Download - KEY AB Calculus A
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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.
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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
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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
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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 +