Download Review Packet for AP Calculus I. Simplify each expression below in

Review Packet for AP Calculus
I. Simplify each expression below in #1-3.
1.
5 9

8 16
2. 24 
3
4
3.
12 63

21 84
II. Exponent Review. Simplify leaving no negative exponents in #4-6. Evaluate in #7-9.
4 x 1 y 3
5.
5 x 4 y 2
4. (2 x ) (3x )
3 4
7. (27)
2 3
2
3
8. (64)
1
2
2
6.
4 x 1 y 3 2
( 4 2 )
5x y
3
9. (16) 4
1 32
+( )
9
1
 (64) 2
III. Polynomial Review. Perform the given operation for each problem in #10-14.
10.
( x  3) 2 (2 x  1)
13. Divide ( (3 x
3
11.
 x 2  7 x  6)
(3x  2)( x 2  4 x  5)
by
( x  2)
12. (8 x
2
 3 x)  (4 x 2  5 x  3)
using long division. Do the same problem using
synthetic division.
14. Cube the binomial
(2 x  3) .
IV. Radicals. Simplify the following radical expressions in #15-20, removing all possible factors from
each radical. Rationalize when necessary. (That is, leave no radicals in a denominator). Solve the radical
equation for x in #21.
6
15.
32x y
19.
2
3  6
9
16.
5b  10b
4
17.
m 2 n5
12m 4
20. (8  3 2)(8  3 2)
18. 5 27  2 48  7 12
21.
x2  3  x  1
V. Factoring/Solving quadratic equations. Completely factor the following polynomials in #22-25. Check
for greatest common factors first.
22. z2 – 81
23. 2x2 + 13x – 24
24. 8z5 – 4z4 + 20z3
25. b4 – 81
Solve the problems in #26-31 by factoring completely.
26. r3 + 3r2 – 54r = 0
29.
27.
x3  3x 2  x  3 = 0
8 x 4  32 x 2  0
30.
10 x 2  9 x
28.
4 x 2  4 x  35 = 0
31.
8 x 4  32 x 2  0
VI. Simplifying rational expressions. Common denominators are needed to add/subtract. Perform the
operations as required in #32-37.
5 y 5 y2
32.

2 x2 8x2
x 2  13x  40
33.
x 2  2 x  35
y2  2 y
y 2  81
34. 2

y  7 y  18 y 2  11y  18
3
4
35.

2
7 x y 21xy 2
4
3

36. 2
x  3x 3x  9
2
x
37.
6
4
x
1
VII. Solving equations/inequalities. This is a mixture of all types of equations/inequalities, from as easy
as linear, to quadratic, to rational, to logarithmic, to exponential .
38.
4
3
( x  10)  ( x  30) 39. 3x  8  14
5
10
42. 2x2  5x  11  0
43.
8 x 2  40 x  0
40. 2 x  5
9 41. 6  (2 x  7)  15  3x  (1  x )
44. x3  216  0
45.
2
5
6

 2
x2 x2 x 4
46. 42 x3  6  14
47. log 4 x  log 4 ( x  1) 
1
2
48. 2ln x  ln3  2
49. x 4  4 x 2  45  0
VIII. Linear Equations/Slope.
In #50-52, find the slope of a line joining the two points.
50. (3, 8) and ( 5, 2)
51. (4,3) and (6,3)
52. (-2,5) and (-2,4)
In #53-55, find the equation of the line described. Use point-slope form when necessary, but pupt your
final answer in slope-intercept form.
53. A line that passes through (0,4) and (-2,3)
54. A line with x-intercept of 3 and y-intercept of 9.
55. A line parallel to x  3 y  6 that passes through the point (-9,6)
56. A line perpendicular to y=2/3x + 4 that passes through the point (-2,-4).
57. A line that passes through (4,3) and (7,3).
58. A line that passes through (-2,-5) and (-2,-1).
IX. Trig Review.
59. Determine two coterminal angles to each of the following angle measures:
a) 5/4
b) 60º
60. Determine the values of all six trigonometric functions for the angle whose terminal side lands on
the ordered pair (-5, 12).
61. Without using a calculator, find the value of the six trig values for each given angle measure below.
t
quadrant
7/6
Reference
Terminal
number
point
Sin t
Cos t
Tan t
Csc t
Sec t
Cot t
8/3
-3/4
-3/2
62. Solve the following trig equations for values between 0    2 .
a) 4sin x  2 3  0
b) tan 2 x  1  0
c) 2sin 2 x  sin x  0
d) 2 cos 2 x  3cos x  1  0
63. Use trig identities (including reciprocal, quotient, and Pythagorean) to prove the following identities.
Do not move terms from one side to the other nor should you multiply/divide each side by anything to
prove the identities.
a) cos x  sin x tan x  sec x
b) (tan 2 x  1)(1  cos 2 x)  tan 2 x
c) tan 2 x sec2 x  tan 2 x  tan 4 x