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COMPASS/ESL Sample Test Questions—A Guide for Students and ParentsMathematicsNumerical Skills/Pre-AlgebraAlgebraAn ACT Program for Educational Planning
Note to StudentsWelcome to the COMPASS Sample Mathematics Test!You are about to look at some sample test questions as youprepare to take the actual COMPASS test. The examples in thisbooklet are similar to the kinds of test questions you are likely tosee when you take the actual COMPASS test. Since this is apractice exercise, you will answer just a few questions and youwon’t receive a real test score. The answer key followsthe sample questions.Once you are ready to take the actual COMPASS test, youneed to know that the test is computer delivered and untimed—that is, you may work at your own pace. After you complete thetest, you can get a score report to help you make good choiceswhen you register for college classes.We hope you benefit from these sample questions, and wewish you success as you pursue your education and career goals!Note to ParentsThe test questions in this sample set are similar to the kinds oftest questions your son or daughter will encounter when they takethe actual COMPASS test. Since these questions are only forpractice, they do not produce a test score; students answer morequestions on the actual test. The aim of this booklet is to give asense of the kinds of questions examinees will face and their levelof difficulty. There is an answer key at the end.
COMPASS Mathematics TestsThe COMPASS Mathematics Tests are organized around five principal content domains:numerical skills/prealgebra, algebra, college algebra, geometry, and trigonometry. To ensurevariety in the content and complexity of items within each domain, COMPASS includesmathematics items of three general levels of cognitive complexity: basic skills, application, andanalysis. A basic skills item can be solved by performing a sequence of basic operations. Anapplication item involves applying sequences of basic operations to novel settings or in complexways. An analysis item requires students to demonstrate a conceptual understanding of theprinciples and relationships relevant to particular mathematical operations. Items in each of thecontent domains sample extensively from these three cognitive levels.Students are permitted to use calculators on all current Windows and Internet versions ofCOMPASS Mathematics Tests. Calculators must, however, meet ACT’s specifications,which are the same for COMPASS and the ACT Assessment. These specifications areupdated periodically and can be found at ACT’s website athttp://www.act.org/aap/taking/calculator.html 2004 by ACT, Inc. All rights reserved.
Numerical Skills/Prealgebra and Algebra TestsNumerical Skills/Prealgebra Placement TestQuestions in the Numerical Skills/Prealgebra Placement Test range in content from basicarithmetic concepts and skills to the knowledge and skills considered prerequisites for a firstalgebra course. The Numerical Skills/Prealgebra Placement Test includes items from more than adozen content areas; however, a majority of the questions come from the following categories:1.2.3.4.5.6.7.Operations with IntegersOperations with FractionsOperations with DecimalsPositive Integer Exponents, Square Roots, and Scientific NotationRatios and ProportionsPercentagesAverages (Means, Medians, and Modes)Sample items for each of these categories are presented later in this section.Algebra Placement TestThe Algebra Placement Test is composed of items from three curricular areas: elementaryalgebra, coordinate geometry, and intermediate algebra. Each of these three areas is furthersubdivided into a number of more specific content areas. Overall, the Algebra Placement Testincludes items from more than 20 content areas; however, the majority of test questions fallwithin the following eight content areas:1.2.3.4.5.6.7.8.Substituting Values into Algebraic ExpressionsSetting Up Equations for Given SituationsBasic Operations with PolynomialsFactoring PolynomialsLinear Equations in One VariableExponents and RadicalsRational ExpressionsLinear Equations in Two VariablesSample items for each of these categories are presented later in this section. 2004 by ACT, Inc. All rights reserved.
Numerical Skills/Prealgebra Placement Test Sample ItemsNumerical Skills/Prealgebra1.54 – 6 2 6 ?624273057A.B.C.D.E.2.The lowest temperature on a winter morning was –8 F. Later that same day thetemperature reached a high of 24 F. By how many degrees Fahrenheit did thetemperature increase?A.3 B.8 C.16 D.24 E.32 3.If ( 34 23 ) ( 12 13 ) is calculated and the answer reduced to simplest terms, what is thedenominator of the resulting fraction?A.24B.12C.6D.4E.34.1 2 3 4 523 456(A.B.C.D.E.) () ?116172713187956 2004 by ACT, Inc. All rights reserved.1
Numerical Skills/Prealgebra Placement Test Sample Items5.Mr. Brown went grocery shopping to buy meat for his annual office picnic. He bought7 34 pounds of hamburger, 17.85 pounds of chicken, and 6 12 pounds of steak. Howmany pounds of meat did Mr. Brown buy?A.32.10B.31.31C.26.25D.22.10E.21.106.Four students about to purchase concert tickets for 18.50 for each ticket discover thatthey may purchase a block of 5 tickets for 80.00. How much would each of the 4 saveif they can get a fifth person to join them and the 5 people equally divide the price ofthe 5-ticket block?A. 1.50B. 2.50C. 3.13D. 10.00E. 12.507.In scientific notation, 20,000 3,400,000 ?A.3.42 106B.3.60 106C.3.42 107D.3.60 107E.3.60 10128.Saying that 4 x 9 is equivalent to saying what about x ?A.0 x 5B.0 x 65C.2 x 3D.4 x 9E.16 x 81 2004 by ACT, Inc. All rights reserved.2
Numerical Skills/Prealgebra Placement Test Sample Items9.What value of x solves the following proportion?96A.5 13B.6 34C.10 12D.11E.12 x810. If the total cost of x apples is b cents, what is a general formula for the cost, in cents,of y apples?A.B.C.D.E.bxyxbyxybbyxbxy11. On a math test, 12 students earned an A. This number is exactly 25% of the totalnumber of students in the class. How many students are in the class?A.15B.16C.21D.30E.4812. This year, 75% of the graduating class of Harriet Tubman High School had taken atleast 8 math courses. Of the remaining class members, 60% had taken 6 or 7 mathcourses. What percent of the graduating class had taken fewer than 6 math courses?A.0%B.10%C.15%D.30%E.45% 2004 by ACT, Inc. All rights reserved.3
Numerical Skills/Prealgebra Placement Test Sample Items13. Adam tried to compute the average of his 7 test scores. He mistakenly divided thecorrect sum of all of his test scores by 6, which yielded 84. What is Adam’s correctaverage test score?A.70B.72C.84D.96E.9814. A total of 50 juniors and seniors were given a mathematics test. The 35 juniorsattained an average score of 80 while the 15 seniors attained an average of 70. Whatwas the average score for all 50 students who took the test?A.73B.75C.76D.77E.78 2004 by ACT, Inc. All rights reserved.4
Numerical Skills/Prealgebra Placement Test Sample ItemsCorrect Answers for Sample Numerical Skills/Prealgebra ItemsItem NumberCorrect Answer1EOperations with Integers2EOperations with Integers3BOperations with Fractions4COperations with Fractions5AOperations with Decimals6BOperations with Decimals7AExponents8EExponents9ERatios and Proportions10DRatios and 14DAverages 2004 by ACT, Inc. All rights reserved.5Content Category
Algebra Placement Test Sample ItemsAlgebra1.2.If x –3, what is the value ofA.–4B.–2C.2D.3 23E.5x2 1x 1?Doctors use the term maximum heart rate (MHR) when referring to the quantity foundby starting with 220 beats per minute and subtracting 1 beat per minute for each yearof a person’s age. Doctors recommend exercising 3 or 4 times each week for at least20 minutes with your heart rate increased from its resting heart rate (RHR) to itstraining heart rate (THR), whereTHR RHR .65(MHR – RHR)Which of the following is closest to the THR of a 43-year-old person whose RHR is54 beats per minute?A.B.C.D.E.3.19716916213480When getting into shape by exercising, the subject’s maximum recommended numberof heartbeats per minute (h) can be determined by subtracting the subject’s age (a)from 220 and then taking 75% of that value. This relation is expressed by which of thefollowing formulas?A.B.C.D.E.hhh.75h220 .75(220 – a).75(220) – a220 – .75a220 – a.75(h – a) 2004 by ACT, Inc. All rights reserved.6
Algebra Placement Test Sample Items4.An airplane flew for 8 hours at an airspeed of x miles per hour (mph), and for 7 morehours at 325 mph. If the average airspeed for the entire flight was 350 mph, which ofthe following equations could be used to find x ?A.B.C.D.E5. 2(350) 15(350) 350 2(350) 15(350) b7bb7bWhat is the sum of the polynomials 3a2b 2a2 b2 and–ab2 a2b2 ?3a2 b3a2 b2a2 b2a2 b3–3a3 b3–– ab2 3a2b2ab2 2a2b23a2 b22a4 b42a4 bWhich of the following is a factor of the polynomialx2 – x – 20 ��3a9a9aA.B.C.D.E.7. – Which of the following is equivalent to3a 4b – (–6a – 3b) ?A.B.C.D.E.6.xx8x8x8xx–5x–4x 2x 5x 10Which of the following is a factor of x2 – 5x – 6 ?A.B.C.D.E.(x(x(x(x(x 2)– 6)– 3)– 2)– 1) 2004 by ACT, Inc. All rights reserved.7
Algebra Placement Test Sample Items9.If 2(x – 5) –11, then x ?A.– 212B.–8C.– 11D.–3E.–110. If2245A.B.C.D.E.3 x 1 1 , then x ? ( 10)221–1–2–1011. For all nonzero r, t, and z values,16 r 3tz 5 4rt 3 z 2 ?4z 3r 2t 24r 2 z 3t24 rztA.–B.–C.–D.E.–4r4t4z7–4r2t2z312. For all x 0 and y 0, the radical expressionA.3 x xy9x yB.3 x xy3x yC.3 x xy9x yD.3 x xy3x yx3x yE. 2004 by ACT, Inc. All rights reserved.8x3 x yis equivalent to:
Algebra Placement Test Sample Items13. For all x –4, which of the following is equivalent to the expression below?x 2 12 x 32x 4A.B.C.D.E.x 3x 8x 11x 16x 2814. Which of the following is a simplified expression equal toA.B.C.D.E.9 x2x 3for all x –3 ?3xx 3x–3–x 3–x – 315. What is the slope of the line with the equation 2x 3y 6 0 ?A.–6B.–3C.–2D.– 23E.2316. Point A (–4,1) is in the standard (x,y) coordinate plane. What must be the coordinatesof point B so that the line x 2 is the perpendicular bisector of AB ?A.(–6, 1)B.(–4,–1)C.(–4, 3)D.(–2, 1)E.( 8, 1) 2004 by ACT, Inc. All rights reserved.9
Algebra Placement Test Sample ItemsCorrect Answers for Sample Algebra ItemsItem NumberCorrect Answer1ASubstituting Values into Algebraic Expressions2DSubstituting Values into Algebraic Expressions3ASetting Up Equations for Given Situations4ESetting Up Equations for Given Situations5EBasic Operations with Polynomials6ABasic Operations with Polynomials7AFactoring Polynomials8BFactoring Polynomials9ELinear Equations in One Variable10CLinear Equations in One Variable11BExponents12CExponents13BRational Expressions14ERational Expressions15DLinear Equations in Two Variables16ELinear Equations in Two Variables 2004 by ACT, Inc. All rights reserved.Content Category10
The test questions in this sample set are similar to the kinds of test questions your son or daughter will encounter when they take the actual COMPASS test. Since these questions are only for practice, they do not produce a test score; students answer more questions on the actual test. The aim of this booklet is to give a
