Function

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Curves

Analytic geometry

equations

Multivariable calculus

Name:________________________ Date:________________________ AP Calculus BC Class Activity 5a: Parametric Equations Complete the value of table below and graph the curve for and y = t x y -2 -1 0 1 2 3 Complete the table below and graph the curve for and . t x y 0 ? 2? For the following problems eliminate the parameter and find y as a function of x. and and Given the function below and an equation for x, find one parametric curve that could represent it: and and Use

Graphs and Graphing Utilities

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Graphing calculators

Programmable calculators

Trigonometric functions

TI-83 series

TI-Nspire series

1.1 - Graphs and Graphing Utilities TI-82 There are several kinds of graphs that the TI-82 or TI-83 will do, but they are accessed from the same key. The [y=] key and the [2nd] [y=] or [StatPlot] key. The two major kinds of plots may cause confusion when mixed, so it is best to turn off all unnecessary plots before trying to graph an equation. To turn off all statistical plots, hit [StatPlot] and choose option 4 - PlotsOff. Hit enter to finish the command. To turn off a regular plot, one can either hit [Clear] while on an equation, or arrow to the left so that the cursor is on the equal sign, and press enter to toggle the display of that equation. Graphing Equations with the Calculator

2008 AP MC

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Section I The Calculus BC Exam AP Calculus BC Exam SECTION I: Multiple-Choice Questions At a Glance Total Time 1 hour, 45 minutes Number of Questions 45 Percent of Total Grade 50% Writing Instrument Pencil required Part A Number of Questions 28 Time 55 minutes Electronic Device None allowed Part B Number of Questions 17 Time 50 minutes Electronic Device Graphing calculator required Instructions Section I of this exam contains 45 multiple-choice questions and 4 survey questions. For Part A, fill in only the ovals for numbers 1 through 28 on page 2 of the answer sheet. For Part B, fill in only the ovals for numbers 76 through 92 on page 3 of the answer sheet. The survey questions are numbers 93 through 96.

2003 AP MC

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Integration by substitution

Trigonometric functions

Taylor series

integral

Technology

? ? ? ? ? ? ? ? ? ? ? ? ? ? M AREA - COMPLETE THIS AREA AT EVERY EXAMINATION. ~The AP"'ADVANCEDTo maintain lhe security 01 lhe exam and the vaftdily 01 my AP grade, I will allow no one other than myseff to see the multiple-ohoice queslicns and wiD seal the appropriate section when asked to do so. t will not discuss these questions .. .. College PLACEMENT PLACE AN AP ? NUMBER LABEL _ Board PROGRAM" Iwith anyone at any time after the completion of the multipl_ section. I em awam 01 and agree 10 the Program'. ~ policies and procecilJteS as outlined in the 2003 Buffetin for AP Stt.tdImts and Parents. OR WRITE YOUR AP NUMBER Answer Sheet for May 2003, Form 3ZBP HERE AT EVERY EXAMINATION. PAGE 1 ,...,. W Plintexamination name:.______________________

exponential logarithmic functions

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Special functions

Exponentials

Base

Seartec Trading (Pty) Ltd. Official SHARP importer & distributor for Southern Africa Worksheet 3 Memorandum: Functions ? Exponential and Logarithmic Grade 12 Mathematics CAPS 1. A quantity representing the power to which a number (the base) must be raised to produce a given number. Remember 2. - if powers with same bases are multiplied the exponents are added ? - if powers with the same bases are divided the exponents are subtracted ? - anything to the power of zero is 1 ? - when a power is raised to another exponent ? the exponents are multiplied ? ( ) - when a power is under a root-sign, the exponent of the power is divided by the root-value ? ?

Calculus AB #2

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Ordinary differential equation

Elementary algebra

equations

Multivariable calculus

Linear equation

Function

Curve sketching

education

?3 ?2 ?1 1 2 3 4 16 ?12 ?8 ?4 4 8 12 Ws 1 ? review intercepts, linear equations, inequalities, symmetry, domain/range Calculus AB SHOW WORK IN YOUR NOTEBOOK. Find the x and y intercepts of each. 1. 1 4 2 y x= ? 2. 2 3 6x y? = 3. 3 24 4 15y x x x= + ? 4. 22 11 6y x x= + ? Name the domain and range of each. Write your answers in interval notation. 5. ( ) 1 3 f x x = ? 6. 3y x= + 7. 236y x= ? 8. ( ) 3xg x x += Linear equations 9. Find the equation of the line that passes through the points (2,-3) and (-3,-1) in standard form. 10. Find the equation of the line that passes through the points (-3,-3) and (5,0) in point slope form. 11. Find the equation of the line that passes through the points (2,-5) and (2,-6) in any form.

AP Calc AB 2002 Free Response Questions

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Advanced Placement Calculus

Differential calculus

L'Hôpital's rule

education

AP? Calculus AB 2002 Free-Response Questions These materials were produced by Educational Testing Service? (ETS?), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle. The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to college and opportunity. Founded in 1900, the association is composed of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the

INTERMEDIATE ALGEBRA EXAM

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Implicit and explicit functions

Inverse functions

polynomials

Completing the square

Function

Logarithm

education

MATH EXAM 1 THRU 4 1 MATH EXAM #1 1. Determine whether the diagram defines y as a function of x. if it does not, indicate a value x that is assigned more than one value of y X y -4 5 -3 7 4 9 4 11 2. GRAPH THE FUNCTION: h(x) =|4-x| X h(x) 3 1 4 0 5 1 6 2 2 2 1 3 3. Determine the graph of the solution of the given system. X + Y > 2 X - Y < 2 MATH EXAM 1 THRU 4 2 3 Determine whether the graph is a function 4. THE GRAPH OF A SYSTEM OF 2 LINEAR INEQUALITES IS SHOWN. TELL WHICH POINT IS A SOLUTION OF THE SYSTEM. MATH EXAM 1 THRU 4 3 6. FIND THE SOLUTION OF THE SYSTEM. X > -2 Y > -4

EXPONENTIAL AND LOGARITHMIC FUNCTION EXAM

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Special functions

logarithms

E

Exam 4 Which of the following ordered pairs is a solutuion of (-2,-36) c. (-2,1/36) (-2,1/12) d. (-2,-12) Use composition to show that the pair of functions are inverses. Let find f-g the graph represents a function use the horizontal line test to decide where function is one to one If the function is one to one, find its inverse Find the inverse of the function. Then graph the function and its inverse on one coordinate system. Show line of symmetry on graph Let find the composition (f ? g)(x) Write in exponential form Evulatate the expression Evaluate the expression. Evualtae the expression Write the logarithm as a sum/ difference of logarithms of a single quanity. Then simplify if possible

FORMULAS, LITERAL EQUATIONS , INEQUALITIES AND FUNCTIONS EXAM

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