Algebra Compass Sample Items

These sample items are designed to illustrate the form of the items in the COMPASS
battery. They have not been pre -tested and have not been subjected to the content and
fairness reviews required for all operational items .

Copyright 1995 by ACT, Inc. All rights reserved.
Permission to reproduce all or part of the contents of this booklet is granted to institutions
with a valid COMPASS license agreement in place. Such institutions are required to
credit ACT as the source of the items and to indicate that the items are being reproduced
with ACT’s permission.

(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?

(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 of 3 times x ?

(Elementary Algebra: Substituting Values in Algebraic Expressions)

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

(Intermediate Algebra: Rational Expressions )
4. For all r ≠ ±2.?

( 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)?

Algebra Diagnostic Test – The Algebra Diagnostic Test can be customized to include
assessment of any or all of the following content areas, each of which consists of a pool
of at least 20 items.

Content Areas

Substituting values into algebraic expressions
Setting up equations for given situations
Basic operations with polynomials
Linear equations in one variable
Rational expressions
Linear equations in two variables

(Linear Equations in One Variable)

1. A certain school’s enrollment increased 5% this year over last year’s enrollment.
If the school now has 1,260 students enrolled, how many students were enrolled
last year?

(Setting Up Equations for Given Solutions)

2. A person travels x miles in y hours and then 10 miles in 2 hours. Which
expression represents the person’s average rate, in miles per hour, for the entire
distance traveled?

(Rational Expressions)

3. A rectangle has an area of (21s2 + 18st) square meters. If its width is 3s meters,
what is the length in meters?

Sample Test- Solving Linear Equations

Choose the correct answer for each of the following questions.

1. The solution of the equation x + 7 = 19 is:

2. The solution of the equation 4x = 52 is:

3. The solution of the equation x-15 = 3 is:

4. The solution of the equation 7x=-35 is:

5. The solution of the equation x+20 = 8 is:

6. The solution of the equation 3x + 2 = 7 is:

7. The solution of the equation is:

8. The solution of the equation 5x-2 = 9x + 4 is:

9. The solution of the equation 6(3x+5) = 5x-9 is:

10. The solution of the equation 5-3(2x-6) = 4(x-6) is:

SAMPLE TEST- Factoring Polynomials

1. The correct factorization of x2 – x – 12 is:

2. The correct factorization of 5x2 + 11x + 6 is:

3. A factor of x2-7x+10 is:

4. A factor of x2-4x-12 is:

5. A factor of 3x2+27x+60 is:

6. A factor of 8x2+22x+15 is:

7. A factor of 12x2 – 41x +15 is:

8. A factor of 2x3 – 26x2 + 72x is:

9. A factor of 9x3 – 24x2 – 20x is:

10. A factor of 8x2 – x – 7 is:

Sample Algebra Test – Extra Questions

1. If 5 x 10n = 0.005, then n=

2. If x = -3, then x2-2x+ 1 =

3. Which of the following gives 6a2b3-3a2b in factored form?

4. For all x ≠ 0 and y ≠0,

5. What are all the real values of x that are solutions for the inequality of |x- 2| ≤6?

6. If 3x-2 = 2y and y = 3z+5, which of the following is equal to x?

7. What is the distance between the points with (x,y) coordinates (3,-2) and (-3,-1)?

Algebra Placement Test

Algebra Diagnostic Test

Sample Test – Solving Linear Equations

Sample Test – Solving Factoring Polynomials

Sample Algebra Test – Extra Questions

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