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.