Free of charge Response Queries 1969-2005

Published by Kaye Autrey for face-to-face student training in the AP Calculus class room


AP Calculus Free-Response Questions

1969 AB 1 Consider the next functions described for all by:

f1 ( x) = x farreneheit 2 ( x) = x cos x f3 ( x) = 3e2 x f 4 ( x) = x в€’ x

Answer the following inquiries (a, b, c, and d) regarding each of these functions. Indicate your answer by writing possibly yes or no in the suitable space in the given rectangular grid. Zero justification is necessary but every single blank space will be scored as the wrong answer. Questions f1 (a) (b) x? (c) (d) Does n (в€’ times ) = в€’ f ( by ) Will the inverse function exist for all those Is the function periodic? May be the function constant at x = 0? f2 Functions f3


1969 STOMACH 2 A particle movements along the x-axis in such a way that where it stands at time t is given by times = 3t 4 − 16t three or more + 24t 2 intended for − 5 ≤ capital t ≤ five. a. Decide the velocity and acceleration of the particle for time big t. b. At what principles of capital t is the molecule at rest? c. At what values of t will the particle transform direction? g. What is the speed when the speed is first no? 1969 ABS 3 Presented f ( x) sama dengan

1 you + ln x, identified only around the closed period ≤ by < electronic. x electronic

a. Demonstrating your thinking, determine the cost of x when f offers its (i) absolute maximum (ii) overall minimum b. For what values of back button is the curve concave up? c. Within the coordinate axis provided, sketch the chart of farrenheit over the 2


d. Given that the mean benefit (average ordinate) of f over the span is 2, state in words a geometrical presentation of this amount relative elizabeth в€’1 to the graph. 69 AB 5 BC 4 The number of bacterias in a traditions at period t is given approximately simply by

1 ≤ x < e. electronic

y sama dengan 1000(25 & te twenty ) for 0 ≤ t ≤ 100.

a. Find the greatest number and the smallest volume of bacteria inside the culture through the interval. b. At what time through the interval may be the rate of change in the number of bacteria a minimum? 1969 ABDOMINAL 5 Allow R represent the region enclosed between the graph of y = back button 2 as well as the graph of y = 2 times. a. Get the area of region Ur. b. Find the volume from the solid obtained by revolving the region R about the y-axis.


1969 ABS 6 A great arched window with foundation width 2b and elevation h is placed into a wall. The arch is to be either an arc of a allegoria or a half-cycle of a cosine curve. a. If the posture is a great arc of the parabola, create an formula for the parabola relative to the coordinate system demonstrated in the physique. (x-intercepts happen to be (в€’b, 0) and (b, 0). y-intercept is (0, h). ) b. In case the arch is actually a half-cycle of a cosine competition, write a great equation for the cosine curve relative to the coordinate system shown in the figure.


c. Of these two window designs, which has the higher area? Warrant your response. 1969 ABS 7

at the x & eв€’ x. 2 n. Let 3rd there’s r be a stage on the shape and let the x-coordinate of Ur be r (r в‰ 0). The tangent line to the shape at R crosses the x-axis at a point Queen. Find the coordinates of Q. c. If P is the level (r, 0), find the length of PQ as a function of r plus the limiting value of this duration as r increases without bound. a. On the organize axes supplied, sketch the graph of y sama dengan 1970 STOMACH 1 BC 1 Offered the parabola y = x a couple of в€’ 2 x & 3: a. Find an equation for the line L, which in turn contains the level (2, 3) and is perpendicular to the range tangent to the parabola by (2, 3). b. Discover the area of these part of the first quadrant which usually lies below both the series L and the parabola. 1970 AB two A function f is described on the closed interval via -3 to three and provides the graph shown below.

a. Sketch the entire graph of y = f ( x). b. Sketch the complete graph of y = f ( x ). c. Design the entire graph of con = farreneheit (в€’ x). пЈ«1 пЈ¶ d. Draw the entire chart of con = farrenheit пЈ¬ times пЈ·. пЈ­2 пЈё elizabeth. Sketch the complete graph of y = f ( x в€’ 1).


1970 ABS 3 BC 2 Consider the function f given by f ( x) =

4 x3 1 & 4x3.

a. Find the coordinates of points where the tangent to the curve is a horizontal line....


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