By Shirley O. Hockett, David Bock
Either Calculus AB and Calculus BC are coated during this accomplished AP try guidance handbook. potential attempt takers will locate 4 perform checks in Calculus AB and 4 extra in Calculus BC, with all questions spoke back and recommendations defined. The handbook additionally presents an in depth 10-chapter assessment masking issues for either tests. The authors additionally provide an outline of the AP Calculus tests, such as suggestion to scholars on making most sensible use in their graphing calculators.
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33 Diagnostic Test Calculus AB 7_3679_APCalc_01DiagnosticAB Diagnostic Test Calculus AB 7_4324_APCalc_01DiagnosticAB 34 10/30/09 10:48 AM Page 34 AP Calculus 33. 5 2 x On the curve of f(x) = ex – x2, the two points labeled are (0,1) and (1,e Ϫ 1). The slope of the secant line is m = Δy e−2 = = e – 2. Find c in [0,1] such Δx 1 that, f Ј(c) = e – 2, or f Ј(c) – (e – 2) = 0. Since f Ј(x) = ex – 2x, c can be calculated by solving 0 = ex Ϫ 2x Ϫ (e Ϫ 2). 351. 34. (B) y y y = ex y = ex y=2 y=2 (x,y) 1 1 x 0 (x,y) 0 Use disks; then ⌬V = R2H = (ln y)2 ⌬y.
177 7_4324_APCalc_02DiagnosticBC 10/4/09 1:31 PM Page 49 Diagnostic Test Calculus BC 49 32. If f (x) is continuous at the point where x = a, which of the following statements may be false? (A) lim f ( x ) exists. (B) lim f ( x ) = f (a). (D) f (a) is defined. (E) lim f ( x ) = lim+ f ( x ). x→a (C) f ′(a) exists. x→a x→a x→a 33. A Maclaurin polynomial is to be used to approximate y = sin x on the interval Ϫπ Ϲ x Ϲ π. 1? (A) 3 (B) 4 (C) 5 (D) 6 (E) none of these 34. Find the area bounded by the y-axis and the curve defined parametrically by x(t) = 4 – t2, y(t) = 2t.
B) When is the object moving to the left? (c) Give one value of t from the interval in part (b) at which the speed of the object is increasing. (d) At t = 1 this object’s position was x = 10. Where is the object when t = 3? 10/3/08 4:18 PM Page 27 Diagnostic Test Calculus AB 5' 24" 5' 60° 12" 12" 60° Note: Scales are different on the three figures. 3. The sides of a watering trough are made by folding a sheet of metal 24 inches wide and 5 feet long at an angle of 60°, as shown in the figure above.
AP Calculus by Shirley O. Hockett, David Bock