To: AP Calculus AB students and those who will take BC Calculus in the spring Re: Course requirements and summer assignment From: Sister Mary Butler

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1 To: AP Calculus AB students and those who will take BC Calculus in the spring Re: Course requirements and summer assignment From: Sister Mary Butler Net year, 08-09, I will teach the Advanced Placement Calculus courses. As you know from the course description, these are college-level courses. Each course culminates with an AP eam administered early May, which you are required to take. Because of the date of the test we will need to finish the course content by mid April, so we can have ample time to review all the topics. Success in the AP eam can result in earned college credit and /or advanced standing in college depending upon your choice of school and its policies. The tet we will use is Calculus Graphical, Numerical, and Algebraic Fifth Edition by Finney, Demana, Waits, Kennedy, and Bressoud. AP students purchase their calculus books so they can highlight important definitions and/or write marginal notes. You are responsible to acquire this tet. You can probably get it cheaper on-line or you can purchase used. Note: this book has a yellow cover design. In order to begin with a fresh, energetic start in Calculus, I am requiring that this summer you will be responsible for the review of precalculus topics. Chapter covers the prerequisites for Calculus that you have studied in a previous course. Be particularly sure you have mastered trigonometry and know, without using a calculator, the trig functions of p, p 3.p 4, p. Knowing the graphs, equations, domain and range of the 6 basic functions is etremely helpful to be successful in the course. The Summer Assignment gives the type of questions you are responsible to know. Khan Academy has helpful videos if you need a refresher lesson The College of William and Mary and the University of Albany have calculus readiness tests on line. I am looking forward to our time together net year - the knowledge we ll share, the truth we ll pursue, and the fun we ll have.

2 REVIEW FOR AP CALCULUS. The value of k for which the line 3 + ky 5 = 0 is perpendicular to the line y + 7 = 0 is A. 3 B. 3 C. 6 D. 6 E. 3. The graph of y 4y = 3 is symmetric to A. the -ais B. the y-ais C. the origin D. the line y = E. none of the preceding 3. An equation of the reflection of y = 3 e in the -ais is ( ) A. y = e 3 B. y = e 3 C. y = 3 e D. y = ln 3 E. y = 3 + e 4. If < 0 and f ( ) = then f ( f ( ) ) is equal to A. B. C. 5. The set of real for which f g( ) D. ( ) = g ( f ( ) ), where f E. undefined ( ) = + and g ( ) = 3, is A. { 0, } B. { 0,} C. {,3} D. { 3,} E. φ ( ) = 6. If f ( ) = and g ( ) = 5, then g f ( ) A B C. 5 D. 305 E If and y are real numbers, the domain of the function f ( ) = + 9 A. all B. > 3 or < 3 C. D. all ecept = 9 E. all ecept = 3 or 3 8. Which of the following is the set of all real numbers such that 5 5? A. R B. { 5} C. { 5} D. { : 0} E. { : 0} is 9. Which of the following has a real root? A = 0 B. ( ) + 3 = 0 C. + = 0 D. + ( ) + = 0 E. + 5 = 0 0. If F ( ) = +3 4, then F 5 ( ) = A. 6 B. 0 3 C. 5 D. 3 4 E. 8

3 . Given a rectangle with sides of length and width y. Suppose the length is doubled and the width y is halved. The new perimeter is A. 4 + y B. ( ) y C. + y. If f ( ) = 7 + 3, then its inverse function f ( ) is 3. If r A B. r r, then 7 +3 C. f ( ) = D. D. + y E. + y E A. r 0 B. r 0 C. r 0 or r > D. r 0 or r E. 0 r < 4. If and y are real numbers, the domain of the function f ( ) = + 4 is A. all ecept = or = B. all ecept = 4 C. D. > or < E. all 5. The graph of y 4 y = is symmetric with respect to A) the origin B) the -ais C) the y-ais D) the line y = E) none of these ( ) + f ( ) = f ( + ) for all real numbers and, which of the following 6. If f could define f? A) f ( ) = + B) f ( ) = C) f ( ) = E) f ( ) = D) f ( ) = e 7. sin ( arctan) = A. 0 B. C. D. 3 E. 8. Which of the following intervals is in the domain of the function f ( ) = ln ( cos )? A. π π B. π < < π C. 0 π D. 0 < < π E. 0 π

4 9. If sin ( sin ) = 0 and 0, π, then = A. 0 B. π 6 C. π 4 D. π 3 E. π 0. If f ( ) =, then the domain of f is : A. all real B. > C. D. = 0 E. None of these. If f ( ) = A. + + ( ) = and g ( ) =, then f g( ) B. C. + + D. E.. What is the domain of the function f given by f ( ) = A. { : 3} B. : { } E. : and 3 D. : and { } C. { : } { }? 3. If f ( ) = +, then the inverse function f ( ) = A. B. + C. D. + E. 4. Which of the following does NOT have a period of π? A. f ( ) = sin ( ) B. f D. f ( ) = tan E. f ( ) = tan ( ) = sin C. f ( ) = sin 5 4 cos( + π 3 ) = A. 3 cos sin B. cos 3 sin C. cos + 3 sin D. 3 cos + sin E. 4 cos + 6. The set of real for which f g( ) ( ) = g ( f ( ) ), where f ( ) = + and g ( ) = 3, is A. { 0,} B. { 0, } C. {,3} D. { 3,} E. 7. Let f and g be odd functions. If p, r, and s are nonzero functions defined as follows, which must be odd? I. p ( ) = f ( g( ) ) II. r ( ) = f ( ) + g ( ) III. s ( ) = f ( ) g ( )

5 A. I only B. II only C. I and II only D. II and III only E. I, II, and III 8. Which of the following represents a function? A. + y = B. y = C. y = 0 D. y = ± E. 9. If f and g are inverse functions and if ( 5,0) is a point on the graph of y = g ( ), which of the following could define f? I. f ( ) = 5 II. f ( ) = III. f ( ) = + 5 A. I only B. II only C. III only D. I and II only E. II and III only 30. If f ( ) = eln A. e, then f ( ) = B. e C. D. 0 E. not defined 3. If f ( ) = eln A. e, then f ( ) = B. e C. D. 0 E. no t defined 3. For π π the line y = intersects the curve y = sin only when = A. 5π 6, π 6, π 6, 5π 6 C. π 6, 7π 6, π 6, 5π 6 B. 5π 6, π 6, 7π 6,π 6 E. π 6, 7π 6, 5π 6, π 6, π 6, 5π 6, 7π 6,π 6 D. π 6, 7π 6, 7π 6,π The set of for which and + > is A. B. < 3 or C. < 3 or > D. < 3 E. None of these 34. If f ( ) =, then f ( + ) f ( ) = A. 7 B.5 C.7 D.5 E. 7

6 35. Which of the following equations has a graph that is symmetric with respect to the origin? A. y = B. y = C. y = ( ) D. y = + E. y = ( +) 36. If the domain of the function y = sin is restricted to π 6 5π 6, then the range of the function is A. y B. y C. 0 y D. 0 y E. y FREE RESPONSE QUESTIONS. Let f ( ) = a. Find the -intercepts of the graph of f. b. Write an equation of the graph that is the reflection across the y-ais of the graph of f. ( ) = and g( ) = 4. Given f a. Find the coordinates of the point(s) common to the graphs of f and g. b. Find all the zeros of f. ( ) = sin, π π, and g( ) = for all. 3. Given f a. Sketch the graph of f. b. Let H ( ) = g( f ( ) ). Write an epression for H ( ). c. Find the domain and range of H. 4. Find the domain and the range of f defined by f ( ) = + 6