Math Review Guide

This guide is intended as a focus for your review before taking the placement test. The questions presented here may not be on the placement test.

Although a basic skills calculator is provided for your use during the test, you are encouraged to practice doing basic arithmetic problems without a calculator.

This review is for levels of math from arithmetic through intermediate algebra. Choose the problems appropriate to your level of skill.

In order that we may reuse these materials, please do not write directly on the review guide.

Part 1: Arithmetic Review Guide

Arithmetic covers the following topics: operations with whole numbers, fractions, decimals, ratios and proportions , and percents.

Directions: All fractions and ratios must be reduced completely. Write your answers on the answer sheet.

Operations with Fractions
1. Reduce the fraction to lowest terms: 28/42
a. 14/21
b. 4/6
c. 2/3
d. 7/10

2. Find the product :
a. 3/10
b. 31/51
c. 595/384
d. 384/595

3. Divide :
a. 3/7
b. 16/21
c. 7/3
d. 21/16

4. Multiply :

5. Subtract:
a. 10/13
b. 7/30
c. 7/15
d. 10/17

6. Find the sum:

Operations with Decimals
7. Add: 4.23 + 3.7 + 2.006
a. 24.66
b. 9.36
c. 9.936
d. 9.306

8. Write 17/10 as a decimal number .
a. .17
b. 1.7
c. 17

9. Round 1928.956 to the tenths place.
a. 1928.9
b. 1929.0
c. 1928.95
d. 1928.96

10. If one square yard of carpet costs $15.45, how much will 45.5 square yards cost?
a. $702.98 b. $2.95 c. $7029.75 d. $70.30

11. If Angie’s gross pay for 21.5 hours was $141.04, what was her pay per hour?
a. $15.24/hr
b. $6.72/hr
c. $6.56/hr
d. $7.29/hr

Operations with Ratios and Proportions
12. Two inches on a map equals 10 miles. Write the ratio of map inches to miles.
a. 5
b. 1/5
c. 20
d. 1/2

13. Find the missing part of the proportion:
a. 36
b. 24
c. 21
d. 28

14. If it takes Tom 48 minutes to walk 3 miles, how many minutes will it take him to walk 5 miles?
a. 16 min.
b. 144 min.
c. 15 min.
d. 80 min.

Operations with Percentages
15. Change the percent to a fraction: 145%
a. 29/20
b. 29/2
c. 29/50
d. 29/5

16. Change the decimal number to a percent : .129
a. 1.29%
b. 12.9%
c. 129%
d. .129%

17. The 1980 Census Report listed the population of Pullman as 17,316. The 1990 Census Report listed the population as 18,373. Find the percent change in the population. Round the percent to the nearest tenth.
a. 4.9%
b. 5.75%
c. 6.1%
d. 6.7%

18. Frost’s Refrigeration decided to increase their basic service call charge by 8%. What will be the new charge for a service call if they had been charging $42.50?
a. $44.80
b. $45.00
c. $45.20
d. $45.90

Part II: Introduction to Elementary Algebra Review Guide

Introduction to Elementary Algebra covers the following topics: introduction to variables, operations with signed numbers, solutions to linear equations and inequalities , operations with positive integer exponents, evaluation and manipulations of formulas, and solving basic word problems.

Operations with Signed Numbers
19. Simplify : (5 - 2) - (2 - 5)
a. 3
b. 0
c. 6
d. –6

20. Simplify: -11 - (-3) + (-1) – 9
a. –18
b. –22
c. –24
d. –16

21. Simplify:
a. –14
b. –16
c. -18/5
d. –1

Variables
22. Translate to an algebraic expression : Twice the sum of 3x and y
a. 2(3x) + y
b. 6x + 2y
c. 3x + 2y
d. 2 + 3x + y

23. Evaluate: (x – 3y) (2x + y) when x = -2 and y = -1
a. 25
b. –25
c. –3
d. –5

24. Simplify: 6x – 7b – 10x + 11b
a. –x + b
b. –4x + 4b
c. 4x – 4b
d. –4x – 4b

25. Simplify: 3(x + 1) – 4(x – 1)
a. –x – 7
b. –x – 1
c. –x + 7
d. –x + 1

26. Multiply:

27. Simplify: 2[9x - 2(3x - 2)]
a. 6x – 2
b. 6x – 4
c. 6x + 4
d. 6x + 8

Solutions to Linear Equations and Inequalities
28. Solve: -2x + 21 = -11
a. –5
b. –16
c. 16
d. 5

29. Solve:
a. 6/5
b. 8/15
c. 12/5
d. 20/15

30. Solve: 2x + 6 > 3x + 32
a. x > -26
b. x > -38
c. x < -26
d. x < 26

31. Solve: 6(x – 5) – 3x = -9
a. –13
b. 7
c. 13
d. –7

Operations with Positive Integer Exponents
32. Simplify: 2² – (-2)³
a. –2
b. 12
c. 10
d. 14

33. Simplify: (2 + 3)² – (2 + 3²)
a. 14
b. 0
c. 2
d. 32

Solving Basic Word Problems
34. A board is 28 feet long and is cut into three pieces. The second piece is twice as long as the first piece and the third is three feet longer than the second. What is the length of each piece?
a. 5, 10, 13
b. 4, 8, 16
c. 6, 12, 10
d. 8, 16, 4

35. The perimeter of a rectangle is 66 feet and the width is 7 feet. What is the length in feet?
a. 26
b. 52
c. 40
d. 20

36. The area of a triangle is 24 square feet. If the base is 12 feet, what is the height of the triangle?
a. 4
b. 2
c. 8
d. 6

37. Seven less than four times a number is 35. What is the number?
a. 7
b. 21/2
c. –7
d. -21/2

Manipulation of Formulas
38. Solve: v = k + gt for t