By Shirley O. Hockett, David Bock
Either Calculus AB and Calculus BC are lined during this finished AP try training guide. potential attempt takers will locate 4 perform assessments in Calculus AB and 4 extra in Calculus BC, with all questions responded and recommendations defined. The guide additionally offers an in depth 10-chapter overview masking subject matters for either checks. The authors additionally provide an summary of the AP Calculus tests, including recommendation to scholars on making top use in their graphing calculators.
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Extra info for AP Calculus
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.
The object reverses direction when the velocity changes sign, that is, when the graph crosses the x-axis. There are two such reversals—at x = a and at x = b. 31. (D) The sign diagram shows that f changes from increasing to decreasing f inc 0 f inc 2 + dec 4 + 5 – and thus f has a maximum at x = 4. Because f increases to the right of x = 0 and decreases to the left of x = 5, there are minima at the endpoints. 32. (D) Since f Ј decreases, increases, then decreases, f Љ changes from negative to positive, then back to negative.
Where should the folds be in order to maximize the volume of the trough? Justify your answer. STOP END OF PART A, SECTION II 27 Diagnostic Test Calculus AB 7_3679_APCalc_01DiagnosticAB Diagnostic Test Calculus AB 7_3679_APCalc_01DiagnosticAB 28 10/3/08 4:18 PM Page 28 AP Calculus Part B TIME: 45 MINUTES 3 PROBLEMS No calculator is allowed for any of these problems. If you finish Part B before time has expired, you may return to work on Part A, but you may not use a calculator. 4. Let C represent the curve determined by f ( x ) = 3 6 for –2 ≤ x ≤ 11.