AP Calculus AB Summer Review Packet

Transcription

1 AP Calculus AB Summer Review Packet Mr. Le Leuzinger High School Rm. G-0 The following packet is designed to help you review topics that are important to your SUCCESS in AP Calculus. Students enrolled in AP Calculus AB at Leuzinger High School in are to complete the following problems in this packet during the summer prior to the start of the school year. All work must be shown in the packet or on a separate piece of paper attached to the packet. Please make reference to your notes from Algebra / Pre-Calculus or online math tutorials if you need support in mastery of any of the types of problems included in the packet. You can also me if you have any questions. I will post worked-out solutions on my Leuzinger.org teacher webpage about every - weeks so you can check your answers and know that you are on the right track. Please put forth your best effort! All problems should be completed without a calculator, unless otherwise stated. Use the summer to freshen up on your algebra skills. Be ready when you step into my class.

2 I. SOLVE MULTI-STEP EQUATIONS Solve for the variable ( + 16) = 7. a = a c c =. + = 7 6 Solve for z yz = 0 6. y + yz 8z = 0

3 II. SOLVE SYSTEMS OF EQUATIONS = + = + c b c b = + = b a b a. = + = y y. 8 5 = = + c b c b

4 III. FUNCTIONS Let f ( ) = + 1 and g ( ) = 1. Evaluate. 1. f () =. f (t + 1) =. f [g( )] =. g [ f ( m + )] = Let f ( ) =, ( ) = + 5 g and h ( ) = 1. Evaluate. 5. h [ f ( )] = 6. g [ h( )] = IV. INTERCEPTS Find the and y intercepts. 1. y = 5. y = +. y = 16. y =

5 V. EQUATION OF A LINE Slope-Intercept form: y = m + b Vertical line: = c (slope is undefined) Point-Slope form: y y = m ) Horizontal line: y = c (slope is 0) 1 ( 1 1. Determine the equation of a line passing through the point (5,-) with an undefined slope.. Use point-slope form to find the equation of the line passing through the point (0,5) with a slope of /. 5. Find the equation of a line passing through the point (,8) and parallel to the line y = Find the equation of a line perpendicular to the y-ais passing through the point (,7). 5. Find the equation of a line passing through the points (-,6) and (1,). 6. Find the equation of a line with an -intercept of (,0) and a y-intercept of (0,).

6 VI. FACTORING AND RATIONAL EXPRESSIONS Simplify each rational epression h

7 VII. LOGARITHMS AND RATIONAL EXPONENTS Evaluate. ln 1. ln 1. e ( 1 ln ). e + 7. ln e 5. log (1/ ) 6. log 1 / 8 / ( a ) 5/ / / 9. (5a )(a / y ) 10. 1/ 5 1 y

8 VIII. SOLVE Solve for, where is a real number = 1. 1 = 0. ( 5) = = 8 5. ( + )( ) = = = 8. < = log + log( ) = 1

9 IX. TRIGONOMETRIC IDENTITIES =. = sin cos. 1 sin =. = tan cos 5. sin + cos = tan = 7. cot +1 = 8. cos = 9. sin = 10. tan = X. TRIGONOMETRIC EXPRESSIONS Without a calculator, determine the eact value of each epression. 1. sin 0. sin π. sin π. cos π 5. cos π 6. tan π 6

10 7. cos π 8. cos0 9. tan π 10. cos π sinπ 1. cos π 1. sin π 1. tan π XI. INVERSE TRIGONOMETRIC FUNCTIONS For each of the following, epress the value for y in radians. 1. y = arcsin. y = arccos(1) 1. y = arcsin. y = arctan(1)

11 Completely fill out the Unit Circle.

12 XII. GRAPH Graph each function. Give the domain and range. 1. y = sin. y = cos Domain: Range: Domain: Range:. y = tan. y = e Domain: Range: Domain: Range:

13 5. y = 6. y = Domain: Range: Domain: Range: 7. y = ln 8. y = + Domain: Range: Domain: Range:

14 9. y 1 = y = 1 Domain: Range: Domain: Range: 11. if y = + if if < 0 0 > 1. y = + if + if 1 > 1 Domain: Range: Domain: Range:

15 XIII. Limits, Continuity, Derivative (using limit definition) 1. Provide a complete definition of a limit.. How do you determine if a limit eists?. Provide a difference between a defined function and a limit of a function.. Provide a complete definition of continuity. 5. Based on the given table, what statement can you make regarding limits? Justify.

16 6. Given the tables below, find the following limit: 7. Given the following table, is the function continuous at a = 5? Justify y What can you conclude given a relation with the following values? Justify y

17 9. Find the limit. If it does not eist, justify: 10. Find the limit. If it does not eist, justify: 11. Is the function continuous or discontinuous? Justify: 1. Find the derivative of the function (using the limit definition) given:

18 1. Graph the following piecewise function: 1. In regards to #1, is the function continuous or discontinuous? Justify.

19 15. Provided the graph to the right, find the following: a. b. c. d. Is the following statement true or false? Please justify. The function is continuous at a =. 16. Sketch a graph satisfying all of the following conditions.