Math Placement Review Problems
The following problems are provided to help you review skills you have previously learned, but may have
forgotten. Use the problems below to refresh those skills which are rusty, rather than to try to learn new
material. If you encounter an unfamiliar problem, you should not spend a lot of time trying to obtain the
background necessary to successfully complete the problem; just skip that problem and try the next one.
These are sample questions for material required to place into Level II (MAT101 and MAT103).
1. Add, subtract, multiply, divide and reduce fractions.
a. Add:
b. Subtract:
c. Multiply:
d. Divide:
2 2
5 3
8 7
 15  3 






5 3
3 4
3 6
 7  5 
2. Simplify expressions using signed numbers.
a. Simplify:
b. Simplify:
c. Simplify:
12
d. Simplify:
3  2  4  (3)
4 | 2 | 5  2
2(5)(1)
4
3. Simplify expressions using order of operations including absolute values
a. Simplify:
c. Simplify:
d. Simplify:
8  6
b. Simplify:
3

2(4)(

1)
|−2| − 3(2 + 3)
−3 − (−2)4 + |1 − 5|
2
4. Solve linear equations and inequalities
a) Solve:
b) Solve:
c) Solve:
d) Solve:
2( x  2)  4 x  10
5  2x  8
3x  7  5
7  3x  13
5. Solve story problems involving percents
a) If a student scores
b) Seven is what
c) A $20 item is on
d) A person making $12 an
28 points on a 32 point percent of twenty?
sale for 25% off, if
hour is asked to take a $1
test, what percentage
there is a 7% sales tax, pay cut. A year later, they
did the student earn?
how much will a
are given a 5% raise, how
person pay for this
much an hour are they
item?
making now?
6. Simplify variable expressions.
a) Simplify:
b) Simplify:
c) Simplify:
d) Simplify:
3x  4 x  2 x
x 2y
3x x
3x x
.


y 5
2 4
4 6
7. Identify equivalent forms of simple algebraic expressions.
a. Simplify:
b. Simplify:
c. Simplify:
2
5x  x  2 x
x  2 x  3x
2 x3  4 x(3x 2 )
8. Evaluate algebraic expressions, given the value of the variables.
a. If x  3 and y  2
b. If x  2 and y  3
c. If x  1 and
2
2
y  3 evaluate
evaluate x  3xy
evaluate y( x  y)  x
x2 y  2 y
d. Simplify:
(2 x)(3x)  4 x5
d. If a  2 and b  5
evaluate b  a  ab
Sample questions for material to place into Level III and Level IV are on the next two pages.
These are sample questions for material required to place into Level III (MAT105 and MAT110).
9. Solve word problems involving addition, subtraction, multiplication, and division
a) What number is 8
b) Twice a number is
c) A number divided
d) Three times the sum of
less than 6 times 5?
increased by 3 and the by 3 is increased by 5. a number and 4 is 24. Find
result is 15. What is
The result is 12. Find
the number.
the number?
the number.
10. Evaluate functions
a) For 𝑓(𝑥) = 5𝑥 3 + 2 b) For 𝑔(𝑥) = |𝑥 − 3| c) For 𝐻(𝑡) = 3𝑡 2 − 𝑡 d) Find the value of 𝑓 (1),
2
find the value of
find the value of 𝑔(0). find the value of
when 𝑓(𝑥) = 7𝑥 − 5.
𝑓(−1).
𝐻(−2)
11. Given a linear equation, graph the line.
3
b) Graph: 3x  2 y  9
c) Graph: x  3
d) Graph: 2 x  3 y  12
a) Graph: 𝑦 = 4 𝑥 − 2
12. Write an equation for a line, given two points on the line or given one point on the line and the
equation of a line parallel or perpendicular to the line.
a) Find the slopeb) Find the slopec) Find the slope of a
d) What is the slope of a
intercept equation of the intercept equation of the line perpendicular to the line parallel to the line
line through the points
line passing through
line that passes through
4x  3y  8 ?
(3,3) and (3, 1) .
(4, 2) and perpendicular the points (2,5) and
4
(4, 2) .
to 𝑦 = 𝑥 − 2
3
13. Solve a system of linear equations.
a) Solve:
b) Solve:
c) Solve:
d) Solve:
3x  4 y  6
x  y  2
x  2 y  1
x  4 y  2




2 x  y  7
2 x  3 y  11
3x  4 y  7
x  2 y  5
14. Find the mean, median, mode of a data set
a) The weights of 10
b) The weights of 10
c) The weights of 10
d) Find the median of: 10,
fifth graders are: 70,
fifth graders are: 70,
fifth graders are: 70,
30, 15, 25, and 40.
65, 71, 80, 77, 68, 72,
65, 71, 80, 72, 68, 72,
65, 71, 80, 72, 68, 72,
77, 85, and 90, what is 77, 85, and 90, what is 77, 85, and 90, what is
the mean weight?
the median weight?
the mode?
15. Solve equations for a variable
a) Solve for r:
c) Solve for h:
d) Solve for h:
b) Solve for 𝑏:
2
2
2
2
𝑆 = 2𝜋𝑟(𝑟 + ℎ)
𝐶 = 2𝜋𝑟
𝐴
=
2𝑟ℎ
+
𝜋𝑟
𝑎 +𝑏 = 𝑐
16. Solve story problems involving permutations, combinations or the fundamental counting principle.
a) How many different b) How many 4 digit
c) How many ways can d) A baseball team has 13
license plates can be
codes can be made if
3 books be chosen
members, how many
made if they all must
letters or numbers can
from a stack of 10
different 9 person batting
have 3 letters followed be used, but cannot be different books?
orders are there for this
by 3 numbers?
repeated?
team?
17. Graphs of basic functions
a) Which graph is
b) Which graph will
always decreasing,
never touch the x-axis,
1 𝑥
𝑦 = 2𝑥 or 𝑦 = √𝑥
𝑦 = (2) or 𝑦 = |𝑥|?
c) Which graph is
always increasing,
𝑦 = 𝑥 2 or 𝑦 = 𝑥 3 ?
d) For which graph can
x not equal zero,
𝑦 = log 2 𝑥 or 𝑦 = |𝑥|?
18. Add, subtract, multiply, divide and find the composition of functions
a) If 𝑓(𝑥) = 𝑥 2 + 5𝑥
and 𝑔(𝑥) = 3𝑥 − 2,
find and simplify
(𝑓 + 𝑔)(𝑥)
b) If 𝑓(𝑥) = 𝑥 2 + 5𝑥
and 𝑔(𝑥) = 3𝑥 − 2,
find and simplify
(𝑓 ∙ 𝑔)(𝑥)
c) If 𝑓(𝑥) = 𝑥 2 + 5𝑥
and 𝑔(𝑥) = 3𝑥 − 2,
find and simplify
(𝑔 ∘ 𝑓)(𝑥)
d) If 𝑓(𝑥) = 𝑥 2 + 5𝑥
and 𝑔(𝑥) = 3𝑥 − 2,
find and simplify
(𝑓 − 𝑔)(𝑥)
These are sample questions for material required to place into Level IV (MAT125 and MAT200).
19. Simplify algebraic expressions involving negative exponents and/or fractional exponents.
a) Simplify (all
d) Simplify (all exponents
b) Simplify: 2  32
2x 5 y 6
c)
Simplify:
exponents should be
should be positive):
z 4
3 5
23 x 4 z 2
x z y
positive): 2 3 4
3x 2 y 3 z 5
z y x
20. Solve by factoring
d) 𝑥(𝑥 − 5) = 14
a) 3𝑥 2 + 14𝑥 − 5 = 0 b) 25𝑥 2 − 49 = 0
c) 4𝑥 2 + 5𝑥 = 6
21. Use the quadratic formula to solve a quadratic equation.
a) Solve:
b) Solve:
c) Solve:
2
2
2 x  x  21  0
x  5x  2  0
x 2  4  6 x
d) Solve:
5x2  2 x  2  2 x2  7 x
22. Add, subtract, multiply, and square polynomials.
a) Simplify:
b) Multiply:
c) Multiply:
(3x  4)(2 x  3)
2 x  3( x  4)
(4 x  3)2
d) Simplify:
( x  5)( x  2)  4( x  1)
23. Use the square root method to solve (answers can be complex).
a) (𝑥 − 4)2 = −1
b) (𝑥 + 7)2 = 12
c) (5𝑥 + 1)2 + 9 = 0
d) 2(𝑥 − 1)2 = 8
24. Simplify the following expressions.
a) Simplify:
b) Simplify:
125
45x 20
c) Simplify:
90
d) Simplify:
32x8
25. Find the domain and range of equations and graphs in interval notation
a)
b)
c)
4
d)
4
2
2
4
4
(0, 2)
2
(-1, 2)
(2, 1)
(-2, 0)
(1, 0)
5
5
2
(2, 0)
5
2
(0, 1)
5
5
(2, -1)
2
5
5
5
2
2
4
4
(-2, -3)
4
4
26. Graph quadratics (parabolas) using transformations.
a) Graph:
b) Graph:
c) Graph:
2
2
y  2( x  3)  4
y  3( x  2)2  4
y  x  3
d) Graph:
𝑦 = (𝑥 − 3)2