Download review guide for mathematics placement test

REVIEW GUIDE
FOR
MATHEMATICS PLACEMENT TEST
MAT 060 – PRE-ALGEBRA
MAT 072 – MATHEMATICAL LITERACY
MAT 098 – INTERMEDIATE ALGEBRA
DEPARTMENT OF MATHEMATICS
Parkland College
Office X212
Phone: 217-351-2225
www.parkland.edu/math
1
Why Mathematics Placement?
Parkland College is committed to helping students achieve success in their course
work. In this effort, the college has designed a mathematics placement program to aid
students in selecting the most appropriate mathematics course while taking into account
their widely varied mathematics backgrounds.
Placement or credit in the listed prerequisite course is required prior to registering in any
mathematics course.
Placement scores are valid for only two years; thereafter, the student must be
reassessed.
Students with transfer credit in mathematics are not required to take the placement test,
but can be placed on the basis of mathematics credits earned within the last five years
(after a review of transcripts).
How Does the Placement Test Work?
Parkland uses a national test called the ACCUPLACER. The test questions are based
on your responses to each question you’ve already answered. Questions increase or
decrease in difficulty depending on your answers as you work through the test.
ACCUPLACER tests are untimed, so you can move at a comfortable pace. It’s
important to give yourself enough time to do your best and complete the test because
your results are the key factor in determining the courses you can take.
This is not a test to pass or fail --- it is an instrument to help select the best level for the
student to have a reasonable chance of success --- not too low and not too high.
What is the Purpose of this Review Guide?
The purpose of this review guide is to help students know what types of questions to
expect on the ACCUPLACER test. The sample questions are taken from our MAT 060,
072, and 098 courses. This review should help the student “knock the rust off” of skills
that may not have been used for a while. This review is not intended to teach the
material.
How to Use this Guide:
The student must decide what course they think is the highest level that they have
already mastered, and then review that material. The student may use the answer key
to determine how well they did on the sample questions.
One way to review this material is to work through the chapter reviews or mastery tests
at the end of each chapter of the appropriate level textbooks.
2
Pre-Algebra Review
Preparation for placement out of MAT 060 into MAT 072
The purpose of the following questions is to help the student gauge their readiness on
the topics taught in MAT 060. (The purpose is not to teach this material.)
SIGNED NUMBERS
Simplify the following problems without using your calculator.
8  9 
89
1.
2.
3.
8  9
4.
5.
8  9 
6.
8
0
8  9
8.
8  9  1
10.
9
9.
72
9
2
 8 
11.
8   9 
12.
9   8 
13.
72
8
14.
8   9 
7.
15.
9   8 
16.
9  8
17.
89
18.
09
19.
72  8   9
20.
72   8   9
21.
8  9  2  9
22.
18   4  7 2
23.
2(5)  4( 3)
8  10
24.
18  33  30  6
FRACTIONS AND MIXED NUMBERS
Simplify the following problems without using your calculator.
5  1
1
5
 
25. 1  1
26.
6  4 
4
8
1
2
3 5 22


27. 4  1
28.
5
3
11 21 25
6 3 3 
7
1


29. 1  6
30.
8
4
5  5 10 
42
2
1 2  1
5
31.
32.
  
63
4 3 2
10
3
DECIMALS
Simplify the following problems without using your calculator.
33.
 0.008 0.09
34.
.03 
35.
3.04  17  16.9  7.015
36.
14.8  12.57
37.
0.09  .5  6  .02
38.
0.03 0.0987
39.
Change
40.
Change 16.15 to a mixed number
41.
Change 0.027 to a fraction.
42.
Change
79
to a mixed number.
6
2
3
to a decimal.
8
43. Write the number for one hundred two and five thousandths.
44. Write the number for one thousand and one hundredth.
45. Round 5,525.2178 to the nearest hundred.
46. Round 5,525.2178 to the nearest thousandths.
ALGEBRAIC EXPRESSIONS
Write the following in symbols.
47. The quotient of 10 and x is ninety.
48. The product of 10 and x is ninety.
49. The difference of 10 and x is ninety.
50. Twice the sum of 10 and x is ninety.
Simplify the following problems.
51. 8  9x  10 
52.
8x  9x
53.
8 x  9  9 x  18
54.
5  3  x  4
55.
4  3 x  2  5  7 x  8 
56.
3  x  2y   4  2x  y 
57.
8x  9x 
58.
59.
61.
 3 xy  5 x y 
 2x  3x  9   3x
4
2
2
8
60.
2
 4x  8

62.
x 
 2x y 
 x  4 x  10    3 x
5
3
3
2
4
3
2
 4 x  10

63. Find the value of the expression 7  2x when x  4
64. Evaluate the polynomial x 2  7 x  12 when x  3 .
4
EQUATIONS
Solve the following problems.
65. x  13  12
66.
4 x  44
67.
3 x  7  5
68.
2  3x  5  11
69.
15 x  1  2  4 x  20
70.
5x  6  7x  4x  3  9
71.
5
x  25
3
72.
1
x 3 8
4
73.
0.2 x  8.62  13.76
74.
2x  3.3  7 x  5.2
You may use a calculator on this part, but appropriate work must be shown.
GEOMETRY
Perimeter, Area and Volume Problems. If necessary, round to the hundredth.
75. Use the formula P  2L  2W to find W when P  112 cm and L  22 cm .
76. Find the perimeter of a rectangle with a length of 12.2 in and a width of 8.47 in.
77. Find the area of a rectangle with a length of 12.2 in and a width of 8.47 in.
78. Find the area of a triangle whose base is 34 inches and height is 12 inches.
79. Find the area of a circle with radius 2 cm. Use   3.14
80. Find the circumference of a circle with diameter 16 miles. Use   3.14
81. Find the volume of a rectangular solid that is 5 m wide, 3 m high, and 6 m long.
82. Find the volume of a cylinder with diameter 10 in and height 10 in. Use   3.14
83. Find the length of the missing side of the right triangle.
3 mi
11 mi
84. A square lot is 85 meters on each side. How much would it cost to fence the lot if
the fence costs $14 per meter?
5
RATIO, RATE AND PROPORTION PROBLEMS
85.
A car travels 310 miles on 12.5 gallons of gas. Find the rate in miles per gallon.
86.
Solve the proportion:
87.
If Kristen is paid $202.32 for 40 hours of work, how much will she be paid for 12
hours of work?
88.
The local health food store is making cereal that has nuts to cereal in a ratio of 3
to 8. If they want to make 209 oz of the mix, how many ounces of cereal will
they need?
6.2 12.4

x
1.7
PERCENT PROBLEMS
89.
Write 5.5 as a percent.
91.
Write
93.
What number is 9.2% of 1803?
94.
One hundred five percent of what number is 50.715?
95.
There is a 33% off sale at the jewelry store. If the regular price of a gold chain
is $183, what would be the sale price of the chain?
96.
If a Biology textbook costs $137.50 at the bookstore and tax is 8.5%, what is the
final cost of the textbook?
97.
A Kindle is priced at $219. There is a 25% discount on the Kindle and tax is
9.25%. What is the final cost of the Kindle?
3
as a percent.
5
90.
Write 35% as a decimal.
92.
3
Write 1 % as a decimal.
4
MEAN, MEDIAN, MODE, AND RANGE
98.
Find the mode and range of 3, 4, 5, 7, 6, 7, 4, 3, and 7.
99.
Austin had bowling scores of 118, 147, 203, 156, 180, and 192 for his last six
games. Find Austin’s mean and median bowling score.
100.
A consumer watchdog group priced a can of tomato soup at five different
grocery stores. They found the following prices: $0.89, $1.39, $1.65, $1.70 and
$1.89. Find the mean and median price. Round to the nearest cent.
SCIENTIFIC NOTATION
101.
Write 678,000 in scientific notation.
102. Write 4.1 10 4 in standard notation
6
English Measures and Equivalents
Length
Weight
12 inches (in) = 1 foot (ft)
3 feet = 1 yard (yd)
5280 feet = 1 mile (mi)
16 ounces (oz) = 1 pound (lb)
2000 pounds = 1 ton (T)
Liquid Volume
8 fluid ounces (oz) = 1 cup
2 cups (c) = 1 pint (pt)
2 pints = 1 quart (qt)
4 quarts = 1 gallon (gal)
Metric System
Kilo
Hecto
Deka
Base Unit
Deci
Centi
Milli
km
kg
kL
hm
hg
hL
dam
dag
daL
Length Meter (m)
Weight Gram (g)
Volume Liter (L)
dm
dg
dL
cm
cg
cL
mm
mg
mL
Conversions between Systems
Length
Area
Weight
Volume
2.54 cm = 1 in
1 m = 3.3 ft
1.6 km = 1 mi
6.5 cm2  1 in2
1 m2  10.8 ft 2
28.3 g = 1 oz
1 kg = 2.2 lb
1 L = 1.06 qt
3.8 L = 1 gal
The following problems involve the U.S. system conversions or conversions
between systems. Convert each measurement by multiplying by the appropriate
conversion factors. If necessary, round to the nearest hundredth.
103.
11 yd = __________ in
104. 2.1 gal = __________ cups
105.
275,200 oz = __________ tons
106. 61.82 lb = __________ kg
107.
4.8 km = __________ ft
108. 5.3 gal = __________ L
109.
A car is traveling at a speed of 45 miles per hour. What is the car’s speed in feet
per second?
110.
A science fair poster is a rectangle 36 inches long and 24 inches wide. What is
the area of the poster in square feet?
The following problems involve the metric system. Convert each measurement.
111. 1.86 km = _______________ cm
112. 3200 m = _______________ km
7
Pre-Algebra MAT 060 Review – Answer Key
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
72
17
72
8
64
17
9
17
1
81
55
11
23
8
38
15
3
10
5
12
2.
4.
6.
8.
10.
12.
14.
16.
18.
20.
22.
24.
26.
28.
1
Undefined
1
72
9
1
17
17
0
1
12
40
13
12
2
35
30.
4
32.
4
3
33.
35.
37.
0.00072
43.955
3.1
34.
36.
38.
0.0009
2.23
3.29
39.
13
1
6
40.
16
41.
27
1000
42.
0.375
43.
45.
102.005
5500
44.
46.
1000.01
5525.218
47.
10
 90 or 10  x  90
x
48.
10 x  90
49.
10  x  90
50.
2 10  x   90
51.
53.
55.
57.
72 x  80
52.
54.
56.
58.
17 x  27
23 x  48
72x 2
3
20
17x
3x  7
5 x  10 y
x15
8
59.
15x 3 y 12
60.
8x 9 y 12
61.
5x 2  x  1
62.
2 x 2  8 x
63.
15
64.
42
65.
x  25
66.
x  11
67.
x  4
68.
x  3.5
69.
x  1
70.
x  3
71.
x  15
72.
x  20
73.
x  25.7
74.
x  0.38
75.
34 cm
76.
41.34 in
77.
103.334 in 2
78.
204 in 2
79.
12.56 cm 2
80.
50.24 mi
81.
90 m 3
82.
785 in 3
83.
11.40 mi
84.
It would cost $4760 to fence the lot.
85.
86.
x  3.4
8
x
89.
24.8 miles per gallon
202.32 x

, x = $60.70
40
12
550%
90.
0.35
91.
60%
92.
0.0175
93.
x  165.88
94.
x  48.3
95.
Sale Price: $122.61
96.
Final Price: $149.19
97.
Final Price $179.44
98.
Mode = 7, range = 4
99.
Mean = 166, Median = 168
100.
Mean = $1.50, Median = $1.65
101.
6.78  10 5
102.
0.00041
103.
396 inches
104.
33.6 cups
105.
8.6 tons
106.
28.1 kg
107.
15,840 ft
108.
20 L
109.
66 feet per sec
110.
6ft 2
111.
186,000 cm
112.
3.2 km
87.
88.
11

209
, x = 152
9
Beginning Algebra Review
Preparation for placement out of MAT 072 into MAT 098
The purpose of the following questions is to help the student gauge their readiness on the
topics taught in MAT 072. (The purpose is not to teach this material.)
ALGEBRAIC EXPRESSIONS
1.
2.
3.
x 2  4x  4 for x  5
xy
Evaluate:
for x  6 and y  2
xy
Simplify the given expression: 4 y  2  y  5  6  y  
Evaluate:
SOLVING LINEAR EQUATIONS/INEQUALITIES AND LITERAL EQUATIONS
4x  4 7x  6

7
4
4.
2  x  1   x  7   3  x  1  2
6.
Solve and express the answer in interval notation: 11  5  4x
7.
Solve and express the answer in interval notation:
8.
9
Solve the following formula for C: F  C  32
5
5.
13 
1
2 5
x   x 1
2
3 6
RULES OF EXPONENTS AND OPERATIONS ON POLYNOMIALS
Simplify the following and write all answers using positive exponents.
2
30c 18d 12
9.
10.
3a 2 b5
12c 6 d 4
9 y 13
3
3
11.
12.
2a 2b 4
4
3y 



2
13.
5
15.
 2x 2 y 4 

2 
 3 xy 
17.
5x
19.
3x  7 
2
 
2

1
14.
 1
6 1   
4
16.
3 0  5  3 
18.
 2 x  3  4 x  5 
20.
(8 x 2  5 y 2 )  3 x 2  2 xy  y 2 
3
 x  1  2 x 2  3 x  7

0
10
GRAPHS
21.
Complete the table and graph the line.
y  3 x  6
x
y
8
y
x
8
-8
-8
22.
Complete the table and graph the line.
y
1
x 1
6
x
y
8
y
x
8
-8
-8
23.
From the graph of the line, find the
slope.
8
y
x
8
-8
-8
24.
Graph the inequality
y  3 x  5
8
y
x
8
-8
-8
11
25.
If the slope of the line L1 is 2 , find the slope of L2 so that L2 is
perpendicular to L1.
26.
If the slope of the line L1 is 2 , find the slope of L2 so that L2 is parallel to
L1.
27.
Write the equation of the line through the points  2,1 and  2,3  . Write the
answer in slope-intercept form.
28.
Given the line 2 x  3 y  6 , find the slope, x-intercept, and y-intercept.
29.
Determine which of the following ordered pairs are a solution to 5 x  3 y  30 .
a. (5,3)
b.  5,  3 
c.  3,  5 
30.
Write an inequality to represent the shaded portion of the graph below:
8
y
x
8
-8
-8
LINEAR SYSTEMS
31.
Solve: 6 x  4y  42
10 x  8y  26
32.
The total receipts for a concert were $650. Adult tickets cost $3, and
children’s tickets cost $2. Seventy-five more adult tickets were sold than
children’s tickets. How many of each type were sold?
33.
How many gallons of a 60% acidic solution must be added to 15 gallons of a
30% solution to obtain a 51% solution?
34.
You and a friend started jogging at the same location but headed in opposite
directions. After 45 minutes, you were 12 miles apart. If your rate was 6 mph
faster than that of your friend, what was your rate?
12
Beginning Algebra Review – Answer Key
1.
7
2.
3.
8 y  60
4.
5.
x6
6.
1
2
x 7
 4,  
7.
( 1,  )
8.
C
9.
9a 4 b10
10.
11.
y
3
12.
13.

15.
1
25
27
8x 3 y 18
14.
5
 F  32 
9
5c12d 8
2
6
a
8b12
23

6
16.
4
8 x 2  2 x  15
24 x 4  16 x 3 y  7 x 2 y 2  10 xy 3  5y 4
17.
7x 2  4x  8
18.
19.
9 x 2  42 x  49
20.
22.
21.
8
23.
m
25.
1
2
2
3
24.
y
x
8
-8
-8
27.
29.
1
x2
2
a and c
y
31.
 5, 3 
33.
35 gallons
26.
–2
28.
m
30.
2
, x-int =  3,0  , y-int =  0,  2 
3
y  x 2
32.
85 children’s & 160 adult tickets
34.
11 miles per hour
13
Intermediate Algebra Review
Preparation for placement out of MAT 098 into 105/107/108/124
The purpose of the following questions is to help the student gauge their readiness on the
topics taught in MAT 098. (The purpose is not to teach this material.)
FUNCTION NOTATION
Determine the domain of each function.
x2
f x 
1.
2 x  12
2.
f  x   3  4x
FACTORING POLYNOMIALS AND SOLVING EQUATIONS BY FACTORING
Completely factor each polynomial.
3.
3 x  x  5 y   2y  x  5 y 
4.
24 x 5 y 7  8 x 8 y 3  12x 2 y 9
5.
2 xm  3 ym  2 xn  3 yn
6.
x 2  3 x  18
7.
 x 2  3 x  28
8.
x 2  8 xy  16y 2
9.
144 x 4  25
10.
2 x 2  7 x  30
11.
5 x 2  20y 2
12.
6 x 3  33 x 2  42 x
13.
27 x 3  64
14.
2 x 3  12  3 x  8 x 2
16.
 x  1
Solve algebraically
15.
 x  12  x  1  40
2
 37  3 x
RATIONAL EXPONENTS, RADICAL EXPRESSIONS, COMPLEX NUMBERS, AND
QUADRATIC EQUATIONS
Simplify the following.

17.
 8 
19.
2
21.
 3  2i  5  i 
22.
i 99
23.
7
3  2i
24.

4
18.
3

2 5 3 2 2 5 3

4
81x 5 y
4
3

3
4
3
20.
7 2
1
3a 4 k
2
3

1
6a 2k
4
3

14
x 2  4 x  9  x  1
25.
Solve:
26.
Write the quadratic formula
27.
Find the solutions to the nearest tenth: 5 x 2  7 x  2  0
28.
Find the exact solutions: 3 x 2  2 x  1  0
29.
Calculate the distance between the points  4,3  and  2,  3  .
30.
Solve the inequality. Write the answer in interval notation:  x 2  15  8 x
RATIONAL EXPRESSIONS AND RATIONAL EQUATIONS
Simplify the following.
31.
3  x2
x2  3
32.
15 x 2  15 y 2
5x3 y 2  5x 2y 3

11x 3  11y 3 4 x 3  4 x 2 y  4 xy 2
33.
x  2 x 3  8 x 2  2x  4


x  3 x2  9
x 3
34.
12 x 2  x 1  1
8 x 2  6 x 1  1
36.
15
x 4 x 3


x  5x x  5
x
Solve for x.
35.
4
3
8


0
x  7 x  10 x  2 x  5
2
2
Solve the following applications.
37.
A boat completes a trip from Riverton to Clear Creek and back each weekday.
The distance one way is 60 miles, and the speed of the current in the river is
4 miles per hour. If the round trip takes 8 hours, determine the speed of the
boat in still water.
38.
A window washer can wash the windows on one side of a building in 112
working hours. With an assistant he can do the job in 63 hours. How many
hours would the assistant need to do the job alone?
Answer the following.
39.
If y is directly proportional to the square of x, and y is 37.5 when x is 5, find y
when x is 12.
40.
If y varies inversely as x, and y is 36 when x is 22, find y when x is 33.
15
Intermediate Algebra MAT 098 Review – Answer Key
4.
6.
 x  6  x  3 
7.
 x  5 y  3 x  2 y 
 m  n  2 x  3 y 
  x  7  x  4 
3

 , 4 


2 3
4 x y  6 x 3 y 4  2x 6  3y 6 
8.
9.
12x
 x  4y 
10.
11.
5  x  2 y  x  2 y 
1.
3.
5.
 , 6   6,  
2
 5 12 x 2  5 
2.
12.
2
 2 x  5  x  6 
3 x  2 x  7  x  2 
13.
 3x  4   9x 2  12x  16 
14.
 2x
15.
x  7, x  4
16.
x  9, x  4
18.
27x 5 y
20.
7 2
17.
19.
1
16
 67
2

 3  x  4
3
17  7i
21 14

i
13 13
22.
i
24.
18a 4 k 2
25.
x4
26.
27.
x  1.6, x  0.2
28.
29.
6 2
30.
31.
1
32.
12
11xy 2
33.
x2
x 2
34.
3x
x2
35.
37.
x  1
The speed of the boat in still
water is 16 mi/h
36.
38.
No solution
The assistant would need 144 hours
to do the job alone
39.
y  216
40.
y  24
21.
23.
3
b  b 2  4ac
2a
1  i 2
x
3
 , 3   5, 
x
16
Center for Academic Success
D 120
The Center for Academic Success (CAS) in D120 is Parkland College’s one-stop learning
center. CAS provides many learning and student development support services to empower
students to achieve their academic goals.
Preparation for Parkland’s assessment tests for entering students is highly recommended.
Assessment results determine course placements; low assessment scores may result in
several semesters in pre-college or developmental academic skill courses. Help in reviewing
math skills is available in CAS for prospective students as well as current students who wish to
re-assess. We invite you to use any of the following services.
FREE WALK-IN TUTORING HELP: CAS has tutoring services for currently enrolled Parkland
students as well as prospective students preparing for assessment tests. Tutoring services
are intended to help students complete assignments and review for tests. They are not
instructional sessions to teach new material.

Math Faculty Tutoring (MFT): Experienced math faculty provide free tutoring services for
students enrolled in pre-college math courses at Parkland. Students preparing to take the
Parkland math assessment may use MFT services to ask questions as they work through
the Mathematics Department’s Math Placement Review Guide. Math Faculty Tutoring is
available in the fall and spring semesters Mondays through Fridays, 10:00 a.m. to 1:00 p.m.

Peer Tutoring: Trained student tutors provide free walk-in tutoring services for currently
enrolled Parkland students. Students preparing for math assessment may use Peer
Tutoring services to ask questions as they review with the Math Placement Review Guide.
Math Faculty Tutoring is available Mondays through Thursdays, 9:00 a.m. to 9:00 p.m.,
Fridays, 9:00 a.m. to 5:00 p.m.
FOR-CREDIT TUTORIALS: Students who need extended instruction to learn and/or review math
knowledge and skills are invited to enroll for CAS one-credit hour tutorials.
 Supplemental Tutorials: A one-credit hour tutorial lasts 8 weeks. Interested students will
take a diagnostic to ascertain level of math ability. The tutorial consists of a weekly onehour conference with an instructor in a small group setting. Students complete an
additional hour or more of homework in CAS each week. A letter grade is assigned to each
tutorial taken.
For more information about CAS and its services, call 217/353-2005 or visit
www.parkland.edu/cas.
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