Download AP Calculus Readiness Questions

AP Calculus Readiness Questions
You CANNOT use a calculator on these questions. Show all work. If you are entering calculus and cannot do the
material on this document you need to learn how to do it before August! Most of the questions relate to algebra II
while the trig is from precalculus. www.purplemath.com is a good site for help.
1. Solve the inequality 2 x  5  3
2. Solve: x  6 < 9
3. Solve the inequality 16  7  2 x  5
4. Write the equation of the line containing the points (3, 7) and (2,5) .
5. Write the equation of the line, in slope-intercept form, that passes through the point (6, 4) and has slope –2.
6. Write the equation of the line that is perpendicular to the line 3x  y  7 and contains the point (4,3)
7. Solve the following system of equations (solve for x and y) 4 x  3 y  7 and 2 x  y  9
8. Evaluate the piecewise-function at the two given values:
f ( x)  x 2  1, x  4
6 x  7, x  4
a) at f (2)
and
b) at f
9. Multiply (3t  4)(2t  3)
(6)
10. Multiply: ( x  2)( x 2  2 x  2)
11. Factor completely: x3  5x2  x  5
12. Factor: 36 y 2  25
13. Factor Completely x3  125
14. Solve by completing the square: 10x = 4 x 2  1
15. Use the quadratic formula to solve: 2 x 2  3x  1 = 0
16. Solve use any method x 2  2 x  24 = 0
17. Solve (13x  5) 2 = 78
18. Solve 5x2  2  3x
19. Solve
x2
16

x4
x4
21. Solve
3x  25
3
5 
x7
x
20. Solve
4x 1 2x  3 7


4
3
12
22. Simplify the rational expression.
n 2  2n  24
n 2  11n  28
23. Multiply
x2  2 x  3
3x  3
 2
2
x 1
x  4x  3
x 2  10 x  24
x6
24. Divide:

2
x  16
x6
25. Add:
1
6
+
x2
x2
2
5
26. Add

x 3 x3
1
2
37. Simplify:
1
3 +
8
3
28. Simplify x  2
6
5
x
29. Simplify
4
1 3
30. Simplify     
2 4
1 +
a 2 (r 3 s )2
a5r 3 s3
2
31. Simplify: 3(-2x-2)-3
32. Solve for x: 4 x+1  4 2= 4 6
33. Write the following using radical notation. Assume that all variables represent positive real numbers.
4
34. Simplify
8
2
3
35.
11x
5
9
 83  9
Simplify  7  (leave your answer as an exponent)
 
36. Solve for x:
38. Simplify:
7 x  58  x  4
37. Simplify and Rationalize
9
1
1


16
64
4
18 
3
10
39. Simplify 5 18  6 8
40 If f ( x)  x 2  2 and g ( x)  x  3 then f ( g ( x))  ?
41. Given f ( x)  x 2 and g ( x)  2  x , find ( f  g )(3)
42. What is f 1 ( x) , the inverse of f ( x) , if f ( x) 
1
x 1
2

43. Find the Domain and Range of the function f ( x)  5  x .
44. Find the Domain and Range of the function f ( x) 
45. Find the horizontal asymptote(s) f ( x) 
7x
x4
3
x 3
46. Find the vertical asymptote(s) f ( x) 
47. Describe the transformation of the graph f(x) = |x| for the graph f(x) = |x + 3| - 1.
x3
x  2x  8
2
48. The log 6 xy 2 is the same as which of the following (expand)
A. log6 x  log6 y  log6 2
B. 2(log6 x  log6 y)
C. log6 x  log 6 2 y
D. log6 x  2log6 y
49. The log 4 16  2 can also be expressed as:
A. log 2 16  4
B. 164  2
C. 42  16
D. 24  16
50. Evaluate (without a calculator): log2 64
Find the value of each. Use exact answers.
51. sin(585 )
52.
sec
10
3
53.
sin
5
4

6
55. tan

3
56. sec
57. tan
15
6
58. cos
3
4
59. cos
60. sin
7
2
61.
cot
11
6
62. tan(210 )
44.
csc

2
If 0    2 , find the value(s) of  That make each statement true.
63.
csc   2
64. cos 
65.
sec  2 and tan  0
66.
sin 
 2
2
1
and cos  0
2