Sample Questions for Elementary Algebra Skills
1. Combine Like terms: 13 a

15 b
 a

2 b
2. Multiply:

2 x

1

4 x

1

3. Solve for x: 5

2 x

3
  x

3


0
4. Find all the factors of x
2  x

12
5. Factor out the greatest common factor: xy
3  yx
3
6. Divide: x
2 y
 y x
2
7. Simplify: b
3 b
5
8. Multiply:



2 x
3 y
9 y
4 x
2 


9. Simplify: 64 x
16
10. The average of x, y , and z is 80. If two of the numbers are 74 and 78, then what is the other number?
11. Find all the solutions of 4
 x
  x

0
12. Find the value of x in the solution of the following system of equations:
13.

 3 x x

 y y


7
5
14. In which quadrants (I, II, III, and/or IV) will you find ordered pairs for which x > -3 and y<0?
15. Find the values of x for which
 x

3

12
16. What are all values of x for which x
2 
9 x

0 ?
17. Factor: 2 x 2 
17 x

30
18. Solve:
5
 z z

9
19. (3 a b )
2 
20.
3

5 x x

2

21. If Sam walks 650 meters in x minutes then write an algebraic expression which represents the number of minutes it will take Sam to walk 1500 meters at the same average rate.
Revised November 13, 2006

Answers For Sample Elementary Algebra Questions
1. 12 a

13 b
2. 8 x
2 
2 x

1
3. 2
4.
5.
 x

3
 x

4
 xy
 y
2  x
2

6. xy
7.
1 b
2
8.
3
2 x
9. 8 x
8
10. 88
11.

3 and
2
3
12. 3
13. III and IV
14. x
 
15
15. x

0 or x

9
16. (2 x

3)( x

10)
17.
1
2
18. 9 a 2 
6 ab b 2
19.
 
6
(

2)
20.
1500 x 30 or
650 13 x
minutes
2