a+b=c AP Calculus The following 15 questions are typical Multiple Choice without a calculator questions. Work through these and then check your answers with the solutions given. 1. The relative maximum of the function 2. Evaluate S x /3dx if x > 0, f(x) = 3x2 -x'is: a. 2 x 2 / 3 + C a. (0, 0) only b. (1, 2) only b. -2x-4/3+ C c. (2, 4) only -2x /3 + C C. - 7X d. (4, -16) only e. (0, 0) and (2, 4) d. 2x /3 + C e . -2x-4 /3 + C 3. Find f' (0), if f (x) = V3 sin x + 2 4. The figure below shows the graph of the a. velocity function of a moving object. At ONIN which of the labeled points is the speed b. the greatest? C. a. A b. B d. C. C e . d. D e . E 5. What is the area in the first quadrant 6. At x = -1, the graph of f (x) = 2x2 + bounded by y = x2 + 1 and y = 5? has an inflection point. What is the value a. of k? b. a. -2 -1 C . C. 0 d. d. 1 e . 2 7. If the position of a particle at time t is 8. The maximum value of given by s(t) = what is the 1-t f(x) = 2x3 - 9x2 + 12x - 1 on [-1, 2] acceleration of the particle at t = 0? is a. -4 a. 0 b. -2 b. 1 c. 2 C. d. 3 d. 2 e. 4 e . 4ly=z a+b=c AP Calculus 9. So (2x3 + 3) dx = 10. The rate of decay of a radioactive a. 8 substance is proportion to the amount of b. 11 the substance present. If currently there c. 14 are 8 grams and four years ago there d. 20 were 12 grams, how many grams will e. 24 there be 8 years from now? a. 0 11. Evaluate lim - x2-5x+2 b . x-00 3x3+2x2-1 C . a. 7 b. 0 d. c. -2 e . d. co e. 3 12. The graph of a function f is shown below. At which value of x is f dx 13. Find ~ when x = 1, for continuous, but not differentiable? x3 + 2x2y - 4y = 7 a. -8 a. a b. b b. - C. C c. -3 d. d d. 0 e. e 7 e . = 14. Find the average value of 15. The graph of a function f (x) is shown f (x) = x3vx4 + 9 on [0, 2]. below. Which of the following 49 a. statements about f is true? I. limf (x) does not exist b. - II. limf (x) =4 C. x-b 125 III. limf (x) = 4 x -a a. I only e. b. II only c. III only d. I and II e. II and IIIPUES T b Caleulus 1. The values of a function are given in the table below. Use a trapezoidal approximation for fum f(x)dx using 10 trapezoids. x Jo [1 [2 /3 J4 15 [6][7 |8 |9 [10 A. 30.825 B. 32.500 C. 33.325 D. 33.333 B, 35.825 2. The area of the region enclosed by the graphs of y = e** 2andy = V4 xZis A. 2,525 B. 4.049 C. 4328 D. 5.050 E. 6.289 3. If A(t) = 4000 + 48(t 3) 4(t 3)* is the amount of a certain item produced in a factory where t is time in hours since 8:00 am. At what time is the production level increasing the fastest? A. 8:00am B. 10:00am C. 11:00am D. 12:00 noon E. 1:00 pm 4. If f'(x) = e*(x* + 3x) 3 for 0 0 measured in hours. If the tank started empty, how many gallons of water are in the tank after 4 hours? A. 600 B. 900 C. 1200 D. 1600 E. 2400 7. The region in the first quadrant enclosed by y = 2 sin x and y = x is revolved about the x- axis. Find the volume of the resulting figure. A. 1.895 B. 2.126 C. 5.811 D. 6.678 E. 13.355 x/y=Z a+b=c AP Calculus 8. The equation of the tangent line to f (x) = x3 - 6x2 at its point of inflection is A. y = -12x + 8 B. y = -12x + 40 C. y = 12x - 8 D. y = -12x + 12 E. y = 12x - 40 9. If f' (x) = sin(x*), then how many critical points does the function f (x) have on the interval [0.2, 2.6]? A. 0 B. 1 C. 2 D. 3 E. 4 10. Find a + b, if f (x) = Sex+2 x is differentiable at x = 0 A. 0 B. 1 C. 2 D. 3 E. 4