Download Professional Mathematics Standards Review Introduction: Setup of

Professional Mathematics Standards Review
Introduction:
The following review is designed to give you an opportunity to experience typical
problems that might appear on the Professional Mathematics Standard Test administered
to Education majors. The 6th Edition of A Problem Solving Approach to Mathematics by
Billstein, Libeskind and Loll, is the textbook used in the Concepts One and Two courses
given here at Kent State. While there are other sources you may chose for practice
problems, this review specifically refers you to chapters and pages in the Billstein Text.
The text is located at the reference desk of the Curriculum Materials Library, White Hal
for your convenience.
Setup of Review:
This Review is structured to cover 7 major topic areas: Problem Solving, Number
Concepts and Operations, Geometry, Measurement, Probability, Averages, and a final
group, Ratio, Proportion, Fractions and Percents. What is available is a two sided single
sheet for each of these areas. Depending on the problems you missed, take the
appropriate sheet and use it to structure your review. Each sheet has sample problems as
well as additional help available from the Billstein text. The answers to all sample
problems are located on the back side of this sheet.
Problem #'s
Concept
9,22,24,31,36,38,40
I Problem Solving
I, 2, 3, 14, 18, 27, 29, 37,39
Chapters 3,4, &6
5,6, 7,8,34
II Number Concepts and
Operations
III Geometry
10, 11, 13, 21, 26,30
IV Measurement
Chapter 12
12, 23, 33
V Probability
Chapter 8
15,32,35
VI Averages
Chapter 9
4, 16, 17, 19, 20, 25, 28, 38,40
VII Ratio, proportion,
fractions, and percents
Chapter 5,6, & 7
Billstein 6th Ed.
Chapters
Chapters 1 & 7
Chapters 10, 11 & 13
I
I
!
l
I
Answers to Practice Sheets
I: Problem Solving
1. c
2. b
3. c
4. b
5. c
VI: Averages
1. b
2. a
3. b
4. a
II: Number Concepts
1. b
2. d
3. b
4. a
5. a
VII: Ratio, Proportion, Fractions & Percents
1. a
2. d
3. c
4. b
5. c
6. d
7. b
Ill: Geometly
1. a
2. c
3. d
4. d
5. b
IV: Measurement
1. a
2:. c
3. d
4. c
5. d
V: Probability
1. a
2.
3.
4.
5.
b
b
b
c
I:.. Proh!emSolviilg
If you missed questions# 9, 22, 24, 31, 36, 38,40 you need to review Problem Solving.
Problem solving is a critical component of developing mathematical ability. It can
involve employing different strategies for differently stated situations. Problem solving
can include solving problems \vhich requiring the ability to use various operations with
different kinds of numbers. .It can also involve the ability to read or compose tables 1
charts, and diagrams. Some application problems involve using variables. It is
recornJnended that you review Chapter 1 and Chapter 7 ofBillstein 6°' Edition, A
Problem Solving Apptoach to Mathematics.
Problem Solving is knowing what to do when you don 1t ¥-..now what to do! There are four
basic steps for problem solving discussed in Chapter L
1. RElill: Understanding the problem sometimes requires you to read it more
than once. Reading a problem more than once helps you to sort the
information given and determine the relative information as well as what is
extraneous information.
2. PLAt'!: There is more than one way to solve a problem. Choose a strategy
that you are comfortable with, and that fits the information given. For
example, look for a pattern) draw a pictUre, uiake a chart or table, work
back\'vards, employ counting, or use a guess and check method.
3. DO: Cru.'T)' out your pian.
4. LOOk BACK: Re-read the problem and reflect on what you have done. Is
your answer reasonable? Does it make sense? Is there a way to check your
answer? Could you have thought about this another way?
BiUstein:
1. Chapter 1,
a. Problem Solving read page 19
b. Sample problems
pages 22-2.8
.
.
Practice problem .set pages 44, 48, 49.
'
2. Chapter 7,
a. Applications of Mathematics- page 338
b. Sample problems pages 338-348
Practice problem set pages 349, 357, 358
Sample Problems:
1. Candy bars cost $3.00 for a box of 12 at Sam's Club. Tne school band is selling each
bar for $0.50 to raise money for their new unifonns. What is the profit on each box
sold?
a. $0.25
c. $3.00
b. $2.50
d. $6.00
2. Mr. and Mrs. Smith bought a new car for $17,500. They made a down-payment of $5000
and choose a 40 month payment plan. Each month they pay $350.00 for their loan. What is
the total finance charge?
c. $700
a. $350
d.$1250
b. $1500
3. If a = 2b2, what happens to a if b is doubled?
a. a is tripled
c. a is multiplied by 4
b. a is doubled
d. a is multiplied by 2
4. The following is a bus route showing stops A, B, and C and a scale in minutes.
Which stop takes longer to get to from B?
c. Stop C
a. Stop A
b. both are the same
d. Not enough information
5. Kauffman's Labor Day end of the season sale began on Friday. A stereo system was
advertised for $200. On Super Saturday, the price was marked an additional40% off.
Customers received bonus coupons which allowed an additional one third off the lowest
sale price for Super Saturday only. What would you pay for the stereo using your coupon
on Super Saturday?
c. $80
a. $120
d. $133.34
b. $54
II: Number Concepts and Operations
If you n1issed questions nun1ber 12} 3 14} 18, 27, 2937, 39 you need to review number
concepts and operations. Having good number sense is an importfu"1t part of doing
mathematics and requires one to think beyond learned skills and develop a flexibility with
numbers. Developing the ability to use mental mathematics and estimation are important
for every day functioning in the real world. Formal pencil and paper operations of
addition, subtraction, multiplication and division over the real numbers (whole numbers,
inte-gers) rational numbers, fractions; and decimals) as wel1 as the properties of our number
system are additional topics ernployed ln this problem set. You should revie"v Chapters 3,
4 and 6 ofBillstein's 6fu Edition of A Problem Solving Approach io A{athematics,
1
Eiilstein:
l. Chapter 3
a. Whole number addition and subtractio!l, page 119-127
Practice problems on page 127-128
b. wnole number multiplication and division, page 129-137
Practice problems on page 137-139
c. Mental mathematics fu"ld estimation:
1. Addition, subtraction page 140-151
Practice problems on page 151-155
2. Multiplication, division on page 156-164
Practice problems on page 165-168
2. Chapter 4
a. Integers, page 176
b. Practice problems:
1. Addition and subtractioupracticeproblems on page 187-189
2. Multiplication and di,ision practice problems on page 196-198
3. Chapter 6
a. Integer exponents, page 294
Practice problems on page 306-307
b. Operations on decimals, page 307-322
Practice problems on page 322-324
c. Real num.bers: square roots, page 325
Practice problems on page 331-333
Sample Problems:
L Troop 122 has 36 girls and 2 leaders. They purchased 10 pounds of hamburger fer
their weekend camping trip. lfthey make quarter pourld burgers would. they have
enough meat so tl1at each person ca11have 1 h<L.'llburger?
a. not enough information
b. yes
c. no
2. Which
a.
b.
c.
3.
of the following statements is equivalent toy'?
4 ( J')
d. J' X y X)' X J'
y+ y+ y+}'
4
Joan returned overdue material to the local libra.)'. The library charges $0.10 a day
for overdue books aud $0.25 a day for overdue cassettes. The total fine was $0.80.
How many cassettes did Joan retu..u?
c. 3
a. 1
b. 2
d. 4
4. The total bill for d.innerwas $36.10 If Jason and Bob wanted to leave a 15% tip
about how much should the tip be?
c. $3.50
a. $5.40
d. $6.25
b. $4.50
5. Which of the fol1owing is p.hvavspositive?
c. -w
a. -(-10)
b.
(0)
d. - ( 7)
III: Geometry
If you missed questions 5, 6, 7, 8, or 34 you need to review some concepts in Geometry.
Some of the specific topics you need to look at for this problem set are: definitions of
· basic terms, d finitions of shapes, and properties of shapes including angle measure, side
lengths and parallel and perpendicular lines. You should review Chapters 10 and 11 in
Biilstein's G'' Edition of A Problem Solving Approach to Mathematics.
BiHstein:
1. Chapter 10
a. Properties and definitions of point, line, ray, angle read page 538-549
Chapter outline on page 610
Problem set on page 550-553
b. Polygor.s, congruence, triangles & quadrilaterals read page 554--560
Problem set on page 561-563
c. imgles and angle measure read page 579
Problem set on page 586- 589
2. Chapter 1.1
a. Properties of quadrilaterals read page 560-561
Practice problems on page 632-633
Sample Problems:
1. Tne measure of one angle in a triangle is 90°. The triangle can be:
l. a right triangle
2.. an isosceles triangle
3.· an equilateral triangle
a. 1 & 2
b. 1 & 3
2.
c. 1, 2 & 3
d. 2 &3
m· triangle ABC, if the measure of angle A is 40° and the measure
then the measure of angle C must be:
a. 90°
b. 60°
c. 80°
d. 100°
of angle B is 60°,
3. Angles 1, 2, 3, and 4 are fanned by two intersecting lines. Angle 1 and angle 2 are
call.ed:
a.
b.
c.
d.
corresponding angles
complimentary angles
vertical angles
supplementary angles
4. If two angles of a tria..TJ.gle are complimenta..ry what is the measure of the third angle?
a. 60°
b. 30°
c. 70°
d. 90°
5. Find the measure of angle 2 given that TRA.P is a trapezoid with line segment TR
parallel to line segment PA.
a. 60°
T ,...,..-----,,.-:/iZ.
b. 30°
c. 70°
cL 90°
TV: Mea!>urement
Ifyou issed problems\ 0, 11, 13,21,26, or 30, then you need to review easureme1it.·
The concept of measurement includes findi..11g length, area, volume, perimeter and
conversionsbetween units of measure1nent.. M.easurements in the United· States are in
Standard Units while tl1e scientificcommunity and most oibernationsuse Metric units,
• ·You oan find more detailed information on measurement in Chapter 126fB111steiri 6"'
. Edition, A Pioblem Solving Approacli to Nfathematics.
·
Billstein:
l. Chapter 12
··· . a.. Al"eafeail.page67E
··Practice problemson p.age 691-695
·b. Surface area read page 713
.
Practice problems on age717-720
· c. Volume readp.age 721
Practice p.r.ob1entssrti
feet
b. 15sct.feet.
c. 10 sq. feel
d. 90 cubic feet
3. John's walls have a total of 384 square feet of surface area. If a can of paint claims it will
cover 10,000 square inches of surface area, how many cans of paint will john need to buy?
a. 3
b. 4
c. 5
d. 6
4. A wheel on the hot dog cart at the baseball game has a 30 em. diameter. What is the area
of the circle formed by the cart's wheel rounded to the nearest centimeter?
a. 699 sq. em.
b. 94sq. em. c.
707 sq. em. d.
148 sq. em.
5. How many square centimeters are there in a square meter?
a. 10 b.
100
c. 1,000
d. 10,000
Y: Prohability
If you missed numbers 12, 23, or 33 you need to review Probability. Probabilities are
ratios expressed as fractions, decimals or percents m1d are determined by considering
results or outcomes of events. A set of all possible outcomes for an experiment is called a
sample space. The probability of an event happening is defined as the number of favorable
outcomes over the number of possible outcomes. For example, suppose you want to know
the probability of getting one head (H) when tossing two pennies. There
are four possibilities in the sample set: two heads (HI1), a head then a tail (HT), a tail
then a head (TH), or two tails (TT). Only two of the outcomes are favorable of the four
possibilities therefore the probability of getting one head when tossing two pennies is 2/4
or 1/2. You can learn more about probabilities ifyou read Chapter 8 ofBillstein 61h
Edition, A Problem Solving Approach to Mathematics.
Billstein:
1. Chapter 8
a. Read and study examples on how probabilities are determined, page
411-420
Practice problems on page 420-423
Sample Problems:
L A drawer contains 6 red socks, 4 blue socks, and 2 white socks. Suppose one sock is
taken from the drawer and tbat it is equally likely than any one of the socks can be
drawn. Find the probability that the sock drawn will be red.
a.Y,
b. 116
c. 5/6
d. y,.
2. A calculus class is composed of35 men and 45 women. There are 20 education
majors, 30 biology majors, 10 math majors, and 20 business majors. If one student is
chosen at random for the Dean's committee, what is the probabilitj it will not be a
math major?
a. 1/8
b. 7/8
d. 3/8
3. Given two standard dice, Joan. rolls a sum of2 (a one and a one, sometimes refened to
as snake eyes) five times in a row. "What is the probability on t'le ne:A1: roll she will roll
a sum of2?
a.· near 0
b. l/36
4.
c. 1/12
d. 1116
Charmel45 kept a record of the daily forecast for most of 1996. Their records show
that the predications have been correct 240 days an.d inconect 120 days out of the 360
days of record keeping. On the basis of this information, What is the best estimate
that can be made of the probability that Channel 45's forecast for some futnre date
will be con-eel?
a. Vz
b. 2/3
c. 2/5
d. 113
5. Any member ofMrs. Fisher's yearbook staff who wants to be editor can put his or her
name :into a hat. This month there are 9 boys names and 6 girls names in the hat.
"What is the probability that the editor will be a girl?
a. 1/6
b. 2/3
c. 2/5
d. 3/5
VI: Averaoes
If you missed problen1s 15, 32, or 35 you need to review Statistics. Statistics invo1ves
interpreting data. Chapter 9 in of Billstein 6°' Edition, A Problem Solving Approach 10
M.athcmatics.
Billstein:
l. Chapter 9
a. Read section 9-2
b. 1-1eastlres of central tendency and variation on page 492
c. Cmnputing the mean (average) on page 493
Practice problems on page 496
d. Extra practice on page 506-507
Sample Problems:
L To receive an A in class Willie needed at least an average of90% on his 5 exams.
Wiliie's grades on the first four exams were 85, 95,88 and 94. What minimum score
does he need on the 5"' exam to get an A in. the class?
a. 87
b. 88
c. 90
d. 92
2. If the mean weight of7 tackles on a team is 230 pounds and the mean weight of the 4
backfield members is 190 pounds, what is the mean weight of the 11 person team?
a. 215.45 lb.
b. 420 lb.
c. 204.50 lb.
d. 210 lb.
3. If 7 students got an 80 average on Mrs. Black's ma.th test aud 3 students got scores of
71, 99, and 50. Vlhat ]s the average grade for the class?
a. 75
h. 78
c. 80
d. 81
4. McDonnell's sells 3,000 hamburgers per day Monday through Saturday. How many
hamburgers do they need to sell on Sunday to have an average sale of 3500 per day?
a. 6500
b. 6000
c. 21,000
d. 500
VII. RATIO. PROPORTION. FRACTIONS & PERCENTS
If you missed problem number 20 you need to review ratio and proportion. If you missed
problem number 16, 17, 19 or 28 you need to review fractions. If you missed problems
number 4, 25, 38, or 40 you need to review percents. You can find more detailed
information on these topics in Chapters 7, and 5 ofBillstein 6"' Edition, A Problem Solving
Approach to Mathematics.
Billstein:
1. Chapter 7
a. Ratio and proportion read section 7-4 on page 374-384.
Practice problems on page 384-385
b. Percents read section 7-5 on page 387-396
Practice problems on page 396-398
2. Chapter 5
a. Fractions read page 352- 360
Practice problems on page 260-263
b. Operations of addition and subtraction of fractions read page 263-273
Practice problems on page 273-276
c. Operations of multiplication and division of fractions, read page 277285
Practice problems on page 285-288
Sample Problems: Ratio/proportion
1. The cL."'EEUa club at Kent put on a play last week. There were 27 people in the cast.
There were twice as many boys as girls in the cast. How many girls were in the play?
v. 16
a. 9
b. 18
d. 30
2. Jacob sketched a drawing for the school paper. His original drawing was too small so
be made the drawing bigger using a scale of 10 millimeters= 2 centimeters. If the
original width of the first drawing was 80 millimeters, wht is the width of the
enlllrgement?
c. 40 em.
a. 10.5 em.
d. 16 em.
b. 4cm.
Sample Problems: Fractions
3. Arrange the following fractions in increasing order: 10/22, 11/16, and 15/45.
a. 15/45, ll/16, 10/22
b. 11116, 10/22, 15/45
c. 15/45, 10/22, 11116
d. 10/22, 11116, 15/45
4. A sixth grade class is collecting cans to take to the recycling center. Becky's group
.brought the. following amounts in pounds: 1 1/8, 3 4110, 5 718, 6110. How many
pounds does her group have altogether?
c. 9 18/36
a. 10
d. 12
b. 11
5. A recipe requires 3 Y2 cups of mille Ryan put in% of a cup. How much more milk
does he need to put in?
a. 3
c. 2%
b. 2 'h
d. l%
Sample Problems: Percent
6. Marc had 84 boxes of candy. He sold 75%. How many boxes did he return to school
unsold?
c. 63
a. 25
d. 21
b. 56
7. A ph.L.'Tlber's wage this year is $19.80 per hour. This is a 110% increase over last
year's hourly wage. Wnat is the dollar amount of in.crease in the hourly wage over
last year?
c. $18
a. $.18
d. $ 21.78
b. $1.80