Orange Coast College
Math Placement Test Review
(Sample Problems)
The following problems are just a small sample of the types of problems students will see on the test and is not
intended as a complete review. It is only provided to aid students in determining their correct Math Level and
as a supplement to their studying for that Assessment Test. All Math tests are timed 1 hour and calculators are
NOT permitted. Students must wait one year to retake the same level test.
Level 1 Algebra Readiness Test
placement may be into one of the following courses:
MATH A005 – Basic Math
MATH A008 – Pre-Algebra
MATH A010 – Elementary Algebra
o
Topics: Integers; Fractions; Decimals and Percent; Exponents and
Square Roots; Simple Equations and Operations with Literal
Symbols; Geometry and Graphing
Study problems 1 through 30
__________________________________________________________________________________________________
Level 2 Elementary Algebra Test
placement may be into one of the following courses:
MATH A010 – Elementary Algebra
MATH A020 – Geometry
MATH A030 – Intermediate Algebra
o
Topics: Arithmetic Operations; Polynomials; Linear Equations
and Inequalities; Quadratic Equations; Graphing; Rational
Expressions; Exponents and Square Roots; Geometry; Word
Problems
Study problems 31 through 56
__________________________________________________________________________________________________
Level 3 Intermediate Algebra Test
placement may be into one of the following courses:
MATH A030 – Intermediate Algebra
MATH A100 – Liberal Arts Math
MATH A115 – College Algebra
MATH A120 – Trigonometry
MATH A140 – Business Calculus
MATH A155 – Finite Math
MATH A160 - Statistics
o
Topics: Simplifying and Evaluating Expressions; Polynomials;
Linear Equations, Inequalities, and Systems; Rational Expressions
and Equations; Quadratic Equations, Inequalities, and Complex
Numbers; Logarithmic/Exponential Expressions and Equations;
Radical Expressions and Equations; Graphing; Applications
Study problems 57 through 82
__________________________________________________________________________________________________
Level 4 Precalculus Test
placement may be into one of the following courses:
MATH A170 – Precalculus
MATH A180 – Calculus I
o
Study problems 83 through 100
Topics: Exponents and Radicals; Functions; Geometric
Applications; Linear Equations and Inequalities, Absolute Values,
and their Graphs; Logarithmic and Exponential Functions;
Polynomials and Polynomial Functions; Rational Expressions and
their Graphs; Trigonometry
Level 1 Questions start here:
1) 0.65 × 18.4 =
2) 1.6 – 0.72 =
3) 3.48 ÷ 0.4 =
4)
6
5) 18 ÷ 5 =
7) 2 × 4
6)
1
=
3
3
4
+
2
3
7
8
9
×
÷
4
5
15
16
=
=
8) What is 35% of 80?
9) If 𝑥 = 4, then 4𝑥 – 13 =
11)
20
10) Jim bought 8 notebooks and 3 pens, costing $1.50
each. How much did he pay?
12) 4𝑥 + 7 = 23. Find 𝑥.
=
13) What is 7% expressed as a decimal?
14) There are 53 palm trees in the park. Park workers
are planting more palm trees today. When they finish,
there will be 78 palm trees in the park. How many
palm trees are the workers planting today?
15) What number multiplied by 8 equals −24?
16) Find the least common multiple of 12 and 15.
17) If √𝑛 = 81, then 𝑛 =
18) (3.1)2 + (0.3)2 =
19) Arrange the following numbers in order from
20) What fraction of the figure is shaded?
1 1
smallest to largest: , , 0.24, 0.26
4 5
1
4
1
3
21) How many bouquets of flowers can you buy with
$136, if each bouquet costs $8?
23) 3(𝑥 + 1) – 2𝑥 =
22) 3(5 + 2) – 8 + 2(3) =
24) Simplify:
25) In the right triangle shown, what is the length of
𝐾, if 𝐽 = 3 and 𝐿 = 4?
𝐾
𝐽
4𝑥𝑦
6𝑦𝑧
26) A sporting goods store has a tennis racket on sale
for $60. This is 80% of its original price. What was
the original price?
𝐿
27) What is the radius of a circle whose area is
64𝜋𝑖𝑛2?
28) Find the perimeter and area of the square.
29) On the number line below, what is the distance
between points 𝐴 and 𝐵, and what number
represents the point half the distance between points
𝐴 and 𝐵?
30) What are the coordinates of point 𝐶 in the figure
below?
𝐴 (−2, 3)
𝐷 (3, 2)
16 𝑖𝑛
𝐴
𝐵
−2
8
𝐵 (−2, −1)
𝐶
Level 2 Questions start here:
31) Convert
19
5
to a decimal.
32)
4
15
×
3
8
=
33) 7.19 – (5 – 1.3) =
34) 8𝑥 – 3𝑦 + 7𝑥 – 10𝑦 =
35) 3√26 is a number between…
36) (𝑥 – 2)(𝑥 + 6) =
37) (𝑥 2 + 7𝑥 − 3) − (−3𝑥 2 + 4𝑥 − 2)
39) (𝑧 − 5𝑦)2
38)
85
82
=
40) If 𝑦 = 𝑥 – 8 and 2𝑥 – 𝑦 = 4, then 𝑥 =
41) 34 ∙ 35 =
43)
45)
4 (𝑥 2 −4)
𝑥−2
2
𝑥+1
−
42) 4𝑥 – 7 > 9𝑥 + 13 is equivalent to…
44) √27 =
=
1
𝑥−1
46) The sum of three consecutive integers is 48. What
are the three integers?
=
47) What is one of the solutions of the equation
(𝑥 + 4)(2𝑥 − 5) = 0?
48) What is one of the solutions of the equation
𝑥 2 + 4𝑥 = 12?
49) On the number line shown, which letter best
50) What percent of 40 is 25?
locates
5
9
?
P Q R S T
0
1
7
2
7
3
7
4
7
6
7
5
7
1
51) What is the area 𝐴 and perimeter 𝑃 of the triangle
shown?
13
5
9
52) Graph all values of 𝑥 such that 𝑥 > −7 and
𝑥 ≤ 5.
−8
20
53) What are the coordinates of point 𝑃 shown in the
figure below?
0
8
54) In the triangle shown, what is the degree measure
of ∠𝐶?
𝐴
80°
(0,0)
𝑃
55) What is the approximate area of a circle whose
radius is 7?
𝐵
60°
56) 64 is the square of twice what number?
Level 3 Questions start here:
57) Write (23 )2 (24 ) as a power of 2.
59) Simplify:
58)|9 – 17| − |8 – 12| =
6.9 × 104
2.3 × 107
60) If 𝑓(𝑥) = 4 – 5𝑥, find 𝑓(𝑎 − 4).
𝐶
61) (4𝑥 2 𝑦 2 – 2𝑥𝑦 + 8𝑦 2 ) – (−2𝑥 2 𝑦 2 + 3𝑥𝑦 − 8𝑦 2 ) =
62) Solve for 𝑥: 8 – 2(3 – 2𝑥) = 3(𝑥 – 1)
63) Solve for 𝑥: − 2𝑥 + 6 ≥ 4
64) Solve for ℎ: 𝑉 =
65)
1
1
+
𝑥 𝑥2
1
𝑥
66)
=
15𝑥
5𝑥+5
∙
𝑥 2 +3𝑥+2
𝑥 2 +2𝑥
1
𝜋𝑟2 ℎ
3
=
67) Solve for 𝑥: (𝑥 – 15)2 = 28
68) 𝑥 2 – 3𝑥 – 1 = 0
5𝑥 − 𝑦 = 1
69) Find the 𝑦-value of the solution of {
−2𝑥 + 3𝑦 = 10
70) What is the midpoint of the segment connecting
(−2, 3) and (4, −3)?
71) (3𝑥 3 𝑦)2 (𝑥𝑦 3 ) =
72) (2 − √−2)(3 − √−2) =
73) (√3 + √2)2 =
74) One of the roots of 𝑥 2 − 2𝑥 − 1 = 0 is…
75) Write the equations of the line with slope
𝑦 −intercept −2.
3
2
and
76) 𝑥 2 − 3𝑥. What number must be added to
complete the square?
77) What is the distance between the points (−2, 1)
and (1,5)?
78) Solve for 𝑥: log 2 (𝑥 + 7) − log 2 𝑥 = 3
79) Solve for 𝑥: 95𝑥 = 272𝑥−4
80) The length of a rectangle is twice the width. If
the perimeter is 66 inches, what are the length and
width of the rectangle?
82) Graph y = 𝑥 2 + 1
81) Write the equation for the
line show.
Level 4 Questions start here:
83) Find the x and y-values in the system of
𝑥−𝑦 =2
equations: {
4𝑥 − 6𝑦 = 4
84) If 𝑓(𝑥) = 2𝑥 − 7 and 𝑔(𝑥) = 2𝑥 2 − 3, then
𝑓(𝑔(3)) =
85) 𝑎−2 (𝑎−1 + 𝑎−4 ) =
86) The inequality |7 − 𝑥| > 8 is equivalent to…
87) One of the roots of 2𝑥 2 − 3𝑥 − 2 = 0 is…
88) Solve for 𝑥: log 3 27 = 𝑥
1
89) Solve for 𝑥: log 4 ( ) = 𝑥
90) Find 𝑓(2) if 𝑓(𝑥) = 4𝑥 2 + 7
91) The graphs of 𝑥 = 2 and 2𝑦 = 𝑥 − 1 intersect at
what point?
92) Solve for 𝑥: |2𝑥 − 5| ≤ 3
4
𝑥
93) 3
√3
95)
=
14−7𝑥
𝑥2 −𝑥
𝑥−2
𝑥−1
3
94) If sin 𝑥 = −
𝑥=
1
cos 𝑥 = 2, and 0 ≤ 𝑥 ≤ 2𝜋, then
96) If 7 = 5𝑠 , then 𝑠 =
=
1
√3
,
2
7
97) If 4 is 2 of 8 of a certain number, then that number
is…
98) What is the radian measure of an angle whose
degree measure is 72°?
99) In the figure shown, 𝑥 =
100) The graph of 𝑦 = 𝑓(𝑥) is shown on the left. On
the right, please graph 𝑦 = |𝑓(𝑥)| = 1.
12
4
𝑥
10
Answer Key
1) 11.96
27) 8
54) 40°
2) 0.88
28) Perimeter = 64𝑖𝑛
Area = 256𝑖𝑛2
55) 153
3) 8.7
4)
25
7
58) 4
59) 3.0 × 10−3
31) 3.8
5
6
32)
2
7) 8
3
1
60) −5𝑎 + 24
10
61) 6𝑥 2 𝑦 2 − 5𝑥𝑦 + 16𝑦 2
33) 3.49
8) 28
62) −5
34) 15𝑥 – 13𝑦
9) 3
63) 𝑥 ≤ 1
35) 15 𝑎𝑛𝑑 17
10) $16.50
11)
57) 210
30) (3, −1)
5) 15
6)
56) 4
29) Distance = 10
Midpoint = 3
64)
36) 𝑥 2 + 4𝑥 – 12
17
37) 4𝑥 2 + 3𝑥 − 1
12
65)
3
12) 𝑥 = 4
38) 8
13) 0.07
39) 𝑧 2 – 10𝑦𝑧 + 25𝑦 2
14) 25
40) −4
3𝑉
𝜋𝑟 2
=ℎ
𝑥+1
𝑥
66) 3
67) 15 ± 2√7
68)
9
3 ± √13
2
15) −3
41) 3
16) 60
42) 𝑥 < −4
69) 4
17) 9
43) 4𝑥 + 8
70) (1,0)
18) 9.7
44) 3√3
1
1
5
4
19) , 0.24, , 0.26
20)
5
45)
𝑥 2 −1
47)
22) 19
48) 2
2𝑥
3𝑧
25) 5
26) $75
73) 5 + 2√6
74) 1 + √2 or 1 − √2
5
21) 17
24)
72) 4 – 5𝑖√2
𝑥−3
46) 15, 16, 17
12
23) 𝑥 + 3
71) 9𝑥 7 𝑦 5
75) 𝑦 =
2
76)
49) Q
9
4
50) 62.5%
77) √53
51) 𝐴 = 50, 𝑃 = 42
78) 1
52)
−8
53) (4, −3)
0
8
79) −3
3
2
𝑥−2
80) Length = 22
Width = 11
81) 𝑦 =
3
5
𝑥−3
82)
83) 𝑥 = 4
𝑦=2
84) 23
85)
1
+
𝑎3
1
𝑎6
86) 15 < 𝑥 or −1 > 𝑥
87) 2 or −
1
2
88) 3
89) −1
90) 23
91) (2,
1
2
)
92) 1 ≤ 𝑥 ≤ 4
3
93)
94)
𝑥 √9
3
5𝜋
3
7
95) −
𝑠
96) √
97)
98)
𝑥
7
5
12
7
2𝜋
5
99) 5
or 1
5
7
100)