belief to which one’s own actions do not conform
hypothesis n: a proposition or assumption put forth as the basis for further investigation
illusory (illusion) adj: deceptive
imitate (imitation) v: to mimic or copy
integrity n: completeness; free from moral corruption
investigate (investigation, investigator) v: to examine a matter thoroughly; to make a systematic search
isolation (isolated) n: unconnected with anything else
lubricate (lubricant) v: to make slippery or smooth in order to minimize friction
manual adj: pertaining to hands, especially labor done by handn: a book of instruction
measure n: a size or quantity determined by measuring; something assessed by judgment or observationv: to ascertain size, quantity, or distance; to regulate or restrain
modest (modesty) adj: having a moderate estimate of one’s ability; not exaggerated or excessive
narrate (narrative, narrator) v: to tell a story
navigate (navigable, navigation) v: to find one’s way
neglect (negligence, negligent) v: to pay no or insufficient attention to
novel (novelty, novelist) v: new, originaln: a usually long prose narrative
obey (obedience) v: to comply with or submit to
observe (observable, observation) v: to watch carefully; to adhere to (e.g., a custom)
offense (offensive) n: an attack; a breach of law, duty, or manners
oppose (opponent, opposition) v: to set oneself against; to confront with objections
perplex (perplexing, perplexity) v: to confuse; to torment
persistent (persistence) adj: enduring; persisting in an action
persuade (persuasive) v: to successfully talk someone into an action or belief
plot n: a small piece of ground; a plan; a conspiracyv: to plan, especially a conspiracy
preserve v: to keep from harm
progress (progressive) n: advancement; developmentv: to proceed; to move by stages; to move forward
prohibitive (prohibit) adj: having the quality of preventing something from happening
prosaic (prose) adj: commonplace, dull
protagonist n: the chief person in a work of fiction; the leading person in a contest
restrain (restraint, restrained) v: to prevent from doing something; to limit
revise (revision) v: to look over repeatedly, as in a plan or piece of writing
satisfactory (satisfy) adj: sufficient, adequate
scrutinize v: to inspect closely; to examine methodically
stimulate (stimulant, stimulation, stimulus) v: to rouse to action; to animate
supplant v: to cause the downfall of; to remove from a position
suppress v: to cause an activity to cease; to cause a person to become powerless
surreptitious adj: obtained by suppression of the truth; acting stealthily or secretly
universal adj: applicable in all cases; including or affecting all members of a particular group; pertaining to the universe
varied adj: of different sorts or kinds
venerate (venerable, venerability) v: to regard with deep respect; to pay honor to something

 

 

Word List - Official SAT Study Guide Test 1

Word Definition
Accolade praise
Allusion indirect reference
Ambivalence uncertainty; having 'mixed' feelings
Ambivalent unable to decide
Analogy comparison
Anecdote short account of something interesting; story
Anomalous odd; not fitting the pattern
Apparition ghost; something that 'appears'
Aspersion negative feeling; damaging remark
Belligerence aggression
Bombastic too elaborate; exaggerated
Candid truthful
Capricious changeable; fickle
Cherished cared for; firmly-held
Cliche over-used expression
Conception 1. idea; view. 2. beginning of pregnancy
Convoluted complicated or long-winded
Credence belief
Cryptic hidden
Currency 1. widespread acceptance, 2. money
Decorous good and correct (used of behavior)
Denunciation act of speaking out against
Derailed thrown off course
Derivative unoriginal
Despotic acting like a tyrant
Detritus rubbish
Diaphanous very thin and transparent
Dictum often-used saying
Dilettante person who dabbles in the arts
Disdained showed contempt for
Dispassionate unbiased; fair
Dowager an elderly woman of elevate social status
Dubious doubtful
Egalitarian equal; believer in equality
Elicit draw out (used mainly for information or feelings)
Elliptical 1. shaped like an ellipse, 2. indirect
Epitomizes acts as a typical example of
Equivocate speak ambiguously/vaguely
Evasiveness trying to avoid something
Explicitly very clear; nothing hidden
Foraging searching for food
Hypothetical based on guesswork; not proven
Iconoclast person who goes against accepted authority
Idiosyncratic quirky; unique to an individual
Imponderable cannot be understood
Indecorous not well-behaved; lacking in dignity
Indigence extreme poverty
Inept clumsy
Inherent inbuilt; genetic
Intricate complicated
Irrefutable cannot be proved wrong
Jingoism using words to stir up exaggerated patriotism
Jubilant joyful
Judicious fair and equal
Lament express regret over something
Loquacious talkative; using too many words
Mendicancy begging
Metaphorical not literal; figurative
Milieu environment; surroundings
Mitigated made less severe
Nascent just begun; in an early stage of development
Nostalgia longing for the past
Obtrusive easily seen
Orthographical concerned with writing and spelling
Ossified become fixed and rigid
Ostentatious showy
Palpable can be felt
Pastoral 1. concerned with the countryside, 2. concerned with the care a pastor gives to someone
Pedestrian 1. boring (adj), 2. person who walks (n)
Perfidy treachery; betrayal
Profligacy wasteful and immoral behavior
Prohibitive very expensive
Prudence wisdom; caution
Pugnacious aggressive
Purveyor one who sells something or causes something to spread
Resonance echo
Respite break (from work etc.)
Resurgence revival
Sparse thin; not thick
Stringent strict
Succumbing giving in to; falling under the influence of
Supercilious arrogant
Tenacity firmness of purpose
Transcend go beyond a limit
Variegated multicolored
Venerable worthy of respect
Viable workable; able to live or grow
Visceral concerned with the 'guts'; physical rather than mental

 

Word List - Official SAT Study Guide Test 2

Word Definition
Ambivalent undecided; having 'mixed' feelings
Apathy lack of energy or interest
Autonomy self-government
Benevolent kindly
Blanched turned pale
Bolster give support to
Bucolic concerned with the countryside and farming
Callous cruel and unfeeling
Cantankerous bad tempered
Capricious changeable; fickle
Chicanery trickery; attempt to deceive
Churlish ill-mannered
Cohesive forming a whole; 'sticking' together
Concur agree
Cryptic hidden; obscure
Decimation extensive destruction
Deft skilful
Delinquency wrong-doing
Depravity moral corruption
Desolate lonely; devoid of life; feeling very sad and hopeless
Devoid of empty of
Didactic intending to teach or give instructions
Disingenuous crafty
Dispassionate unbiased
Disposition tendency; personality
Dissent disagreement
Effusive overly expressive of emotions; 'gushing'
Endorse support
Enigma puzzle
Enumerate count out; list
Ephemeral short-lived
Erroneous wrong
Erudition great knowledge or learning
Esoteric obscure
Fabrication something made up; untrue
Facetious cheeky; not to be taken seriously
Factions sides in a dispute; groups with common interests
Flotsam floating rubbish
Fostered encouraged
Hackneyed stale and over-used
Harbored held [as in 'harbored and idea']
Hodgepodge strange mixture
Hypothetical not proven; based on guesswork
Impetuous impulsive
Implacable cannot be appeased; relentless
Impugned challenged; attacked in words
Incorrigible cannot be corrected (of behavior)
Indigenous native to a particular place
Ineffable cannot be expressed in words
Irascible easily angered
Ironic unexpected
Lament express regret
Languid having no energy or interest
Lassitude lack of energy
Lugubrious mournful; very sad
Mercurial rapidly changing
Misnomer wrong name for something
Mollified calmed; pacified
Multifaceted having many aspects
Mundane dull; ordinary
Nostalgic longing for the past
Obtrusive easily seen; 'sticking out'
Omnipotent all powerful
Pedagogy science of teaching
Phlegmatic calm
Plausible believable
Precursor fore-runner; earlier version
Preeminence fame; top position
Pretentious putting on an act
Prognosis outlook
Prolific producing a lot
Provocative provoking
Raiment clothes; garments
Reciprocate pay back
Reconcile bring disputing side together again
Remiss wrong
Remonstrance criticism
Resilient able to spring back; strong
Retrenchment reducing staff or forces; conserving resources
Robust firm and strong
Skeptical doubtful
Skewed distorted; bent
Stringent strict
Subtle not obvious
Succinct clear, short and well-expressed
Sundry miscellaneous
Sustenance support; food
Tenable can be held (of an opinion, for example)
Tenuous shaky; not firm
Torrid hot and steamy
Undermine attempt to overthrow; weaken
Underscore emphasize
Unequivocal clear; cannot be misunderstood
Vector carrier (of disease, for example)
Verbose wordy
Whimsical fickle; changeable
Wistful full of sadness and longing

 

 

Word List - Official SAT Study Guide Test 3

Word Defintion
Abashed ashamed or sorry
Allusion indirect reference
Ambivalent undecided; unclear
Analogy comparison
Anecdote short account/story
Annihilated wiped out
Anomalies oddities; things that don't fit the pattern
Antipodes places on opposite sides of the globe
Apprehension worry; nervousness
Arduous hard and difficult
Articulate (adj.) able to express something well in words
Assuage to make less
Auspicious fortunate; indicative of a successful outcome
Avuncular acting like an uncle; kindly
Axiom something that is taken to be true; basic idea that can't be questioned
Banal dull; unoriginal
Bellicose aggressive
Benign kindly
Bereft of without; deprived of
Bifurcation division into two
Blatantly obviously
Cacophonous very noisy; unpleasant sounding
Cantankerous irritable and difficult to please
Captivating fascinating
Chided scolded
Clairvoyant able to see into the future/another dimension
Coddled over-protected; kept warm
Comely attractive
Complacent smug; over-confident
Conducive to suitable for; leading to
Convivial sociable and friendly
Cornucopia literally a horn filled with fruits etc; symbol of plenty
Cosmopolitan composed of varied nationalities
Counterfeiter faker; someone who makes fake money, for example
Decipher decode; work out meaning
Deferential showing respect
Deterrent something that puts one off; a preventive
Dichotomies divisions into two parts
Diffident shy; hesitant
Digression going off the point
Discriminating 1. able to make fine distinctions between; having good taste, 2. favoring one side/group and acting against another
Docile placid; easily lead
Elite the upper levels in a society; the privileged ones
Equitable fair and equal
Equivocal ambiguous; something that can be interpreted in more than one way
Exhilarating exciting
Fathom 1. (v) work out; understand, 2. (n) measure of depth
Fervent passionate
Filial concerned with the relationship between child and parent
Foreboding sense of doom
Funerary concerned with funerals
Galvanized 1. stirred into action; stimulated, 2. coated with zinc
Grandiose exaggerated; too great; on a grand scale
Haughty arrogant
Hilarious very funny
Hyperbole over-exaggeration
Impetuous impulsive
Indecipherable cannot be decoded; cannot be worked out
Irresolute lacking firmness; inability to decide or commit
Levity lack of seriousness; humor
Loquacious talkative
Mediocre average
Mellifluous pleasant-sounding
Metaphor figurative speech; using implied comparisons
Miscreants wrong-doers
Mitigated made less severe
Naive unsophisticated; simple and inexperienced
Nonchalant assuming an appearance of not caring; indifferent
Obliterated wiped out
Ousted pushed out of a position
Pacifists people who oppose war
Panacea remedy for all ills
Paradoxically counter to what one would think; contradictory
Personification 1. attributing human qualities to something non-human, 2. acting as an example of
Perusal careful reading
Placid calm and peaceful
Presumptuous assuming too much; arrogant
Profiteer someone who seeks to make unjustified profits
Propagandist someone who spreads ideas
Proximity closeness
Qualification something added to modify an opinion
Reconcile bring disputing sides together; overcome bad feeling
Respite break from work etc.
Reticent shy; unwilling to reveal information
Reverential showing respect
Revisionists people who revise; anti-revolutionaries
Sanctimonious hypocritically holy; making a pretense of religious feeling
Stoic brave; able to tolerate whatever life throws at you
Symbiotic mutually advantageous; close relationship
Syncopated with strongly accented rhythm
Tacit unspoken; understood even thought not expressed in words
Taunted teased; mocked
Temperate mild; moderate
Understatement making something seem less important than it is
Unqualified without hesitation; complete and total
Unrelenting never giving up; non-stop
Unwarranted unjustified
Watershed 1. area between two river basins, 2. turning point

 

 

Word List - Official SAT Study Guide Test 4

Word Definition
Advocate support
Ambiguous vague
Animosity hostility; hatred
Boorishness rudeness; ill-mannered behavior
Censure blame; criticize
Concord agreement
Conflagration big fire
Consecrated dedicated; made holy
Consummate supremely good
Contagious passed on through touch; infectious
Cursory superficial
Dalliance non-serious involvement; toying or playing with something
Deleterious harmful
Disparaging critical
Dubious doubtful
Equitable fair and equal
Eulogy praise
Fastidious very fussy; excessively concerned (esp. about cleanliness)
Fidelity faithfulness; loyalty
Formidable inspiring awe
Futile useless; waste of time and effort
Futility uselessness
Holistic whole; entire (Holistic viewpoint = seeing things as a whole)
Idiosyncratic quirky; eccentric; unique to an individual
Ineffable can’t be expressed in words
Infelicity unsuitability; inappropriateness
Integrity honor; honesty
Intermittent on and off; not continuous
Judicious fair; wise
Legitimate to make legal; give approval to
Mercenary seeking money above all else
Meticulous thorough; taking care of details
Petulant sulky
Polarized divided into two extremes
Pragmatism practicality
Presumptive presumed
Propensity tendency; leaning’ predilection
Prosaic ordinary
Quelled suppressed
Regressive moving backwards (literal or metaphoric)
Remiss neglectful
Rhetoric persuasive language
Sedulous thorough; eager
Sermonized gave moral lecture
Shroud 1. a cover for dead body, 2. to cover
Steadfastness loyalty; firmness of purpose
Temporize put off; procrastinate
Treacly too sweet; over sentimental
Vacillated wavered; hesitated
Vindication proving right
Vindictive seeking revenge

 

Word List - Official SAT Study Guide Test 5

Word Definition
Abstruse difficult to comprehend
Acumen sharpness of mind
Adroit skilful
Anachronistic out of normal time range
Arcane obscure; known only to few people
Autonomy self-government
Belittlers people who criticize/disparage
Byzantine excessive; decadent
Consecration dedication
Corollary consequence; inference
Curtail cut short
Debunkers people who expose/throw out old ideas
Devious cunning
Didactic intending to preach or teach
Effacement wiping out; (self-effacement = excessive modesty)
Egotistical selfish
Embodiment living example of
Epitome essence; typical example or symbol of
Esoteric obscure
Extrapolated predicted on the basis of existing data; extended
Foster encourage
Inane silly
Incoherence lack of clarity
Inconspicuous not easily seen
Indiscriminate without thought; random; careless
Ingenuous naïve
Insolence lack of respect; rudeness
Insurrectionists rebels
Intemperance lack of moderation
Irreverence lack of respect
Jeopardize put at risk
Lackadaisical lazy; careless; lax
Lucid clear
Magnanimity generosity (of spirit)
Multifarious having many aspects
Nefarious infamous
Onerous burdensome
Opportunism grabbing opportunities; seeking unprincipled advantage
Ornate highly decorated
Precursor forerunner
Proponents supporters
Resolute firm of purpose
Sanctity holiness
Seditious causing division or rebellion
Slipshod careless; untidy
Solicitousness expressing care/concern
Sophistry devious logic
Substantiate give supporting evidence
Subversive intending to overthrow
Sustain support
Tenacious holding firmly to idea or purpose
Volatile 1. evaporates easily, 2. easily angered; emotional

 

Word List - Official SAT Study Guide Test 6

Word Definition
Adroit skilful (Maladroit = clumsy)
Agnostic unsure of the existence of god
Ameliorating making better
Arboreal living in trees
Ascertain find out; make sure
Barrage bombardment; stream (of abuse etc.)
Belabor over-emphasizing
Brevity briefness
Cacophony noise; din
Censured blamed
Circumvent avoid
Coerced forced
Condoning tolerating
Congenial friendly; sociable; suitable
Demagogues mob leaders; agitators
Disparaged criticized
Docile tame; subservient
Eclectic taking things from different sources
Elitist favoring top group; snob
Elusive difficult to pin down
Empiric found by experiment/practice
Endorsed supported
Envisioning imagining, predicting
Extolled praised
Foster support; encourage
Furtiveness secretiveness
Gluttonous greedy
Indictment charge; legal accusation
Indigenous native to a locality
Irreproachable cannot be criticized. (Reproach = criticize)
Knack trick; skill
Libelous open to prosecution for libel (Libel = written slander)
Naiveté innocence; lack of worldliness
Nihilism belief in nothing; anarchy
Paucity shortage
Penchant tendency; leaning toward
Perquisites ‘perks’
Phobic fearful
Pilfer steal
Pliant flexible
Predilection liking for; penchant
Presumption assuming too much
Profundity depth (of ideas)
Quixotic idealistic; impractical
Reclusive avoiding other people; solitary
Rehash revamp hurriedly/carelessly
Repertoire range; set of skills
Repertory story; stock; repertoire
Reprehensible very bad
Sarcasm sneering, bitter remarks; ironic or taunting
Supple flexible; pliant; lithe
Temperamental volatile; changeable
Transitory shot-lived
Tribulations troubles
Unwitting not deliberate
Venality corruption
Vulnerable open to attack; susceptible

 

Word List - Official SAT Study Guide Test 7

Word Definition
Aberration deviation; abnormality
Abstruse difficult to comprehend
Affability friendliness; cordiality
Affluence wealth and status
Alleviation making less severe
Amalgamation mixture or joining of different components
Amassed accumulated
Arcane esoteric
Augmenting increasing in size or number
Belied contradicted
Benevolent kindly
Callous cruel and unfeeling
Candid truthful; honest
Coalition a union of two parts
Concordance agreement
Conflagration big fire
Copious in large amounts
Dearth shortage
Debacle disaster
Disarming charming; unthreatening
Disillusioned freed from wrong ideas
Disparaging criticizing
Embellished decorated
Empathetic understanding in an insightful way
Encompassed included; surrounded
Endorsement support; approval
Entourage group of followers; retinue
Equanimity peace of mind; balance; calm
Eradicating wiping out; destroying
Esoteric obscure
Exacerbated made worse
Excised cut out
Exotic strange; foreign
Faction section; group with common interests
Finagle wheedle; wangle; trick
Grating harsh; rasping
Gratuitous free; unwarranted
Hackneyed commonplace; over-used
Insightful perceptive
Insolence rudeness
Intrigued interested and curious
Intuition sixth sense; ‘gut feeling’
Languid lacking energy; weak
Lobby 1. to try to persuade, 2. entrance hall
Lucid clear
Marred spoiled; ruined
Meager small; scanty
Monotonous dull; repetitive
Motley varied; miscellaneous
Opting choosing
Overhaul renovate
Preclude prevent
Precursors forerunners
Purportedly apparently claiming
Ratify give official approval to
Resilience strength; ability to withstand
Retraction removal; ‘taking back’
Sporadic intermittent; on and off
Spurned shunned; rejected
Substantiated backed up; given supporting evidence
Supplant replace
Truculence stubbornness
Unequivocal certain; cannot be disputed
Voluminous large; bulky; extensive
Winnow sift; separate good from bad

 

Word List - Official SAT Study Guide Test 8

Word Definition
Alacrity speed and eagerness
Amiable friendly; lovable
Apathetic lacking energy or interest
Bypasses avoids; finds a way around
Capricious whimsical; changeable
Censures blames
Conciliatory seeking compromise
Convergence coming together
Cumulative building up
Deferment putting off
Deliberation careful thought
Delineates outlines
Derelict rundown; abandoned
Discrepancy inconsistency
Embittered full of bitter feelings
Encroaching trespassing
Eradicate wipe out
Exacerbates makes worse
Exasperation frustration and annoyance
Exorbitant excessive
Flabbergasted shocked; speechless
Foil for person that shows another to advantage
Frugal economical
Glacial icy; unfriendly
Grimy dirty
Inconsequential unimportant
Indiscernible not easy to see
Infusion influx
Integrity honesty
Jaded tired; bored
Juxtaposition placing two thing nest to each other
Lithe flexible
Miffed annoyed
Mitigator moderator
Modicum tiny amount
Negate wipe out
Nondescript having no special qualities; ordinary
Penurious miserly
Phlegmatic calm; imperturbable
Razing cutting down
Recrimination blame
Reprieve let off (at least temporarily)
Rousing stirring
Salvageable can be saved
Scouring cleaning thoroughly; thorough searching
Secluded lonely; isolated
Solace comfort
Squelch suppress; crush
Stifling suppressing
Surfeit excess
Tangential off the point; irrelevant
Temper moderate
Tremulous hesitant
Unyielding not giving up
Vigilant wary; watchful
Waning declining
Warped twisted; distorted
Wary cautious
Wrath anger

 

Word List - Official SAT Study Guide Test 9

Word Definition
Alleviate make less severe
Amalgam mixture
Astute wise; mentally sharp
Autonomous self-governing
Belied contradicted
Callousness cruelty; unfeeling behavior
Circumstantial accidental; indirect (as in circumstantial evidence)
Corroborated supported; given supporting evidence
Credulity belief
Debilitated weakened
Deliberation careful thought
Denuded stripped
Derided mocked
Despoiled spoiled
Dilatory slow; sluggish
Dispatch speed and eagerness
Empathetic exhibiting deep emotional understanding
Eradicate wipe out
Estrangement separation
Expeditious speedy
Extant still in existence
Flag 1. to lose energy, 2. to signal
Foundered sank
Fraudulent crooked; intending to cheat
Hubris excessive pride
Idiosyncratic eccentric
Impetuosity impulsiveness
Impudent cheeky
Indomitable unshakeable; fearless
Innocuous harmless
Insolvent bankrupt
Irresolute lacking firmness of purpose; hesitant
Irreverent lacking respect
Manipulative deceptive; skilful at handling people
Morbidity concern with death and disease
Myopic short-sighted (literal or metaphoric)
Occlusion shutting out
Officious interfering
Peevishness childish sullenness; irritability
Placid peaceful
Prudent wise; cautious
Punctilious meticulous
Rambunctious boisterous
Rancor bitterness and bad feeling
Scrutinize examine carefully
Scuttled sunk
Sedate calm; placid
Serene peaceful
Squander waste
Validated proved right
Valor bravery
Vulnerable open to attack; susceptible

 

Word List - Official SAT Study Guide Test 10

Word Definition
Adroitness skill
Altruism self-sacrifice
Arbitration mediating between disputing sides
Archaic old-fashioned
Aural through the sense of hearing
Cognitions mental knowledge
Discernment judgment;
Disingenuous crafty
Distension swelling
Egotists selfish people
Emancipators those who set others free
Enigmas puzzles
Erudition learning; scholarly knowledge
Exemplars excellent examples of
Exonerated proved not guilty
Extirpation destruction
Fawning groveling; ‘sucking up’ to people
Finesse skill
Fitful intermittent; on and off; not continuous
Gestures signals
Hilarity great laughter
Husbandry careful management of resources
Ignominy shame
Ineptitude lack of ability
Insipid flavorless; bland
Intuitions gut feelings
Invocation prayer
Irony something unexpected; use of words to convey opposite meaning
Lackadaisical lazy
Lamentable regrettable
Mandate permission
Manifesto statement of values
Modicum tiny amount
Notoriety infamy
Obsequious groveling
Opulence lavish display of wealth
Pathos sadness; stirring the emotions
Plaudits praise
Prospectus brochure
Raze knock down
Rectitude uprightness
Reprimanded scolded
Rudimentary elementary; basic
Sarcasm mockery
Soporific sleep-inducing
Stipulated insisted
Tactile through the sense of touch
Tenacity firmness of purpose
Versatility ability to do many things
Vicarious experienced indirectly; at secondhand

 


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