Download Math resources - Peirce College

Dear student,
This preparation packet is intended to help you prepare yourself for the mathematics placement test at
Peirce. The placement test has questions relating to a number of basic math skills. Each of these skills
has a section which links to an instructional video and practice questions. Watch the video associated
for each skill and try out the practice questions. You can check your answers afterwards to see if you
have done them correctly.
Some of the questions on the placement test will require you to explain your answers. Make sure to use
complete sentences when doing so. You may want to practice this by writing out a sentence or two to
explain your answers for the practice questions below. If you have further questions about the
mathematics placement exam, please consult with your Undergraduate Enrollment Specialist.
Reading and Writing Whole Numbers
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=pZKTBjg7wiU
Sample questions:
Write each of the following numbers in words:
1) Twenty million, two hundred one
2) Five billion, sixty million, eight hundred thousand
3) Forty-four million, four
4) Nine hundred million
5) Sixty-five trillion, four hundred million
Solutions:
1) 20,000,201
2) 5,060,800,000
3) 44,000,004
4) 900,000,000
5) 65,000,400,000,000
Rounding Whole Numbers
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=1tC2cJYH4rc
Sample questions:
Round each number as directed:
1) Round 253 to the tens place
2) Round 725 to the tens place
3) Round 34,860 to the thousands place
4) Round 1,342,870 to the hundred thousands place
5) Round 3,697,483 to the ten thousands place
Solutions:
1) 250
2) 730
3) 35,000
4) 1,300,000
5) 3,700,000
Rounding Decimal Numbers
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=HQYfNP9GCu8
Sample questions:
Round each number as directed:
1) Round12.348 to the tenths place
2) Round 7.081 to the tenths place
3) Round 0.8356 to the hundredths place
4) Round 9.3501 to the thousandths place
5) Round 16.4986 to the hundredths place
Solutions:
1) 12.3
2) 7.1
3) 0.84
4) 9.350
5) 16.50
Adding Negative Numbers
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=COO1Sa3dDtM
Sample questions:
Compute the value:
1) −7 − 4
2) −12 + 11
3) 2 – 5
4) −10 – 4 – 2
5) – 8 + 13 − 1
Solutions:
1) −11
2) −1
3) −3
4) −16
5) 4
Reducing Fractions to Lowest Terms
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=uro3ApfNJZg
Sample questions:
Reduce to lowest terms:
35
1) 49
2)
3)
4)
5)
42
70
32
2
121
132
125
128
Solutions:
5
1) 7
2)
3
5
3) 16
4)
5)
11
12
125
128
(This fraction can not be reduced further)
Multiplying Fractions
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=AKC5tf715UM
Sample questions:
Multiply the following fractions. Write your answer in lowest terms:
14 15
1) 75 ∙ 28
2)
3)
4)
5)
9
10
∙
3)
4)
5)
8
7 5 12
∙ ∙
4 6 35
35 56
8
69
16
∙ 25
∙3
Solutions:
1
1) 10
2)
21
189
80
1
2
49
5
207
16
Dividing Fractions
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=YmkcPVVaelY
Sample questions:
Divide the following fractions. Write your answer in lowest terms.
2
7
1) 5 ÷ 3
2)
3)
4)
5)
Solutions:
6
1) 35
2)
3)
4)
5)
12
35
8
15
27
10
4
7
9
10
12
÷
21
8
9
25
÷ 10
45
25
÷ 21
14
12
7
÷3
Adding and Subtracting Fractions
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=3Fp6mg7QrZs
Sample questions:
Add or Subtract the fractions. Write your answer in lowest terms.
1)
2)
3)
4)
5)
5
1
12
3
6
4
9
3
−3
1
+ 16
8
+ 15
5
−6
4
2
7
−2
Solutions:
1)
2)
3)
1
12
9
16
44
45
1
4) − 12
5) −
12
7
5
(or −1 7)
Converting Between Percent, Decimal, and Fraction Notation
Video Links: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=8yvjaufjon0
https://www.youtube.com/watch?v=9mPBKJhieWU
Sample questions:
1) Convert 12%
a) to a fraction
b) to a decimal
1
2) Convert 25
a) to a decimal
b) to a percent
3) Convert .953
a) to a fraction
b) to a percent
Solutions:
3
1)
a) 25
b) 0.12
2)
a) 0.04
b) 4%
3)
a) 1000
953
b) 95.3%
Solving Percent Word Problems.
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=DgtK_XnV6BM
Sample questions:
1) Jane earns 6% commission on all sales she makes. If she sells $46,500 in merchandise one week,
how much commission will she make?
2) Of the 48,000 podiatrists in the United states, 40,800 are board certified. What percentage of
podiatrists is board certified?
3) According to the Pew Charitable Trusts 2013 State of the City report, there are about 274,800 adults in
the city of Philadelphia who have graduated from college. If this is about 24% of all adults in the city,
how many adults are there living in Philadelphia?
Solutions:
1) $2790 (You are given the Base of $46,000 and the Rate of 6% and are asked for the Part/Amount)
2) 85% (You are given the Base of 48,000 and the Part of 40,800 and are asked for the Rate)
3) 1145000 (You are given the Part of 274,800 and rate of 24% and are asked for the Base)
Solving Linear Equations
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=u9ldizmwWDE
https://www.youtube.com/watch?v=3BrYy5CVxL0
https://www.youtube.com/watch?v=ir0qVgQzDGo
Sample questions:
1)
9 x  28  55
2)
14  5x  8
3)
5𝑥 − 30 = 8𝑥 − 3
4)
4(5 − 2𝑥) = 2𝑥 + 10
Solutions:
1)
x3
2)
x
3)
𝑥 = −9
4)
𝑥=1
22
or x = 4.4
5
Graphing points
Video Link: Please pause and take notes as you watch.
https://www.youtube.com/watch?v=k41lBGDLy8w
Sample questions: Identify the points in the graph below
Solutions:
A (6, 4)
B (-5, -2)
C (2, -5)