Sample Arithmetic Skills Test

The Arithmetic Skills Test measures your abilities in three primary categories. The first is operations with
whole numbers and fractions . The second category involves operations with decimals and percents. The
last category involves applications and problem solving. There are 17 questions on the actual test.

Solve the following problems and choose your answer from the alternatives given.

Question 1: Three people work full time are to work together on a project, but their total time on
the project is to be equivalent to that of only one person working full time. If one of the people is
budgeted for ½ of her time to the project and a second person for 1/3 of his time, what part of the third
workers’ time should be budgeted to this project?

A. One third
B. One forth
C. One sixth
D. One eighth

Question 2: 12 is what percent of 16?

A. 82%
B. 45%
C. 75%
D. 90%

Question 3: If one shirt requires 2/3 of a yard of cloth, how many shirts can be made from 20 yards
of cloth?

A. 10
B. 30
C. 60
D. 80

Question 4:

A. .04
B. 4.0
C. .4
D. .44

Question 5: 6.18 ÷ 6 =

A. 1.03
B. 13
C. .103
D. 10.3

Question 6: 5.2 × 3.1 is between

A. 15 and 16
B. 16 and 17
C. 17 and 18
D. 18 and 19

Question 7: A plane travels 300 kilometers on Monday, 148 kilometers on Tuesday, and 275
kilometers on Wednesday, how many kilometers did it average per day?

A. 280
B. 241
C. 233
D. 267

Question 8: How many fourths are there in 4.8?

A. 12
B. 1.2
C. 19.2
D. 16.32

Question 9:

Question 10: Mr. and Mrs. Baggett’s house sits in the middle of their lot. The lot is rectangular and
except for the house, their lot is covered with grass. How many square feet of grass are on the lot?

A. 200
B. 9600
C. 1250
D. 8350

Question 12: 5/8 – 3/5

A. 2/3
B. 1/40
C. 8/13
D. 1/20

Question 13: A man has 9 pounds 5 ounces of dog food. How much will he have after his Great Dane
eats 5 pounds 8 ounces of it?

A. 4 pounds 3 ounces
B. 14 pounds 12 ounces
C. 3 pounds 7 ounces
D. 3 pounds 13 ounces

SAMPLE ELEMENTARY ALGEBRA SKILLS TEST:
There are three categories in the Elementary Algebra test. First, operations with integers and rational
numbers include computation with integers and negative rationals, the use of absolute values , and
ordering . The second category is operations with algebraic expressions. This will test your abilities in the
evaluation of simple formulas and expressions and adding and subtracting monomials and polynomials.
Both of these categories include questions about multiplying and dividing monomials and polynomials.
Both of the evaluation of positive rational roots and exponents , simplifying algebraic fractions and
factoring. The third category tests abilities in equation solving , inequalities , and word problems. These
questions include solving systems of linear equations , solving quadratic equations by factoring, solving
verbal problems presented in algebraic context, geometric reasoning, translating written phrases into
algebraic expressions and graphing .

On the actual CPT Elementary Algebra test there will be 12 multiple choice questions. When answering
those questions, remember that the test is not timed. So be careful, take your time, and double check
your answers. You will be given pencils and scratch paper and you may use a calculator. This practice
packet is not multiple choice, but does cover the topics you could see on the actual test.

Elementary Algebra
Self‐Assessment Exam

1. In which quadrant does the point (‐3, ‐4) lie?

a. Quadrant I
b. Quadrant II
c. Quadrant III
d. Quadrant IV

2. (3x ÷ 2) (3x + 2) is the factored expression of which trinomial?

a. 9x² ÷ 4
b. 9x² ÷ 6x ÷ 4
c. 9x² ÷ 12x ÷ 4
d. 9x² ÷ 35x ÷ 4

3. If 4(3x + 2)‐ (x ÷ 5) = ‐3 then ‐x =?

a. 11/6
b. ‐11/6
c. 6/11
d. ‐6/11

4. (3x³y)³ = ?



5. (x – 2) is a factor of which polynomial?
I. x² ‐ 4x ÷4
II. x² ÷ x – 6

a. I only
b. II onIy
c. I and II
d. neither

7. x = I ‐4 – 5 I y = l ‐4 – (‐5) l z = l ‐4 l – l ‐5 l
Which is true about x, y, and z?

a. x < z
b. z < y
c. x = z
d. y = z



a. 4y/3
b. 4y/9
c. 4y/3x
d. 4y/9x

9. Solve for x and y:
2x ÷ y = 3
X – 3y = 12

a. (3, 9)
b. (3, ‐9)
c. (3, ‐3)
d. (3, 3)

10. M is 8 more than a second number. Which of the following represents the second number?

a. M – 11
b. M – 8
c. M ÷ 8
d. M ÷ 17

11. Which pair of equations does NOT have a common solution ?

a. x ÷ y = ‐1
4x – 3y = 24

b. 4x ÷ 6y = 12
6x ÷ 9y = 12

c. 2x ‐3y = ‐4
2x ÷ y = 4

d. 5x – 4y = 9
x – 2y = ‐3

12. 24x – 8 = ?

a. 8x
b. 8(3x – x)
c. 8(3x – 1)
d. 8(3x – 8)

13. (2x – 5y)² = ?

a. 4x² ‐ 25y²
b. 4x² ‐ 10xy ÷ 25y²
c. 4x² ÷ 20xy – 25y²
d. 4x² ‐ 20xy ÷ 25y²

14. (9‐7)‐(7‐9)=?

a. 0
b. 4
c. ‐4
d. ‐14

15.

a. 15x²
b. 45x²
c. 75x²
d. 75x

16.

a. 3x/30
b. x/10
c. 19x/30
d. 19/30

17. Which of the following is equal to x² ‐10x ÷24?

a. (x‐4)(X÷6)
b. (x÷4)(x‐6)
c. (x‐4)(x‐6)
d. (x÷4)(x÷6)

18.

a. X‐5x
b. X‐5
c. x²‐5x
d. x²‐5

19. Which of the following equals 12x?

a. 6x∙6x
b. 13x² ‐ x
c. ‐8x ÷ 20x
d. 12 ÷ x

20. If x² ÷ m – 6y²= (x ÷ 3y) (x‐2y) then m=?

a. xy
b. –xy
c. 5xy
d. ‐5xy

21.

a. 4
b. ‐4
c. 1
d. ‐1

22.

a. 12/6x²
b. 2/x²
c. 2/x
d. 2

23.

a. xy²/12
b. xy³/12
c. x²y³/12
d. x²y/12

24. Which of the following statements represents this equation? x/3 – 5 = 8

a. One‐third a number x less than five equals eight
b. Five minus one‐third a number x equals eight
c. Five less than one‐third a number x equals eight
d. Eight is one‐third a number x less than 5

25. If x=5 and y=3 then

a. 19/2
b. 1/8
c. 1/2
d. 19/8

26. Which is NOT between ‐1 and 1?

a. ‐5/6
b. 7/8
c. ‐1/2
d. 3/2

27. Which is the correct factored form of 24x² ‐ 2x ‐15?

a. (4x‐3) (6x ÷5)
b. (4x ÷3)(6x‐5)
c. (4x‐3)(6x‐5)
d. (4x÷3)(6x÷5)

28. (‐3)(‐1) ÷ (4)(‐3) / (‐2) =?

a. ‐3
b. 9/2
c. 9
d. 15

SAMPLE COLLEGE LEVEL MATHMATICS SKILLS TEST:

If you score into college level on the Elementary Algebra Test, you will have the opportunity to take the
College Level Mathematics Test in which you could possibly receive credit for college level mathematics.
 

 
ANSWERS TO SAMPLE QUESTIONS

Arithmetic Answers:

Elementary Algebra
Self‐Assessment Exam KEY

College Level Mathematic Answers: