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Algebra Compass Sample Items
These sample items are designed to illustrate the form of
the items in the COMPASS
battery. They have not been pretested 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 x15 = 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 5x2 = 9x + 4 is:
9. The solution of the equation 6(3x+5) = 5x9 is:
10. The solution of the equation 53(2x6) = 4(x6) 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}4x12 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 3x2 = 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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