8/7/2019 KEY AB Calculus A

1/4

AP CALCULUS AB A Exam Review KEY Page 1 of 4

1.

a. 6 b.5

3c.

1

2 d. ,dne

b. 0 f.3

cos6 2

= g. 6 h.

1, 0

2a

a>

2. Only ( )h x is continuous at x = 1.

3. a.2

1 9

x x+ b.

2

10

( 2)x +c. 26 cos (3 5)sinx x x x +

d.2

3

3

2 7

x

x +e.

1

34

12sin6 cos63

x x x+ f. [ ]( ) ( )f g x g x

g. 22 sin cost t t t + h. 242

3 3sec

1 9x

xx+ +

i.2

2

10

30 1 4x x+ +

4.

a. 22 ( 1)xf x + b. 4 (5)f

c. 3 62 ( 1)x f x + d. 5 66 ( 1)x f x +

5.

a. all reals except x = -1 b. All reals except at x = -1,0,2,36.

a.1

2b. there are no values ofa

7.

8/7/2019 KEY AB Calculus A

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AP CALCULUS AB A Exam Review KEY Page 2 of 4

8. a, x = 1, 2

b. Increasing on ( ) ( ),1 , 2, . Decreasing on (1,2)c. Relative max at x = 1, relative min at x = 2d. Absolute max value is 9e. Inflection point at x = 3/2f. Concave up on 3 ,

2

. Concave down on

3,2

9. 0.7

10.

a.( )

( ) (1) (1)( 1)

3(1) ln 4 1

2

L x f f x

L x

= +

= +

b. (1.2) 1.686f = c. The approximation is too large because the graph offis concave downward.

11.

a.2

2

dy x y

dx x y

=

+

b. The tangent is horizontal at the points (3,-6) and (-3,6)c. The tangent is vertical at the points (-6,3) and (6,-3)

12. a. 11b. 10

13. a.2

16 12cos 2x x

x+

b.

( )3

2

4

4 3x

c.2 2

3 3

25y x

y y

=

14. 372 / minft

15. 6 ft by 6 ft

8/7/2019 KEY AB Calculus A

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AP CALCULUS AB A Exam Review KEY Page 3 of 4

16.

a.

b,c. 1.423, .312c

17.

a. f is increasing on (-3,1) and (3,4], since f is positive on those intervalsf is decreasing on [-4,3) and (1,3) since f is negative on those intervals.

b. Critical points are at x = -3, 1, and 3c. Relative maximum occurs at x = 1. f changes sign from positive to

negative. Relative minimum occurs at x = -3, and 3. f changes from

negative to positive at those points.d. Inflection points occur at x = -1 and x = 2.e. f is concave upward on (-4,-1) and (2,4). f is concave downward on (-1,2)

18. a. t = 7 seconds.

b. t = 10 seconds.c. 1.5 ft/s2

19. a. ( )8

0

1 1( ) 2 40 38 36 30 36 /

8 8R t dt gal hr + + + = by left Riemann Sum

( )1

2 38 36 30 26 32.5 / 8

gal hr + + + = by Right Riemann Sums

20. f = b, f = a, f = c

21. 2 8( 3) 8 22y x or y x= + =

22. Slope of cos5y x at x = = is 0, therefore the slope of the normal is

undefined.

23. Minimum value is9

16

8/7/2019 KEY AB Calculus A

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AP CALCULUS AB A Exam Review KEY Page 4 of 4

24.

a. Falseb. Sometimes truec. Sometimes trued. Sometimes truee.

Sometimes truef. Always true

g. Always trueh. Always true

25.

a. 2( ) 3 12 9v t t t = +

b. Particle at rest when t = 1, 3, moving left on (1,3); moving right on( ) ( ),1 , 3,

c. (2) 3v = d. ( ) 6 12a t t= e. minimum velocity is 3

26. a. 2secx C+ b.3

7sinx Cx

+ +

27. a. 3 tanx C+ b.

7

244

2 77

x x x C + +

c.41

6ln4

x x C +