# 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 2x^{3}-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

Exponents

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 (21s^{2} + 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 x^{2} – x – 12 is:

2. The correct factorization of 5x^{2} + 11x + 6 is:

3. A factor of x^{2}-7x+10 is:

4. A factor of x^{2}-4x-12 is:

5. A factor of 3x^{2}+27x+60 is:

6. A factor of 8x^{2}+22x+15 is:

7. A factor of 12x^{2} – 41x +15 is:

8. A factor of 2x^{3} – 26x^{2} + 72x is:

9. A factor of 9x^{3} – 24x^{2} – 20x is:

10. A factor of 8x^{2} – x – 7 is:

**Sample Algebra Test – Extra Questions
**

1. If 5 x 10

^{n}= 0.005, then n=

2. If x = -3, then x^{2}-2x+ 1 =

3. Which of the following gives 6a^{2}b^{3}-3a^{2}b 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

Prev | Next |