AP Calculus Chapter 2 Practice Test

Transcription

1 AP Calculus Chapter 2 Practice Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Assume that a watermelon dropped from a tall building falls y = 16t2 ft in t sec. Find the watermelon's average speed during the first sec of fall. A) 40 ft/sec B) 81 ft/sec C) 160 ft/sec D) 80 ft/sec 1) Determine the it by substitution. 2) (x2 - ) A) Does not exist B) 0 C) - D) 2) 3) x3-6x + 8 x - 2 A) 4 B) -4 C) 0 D) Does not exist 3) 4) x 3 x2 + 12x + 36 A) Does not exist B) 9 C) ± 9 D) 81 4) 1

2 Complete the table and state the f(x). Round table values to six decimal places when necessary. ) f(x) = x 2 + x + 12 x + 4 ) f(x)???????? A) B) f(x) = 3 f(x) = 4 C) none of these D) f(x) = 3 Determine the it algebraically, if it exists. 6) x -4 x2-16 x + 4 A) -4 B) Does not exist C) -8 D) 1 6) 7) x2 + 3x - 10 x 2 x - 2 A) 3 B) Does not exist C) 0 D) 7 7) 8) 1 x x 8) A) 0 B) C) 1 36 D) Does not exist 2

3 Determine the it graphically, if it exists. 9) f(x) x -1/2 9) A) Does not exist B) -2 C) 0 D) -1 Find the indicated it. 10) x 7 - int x A) 6 B) -6 C) 0 D) 7 10) 11) + 9x x A) 0 B) Does not exist C) -9 D) 9 11) Find the it. 12) Let f(x) = 8 and x -1 A) 16 2 g(x) = 8. Find x -1 B) 32 x -1 [f(x)]2 2 + g(x). C) -1 D) 4 12) Evaluate or determine that the it does not exist for each of the its (a) x d- f(x), (b) x d+ f(x), and (c) x d f(x) for the given function f and number d. 13) f(x) = 7x - 10, for x 1, 3x - 6, for x > 1 13) d = 1 A) (a) -10 (b) -6 (c) Does not exist C) (a) -3 (b) -3 (c) Does not exist B) (a) -3 (b) -3 (c) -3 D) (a) -6 (b) -10 (c) Does not exist 3

4 Provide an appropriate response. 14) If x 3 f(x) x for x in [-1, 1], find f(x) if it exists. A) -1 B) 1 C) 0 D) Does not exist 14) Find the it. 1) x 6x x - 7 1) A) 3 8 B) C) D) 0 Find the indicated it. 16) x 1- cos x x2 A) B) - C) 1 D) 0 16) Find the it. 17) x (-2) + 1 x ) A) 1 2 B) - C) D) ) x (π/2) + tan x A) 0 B) 1 C) D) - 18) 19) + (1 + csc x) A) - B) C) 1 D) 0 19) Find the vertical asymptotes of the graph of f(x). 20) f(x) = csc x 20) A) x = nπ, n is any integer B) no vertical asymptotes C) x = 0 D) x = π 2 + nπ, n is any integer Find a power function end behavior model. 21) y = 8x 2 + x - 1 x3 - x2 A) y = 8x B) y = 8x + 1 x2 - x C) y = x 8 D) y = 8 x 21) 4

5 Find the points of discontinuity. Identify each type of discontinuity. 22) y = 1 (x + 3) A) x = -3, jump discontinuity B) x = -3, infinite discontinuity C) None D) x = 1 22) 23) y = x ) A) x > - 9, all points not in the domain B) x = - 9, infinite discontinuity C) x < - 9, all points not in the domain D) x = - 9, jump discontinuity Provide an appropriate response. 24) Given f(x) = 3 3x and g(x) = x - 7, where is the function f(x)/g(x) continuous? A) The function f(x)/g(x) is continuous for all x except x = 7. B) The function f(x)/g(x) is continuous for all x. C) The function f(x)/g(x) is continuous for all x except x < 0 and x = -7. D) The function f(x)/g(x) is continuous for all x except x = ) Solve the problem. 2) The graph below shows the amount of income tax that a single person must pay on his or her income when claiming the standard deduction. Identify the income levels where discontinuities occur and explain the meaning of the discontinuities. 2) Income Tax, 1000's of dollars Income, 1000's of dollars A) Discontinuities at x = $22,000, x = $44,000, and x = $60,000. Discontinuities represent tax cheating on the part of high-income earners. B) Discontinuities at x = $44,000 and x = $60,000. Discontinuities represent boundaries between tax brackets. C) Discontinuities at x = $22,000, x = $44,000, and x = $60,000. Discontinuities represent boundaries between tax brackets. D) Discontinuities at x = $44,000 and x = $60,000. Discontinuities represent tax shelters.

6 Find the average rate of change of the function over the given interval. 26) f(x) = x 2 + 2x, [2, 6] A) 8 B) 20 3 C) 10 D) 12 26) 27) f(x) = 8 + cos x, [0, π] 27) A) 0 B) 1 π C) 8 π 2.46 D) - 2 π Find the slope of the line tangent to the curve at the given value of x. 28) f(x) = -10x x; x = 8 A) -148 B) -192 C) -106 D) ) 29) f(x) = -4 x at x = 11 29) A) B) C) 4 11 D) 11 4 Find the instantaneous rate of change of the position function y = f(t) in feet at the given time t in seconds. 30) f(t) = t3-4t2 + 2, t = 3 A) 21 ft/sec B) 66 ft/sec C) 113 ft/sec D) 111 ft/sec 30) Solve the problem. 31) Find the points where the graph of the function has horizontal tangents. f(x) = x2 + 3x - 4 A) 3 10, B) , C) (0, 4) D) (-13, 182) 31) 32) For a motorcycle traveling at speed v (in mph) when the brakes are applied, the distance d (in feet) required to stop the motorcycle may be approximated by the formula d = 0.0v2 + v. Find the instantaneous rate of change of distance with respect to velocity when the speed is 41 mph. A) 10.2 mph B) 4.1 mph C).1 mph D) 42 mph 32) 33) A cubic salt crystal expands by accumulation on all sides. As it expands outward find the rate of change of its volume with respect to the length of an edge when the edge is 0.31 mileter. 33) A) 0.09 mm3/mm B) mm3/mm C) 2.88 mm3/mm D) mm3/mm 6

7 Answer Key Testname: CHAPTER 2 PRACTICE 1) D 2) C 3) B 4) B ) D 6) C 7) D 8) B 9) D 10) A 11) D 12) B 13) B 14) C 1) A 16) D 17) C 18) D 19) B 20) A 21) D 22) C 23) C 24) A 2) C 26) C 27) D 28) A 29) B 30) D 31) B 32) C 33) D 7