Elementary Algebra sample problems

The following sample questions will help you to determine which algebra topics you understand
and which you need to review. This list of questions covers many of the basic concepts of
elementary algebra, but it is not meant to include all of the types of questions asked on the
placement test.
Simplify:
−4 + (−6)
8(−3)
− 6+ 4
2
6a − 3(b − 2)
Solve:
x x
− 3 = + 1
4 2
Solve:
x 2 + 25 = −10x
Twice a number
decreased by 8 is
equal to the number
increased by 10. Find
the number.
7 + (−11)
(−5)(−7)
−5x + x − 6x
Evaluate:
a + 3b − c
for a = −3, b = 2
and c = −1
Solve:
7 3
s+ 1 s
= −
3
Solve:
x 2 − 8x + 7 = 0
Simplify:
(−2) 2 (3) 3
5 − 12
− 25
− 5
5(4y − 2) − (y + 7)
Evaluate:
−2a 2 − 6a + 4
for a = −3
Solve:
3x + 4 < 12 − x
Four times a number
increased by 10 is
equal to 34. What
is the number?
Simplify:
(4a 2 b)(−3a 5 b 3 )
10 − (−2)
− 12
4
1
( 24c − 9)
3
Solve:
4y − (2y + 6) = 10
Solve:
6 − 2(t + 1) ≥ 8
Samantha is three
times as old as
Susan. The sum of
their ages is 48.
How old is each?
Simplify:
(r 3 s 5 ) 4
Algebra Problems Page 1 of 3

Simplify:
27x
y
8
18x
y
6 4
Simplify:
64
Graph and find
the slope of this line:
2
y =− x+
4
5
(x − 7)(2x + 3)
Simplify:
2x 4 (3x 2 − 2x + 4)
Simplify:
4 2
8a −6a −2a 2
2a
Simplify:
7 9
−
10y
y
5 2
Simplify:
−2 3
2 ⋅ 4
Simplify:
2 4
49ab , a ≥ 0
Write an equation of
the line whose slope is
2 and whose
y-intercept is (0, 5).
Simplify:
(3x − 5) 2
Factor:
3x 2 + 6x
Simplify:
2
a −3a−18 2
a − 9
Simplify:
x + 5
x
Simplify:
−
y ⋅ y
− 5
y
4 2
Simplify:
27 12 3
x
Find the slope of the
line that passes
through the points
(−2, 7) and (3, −3)
Simplify:
7b(−4b 2 ) + 3b 2 (−b)
Factor:
x 2 + 6x − 16
Simplify:
2
x + 7x
3x+ 15
2 ⋅ 2
x − 25 x
Simplify:
3 5
−
x x+
3
Simplify:
x x
2 ÷ 3
y y
Graph and find
the slope of this line:
3x − 2y = 6
Solve this system
of equations:
3x + 2y = 25
x − 3y = −21
Simplify:
3x(x + 5) − 2(x 2 + 4x − 1)
Factor:
3x 2 + x − 2
Simplify:
2 5
a− 3 2a 6
÷
−
Simplify:
3
1+
x
9
x −
x
As you prepare for the mathematics placement test, you should review the topics listed on the
next page:
Arithmetic of real numbers (including integers, rational numbers, and irrational numbers)
Algebra Problems Page 2 of 3

Simplifying algebraic expressions
Evaluating algebraic expressions
Absolute value
Simplifying rational expressions
Definition of integer exponents and operations involving expressions that contain
exponents
Solving linear equations
Solving equations involving fractions
Ratio and proportion
Solving linear inequalities
Graphing linear equations in two variables
Writing equations of lines
Solving systems of linear equations
Operations with polynomials
Factoring polynomials
Operations with rational expressions
Simplifying square root expressions
Solving quadratic equations
Algebra Problems Page 3 of 3