Algebra and Probability Practice Problems for McGraw-Hill's ASVAB

The study guides for this practice quiz can be found at:

• Algebra and Probability Study Guide 1 for McGraw-Hill's ASVAB
• Algebra and Probability Study Guide 2 for McGraw-Hill's ASVAB

Circle the letter that represents the best or correct answer. If any of your answers were wrong, go back and study the relevant section of the algebra review.

1. The phrase "some number plus 20" is the same as
   1. j + 20
   2. j – 20
   3. 
   4. j × 20
2. Evaluate: a + 2(b) – c if a = 5, b = 3, and c = 2
   1. 7
   2. 9
   3. 10
   4. 11
3. Solve for z: 32 + –z = 12
   1. –20
   2. –12
   3. 12
   4. 20
4. The proportion "a is to b is as 3 is to 6" can be represented as
   1. a + b = 3 + 6
   2. a × b = 3 × 6 + 45
   3. a(3) + b(6)
   4. 
5. Solve for each variable.
   y + g = 12 and 2y + 3g = 16
   1. g = 15, y = —3
   2. g = 5, y = 7
   3. g = 1, y = 11
   4. g = –8, y = 20
6. Add:
   
   1. –45g
   2. 45g
   3. 45g²
   4. 135g
7. Subtract:
   
   1. –230
   2. –30
   3. 30
   4. 230
8. Multiply: (g³)(g¹²)
   1. g^–3
   2. g¹⁵
   3. g^–15
   4. g³⁶
9. Add:
   g² + gh + h² + 3g² + 4gh + 3h² =
   1. 2g² + 3gh + 2h²
   2. 2g² + 5gh + 4h²
   3. 4g² + 5gh + 4h²
   4. 4g² + 3gh + 2h²
10. Multiply:
    3h – 2m
    × 2h + m
    1. 5h² + 3m²
    2. 6h² – hm – 2m²
    3. 6h² + 5hm + 2m²
    4. 6h² + 4hm + 2m²
11. Factor: x² + 4x – 12
    1. (2x² + 1 + 6)(–x² + 3x – 2)
    2. (x + 6)(x – 2)
    3. (x + 4)(x + 3)
    4. (x² + 2)(x^–2 + 4)
12. Reduce to lowest terms:
    
    1. x – 2
    2. 
    3. 
    4. _
13. Multiply:
    
    1. 
    2. 
    3. 
    4. 
14. Divide:
    
    1. 
    2. 
    3. 
    4. 
15. Which equation is represented by the following graph?
    
    1. 2x + y = 0
    2. x² + 1 = 0
    3. x + y = 5
    4. 2x + y = 7
16. Using a number cube with sides labeled 1 through 6, what is the probability of throwing a 3 or a 4?
    1. 2 in 4
    2. 1 in 3
    3. 2 in 8
    4. 1 in 9

Answers