By William Ma

ISBN-10: 007137714X

ISBN-13: 9780071377140

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**Additional resources for AP Calculus AB**

**Example text**

Draw a possible graph of f ′ on (a, b). Figure D-2 y 10. If h( x) = f x ∫π 2 sin t dt , find h′(π). 11. What is the average value of the function y = e−4x on [−ln 2, ln 2]? a c 0 d e f b x 12. The graph of f consists of four line segments, for −1 ≤ x ≤ 5 as shown in Figure D-3. What is the value of ∫ f ( x)dx ? 5 −1 y Figure D-1 6. If f ( x) = 2xe x , what is the value of lim f ′( x) ? f x → 0+ 7. Evaluate 8. If ∫ 1 − x2 dx. x2 ∫ (2x − 3)dx k −1 –1 0 1 2 3 = 6, find k. 9. The graph of the velocity function of a moving particle is shown in Figure D-2.

Set v(t ) = 0 ⇒ t (t − 1) = 0 ⇒ t = 0 or t = 1 16. From Chapter 8 Let u = 3x; du = 3dx or ∫ g(3x)dx a(t ) = v ′(t ) = 2t − 1 du = dx 3 Set a(t ) = 0 ⇒ 2t − 1 = 0 or t = du 1 g(u) = ∫ g(u)du 3 3 = ∫ = 1 1 f (u) + c = f (3x) + c 3 3 ∫0 g(3x)dx = Since the graph of g is decreasing and then increasing, It is not monotonic. Thus only statements II and III are true. At x = 0, y = cos( xy) = cos(0) = 1; (0, 1) 2 d ( tan x) x 4 dx π = sec2 = 4 15. From Chapter 6 y = cos( xy) ; ∆x 1 Since v(t ) < 0 and a(t ) > 0 on , 1 , 2 the speed of the particle is decreasing on 2 1 1 1 f (3x)]0 = f (6) − f (0) [ 3 3 3 1 , 1 .

Org/ap/calculus. What Are the Advanced Placement Exam Grades? Advanced Placement Exam grades are given in a 5-point scale with 5 being the highest grade. The grades are described below: 5 4 3 2 1 Extremely Well Qualified Well Qualified Qualified Possibly Qualified No Recommendation 0267-02/Part II 12/18/2001 17:23 Page 14 14 • What You Need to Know About the AP Calculus AB Exam How Is the AP Calculus AB Exam Grade Calculated? • The exam has a total raw score of 108 points: 54 points for the multiple-choice questions in Section I and 54 points for the free-response questions for Section II.

### AP Calculus AB by William Ma

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