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Unformatted text preview: AP Calculus (BC) Chapter 3 Test No Calculator Section
Name: Date: Period: Part I. MultipleChoice Questions (5 points each; please circle the correct answer.) 3x2 + x , then g (x) = 3x2 − x 1. If g (x) = (A) 1 6x2 + 1 (B) 2 6x − 1 −6 (C) (3x − 1)2 −2x2 (D) 2 (x − x)2 36x2 − 2x (E) 2 (x − x)2 2. If the function f (x) is differentiable for all x and if f (x) = then a = (A) 0 (B) 1 (C) −14 (D) −24 (E) 26 ax3 − 6x bx2 + 4 if x ≤ 1 if x > 1, 3. Find the slope of the normal line to the graph of y = x + cos xy at the point (0, 1). (A) 1 (B) −1 (C) 0 (D) 2 (E) Undeﬁned The next two questions pertain to the function f , whose graph is given below: 10 y y=f(x) 5 x 6 4 2 5 10 2 4 6 4. For the function f , I. f (−3) > 0 II. f (0) < 0 III. f is differentiable on the interval (0, 1) (A) I only (B) II only (C) III only (D) I and II (E) I, II, and III 5. For the function f I. f (x) > 0 on the interval (−5, −4) II. f (x) is constant on the interval (4, 6) III. f is not deﬁned at all points of (1, 5) (A) I only (B) II only (C) III only (D) I and II (E) II and III Part II. FreeResponse Questions 6. The graph below depicts the velocity v = s (t) of a particle moving along a straight line, where on this straight line positive direction is to the right. s=0
(negative direction = left) 5 (v = velocity) 4 3 2 1 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 10 (t = time) (positive direction = right) (a) (1 point) Would you say that at time t = 1 the particle is moving to the left, moving to the right, or not moving at all? Please explain. (b) (1 point) Would you say that at time t = 3 the particle is moving to the left, moving to the right, or not moving at all? Please explain. (c) (2 points) Find (estimate) two values of t at which time the particle is not accelerating. (d) (2 points) Find (estimate) a value of t at which time the particle is moving to the left, but with zero acceleration. (e) (2 points) According to this graph, at how many distinct times is the particle at rest? (f) (2 points) For which values of t is the particle not only at rest, but is not accelerating (i.e., has no forces acting on it)? (g) (2 points) According to this graph, at how many distinct times is the particle not accelerating? 7. (6 points) Let f and g be differentiable functions and assume that f (1) = 2, f (1) = 1, g (1) = −1, g (1) = 0. Compute h (1), given that h(x) = x2 f (x)g (x). 8. Note that the point (1, 2) is on the curve deﬁned by y 3 − xy 2 − x2 y − 2 = 0. (a) (3 points) Compute
dy dx at the point (1, 2). (b) (4 points) Find an equation of the straight line normal to the above curve at the point (1, 2). AP Calculus (BC) Chapter 3 Test Calculators Allowed
Name: Date: Period: Part III. MultipleChoice Questions (5 points each; please circle the correct answer.) √ 9. You are given the function g (x) = (A) x = (B) x = 22 1 (C) x = ± 2
1 2 √ xe−x . The solutions of g (x) = 0 are 2 (D) x = ± 22 (E) g (x) = 0 has no solutions. √ 10. What is the equation of the line tangent to the graph of y = sin2 x at x = π 1 =− x− 2 4 π 1 (B) y − = x − 2 4 1 π (C) y − √ = x − 4 2 1 1 π (D) y − √ = x− 2 4 2 1 1 π x− (E) y − = 2 2 4 (A) y − π ? 4 11. If f (x) = 3x2 − x and g (x) = f −1 (x), then g (10) could be (A) 59 1 (B) 59 (C) 11 1 (D) 11 1 (E) 10 √ 12. If f (x) = x2 3x + 1, then f (2) ≈ (A) −6.05 (B) 15.12 (C) −10.58 (D) 12.85 (E) 8.31 13. The position of a particle moving along the xaxis at time t is given by x(t) = ecos 2t , 0 ≤ t ≤ π . For which of the following values of t will x (t) = 0? I. t = 0 π II. t = 2 III. t = π . (A) I only (B) II only (C) I and III only (D) I and II only (E) I, II, and III Continue to the next page Part IV. FreeResponse Questions 14. In the ﬁgure to the right, a line is given tangent to the 1 graph of y = 2 at point the P , whose coordinates are x 1 w, 2 , where w > 0. Point Q has coordinates (w, 0). w This line crosses the xaxis at the point R, with coordinates (k, 0). (a) (5 points) For all w > 0, ﬁnd k in terms of w.
y .
Q y=1/x 2 P . R . x (b) (5 points) Suppose that w is increasing at the constant rate of 7 units per second. When w = 5, what is the rate of change of k with respect to time? (c) (5 points) Suppose that w is increasing at the constant rate of 7 units per second. When w = 5, what is the rate of change of the area of P QR with respect to time? Determine whether the area is increasing or decreasing at this instant. 15. (10 points) Two particles leave the origin at the same time and move along the y axis with their respective positions determined by the functions y1 = cos 2t and y2 = 4 sin t. For which values of t, 0 ≤ t ≤ 2π do these particles have the same acceleration? End of test ...
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This note was uploaded on 12/01/2009 for the course BIO 071265836 taught by Professor Solana during the Spring '09 term at Air Force Institute of Technology, Ohio.
 Spring '09
 Solana
 Biology

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