f( X 3-3x )dx = x 2 --3x +C (A) 3x 2-3+C (B) 4x 4-6x 2 +C (C) x 4 3x 2 x 4 5x 3 +15x 2 +20x+25 5x 2 +15x+25 (E) 5 (D) 225 (B) (A)

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1 . f( X -x )dx = x -+C x -6x +C x x x --x+c ---+C x --x +C. If f(x)=x +x +x+5 and g(x)=5, then g(f(x))= 5 5x +5x+5 5 5x +5x +0x+5. The slope of the line tangent to the graph of y = In (x ) at x = e is e e e e e. If f(x) = x + sin x, then f'(x) = + cosx l-cosx cosx smx-xcosx sinx+xcosx x-i If f(x)=- for all x:t:-l, then f'(l) = x+l Copyright 005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.

x+l y=x y = _X 5 +x y = X -x +6 8. A particle moves in a straight line with velocity vet) = t. How far does the particle move between times t = and t =? 9.

2 x+l y=x y = _X 5 +x y = X -x A particle moves in a straight line with velocity vet) = t. How far does the particle move between times t = and t =? 9. If Y = cos x, then dy = dx -6sinxcosx -cosx 6cosx sinxcosx 5 0. The derivative of f(x) = ~-~ S attains its maximum value at x = - 0. If the line x - Y = 0 is tangent in the first quadrant to the curve y = x + k, then k is. If f(x)=x +Ax +Bx-S andiff()= and f(-)=-7, what is the value of A+B? Copyright 005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.

3 ---. The acceleration a of a body moving in a straight line is given in terms of time t by a = 8-6t. If the velocity of the body is 5 at t = and if set) is the distance of the body from the origin at time t, what is s( ) - s()? I - -. If j(x)=x (x-) for all x, then the domain of j' is {xlx:;z':o} {x I x > O} {xi0:s;x:s;} {x Ix :;z': 0 and x:;z':} {x Ix is a real number} e- ( e-) t 6. The number of bacteria in a culture is growing at a rate of 000e 5 per unit of time t. At t = 0, the number of bacteria present was 7,500. Find the number present at t = 5.,00e 7,500e 5 5, e 7 7. What is the area of the region completely bounded by the curve y = - x + x + 6 and the line y=? 8. ~(arcsinx)= dx - ~-x ~-x - ~x - ~x - Copyright 005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.

9. Suppose that f is a function that is defined for all real numbers. Which of the following conditions assures that f has an inverse function? The function f is periodic.

4 9. Suppose that f is a function that is defined for all real numbers. Which of the following conditions assures that f has an inverse function? The function f is periodic. The graph of f is symmetric with respect to the y-axis. The graph of f is concave up. The function f is a strictly increasing function. The function f is continuous. 0. IfF and f are continuous functions such that F'(x) = f(x) for all x, then f: f(x)dx is F'(a) - F'(b) F'(b) - F'(a) F(a)-F(b) F(b) - F(a) none of the above. Given the function defined by f(x) = x 5-0x, find all values of x for which the graph of f is concave up. x> 0 -.J < x < 0 or x >.J - < x < 0 or x> x>.j - <x< Copyright 005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.

$[._ 97 AP Calculus AB: Section I. Im- Iln(+h). -- IS h~o h. Let f (x) = cos ( arctan x). What is the range of f? {xl-~<x<~} {xio<x~l} {xio~x~l} {xl-l<x<l} {xl-l~x~l} f t/ 5.$

5 [._ 97 AP Calculus AB: Section I. Im- Iln(+h). -- IS h~o h. Let f (x) = cos ( arctan x). What is the range of f? {xl-~<x<~} {xio<x~l} {xio~x~l} {xl-l<x<l} {xl-l~x~l} f t/ 5. o tan xdx= n n n J The radius r of a sphere is increasing at the uniform rate of 0. inches per second. At the instant when the surface area S becomes loon square inches, what is the rate of increase, in cubic inches per second, in the volume V? ( S = n r and V = ~ n r ) IOn n.5n 5n 0n 7. (/ x dx= o ~-x - J n n!ln~ J 8. A point moves in a straight line so that its distance at time t from a fixed point of the line is 8t - t. What is the total distance covered by the point between t = and t =? Copyright 005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.

I -- ------- l _ 9. Let f (x) = Isin x - ~ I The maximum value attained by f is n n - - 0. r x- dx = I x -- In- In In+. If loga ( a ) = :' then a = J_5_dx= +x -lox +C ( + x ) 5 5x--+C x.

6 I l _ 9. Let f (x) = Isin x - ~ I The maximum value attained by f is n n r x- dx = I x -- In- In In+. If loga ( a ) = :' then a = J_5_dx= +x -lox +C ( + x ) 5 5x--+C x. Suppose that f is an odd function; i.e., f( -x) = - f(x) for all x. Suppose that f' (xo) exists. Which of the following must necessarily be equal to f' (- Xo )? f'(xo) - f'(xo) f'(xo) - f'(xo) None of the above Copyright 005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.

. The average value of ~ over the interval 0 ~ x ~ is ~J '!:J 5. The region in the first quadrant bounded by the graph of y = secx, x = n, and the axes is rotated about the x-axis.

7 . The average value of ~ over the interval 0 ~ x ~ is ~J '!:J 5. The region in the first quadrant bounded by the graph of y = secx, x = n, and the axes is rotated about the x-axis. What is the volume of the solid generated? n n-l n n 8n d n 6. If y = e nx, then -.L = dx n nn e nx n!e nx ne nx nn ex n!e x 7. If dy =y andify=whenx=0, theny= dx e x e x +e x +e x x + 8. If L f (x - c) dx = 5 where c is a constant, then fl~~cf (x) dx = 9. The point on the curve y = x nearest to (,) is (,) (J,I) (J,) (,8) 0. If tan(xy) = x, then dy = dx - y tan(xy)sec(xy) x tan(xy) sec(xy) cos (xy) sec (xy)- --- y AP CalculusMultiple-ChoiceQuestionCollection Copyright 005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.

8 L_- ~ { X + for x < 0,. Given f(x) = cos rc x for x ~ 0, fl f(x)dx= rc rc rc y 0 X. Calculate the approximate area of the shaded region in the figure by the trapezoidal rule, using 5 divisions at x = - and x = lfthe solutions of f(x) = 0 are - and, then the solutions of f(~) = 0 are 5 -land --and- -- and- -- and. For small values of h, the function ~6+h is best approximated by which of the following? h +- -l!- Copyright 005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.

9 5. If f is a continuous function on [a, b], which of the following is necessarily true? f' exists on (a,b). If f (xo) is a maximum of j, then l'(xo) = 0. lim f(x)=f( lim x) for Xo E(a,b) x~xo x~xo f'(x)=o for some xe[a,b] Copyright 005 by College Board. All rights reserved. Available at apcentral.collegeboard.com.

1993 AP Calculus AB: Section I

1993 AP Calculus AB: Section I 99 AP Calculus AB: Section I 9 Minutes Scientific Calculator Notes: () The eact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among