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ISBN: 0-07-865247-2 (Ohio Student Edition)
ContentsOhio Teacher Advisory Board . . . . . . . . . . . . . . . . . . . .OH2Ohio Academic Content Standards, Grade 9
Indicators, Correlated to Glencoe Algebra 1 . . . . . . .OH3How to Prepare for the OGT . . . . . . . . . . . . . . . . . . . . .OH6Countdown to OGT . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OH8
Melissa BalkoMathematics TeacherPickerington High School CentralPickerington, Ohio
Sue BashoorMathematics SpecialistCanton City SchoolsCanton, Ohio
Jane S. BaxterMathematics Department Chairperson Worthington Kilbourne High SchoolColumbus, Ohio
Yvette DaughertyMathematics ManagerCleveland Municipal School DistrictCleveland, Ohio
Carolyn A. DayDirector of Programs, Mathematics/ScienceDayton Public SchoolsDayton, Ohio
Richard L. GastMathematics Department ChairpersonElyria High SchoolElyria, Ohio
Image Credits: OH1 Gary W. Carter/CORBIS;OH2 Wes Thompson/CORBIS
Laurie Enia GodfreyDirector of Curriculum Development Lorain City SchoolsLorain, Ohio
Marilyn Mann LeslieMathematics and Science SupervisorYoungstown City SchoolsYoungstown, Ohio
Stephen W. MillerLearning Specialist, MathematicsAkron Public SchoolsAkron, Ohio
Paul PennCurriculum Team Leader, Mathematics Lima City SchoolsLima, Ohio
Anthony W. WagnerMathematics Department ChairpersonSidney High SchoolSidney, Ohio
Cindy WismarMathematics Department ChairpersonMedina High SchoolMedina, Ohio
Ohio Algebra 1 OH3
N2 Compare, order and determine equivalent forms for rational andirrational numbers.
2-1, 2-7
N3 Explain the effects of operations such as multiplication ordivision, and of computing powers and roots on the magnitudeof quantities.
1-1, 1-2, 2-3, 2-4, 2-7, 11-1
N4 Demonstrate fluency in computations using real numbers. This objective is addressedthroughout the text andfound in every lesson.
N5 Estimate the solutions for problem situations involving squareand cube roots.
2-7, 11-1
N1 Identify and justify whether properties (closure, identity, inverse,commutative and associative) hold for a given set of operations;e.g., even integers and multiplication.
1-4, 1-6
M1 Convert rates within the same measurement system; e.g., milesper hour to feet per second; kilometers per hour to meters persecond.
12-3, 12-4
Standards and Indicators Student Edition Lesson(s)
Standard 1 NUMBER, NUMBER SENSE AND OPERATIONS
Ohio Academic Content Standards, Grade 9 Indicators, Correlated to Glencoe Algebra 1Lessons in which the standards are a primary focus are indicated in bold.
Number and Number Systems
Meaning of Operations
Computation and Estimation
Measurement Units
Use Measurement Techniques and Tools
M3 Use the ratio of lengths in similar two-dimensional figures orthree-dimensional objects to calculate the ratio of their areas orvolumes respectively.
11-6;Glencoe Pre-Algebra:11-6P, 11-6
M4 Use scale drawings and right triangle trigonometry to solveproblems that include unknown distances and angle measures.
3-6, 11-7
M2 Use unit analysis to check computations involving measurement. 3-8
M5 Solve problems involving unit conversion for situations involvingdistances, areas, volumes and rates within the same measurementsystem.
3-8
Standard 2 MEASUREMENT
P � Preview Lesson, F � Follow-Up Lesson, RM � Reading Math
OH4 Ohio Algebra 1
Standards and Indicators Student Edition Lesson(s)
G3 Analyze two-dimensional figures in a coordinate plane; e.g., useslope and distance formulas to show that a quadrilateral is aparallelogram.
4-2, 5-6, 11-5
P1 Define function with ordered pairs in which each domain elementis assigned exactly one range element.
4-3, 4-6
P2 Generalize patterns using functions or relationships (linear,quadratic and exponential), and freely translate among tabular,graphical and symbolic representations.
4-6, 4-8, 10-1, 10-5
P3 Describe problem situations (linear, quadratic and exponential) byusing tabular, graphical and symbolic representations.
4-8, 10-1, 10-5
G1 Define the basic trigonometric ratios in right triangles: sine,cosine and tangent.
11-7
G2 Apply proportions and right triangle trigonometric ratios to solveproblems involving missing lengths and angle measures insimilar figures.
11-6, 11-7P, 11-7
P5 Describe and compare characteristics of the following families offunctions: linear, quadratic and exponential functions; e.g., generalshape, number of roots, domain, range, rate of change, maximumor minimum.
5-2, 5-3F, 10-1F, 10-5
P6 Write and use equivalent forms of equations and inequalities inproblem situations; e.g., changing a linear equation to the slopeintercept form.
5-2, 5-3, 5-4, 5-5, 6-1, 6-2,6-3, 6-4
P7 Use formulas to solve problems involving exponential growthand decay.
10-6
P8 Find linear equations that represent lines that pass through a givenset of ordered pairs, and find linear equations that represent linesparallel or perpendicular to a given line through a specific point.
5-4, 5-6
P4 Demonstrate the relationship among zeros of a function, roots ofequations, and solutions of equations graphically and in words.
4-5, 10-2, 10-4
P9 Solve and interpret the meaning of 2 by 2 systems of linearequations graphically, by substitution and by elimination, withand without technology.
7-1P, 7-1, 7-1F, 7-2, 7-3,7-4
P10 Solve quadratic equations with real roots by factoring, graphing,using the quadratic formula and with technology.
10-2, 10-3, 10-3F,10-4
Characteristics and Properties
Standard 3 GEOMETRY AND SPATIAL SENSE
Visualization and Geometric Models
Use Algebraic Representations
Use Patterns, Relations and Functions
Standard 4 PATTERNS, FUNCTIONS AND ALGEBRA
P � Preview Lesson, F � Follow-Up Lesson, RM � Reading Math
Ohio Algebra 1 OH5
Standards and Indicators Student Edition Lesson(s)
P13 Model and solve problems involving direct and inverse variationusing proportional reasoning.
5-2, 12-1
P14 Describe the relationship between slope and the graph of a directvariation and inverse variation.
5-2, 12-1
D1 Classify data as univariate (single variable) or bivariate (twovariables) and as quantitative (measurement) or qualitative(categorical) data.
1-9, 2-5, 5-7, 13-3, 13-4, 13-5
D2 Create a scatterplot for a set of bivariate data, sketch the line ofbest fit, and interpret the slope of the line of best fit.
5-7
D3 Analyze and interpret frequency distributions based on spread,symmetry, skewness, clusters and outliers.
2-5, 13-3, 13-4, 13-5
D4 Describe and compare various types of studies (survey, observation,experiment), and identify possible misuses of statistical data.
13-1
D5 Describe characteristics and limitations of sampling methods, andanalyze the effects of random versus biased sampling; e.g.,determine and justify whether the sample is likely to berepresentative of the population.
13-1
D6 Make inferences about relationships in bivariant data, andrecognize the difference between evidence of relationship(correlation) and causation.
5-7
D7 Use counting techniques and the Fundamental Counting principle todetermine the total number of possible outcomes for mathematicalsituations.
14-1
D8 Describe, create and analyze a sample space and use it to calculateprobability.
14-2, 14-3
D9 Identify situations involving independent and dependent events,and explain differences between, and common misconceptionsabout, probabilities associated with those events.
14-3
D10 Use theoretical and experimental probability, including simulationsor random numbers, to estimate probabilities and to solve problemsdealing with uncertainty; e.g., compound events, independentevents, simple dependent events.
14-4, 14-5
P11 Add, subtract, multiply and divide monomials and polynomials(division of polynomials by monomials only).
8-1, 8-5P, 8-5, 8-6, 8-7P, 8-7,RM12, 12-3
P12 Simplify rational expressions by eliminating common factors andapplying properties of integer exponents.
8-2, 12-2, 12-3, 12-4, RM12,12-5
Analyze Change
Data Collection
P15 Describe how a change in the value of a constant in a linear orquadratic equation affects the related graphs.
5-2, 5-3F, 10-1F
Statistical Methods
Probability
Standard 5 DATA ANALYSIS AND PROBABILITY
P � Preview Lesson, F � Follow-Up Lesson, RM � Reading Math
The Ohio Graduation Test (OGT) Preparation and PracticeWorkbook contains a practice for each of the Ohio Academic Standardsand two sample tests.
Your teacher may also ask you to take a sample test at various pointsthroughout the year to see if you’re ready to take the real OGT.
Pages OH8–OH32 of this text include a section called Countdownto OGT. Each page contains 7 problems that are just like those on theOGT. You should plan to complete one page each week to help youprepare for the test.
Plan to spend a few minutes each day working on the OGT problem(s)for that day unless your teacher asks you to do otherwise. For each week,individual days have the same type(s) of problem. If you have difficultywith any problem, you can refer to the lesson that is referenced inparentheses after the problem.
Monday Extended ResponseTuesday Multiple Choice, Short AnswerWednesday Multiple Choice, Short AnswerThursday Multiple ChoiceFriday Multiple Choice
A printable answer sheet to record your work and your answers foreach week. is available at oh.algebra1.com. At the end of the week,your teacher may want you to turn in the answer sheet.
Prepare for the OGT
Preparation and Practice Workbook
Ohio Graduation Test (OGT)Preparation and Practice Workbook
Ohio Graduation Test (OGT)
INCLUDES:
• Ohio Mathematics Academic Content Standards
• Test-Taking Tips
• Practice for Each Academic ContentStandard in Mathematics
• 2 Sample Tests
BASED ON THE OHIOMATHEMATICS ACADEMIC
CONTENT STANDARDS
�
Copy
right
© G
lenc
oe/M
cGra
w-H
ill
Week ____Name Date
7.6.
4.
5. Show your work.
2.
3. Show your work.
1. Show your work.
Florida Algebra 1 OH7
Your textbook contains many opportunities for you to get readyfor the OGT every day. Take advantage of these so you don’t needto cram before the test.
• Each lesson contains at least two OGT practice problems. Youcan use these problems every day to keep your OGT skillssharp. The Chapter Practice Test also includes an OGT practiceproblem.
• Worked-out examples in each chapter show you step-by-stepsolutions of OGT problems. Just like the practice problems,these are in multiple-choice, gridded-response, short-response,and extended- response formats. Test-Taking Tips are alsoincluded.
• Two pages of OGT Practice are included at the end of eachchapter. These problems may cover any of the content up toand including the chapter they follow.
• Pages 867–871 and 876–884 of the Preparing for StandardizedTests section of your textbook discusses various strategies forattacking questions like those that appear on the OGT.Additional practice problems are also provided.
Go to bed early the night beforethe test. You will think moreclearly after a good night’s rest.
Read each problem carefully andthink about ways to solve theproblem before you try to answerthe question.
Relax. Most people get nervouswhen taking a test. It’s natural.Just do your best.
Answer questions you are sureabout first. If you do not know theanswer to a question, skip it andgo back to that question later.
Become familiar with commonformulas and when they shouldbe used.
Think positively. Some problemsmay seem hard to you, but youmay be able to figure out what todo if you read each questioncarefully.
If no figure is provided, drawone. If one is furnished, mark itup to help you solve the problem.
When you have finished eachproblem, reread it to make sureyour answer is reasonable.
Make sure that the number ofthe question on the answersheet matches the number ofthe question on which you areworking in your test booklet.
Ohio Algebra 1 OH7
Lesson 9-5 Factoring Differences of Squares 503www.algebra1.com/extra_examples
Applying the Zero Product Property, set each factor equal to 0 and solve theresulting three equations.
2x � 0 or 3x � 5 � 0 or 3x � 5 � 0
x � 0 3x � �5 3x � 5
x � ��53
� x � �53
�
The solution set is ���53
�, 0, �53
��. Check each solution in the original equation.
Use Differences of Two SquaresExtended-Response Test Item
Read the Test Item
A is the area of the square minus the area of the triangular corner to be removed.
Example 6Example 6StandardizedTest Practice
A corner is cut off a 2-inch by 2-inch square piece of paper. The cut is x inches from a corner as shown.
a. Write an equation in terms of x that represents thearea A of the paper after the corner is removed.
b. What value of x will result in an area that is �79
� the
area of the original square piece of paper? Showhow you arrived at your answer.
x
x
2 in.
2 in.
(continued on the next page)
Test-Taking TipLook to see if the area ofan oddly-shaped figure canbe found by subtractingthe areas of more familiarshapes, such as triangles,rectangles, or circles.
OH8 Ohio Algebra 1
2. Multiple Choice Which point on the numberline is closest to ��17�? (Lesson 2-7)
A B C D
3. Short Answer Mr. Watkins left his house inCincinnati at 8:47 A.M. and arrived at BowlingGreen State University at 11:36 A.M. to pickup his son. They then left Bowling Greenat 12:20 P.M. and drove to Port Clinton for afishing trip. They arrived at Port Clinton at1:53 P.M. What was the total amount of timethat Mr. Watkins spent driving? Show yourwork. (Prerequisite Skill)
DCBA
�5 �4 �3 �2 �1 0
A B C D
4. Multiple Choice Name the property used to
solve 2 � �14
�a. (Lesson 1-4)
Multiplicative IdentityMultiplicative InverseAdditive IdentityReflexive Property
5. Short Answer Many board games use astandard die with sides having 1, 2, 3, 4, 5,and 6 dots. The sum of the number of dots oneach pair of opposite faces is 7. Determinewhether the net represents a standard die.Explain your reasoning. (Prerequisite Skill)
D
C
B
A
6. Multiple Choice The Spanish Club presidentsurveyed the club members to determine thepreferred type of fund-raiser. The results showed that 0.3 chose a car wash, �
270� chose a
bake sale, and 10% chose a gift wrap sale. Theremainder of the members chose a raffle. Whatfraction of the members chose a raffle?(Prerequisite Skill)
�15
� �14
�
�27
� �1230�DC
BA
7. Multiple Choice Tyron wants to build a brickpaver patio in his backyard. The length of thepatio needs to be at least 20 feet. The widthneeds to be greater than 12 feet, and thedistance around needs to be no more than75 feet. Which of the following could be thedimensions of the brick paver patio?(Prerequisite Skill)
25 feet by 14 feet22 feet by 16 feet25 feet by 12 feet 21 feet by 15 feetD
C
B
A
1. Extended Response The stem-and-leaf plot shows weights onpackages in pounds. Find the mean, median, and mode of the data.Determine which measure of central tendency best represents thedata. Show your work. (Lesson 2-5)
Stem Leaf6 7 8 97 2 2 2 2 2 3 4 4 689 8
10 6 8 6|9 � 0.69 lb
Ohio Algebra 1 OH9
1. Extended Response One of the following statements is true for the bar graph shown.
1. The mean, median, and mode are all the same.
2. The mode is less than the median.
3. The median is greater than the mean.
Explain which statement is true. Describe how you came to your conclusion. (Lesson 2-5)
6. Multiple Choice Some of the runways atO’Hare International Airport are shown below.If p � �, n � r, and m � q, which pair of angles willalways be congruent? (Prerequisite Skill)
�1 and �5 �8 and �11�1 and �9 �7 and �9DC
BA
7. Multiple Choice Jackie earns $12.50 per houras an assistant manager at a department store. She earns 1�
12
� times her hourly rate for each hour she works over 40 hours per week.During a 3-week period around the holidays,Jackie works 46 hours each week. What willbe her gross pay for this 3-week period?(Prerequisite Skill)
$337.50$1,725.00$1,837.50$2,587.50D
C
B
A
2. Multiple Choice Evaluate 0.5[6 � (5 � 1)].(Lesson 1-4)
0.51.522.5
3. Short Answer Tessa said “I can square anypositive number x and the result will be greaterthan x.” Juana said, “That statement isn’talways true.” Who is correct? Give a reason foryour answer. (Lesson 1-7)
D
C
B
A
4. Multiple Choice Bob Schul of West Milton,Ohio, won the gold medal in the 5,000-meterrun in the 1964 Olympics in Tokyo. If Bobbegan the race at 9:35:00 A.M. and crossed thefinish line at 9:48:48.8 A.M., what was hiswinning time? (Prerequisite Skill)
12 min 11.2 s 12 min 48.8 s13 min 48.8 s 14 min 48.8 s
5. Short Answer Graph the solution set for 2x � ��36�. Show your work. (Lesson 2-7)
DC
BA
Blue
Pink
Green
Yellow
4
6
20
810
Red
Turq
uoise
Purp
le
Freq
uen
cy
Control Tower
�
n
m
r
q
p
1 2 34
5 678
9
10 11
1. Extended Response The data listedrepresent the rainfall in inches forColumbus for the months of Januarythrough December, 2002. Create a bargraph displaying the data. Find the mean,median, and mode for the data. Write aconclusion based on the data. (Lesson 2-5)
Source: Channel 4, WCMH
OH10 Ohio Algebra 1
6. Multiple Choice Which of the followingcorrectly completes the following statement?(Lesson 1-7)
If two numbers are odd,
then their difference is even.then their product is even.then their sum is odd.then their quotient is an irrational number.
D
C
B
A
7. Multiple Choice Jolon observed the followingprisms. Which of the following statements is avalid conjecture? (Prerequisite Skill)
The number of sides of the base of theprism is 2 less than the number of facesof the prism.The number of faces of a prism is greaterthan the number of vertices of a prism. The number of edges of a prism is 1 lessthan twice the number of faces of the prism.The number of vertices of a prism is 2less than the sum of the number of facesand edges of a prism.
D
C
B
A
4. Multiple Choice Kayla is performing anexperiment in chemistry class. She needs tomix 20 liters of 40% acid solution with a70% acid solution to get a mixture that is50% acid. How many liters of the 70% acidsolution should she use? (Lesson 3-9)
5 L 7.5 L10 L 15 L
5. Short Answer What is the height of atrapezoid with an area of 88 squarecentimeters and bases 15 centimeters and24 centimeters? Round to the nearest tenth.Show your work. (Lesson 3-8)
DC
BA
2. Multiple Choice Mykia jogs 3.5 miles fourtimes a week. It takes her 25 minutes tocomplete her jog. At this rate, how far canshe jog in 1 hour? (Lesson 3-6)
5.8 mi8.4 mi9.1 mi14.3 mi
3. Short Answer Mark works at a car washwhere his hourly wage is $6.40. After 3 months,his hourly wage will increase to $7.36. Whatpercent of increase does Mark’s raise represent?Show your work. (Lesson 3-7)
D
C
B
A
Month Rainfall (in.) Month Rainfall (in.)
Jan. 2.02 Jul. 4.13
Feb. 1.67 Aug. 2.13
Mar. 3.43 Sept. 4.35
Apr. 4.02 Oct. 2.68
May 6.61 Nov. 2.94
Jun. 3.47 Dec. 2.77
Ohio Algebra 1 OH11
1. Extended Response Cans of soda are packaged with 12 cans in abox. The marketing department of a soda company is deciding whichpackaging will require the least amount of cardboard for the box. Theyare deciding between a box that holds two rows of six cans and a boxthat holds three rows of four cans. Based on the dimensions of a sodacan, which box will require less cardboard? Show your work.(Prerequisite Skill)
6. Multiple Choice The volume of a cylinder is300� cubic inches. If the height of a cone withthe same base is 12 inches, what is the diameterof the cone? (Lesson 3-8)
5 in.10 in.25 in.50 in. D
C
B
A
7. Multiple Choice The general equation for acircle is (x � h)2 � (y � k)2 � r2, when (h, k) isthe center and r is the radius of the circle.Which of the following is an equation of acircle with center at (3,�2) and a diameterof 8? (Lesson 1-4)
(x � 3)2 � (y � 2)2 � 64(x � 3)2 � (y � 2)2 � 16(x � 3)2 � (y � 2)2 � 64(x � 3)2 � (y � 2)2 � 16D
C
B
A
2. Multiple Choice In which of the followingsets does the number �103 not belong?(Lesson 2-7)
integerrealrationalnatural
3. Short Answer Mr. Cortez was on a jet when thecaptain announced that the speed of the jet was410 miles per hour and that they would reach Dayton in 3�
12
� hours. At the moment of the announcement, how far were they from Dayton?Show your work. (Lesson 3-9)
D
C
B
A
4. Multiple Choice Thirty is 15% of whatnumber? (Lesson 3-7)
2050200450
5. Short Answer Kenji biked 6 miles to thebeach in 45 minutes. The return trip took him 1�
15
� hours. What was his average speed for the round trip? Round to the nearesthundredth of an hour. Show your work.(Lesson 3-9)
D
C
B
A
2.5 in.
4.75 in.
1. Extended Response The data in the table shows the relationship between the number of sides of apolygon and the number of triangles formed by drawing all the diagonals from one vertex. Draw agraph of the data. Use the data to predict the number of triangles formed in an octagon, nonagon,and decagon. (Lesson 1-8)
OH12 Ohio Algebra 1
6. Multiple Choice What is the 20th term ofthe arithmetic sequence 12, 23, 34, 45, . . . ?(Lesson 4-7)
188199210221D
C
B
A
7. Multiple Choice The attendance at JacobsField, home of the Cleveland Indians,dropped 17.6% from 2001 to 2002. Theattendance in 2001 was 3,175,523. What wasthe 2002 attendance at Jacobs Field to thenearest thousand? (Lesson 3-7)
559,0001,804,0002,617,0002,739,000D
C
B
A
4. Multiple Choice Which equation bestrepresents the data in the table? (Lesson 4-8)
y � 2x � 1y � x � 2y � 3x � 2y � x � 3
5. Short Answer Show a table of values for x � 4y � 12. Then draw its graph. (Lesson 4-5)
D
C
B
A
2. Multiple Choice The transformation of thesquare shown represents all but a .(Lesson 4-2)
reflectiontranslationdilationrotation
3. Short Answer During a business trip toLondon, Mr. Lehnert spent 250 British pounds.He returned with $82.50. How many U.S.dollars did he take to London if 1 Britishpound equals $1.57? (Lesson 3-6)
D
C
B
y
xO
A
?
Polygon triangle quadrilateral pentagon hexagon heptagon
Number of Sides 3 4 5 6 7
Number of Triangles 1 2 3 4 5
x 1 2 3 4 5 6
y 1 3 5 7 9 11
Ohio Algebra 1 OH13
1. Extended Response Certain sets of numberscan be represented by geometric patterns.These are examples of triangular numbers.Draw the triangular figure for Stage 6. Whatnumbers are represented by Stages 1 through6? Use the pattern to determine the triangularnumber for Stage 10. (Lesson 4-7)
6. Multiple Choice Given ABC withcoordinates A(3, 6), B(6, 2), and C(9, 3), whatare the coordinates of the image of A when
ABC is reflected across the x-axis?(Lesson 4-2)
A′(�3, 6) A′(�3, �6)A′(6, �3) A′(3, �6)DC
BA
7. Multiple Choice PQRS is a rectangle withits center at the origin. If the coordinates ofvertex R are (7, �4), what are the coordinatesof vertex P? (Lesson 4-1)
(�7, 4) (�7, �4)(�4, 7) (4, �7)DC
BA
2. Multiple Choice A coat is on sale for 20% off.If you buy the coat before 10 A.M., there is anadditional early-bird discount of 10% off thesale price. If the original cost of the coat was$80, what is the sale price? (Lesson 3-7)
$22.40 $24.00$56.00 $57.60
3. Short Answer Theformula for the area ofa circle is A � �r2,where r is the radius.What is the area of theshaded region? Leaveyour answer in termsof �. Show your work.(Lesson 3-1)
DC
BA
4. Multiple ChoiceWhich equation bestrepresents the graph?(Lesson 4-8)
2x � y � 1x � y � �23x � y � 2x � y � �3
5. Short Answer After Virginia, the most U.S.Presidents were born in Ohio, includingGrant, Hayes, Garfield, Harrison, McKinley,Taft, and Harding. What percent of the43 U.S. Presidents were born in Ohio?Round to the nearest tenth. Show your work.(Lesson 3-7)
D
C
B
A
Stage5
Stage4
Stage3
Stage2
Stage1
12
18
y
xO
y
x
Q
R
O
S
P
1. Extended Response The table shows the weights of various lengths of pipe. Draw a scatter plotwith length on the x-axis and weight on the y-axis. Determine if a correlation exists. If so, what typeof correlation is it? Explain your answer. (Lesson 5-7)
OH14 Ohio Algebra 1
6. Multiple Choice An insurance companyprepared a graph showing the correlationbetween the value of a car and its age.Which graph shows a negative correlation?(Lesson 5-7)
Val
ue
Age of Car
D
Val
ue
Age of Car
C
Val
ue
Age of Car
B
Val
ue
Age of Car
A
7. Multiple Choice Which of the followingtypes of lines has a rate of change of 0?(Lesson 5-1)
horizontal linevertical lineline slanting upward to the rightline slanting downward to the rightD
C
B
A
4. Multiple Choice The scale of a map is2 inches � 125 miles. The distance betweenCincinnati, Ohio, and Washington, D.C., on the map is about 6�
34
� inches. What is the approximate distance between these twocities? (Lesson 3-6)
370 mi 420 mi480 mi 1,680 mi
5. Short Answer The rim of a basketball hoophas a circumference of about 56.55 inches. Findthe radius of the rim to the nearest tenth of aninch. Show your work. (Lesson 3-3)
DC
BA
2. Multiple Choice Assume that y variesdirectly as x. If y � �11 when x � �4, findy when x � 6. (Lesson 5-2)
2.18—
716.5264
3. Short Answer Write and graph the equationbest representing the data in the table. Showyour work. (Lesson 4-8)
D
C
B
A
Length (ft) 20 22 25 26 29 30 31
Weight (lb) 18 29 17 25 22 24 26
x �3 �2 �1 0 1 2 3
y �10 �8 �6 �4 �2 0 2
Ohio Algebra 1 OH15
1. Extended Response The graph shows theamount Shakeel saved from 1980 to 2000.Find the rate of change for 1980 to 2000.Explain the meaning of the slope for theyears 1980 to 2000. (Lesson 5-1)
6. Multiple Choice Which of the following doesnot represent a linear function? (Lesson 4-5)
�2x � 3y � 6
�25
�x � �34
�y � 10
y � 3x2 � 5
y � xD
C
B
A
7. Multiple Choice If the two angle measuresgiven are equal, find the value of x.(Lesson 3-5)
1.34.9613D
C
B
A
2. Multiple Choice Which pair of equationsrepresent lines that are parallel andperpendicular to the graph of 2x � 3y � 6?(Lesson 5-6)
y � �23
�x � 1 and y � ��32
�x � 3
y � ��23
�x � 2 and y � �32
�x � 4
y � �32
�x � 7 and y � ��32
�x
y � 3x � 2 and y � ��13
�x � 1
3. Short Answer Chelsea works part-time at theUniversity of Cincinnati Library. In a 22.5-hourwork week, she earned $193.50. Write a directvariation equation for the amount she earnsworking any number of hours. Show yourwork. (Lesson 5-2)
D
C
B
A
4. Multiple Choice The coordinates of thevertices of trapezoid ABCD are A(5, 6), B(1, �6), C(�5, �2), and D(�3, 4). If thetrapezoid is moved down 2 units and right4 units, which point has the correctcoordinates? (Lesson 4-2)
A′(9, 8) B′(5, �5)C′(�9, �4) D′(1, 2)
5. Short Answer Chin is saving money to buy aDVD player. She has already saved $40 andplans to save $15 more each week until shehas enough money. Write an equation for thetotal amount T she will have saved w weeksfrom now. Find the total amount Chin willhave saved after 8 weeks. Show your work.(Lesson 5-3)
DC
BA
Shakeel’s Savings
Am
ou
nt
(do
llars
)
1000
200300400500600700
1100
800900
1000
Year1980 1985 1990 1995 2000
(8x � 2)˚(25x � 20)˚
6. Multiple Choice Which statement is true basedon the 2000–2001 data about yearly in-statetuition and enrollment? (Lesson 1-9)
The enrollment is 4 times the tuition.The tuition has a much narrower rangethan the total enrollment.The greater the enrollment, the less thetuition.The greater the enrollment, the greater the tuition.
D
C
B
A
7. Multiple Choice Which of the followingordered pairs is not part of the solution setfor 3x � 4y � 10? (Lesson 6-6)
(�2, �3)(3, 2)(6, 2)(�5, �7)D
C
B
AUniversity Tuition Enrollment
Kent State University $5,598 21,924
Ohio State University $4,788 47,952
Ohio University $5,493 19,920
University of Cincinnati $5,823 27,327Source: www.areaconnect.com
4. Multiple Choice Thenumbers on the spinnerare equally likely. What isthe probability that in onespin, you land on amultiple of 3? (Lesson 2-6)
0.25 0.330.5 0.75
5. Short Answer Nations One Bank requires aminimum balance of $300 to maintain freechecking services. If Mrs. Garcia knows shemust write checks for $829 and $137, howmuch money should she have in her accountbefore writing the checks? Show your work.(Lesson 6-1)
DC
BA
2. Multiple Choice Solve �3y � 4 � 15.(Lesson 6-3)
y � ��131� y ��
131�
y � ��131� y ��
131�
3. Short Answer Sam is doing a traffic study thatcounts the number of vehicles driving throughan intersection. Write a statement describingthe correlation of the data in the traffic study.(Lesson 5-7)
DC
BA
12
345
6
78
Hour 1 2 3 4 5
Number of43 42 39 23 19
Vehicles
1. Extended Response Tickets for the high school production of The King and I cost $10 for adultsand $5 for children under 12. The high school drama club must take in $2,500 to cover theirexpenses for producing the play. Using A as the number of adult tickets sold and C as the numberof children’s tickets sold, write an equation representing the minimum number of tickets to besold. Write an inequality representing the play’s not going into debt. Then graph the inequality.(Lesson 6-6)
OH16 Ohio Algebra 1
Ohio Algebra 1 OH17
6. Multiple ChoiceWhich inequalityrepresents thegraph shown?(Lesson 6-6)
y 2x � 2y � 2x � 2x 2y � 2x � 2y � 2D
C
B
A
7. Multiple Choice Which of the following isnot a correct representation of the relation{(0, 1), (2, 5), (3, 4), (4, 2)}? (Lesson 4-3)
Dy
xO
C
4203
2514
x yBA
2. Multiple Choice Point A has coordinates(0, 0), and point B has coordinates (a, b). Whatare the coordinates of point C so ABC is aright triangle? (Prerequisite Skill)
(2a, 2b) (a, 2b)(a, 0) (b, a)
3. Short Answer Theheight of a triangle ismeasured on asegment that isperpendicular toa base. In ABC,can BD
— be used tomeasure the height ofthe triangle? Explain.(Lesson 5-6)
DC
BA
4. Multiple Choice Which of the followingvalues for a and b are counterexamples toshow that the following statement is not true?(Lesson 6-2)
If a � b, then a2 � b2.
a � 4, b � 5
a � �1, b � 0
a � �12
�, b � �23
�
a � 1.27, b � 1.28
5. Short Answer Alonzo’s first four math testscores are 93, 88, 91, and 79. What must hescore on the fifth and final test if he wants atleast a 90 average in math? Show your work.(Lesson 6-3)
D
C
B
A
1. Extended Response The yearly family membership to the Columbus Zoo and Aquarium is $64. Theregular admission to the zoo is $9 for each adult and $5 for each child. How many times should afamily of two adults and two children plan to visit the zoo in a year to make the membership lessexpensive than paying admission? Show your work. (Lesson 6-2)
y
xO
A
B
C
D
y
xO
�4�6�8
�2�4�6�8
8642
2 4 6 8 x y
0 1
2 5
3 4
4 2
x y
1 0
5 2
4 3
2 4
1. Extended Response Last year the Wilsons invested a total of $6,500 in two different savings plans.One plan earned 5% simple interest per year. The other plan earned 4% simple interest per year.Last year, the Wilsons earned a total of $290 in interest from the two accounts. Write a system ofequations that could be used to find the amount of money the Wilsons invested in each plan. Let rrepresent the amount invested at 5% and s represent the amount invested at 4%. Solve this systemto find the amount of money invested in each plan. Show your work. (Lesson 7-1)
OH18 Ohio Algebra 1
6. Multiple Choice Which figure represents arotation of ABC 90° clockwise? (Lesson 4-2)
O
y
x
B'
C'A'
A
C B
D
O
y
x
B'C'
A'
A
C B
C
O
y
x
B'
C' A'
A
C B
B
O
y
x
B'
C'A'
A
C B
A
7. Multiple Choice All members of Team A alsobelong to Team B, but only some members ofTeam B also belong to Team C. Determinewhich of the following statements is true.(Lesson 1-7)
If a person is a member of Team C, thenthe person is not a member of Team A.If a person is not a member of Team B, thenthe person is not a member of Team A.No person that is a member of Team Acan be a member of Team C.all of the aboveD
C
B
A
4. Multiple Choice Tickets for generaladmission to COSI in Columbus are $12 foradults and $7 for youth. If the ticket boothtakes in $3,780 on a given Saturday selling atotal of 415 tickets, how many adult ticketswere sold? (Lesson 7-2)
175 240280 521
5. Short Answer The Troy High School girlsbasketball team scored the following numberof points in their first 10 basketball games thisseason.
65, 58, 52, 60, 61, 50, 29, 55, 73, 65
If the outlier, 29, is removed from the data, byhow much does the mean score change? Showyour work. (Lesson 2-5)
DC
BA
2. Multiple Choice When solving the followingsystem of equations using substitution,which expression can be substituted for x?(Lesson 7-2)
3x � 6y � 8x � 2y � 12
�6y � 8 2y � �83
�
2y � 12 2y � 12
3. Short Answer The sum of two numbers is 21,and their difference is 5. Find the two numbers.Show your work. (Lesson 7-3)
DC
BA
Ohio Algebra 1 OH19
1. Extended Response Mr. Junkin, a furniture builder, sold two tables and one entertainment centerfor $2,335. Then he built and sold three entertainment centers and one more table for $3,255. Writea system of equations to represent the furniture Mr. Junkin made and sold. What is the cost of anentertainment center? What is the cost of a table? Show your work. (Lesson 7-4)
6. Multiple Choice The freshman class is sellingtickets to the homecoming dance. On Thursdaybefore the dance they sold 20 less than twice asmany tickets as they had sold on Wednesday. Theticket sales for Wednesday and Thursday totaled418. Let w � the number sold on Wednesday andt � the number sold on Thursday. Which of thefollowing systems of equations reflects thisinformation? (Lesson 7-2)
t � w � 418 t � w � 418t � 20 � 2w t � 2w � 20t � w � 418 t � w � 418w � 20 � 2t t � 20 � 2w
DC
BA
7. Multiple Choice The solution of the system4x � 5y � �4 and x � y � b is (4, a). What isthe value of b? (Lesson 7-4)
�8�408D
C
B
A
2. Multiple Choice The Terminal Tower inCleveland is 240 feet shorter than the SocietyCenter, which is also in Cleveland. The total ofthe heights of the two buildings is 1,656 feet.What is the height of the shorter building?(Lesson 7-3)
708 feet 816 feet840 feet 948 feet
3. Short Answer The geographic center of Ohio islocated in Delaware County. The closest NationalDoppler weather radar is in Wilmington. If thegeographic center is designated as the origin,then Wilmington has coordinates (�61, �61),where each unit is one mile. If the radar has aradius of 80 miles, write an equation for thecircle that represents the radar coverage fromWilmington. The general equation for a circle is(x � h)2 � (y � k)2 � r2, where (h, k) is thecenter and r is the radius. (Lesson 3-1)
DC
BA
4. Multiple Choice What solid will the patternform when folded along the dotted lines?(Prerequisite Skill)
triangular prismcubesquare pyramidrectangular pyramid
5. Short Answer The average age of the sevenemployees working at a greeting card store is33. If two more people are hired, ages 18 and39, what is the new average age of theemployees working at the store? Show yourwork. (Lesson 2-5)
D
C
B
A
1. Extended Response The district manager of a cellular phone company wants to promote anemployee to sales manager. The quarterly sales for the two employees for the last two years arelisted below. Find the mean, median, mode, and range of the quarterly sales data for each employee.Based on the sales, who should be promoted to sales manager? Explain. (Lesson 2-5)
OH20 Ohio Algebra 1
6. Multiple Choice The population of the UnitedStates in December of 2002 was approximately289 million. What is this number expressed inscientific notation? (Lesson 8-3)
2.89 108 2.89 107
2.89 10�8 2.89 10�7DC
BA
7. Multiple Choice Which expression representsthe area of a circle with a radius of (2x � 5)units? (Lesson 8-7)
(4x � 10)� units2
(4x2 � 7x � 25)� units2
(4x2 � 20x � 25)� units2
(16x2 � 80x � 100) units2D
C
B
A
4. Multiple Choice The area of a triangle is75x3y2 square units, and its height is 10xy2
units. What is the base of the triangle?(Lesson 8-2)
7.5x2 units 15x2 units15x2y units 375x4y4 units
5. Short Answer The graph shows the weeklyallowance for students in grades 6 through 12.If a student is chosen at random, what is theprobability that the student receives $10 ormore as a weekly allowance? Show yourwork. (Lesson 2-6)
DC
BA
2. Multiple Choice The table shows thepopulation of Ohio from 1910 to 2000. Which ofthe following graphical representations wouldbest illustrate the steady increase in Ohio’spopulation over the 90-year period?(Prerequisite Skill)
bar graph line graphcircle graph histogram
3. Short Answer Determine whether thefollowing statement is true or false. If true,explain your reasoning. If false, give acounterexample.
For any real number a, �(�
1a)2� � ��
a12�. (Lesson 8-1)
DC
BA No allowance
less than $5
$5–$9.99
$10–$14.99
$15–$19.99
$20 or more
Number
Am
ou
nt
(do
llars
)
Weekly Allowance
45
5
16
3
4
17
Source: USA Weekend
Employee Quarterly Sales (thousands of dollars)
Ms. Diaz 200.8 190.9 200.0 210.0 200.1 200.5 200.7 210.0
Mr. Cruz 210.0 180.1 191.2 239.2 210.8 190.8 180.9 210.0
Year Population Year Population
1910 4,767,121 1960 9,706,397
1920 5,759,394 1970 10,657,423
1930 6,646,697 1980 10,797,603
1940 6,907,612 1990 10,847,115
1950 7,946,627 2000 11,353,140
Ohio Algebra 1 OH21
1. Extended Response A hot pretzel stand in the mall sells regular pretzels for $1.50 each and jumbo pretzels for $2.25 each. On Saturday, they sold 36 more jumbo pretzels than regular pretzels. The total sales for both types of pretzels were $984.75.How many regular pretzels were sold on Saturday? (Lesson 3-9)
6. Multiple Choice The data in the bar graphshows the annual attendance at the Ohio StateFair from 1998 to 2003. Which of the followingstatements is a logical conclusion from the datain the graph? (Lesson 1-9)
The attendance has increased since 1998.The attendance in 2003 was the greatest ithad been in at least 6 years.The attendance in 2001 was the lowest ithas ever been.The attendance in 2004 will be less thanthe attendance in 2003.
D
C
B
A
7. Multiple Choice The volume of the prism is240a3b3 cubic units. What is the height of theprism? (Lesson 8-2)
3ab units6ab2 units6a units6ab unitsD
C
B
A
4a2b10b
2. Multiple Choice Which of the following isequivalent to 425 10�5? (Lesson 8-3)
4.25 10�5 0.425 10�4
4.25 10�4 4.25 10�3
3. Short Answer Determine whether thefollowing statement is true or false. If true,explain your reasoning. If false, give acounterexample. For all real numbers m and n,and all positive integers a, b, and c,(manb)�c � �
ma1cnbc�. (Lesson 8-2)
DC
BA
4. Multiple Choice The distance from Earth to theSun is about 150,000,000 kilometers. What is thisnumber in scientific notation? (Lesson 8-3)
1.5 10�8 1.5 108
15 10�9 15 109
5. Short Answer What is the probability thata number chosen at random from the domain{�7, �6, �5, �4, �3, �2, �1, 0, 1, 2, 3, 4, 5, 6, 7}will satisfy the inequality 4x � 17 � 5? Showyour work. (Lesson 2-6)
DC
BA
Ohio State Fair Attendance
1998 1999 2000 2001 2002 2003
Att
end
ance
(th
ou
san
ds)
1,050
1,000
950
900
850
800
Year
Source: www.ohioexpocenter.com
Roller Coaster Ride Time
Mantis 2�23� min
Mean Streak 2.75 min
Millennium Force 2 min 20 s
Raptor 2�145� min
1. Extended Response Consider a rectangle that has whole-number dimensionsand a perimeter of 28 units. Draw all possible combinations of dimensions(length and width) for such a rectangle. What are the dimensions of the rectanglewith the minimum area? What are the dimensions of the rectangle with themaximum area? What conclusions can you draw? Show all your drawings.(Lesson 9-1)
OH22 Ohio Algebra 1
4. Multiple Choice Factor 27a2b � 9b5.(Lesson 9-2)
27(a2b � 9b5) 9(3a2b � b5)9b(3a2 � b4) 9b2(3a2 � b3)
5. Short Answer Kyle made a scale drawing ofan airplane. In his drawing, the angle the wingmakes with the body of the airplane is 58°.Kyle used a scale ratio of 1:20 for his drawing.What is the actual measure of the angle thewing makes with the body? Explain.(Prerequisite Skill)
DC
BA
2. Multiple Choice Solve 2t2 � 10t � 48 � 0.(Lesson 9-4)
t � 8 or 3 t � �8 or 3t � �8 or �3 t � 8 or �3
3. Short Answer Angle X and angle Y aresupplementary angles that are formed byintersecting lines. The measure of angle X is44° greater than the measure of angle Y. Findthe measures of angles X and Y. Show yourwork. (Lesson 7-2)
DC
BA
6. Multiple Choice If an object is propelled fromground level at an initial velocity of 96 feet persecond, after t seconds its height h in feet isgiven by the formula h � �16t2 � 96t. Afterhow many seconds will its height be 128 feet?(Lesson 9-6)
2 s and 4 s2 s and 6 s3 s and 4 s3 s and 6 sD
C
B
A
7. Multiple Choice The ride times of four rollercoasters at Cedar Point are listed. Which of thefollowing lists the roller coasters in order fromleast to greatest ride time? (Lesson 2-7)
Millennium Force, Raptor, Mean Streak,MantisMillennium Force, Raptor, Mantis, MeanStreakMean Streak, Mantis, Raptor, MillenniumForceRaptor, Millennium Force, Mantis, MeanStreak
D
C
B
A
Source: www.ultimaterollercoaster.com
Ohio Algebra 1 OH23
6. Multiple Choice On a car trip to the HockingHills, Marin kept a record of her gas mileage asshown below. Which equation describes therelationship shown in the table? (Lesson 4-8)
y � x � 31y � 31xx � y � 31x � 31yD
C
B
A
7. Multiple Choice What is the solution of �3 � �2x � 9 � 3? (Lesson 6-4)
x � �6 and x �3x � �6 and x > �3�6 � x � �3�6 � x � 3D
C
B
A
1. Extended Response The Turner family has a rectangular pool measuring 25 yards by 15 yards in their backyard. They want to build a wooden walkway all around the pool. The entire walkway must be the same width. If the area of the wooden walkway and pool cannot exceed 759 square yards, what is the maximum width they should make the wooden walkway? Show your work. (Lesson 9-4)
2. Multiple Choice A car tire has a diameter of17 inches. About how many revolutions doesthe tire make to travel a distance of 100 feet?(Prerequisite Skill)
19 2245 53
3. Short Answer If a car skids on dry concrete,the Ohio State Highway Patrol can use the formula �
214�s2 � d to approximate the speed s
of a vehicle in miles per hour given thelength d of the skid marks in feet. If thelength of skid marks on dry concrete is96 feet, how fast was the car traveling whenthe brakes were applied? Show your work.(Lesson 9-5)
DC
BA
4. Multiple Choice Solve 3x2 � 8x � 4 � 0.(Lesson 9-6)
x � �2 or ��23
� x � �2 or �23
�
x � 2 or ��23
� x � 2 or �23
�
5. Short Answer Nikki and Kendra are solvinga2 � 7a � �6. Who is correct? Explain yourreasoning. (Lesson 9-3)
DC
BA
Nikki
a2 + 7a = –6a(a + 7) = –6a = –6 or a + 7 = –6
a = –13
Kendra
a2 + 7a = –6
a2 + 7a + 6 = 0(a + 1)(a + 6) = 0a + 1 = 0 or a + 6 = 0
a = –1 a = –6
Gasoline x1 2 3 4 5(gallons)
Distance y31 62 93 124 155(miles)
1. Extended Response Imagine you have a huge sheet of paper that is �1,0100�-inch
thick. You cut the sheet in half and put 1 piece on top of the other. You cutthese 2 pieces in half and put the 4 pieces together in a stack. Then cut thestack in half and repeat the pattern. You do this until you have cut the pile 30times. Complete a table comparing the number of cuts and the number ofresulting pieces. What is the pattern? How many pieces are there after the 30thcut? About how high will the pile be in miles? (Lesson 10-7)
OH24 Ohio Algebra 1
6. Multiple Choice A floor plan is shown for thefirst floor of a new house. One inch represents24 feet. What are the dimensions of the livingroom? (Lesson 3-6)
18 ft by 15 ft 19 ft by 16.5 ft30 ft by 18 ft 32 ft by 38.4 ft DC
BA
7. Multiple Choice A small airplane is landing atthe Akron-Canton Regional Airport. The pilotlowered the wheels at an altitude of 2,160 feet.Three minutes later, the airplane landed. Whatwas the airplane’s rate of descent in feet persecond from the time the wheels were lowereduntil landing? (Lesson 5-1)
81283720D
C
B
A
4. Multiple Choice To the nearest tenth,what are the solutions of 3x2 � 5x � 5 � 0?(Lesson 10-4)
�1.2 or �1.4�0.8 or 0.2�1.6 or 1.2�2.4 or 0.7
5. Short Answer Write a valid conclusion thatfollows from statements (1) and (2). (Lesson 1-7) (1) If a parallelogram has four congruent sides,
it is a rhombus.(2) If a figure is a rhombus, then the diagonals
are perpendicular.
D
C
B
A
2. Multiple Choice Which of the followingequations represents the graph of y � x2
shifted up on the y-axis? (Lesson 10-1)
y � 4x2
y � (x � 3)2
y � x2 � 4y � x2 � 3
3. Short Answer Find the two roots of y � x2 � x � 12. List the roots as ordered pairs. Sketch a graph of the equation. (Lesson 10-2)
D
C
B
A
1 in.
in.58
14
in.38
in.34
LivingRoom
DiningRoom
MasterSuite
Kitchen
Deck
Ohio Algebra 1 OH25
1. Extended Response The Weber family is putting in a garden intheir backyard. They have 120 meters of fencing to border theirgarden. What are the possible whole-number dimensions thatsatisfy the measure given in the diagram? What dimensions willmaximize the area of the garden? Explain. (Lesson 10-1)
6. Multiple Choice The graph of y � 2x is shownbelow. The graph of y � 2x � 3 will be thesame, but shifted how? (Lesson 10-5)
3 units down3 units up3 units left3 units rightD
C
B
A
7. Multiple Choice Find a counterexample forthe following statement. (Lesson 1-7)
If a parallelogram has four right angles, then itis a square.
The parallelogram can be a rhombus.The parallelogram can be a trapezoid.The parallelogram can be a rectangle.The square can be a parallelogram.D
C
B
A
2. Multiple Choice Solve y2 � 10y � 25 � 81.(Lesson 9-4)
y � 4 or 14y � �4 or 14y � 4 or �14y � �4 or �14
3. Short Answer In Cincinnati, fireworks arelaunched from a barge on the Ohio River fora Labor Day celebration. Their flight can bemodeled by the function h(t) � �4.9(t � 4)2 � 80,where h is the height in meters and t is the timein seconds. Suppose the fireworks are launched30 seconds later than planned. Write a newfunction to model the path of the fireworks in thenew location. Show your work. (Lesson 10-1)
D
C
B
A
4. Multiple Choice What is the seventh term ofa geometric sequence in which a1 � �10 andr � 4? (Lesson 10-7)
�163,840 �40,9604,096 4,000,000
5. Short Answer The table shows the amountof Lyla’s monthly cell phone bill based onthe number of minutes she uses. Write anequation in slope-intercept form to representthe total cost t of Lyla’s cell phone bill for mminutes. Show your work. (Lesson 5-4)
DC
BA
(60 � x ) m
x m
y
xO
Minutes 40 80 120 160 200
Monthly Bill $19 $25 $31 $37 $43
1. Extended Response An isosceles triangle has two sidesthat are the same length. Show that ADC is isosceles.(Hint: Use the distance formula.) (Lesson 11-5)
OH26 Ohio Algebra 1
6. Multiple Choice If ABC � DEF andAB � 6, BC � 8, AC � 12, DE � 4, and DF � 8, find the length of EF.—
(Lesson 11-6)
4 5�13
�
5�23
� 6DC
BA
7. Multiple Choice Calculate the approximateheight of the falls given the informationshown. (Lesson 11-7)
75 ft 82 ft90 ft 93 ftDC
BA
4. Multiple Choice Find the distance betweenthe points at (3, 2) and (�2, �4) to the nearesthundredth. (Lesson 11-5)
5.00 7.818.06 11.03
5. Short Answer Determine whether thefollowing conjecture is true or false basedon the given information. If the conjectureis false, provide a counterexample. (Lesson 1-7)
Given: JK � KL � LM � MJ
Conjecture: JKLM forms a square.
DC
BA
2. Multiple Choice Simplify �48�. (Lesson 11-1)
4�12� 2�2�4�3� 16�3�
3. Short Answer The band members atMansfield High School are having a car washto raise money. The supplies for the car washcost a total of $105, and each customer will pay$5 to have their car washed. Write and solve aninequality to find the number of cars they mustwash in order to make a profit of at least $300.Show your work. (Lesson 6-1)
DC
BA
O(0, 0)
(a, 0)A
C
D ( , b)a2
y
x
110 ft5 ft
30 ft
20˚Transit
A
B
D
E
C
F
Ohio Algebra 1 OH27
1. Extended Response Trapezoid FGHI has vertices located at F(�2, 0), G(0, 2),H(6, 4), and I(�4, �6). Sketch the trapezoid on a coordinate graph. Thendetermine whether the trapezoid is isosceles by calculating the lengths of thetwo diagonals. Explain another way to confirm that the trapezoid is isosceles.(Lesson 11-5)
6. Multiple Choice The length of a leg of a45°-45°-90° triangle can be determined bydividing the length of the hypotenuse of thetriangle by �2�. If the length of the hypotenuseof a 45°-45°-90° triangle is 16 centimeters, whatis the length of each leg? (Lesson 11-1)
8�2� cm8�3� cm16�2� cm16�3� cmD
C
B
A
7. MultipleChoice Whatformula shouldyou use toprove that thediagonals ofrectangle QRSTare congruent?(Lesson 11-5)
Midpoint FormulaSlope FormulaArea FormulaDistance FormulaD
C
B
A
2. Multiple Choice The stem-and-leaf plotshows the number of hot dogs eaten during acontest. What is the mode of hot dogs eaten?(Lesson 2-5)
131414.517
3. Short Answer If a 30-foot sign casts a shadowthat is 12 feet long, how tall is the building nextdoor that casts a 36-foot shadow? Draw asketch. Show your work. (Lesson 11-6)
D
C
B
A
4. Multiple Choice When the Sun’s angle ofelevation is 70°, a building casts a shadow25 meters long. What is the approximateheight of the building? (Lesson 11-7)
24 m42 m69 m82 m
5. Short Answer If r � s and p � q, is it true thatrp � sq? If so, explain. If not, provide acounterexample. (Lesson 6-1)
D
C
B
AStem Leaf0 8 8 91 1 2 2 4 7 7 72 1 1 2 2|1 � 21
O T (0,0) S (a, 0)
Q (0,b) S (a, b)y
x
1. Extended Response As a student at The Ohio State University in 1935, JesseOwens set a world record in the 220-yard dash with a time of 20.3 seconds.What was his winning speed in miles per hour? Round to the nearesthundredth. Show your work. (Lesson 12-3)
OH28 Ohio Algebra 1
6. Multiple Choice Which expression representsthe length of the rectangle? (Lesson 12-5)
n � 12n � 12n � 10n � 10D
C
B
A
7. Multiple Choice The table shows theage group and number of people that aremembers at Western Lake Country Club.Use this information to write the fraction ofthe members that are 60 years and older.(Lesson 12-6)
�75536
�
�13,54192
�
�14,55152
�
�479516
�D
C
B
A
4. Multiple Choice Simplify 60a4b3c2.(Lesson 11-1)
2a2 �bc� �15b�6a2 �bc� �10b�2a4b2c2 �15b�6a4b2c2 �10b�
5. Short Answer A rhombus is shown on acoordinate plane. Determine whether thediagonals are perpendicular. Show your work.(Lesson 5-6)
D
C
B
A
2. Multiple Choice A publisher determinedthat the cost of printing a certain bookvaries inversely as the number produced. If10,000 books are printed, the cost is $2 per unit.Find the cost per unit to print 25,000 books.(Lesson 12-1)
$0.50 $0.80$0.95 $1.05
3. Short Answer A triangle has coordinatesA(�6, 6), B(4, �4), and C(�4, �2). Classify
ABC by its sides. Show your work.(Lesson 11-5)
DC
BA
y
xO
P
LM
N
Age Number ofMembers
0–19 114
20–39 416
40–59 527
60–79 349
80+ 106
A � n2 � 4n � 60 n�6
Ohio Algebra 1 OH29
1. Extended Response Determine whetherquadrilateral WXYZ is a square. Show yourwork. (Lesson 11-5)
6. Multiple Choice If y varies inversely as xand y � 4 when x � 12, find x when y � 6.(Lesson 12-1)
6789D
C
B
A
7. Multiple Choice Melissa takes care of herneighbor’s cats while they are out of town.One week she is taking care of three cats. Thefirst cat eats a bag of food every 10 days, thesecond cat eats a bag every 11 days, and thethird cat eats a bag every 14 days. How manybags of food should Melissa buy for oneweek? (Lesson 12-7)
1234D
C
B
A
2. Multiple Choice The length of a violin stringvaries inversely as the frequency of itsvibrations. A violin string 10 inches longvibrates at a frequency of 512 cycles persecond. Find the frequency of a 16-inch string.(Lesson 12-1)
240 cycles per second320 cycles per second360 cycles per second480 cycles per second
3. Short Answer Jordan says that �317� is closerto 18. Gabriella says that it is closer to 17. Whois correct? Explain your answer. (Lesson 11-1)
D
C
B
A
4. Multiple Choice Mi-Ling is working on theschool yearbook. She must reduce a photo thatis 4 inches wide by 5 inches long to fit in aspace 3 inches wide. How long will thereduced photo be? (Lesson 3-6)
2�25
� inches 3�13
� inches
3�34
� inches 6�23
� inches
5. Short Answer The distance from Dayton toAkron is 198 miles by road. How long will ittake you to reach Dayton from Akron if youtravel an average of 58 miles per hour? Roundto the nearest quarter of an hour. Show yourwork. (Lesson 12-4)
DC
BA
y
xO
W (�1, 3)
Y (2, �4)
Z (�3, �2)
X (4, 1)
6. Multiple Choice To predict the president ofthe Student Government Association, whichmethod would give the school newspapereditor the most accurate result? (Lesson 13-1)
Ask only the freshman class.Ask all of the teachers.Publish a survey and ask each student toreply.Ask every 10th student who enters thecafeteria.
D
C
B
A
7. Multiple Choice In the figure shown, ABE � ACD. What is CD? (Lesson 11-6)
3 cm6 cm9 cm12 cm D
C
B
A
9,000 ft
3,500 ft
A
CB
A
D C
E B9 cm
x
6 cm
18 cm
1. Extended Response Construct a bar graph of the 2002 population of the seven most populouscounties in Ohio as shown below. Find the mean, median, and range of the data for the counties inOhio. Compare the median and mean. Make a statement that supports your findings. (Lesson 13-4)
Source: U.S. Census Bureau
OH30 Ohio Algebra 1
4. Multiple Choice If the box-and-whisker plotbelow represents the percent of studentsparticipating in extra-curricular activities inhigh schools in Ohio, what is the smallestpercent of students participating in extra-curricular activities? (Lesson 13-5)
50% 60%72% 76%
5. Short Answer Alex scored 131, 128, 130, 147,131, 159, 135, 131, 132, and 124 in 10 games ofbowling. Find the range, mean, median, andmode of his scores. If Alex wanted to impresssomeone with his scores, should he give themean, median, or mode? Explain your answer.(Lesson 13-4)
DC
BA
2. Multiple Choice Triangle RST has coordinatesR(4, 9), S(�5, �2), and T(2, �7). What are thecoordinates of S′ after RST is reflected overthe y-axis? (Lesson 4-2)
(5, �2) (�5, 2)(�2, �5) (5, 2)
3. Short Answer Carlotta Bonilla is piloting a smallcargo plane bound for Wright Patterson Air ForceBase. She determined that she was flying 3,500feet parallel to the ground and that the grounddistance to the landing strip was 9,000 feet.Approximately what is her plane’s angle ofdepression to the landing strip, represented by�A? Round to the nearest degree. Show yourwork. (Lesson 11-7)
DC
BA
50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86
Ohio County Butler Cuyahoga Franklin Hamilton Lucas Montgomery Summit
2002 Population3.41 13.79 10.87 8.34 4.54 5.54 5.46
(100,000s)
Ohio Algebra 1 OH31
6. Multiple Choice Use the histogram todetermine the measurement class in which themedian occurs. (Lesson 13-3)
150–200200–250250–300350–400D
C
B
A
7. Multiple Choice Which algebra class had thegreater median test score? (Lesson 13-4)
period 1period 6about the samecan’t tellD
C
B
A
1. Extended Response The data below represents the ages of the first 8 people to arrive at the Rockand Roll Hall of Fame in Cleveland on a given Saturday.
18, 20, 17, 32, 15, 17, 28, 16
Draw a box-and-whisker plot for the data. Explain your reasoning. What are the range and theinterquartile range? What is the median? (Lesson 13-5)
2. Multiple Choice Jada was standing next to theEiffel Tower at Kings Island. The shadow ofthis replica is 241 feet, and Jada’s shadow is4 feet. If Jada is 5 feet 6 inches tall, how tallis the Eiffel Tower at Kings Island to thenearest foot? (Lesson 11-6)
109 ft 175 ft331 ft 337 ft
3. Short Answer A rectangle is 5 inches by12 inches. The rectangle is cut in half, and onehalf is discarded. The remaining rectangle is cutin half, and one half is discarded. This is repeatedtwice. List the areas of the five rectangles formed.Describe a pattern in the areas of the rectangles.(Lesson 10-7)
DC
BA
4. Multiple Choice Express 0.00008451 inscientific notation. (Lesson 8-3)
8.45 10�5
8.45 105
84.5 10�4
84.5 104
5. Short Answer Fifty shoppers outside adepartment store are asked to name theirpreferred clothes designer among fourchoices. State whether the sample is unbiased(random) or biased. If unbiased, classify itas simple, stratified, or systematic. If biased,classify it as convenience or voluntary response.(Lesson 13-1)
D
C
B
A
Money Spent per Family During the Holiday Weekend
150-200100-15050-1000-50
4
6
2
0
8
Freq
uen
cy
200-250 250-300 300-350 350-400Money Spent (dollars)
81–9
0
71–8
0
61–7
0
50–6
0
4
6
2
0Nu
mb
er o
f St
ud
ents
91–1
00
81–9
0
71–8
0
61–7
0
50–6
0
91–1
00
Period 1 Scores
4
6
2
0Nu
mb
er o
f St
ud
ents
Period 6 Scores
Score Score
1. Extended Response Lima Senior High School art students are designing greeting cards to sell as a fund-raiser. They must choose from glossy (G), satin (S), or textured (T) paper. Choices for lettering fonts are block (B) or script (S). Color scheme choices are black and white (BW) or tri-color (TC). Use a tree diagram to determine the number of possible greeting card designs. Make a statement reflecting your findings. (Lesson 14-1)
OH32 Ohio Algebra 1
6. Multiple Choice Describe the transformationof rectangle PQRS with P(3, 2), Q(6, 0), R(2, �6),and S(�1, �4) if the coordinates of its image areP′(2, 3), Q′(0, 6), R′(�6, 2), and S′(�4, �1).(Lesson 4-2)
reflection over y-axisreflection over x-axisreflection over line y � xreflection over line y � �xD
C
B
A
7. Multiple Choice One hundred students atYoungstown Chaney High School were askedwhether they had seen any of three givenmovies. The results are shown in the Venndiagram. Based on the sampling, what is theprobability that a randomly selected highschool student would have seen at least two ofthe movies listed? (Lesson 14-3)
�510�
�275�
�130�
�13070
�D
C
B
A
4. Multiple Choice Solve (w � 3)2 � 64.(Lesson 9-6)
w � 5 or �11w � �5 or 11w � 5 or 11w � �5 or �11
5. Short Answer A high school usescombination locks on their gym lockers. Thelocks have 6-digit combinations, using thedigits 2, 3, 4, 5, 6, and 7. Each number is usedand no number is used more than once. Ifthere are 711 students taking physicaleducation at any one time, are there enoughdifferent locker combinations for no repeats?Show and explain your work. (Lesson 14-2)
D
C
B
A
2. Multiple Choice Determine the constant ofvariation if y varies inversely as x and y � 6.5when x � �1.2. (Lesson 12-1)
�7.8 �5.35.3 7.8
3. Short Answer Niko tossed three differentcoins 200 times and recorded his results inthe table below. What was Niko’s experimentalprobability of getting a THT on a toss of3 coins? What is the theoretical probability ofgetting a THT? Why aren’t both probabilitiesthe same? (Lesson 14-5)
DC
BA
Results of Tossing 3 Coins 200 Times
HHH 26 TTT 21
HHT 18 TTH 41
HTH 15 THT 20
HTT 29 THH 30
39 24
8
7
9
11
2
Mrs.Doubtfire
Awakenings
Dead PoetsSociety
