Algebra Placement Exam
Review Problems
3
1. Multiply and simplify x 6  x 
y3  4y
y 2  4 y  12
2. Simplify the expression
3. Subtract and simplify
2
y
x

x  xy xy  y 2
2
4. Divide 10 x 3  15 x 2  4 x  6 by 5 x 2  2
2x2  7x  6
 2x  1
5. Solve
x2
6. Evaluate 125
7. Evaluate 16
8. Simplify
3
2
3
3
2
24
9. Multiply and simplify

10. Combine and simplify
11. Solve for y
10
y2  9
2x  3 y  4
12. Solve
4x  y   6
13. Solve x 2  4 x  9  0
14. Solve  2 x  1  15

5 1
2
53
27 7 5

4
8

15. Determine how many gallons each of a 20% alcohol solution and a 60% solution must be
combined to obtain 100 gallons of a 30% solution.
16. A square, x feet on a side, is the same area as a triangle with base of length 4x feet and
height x-3 feet. What’s x?
17. You can mow a lawn in 3 hours and your friend can mow it in four hours. Let x be the time
it takes both of you to mow the lawn working together. Write the equation to determine x.
18. After a 30% discount, the price of a CD is $10.50. What was the original price?
1
19. Are the lines y  3 x  4 and y   x  17 parallel, perpendicular, or neither?
3
20. Find the slope of the line 4 x  9 y  3  0 .
3
5
21. Find the equation of the line perpendicular to the line y   x  1 and through the point
0,7.
22. Find the equation of the circle which has the points 1,4 and 3,6 as endpoints of a
diameter.
23. Write the equation of the parabola shown to the right.
24. Write the equation of the ellipse graphed to the right.
25. Find the set of all real numbers x so that
x 2  4 is a real number.
26.What is the domain of the function graphed to the right?
27.If f  x   x 2  2 x  5 , find f  x  1 .
28. If f  x   4  x  2 and g x   2x 5 , find f g 2 .
29. If f g x   x 3  1 and g x   x 3  1, what is g f  x  ?
2
30. Use the table of values for y  f  x  to complete the table for y  f
-2
-1
0
1
2
3
x
f x
-2
0
2
4
6
1
x .
8
x
f
1
x
31. Simplify
2  5i
7  3i
5
3
32. Factor completely x  5 x  36 x
3
2
33. Use the root x  5i to find all roots of the polynomial 2 x  3 x  50 x  75
34.Solve for x
2 x  3  32
x
9
35. Solve for x b b 
2
36. Solve for x
1
b6x
log x 81  4
37. Simplify log2 125  log2 25
38.Simplify the expression
n  2 !
n!
39. What is the 5th term of the arithmetic sequence? -1, 2, __, __, __
40. What is the 6th term of the geometric sequence? 5, 15, 45, __, __, __

 2
41. Find the sum of the infinite geometric series  4   
 3
n 0
42. If A and B are the given matrices, find 2A + 4B.
43. If
a
b
c
d
 ad  bc , evaluate
3
4
1 2

2 1
0 5
n
 3 4
A 

  1 2
 2 1
B

 0 5