# Math Skills

# Sample Math Skills

The COMPASS Math test will start you off with numerical skills/prealgebra section. As you answer correctly, the next question will be more difficult. RELAX! And do your best on each item and the test will stop when the top end of your abilities is reached.

### COMPASS SAMPLE ITEMS MATH -- Numerical Skills/Prealgebra Placement Test

**(Computing an Arithmetic Average)**

1. What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2 ?

A. 3

B. 4

C. 4

D. 5

E. 6

**(Basic Operations with Decimals)**

2. Ben is making wooden toys for the next arts and crafts sale. Each toy costs Ben $1.80 to make. If he sells the toys for $3.00 each, how many will he have to sell to make a profit of exactly $36.00?

A. 12

B. 20

C. 30

D. 60

E. 108

**(Basic Operations with Fractions)**

3. How many yards of material from a 24-yard length of cloth remain after 3 pieces, each 3 yards long, and 5 pieces, each 2 yards long, are removed?

A. 2

B. 4

C. 4

D. 10

E. 10

**(Percentages)**

4. Phillip charged $400 worth of goods on his credit card. On his first bill, he was not charged any interest, and he made a payment of $20. He then charged another $18 worth of goods. On his second bill a month later, he was charged 2% interest on his entire unpaid balance. How much interest was Phillip charged on his second bill?

A. $8.76

B. $7.96

C. $7.60

D. $7.24

E. $6.63

### COMPASS SAMPLE ITEMS MATH -- Algebra Placement Test

**(Elementary Algebra: Linear Equations in One Variable)**

1. A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the student wants an average (arithmetic mean) of exactly 87, what score must she earn on the fourth test?

A. 85

B. 86

C. 87

D. 92

E. 93

**(Elementary Algebra: Basic Operations with Polynomials)**

2. Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?

A. -6x2 + 25x + 6

B. 6x2 + 5x + 6

C. 6x2 – 5x + 6

D. 6x2 – 5x – 6

E. 6x2 – 13x – 6

**(Elementary Algebra: Substituting Values in Algebraic Expressions)**

3. If x = -1 and y = 2, what is the value of the expression 2x3 – 3xy ?

A. 8

B. 4

C. -1

D. -4

E. -8

**(Intermediate Algebra: Rational Expressions)**

4. For all r ±2,

?

A.

C.

D.

E.

**(Coordinate Geometry: Linear Equations in 2 Variables)**

5. What is the equation of the line that contains the points with (x,y) coordinates (-3,7) and (5,-1) ?

A. y = 3x – 2

B. y = x + 10

C. y = - + 8

D. y = - +

E. y = -x + 4

### COMPASS SAMPLE ITEMS -- College Algebra Placement Test

**(Complex Numbers)**

1. For i = , if 3i (2+5i) = x + 6i, then x =

A. -15

B. 5

C. 5i

D. 15i

E. 27i

**(Functions)**

2. If f(4) = 0 and f(6) = 6, which of the following could represent f(x) ?

A. x - 4

B. x + 2

C. x - 4

D. x + 6

E. 3x - 12

### COMPASS SAMPLE ITEMS - Answers to Sample Items

### Numerical Skills/Prealgebra Placement Test

1. C

2. C

3. A

4. B

### Algebra Placement Test

1. D

2. D

3. B

4. A

5. E

### College Algebra Placement Test

1. A

2. E

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