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AP Calculus by Shirley O. Hockett, David Bock PDF

By Shirley O. Hockett, David Bock

Either Calculus AB and Calculus BC are lined during this finished AP attempt education guide. potential attempt takers will locate 4 perform tests in Calculus AB and 4 extra in Calculus BC, with all questions responded and strategies defined. The handbook additionally presents an in depth 10-chapter assessment protecting subject matters for either assessments. The authors additionally supply an outline of the AP Calculus checks, inclusive of suggestion to scholars on making most sensible use in their graphing calculators.

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0 13. (E) Since y ′ = 2(x – 3)–2 and y′′ = −4( x − 3)−3 = −4 ( x − 3)3 , y Љ is positive when x Ͻ 3. dM represents the rate of change of mass with respect to time; y is dt directly proportional to x if y = kx. 14. (D) 15. (B) 16. (E) [cos (x2)]Ј = Ϫsin (x2) . 2x. The missing factor 2x cannot be created through introduction of constants alone. 17. (E) As the water gets deeper, the depth increases more slowly. Hence, the rate 1 π /3 3 3⎛ 1⎞ π /3 tan x dx = [ − ln cos x ]0 = ⎜ − ln ⎟ . ∫ 2⎠ π/3 0 π π⎝ of change of depth decreases: d 2h dt 2 < 0.

4 dt dt (E) Let u = 2x and note that F ′( x ) = 1 . 1 − u3 Then F ′( x ) = F ′(u)u ′( x ) = 2 F ′(u) = 2 i 43. (D) v(5) Ϫ v(0) = ∫ 5 0 dx = 3 . dt 1 i . 1 − (2 x )3 a(t ) dt = − 1 π i 22 + 1 (3) (2) = − π + 3 . Since v(5) = 0, 4 2 Ϫv(0) = Ϫπ ϩ 3; so v(0) = π Ϫ 3. 102 5 44. (C) 45. (D) Let y = (x3 Ϫ 4x2 ϩ 8)ecos(x ). The equation of the tangent at point (2,y (2)) is y Ϫ y(2) = yЈ(2)(x Ϫ 2). Note that y(2) = 0. To find the y-intercept, let x = 0 and solve for y: y = Ϫ2yЈ(2). 161. 0 2 10/3/08 4:18 PM Page 37 Diagnostic Test Calculus AB Free-Response Part A AB 1.

If, when t = 0, its velocity, v, is 1 and its position, s, is 3, then at any time t (A) s = t3 ϩ 3 (D) s = (B) s = t3 ϩ 3t ϩ 1 t3 +t+3 3 (E) s = (C) s = t3 ϩ t ϩ 3 t3 t2 + +3 3 2 37. If y = f(x2) and f ′( x ) = 5 x − 1 then dy is equal to dx (A) 2 x 5 x 2 − 1 (B) 5x − 1 2x (D) 5x − 1 (C) 2 x 5 x − 1 (E) none of these 38. Find the area of the first quadrant region bounded by y = x2, y = cos (x), and the y-axis. 921 39. If the substitution x = 2t ϩ 1 is used, which of the following is equivalent to ∫ 3 4 0 (A) 2t + 1 dt ?

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