An ACT Program for Educational PlanningCOMPASS/ESLSample Test Questions—A Guide for Students and ParentsMathematicsCollege AlgebraGeometryTrigonometry®5281_COMPASS/ESL Cover&Intro 7/1/04 9:13 AM Page 1Note 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.5281_COMPASS/ESL Cover&Intro 6/25/04 12:20 PM Page 2© 2004 ACT, Inc. All rights reserved.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 ACT, Inc. All rights reserved.College Algebra, Geometry, and Trigonometry Placement TestsCollege Algebra Placement TestItems in the College Algebra Test focus on algebra knowledge and skills in a variety of contentareas. The majority of items come from the following content areas:FunctionsExponentsComplex NumbersArithmetic and Geometric Sequences and SeriesMatrices (basic operations, equations, and determinants)Sample items for each of these categories are presented later in this section.Geometry Placement TestPrimary content areas included in the Geometry Placement Test include:Triangles (perimeter, area, Pythagorean theorem, etc.)Circles (perimeter, area, arcs, etc.)Angles (supplementary, complementary, adjacent, vertical, etc.)Rectangles (perimeter, area, etc.)Three-dimensional conceptsHybrid (composite) shapesSample items for each of these categories are presented later in this section.Trigonometry Placement TestThe primary content areas assessed by the Trigonometry Placement Test include:Trigonometric functions and identitiesRight-triangle trigonometryTrigonometric equations and inequalitiesGraphs of trigonometric functionsSpecial angles (multiples of 30 and 45 degrees)Sample items for each of these categories are presented later in this section.College Algebra Placement Test Sample Items© 2004 ACT, Inc. All rights reserved.1College Algebra1. What is the next term in the geometric sequence 16, –4, 1, –14, … ?A. –18B. 0C. 116D. 18E. 122. A manufacturing company processes raw ore. The number of tons of refined materialthe company can produce during t days using Process A is A(t) = t2 + 2t and usingProcess B is B(t) = 10t. The company has only 7 days to process ore and must choose 1of the processes. What is the maximum output of refined material, in tons, for this timeperiod?A. 8B. 10C. 51D. 63E. 703. For the 2 functions, f (x) and g(x), tables of values are shown below. What is the valueof g(f (3)) ?xf (x) xg(x)–57–23–2–5 1–113 2–332 3–5A.–5B.–3C.–1D. 2E. 7College Algebra Placement Test Sample Items© 2004 ACT, Inc. All rights reserved.24. For positive real numbers x, y, and z, which of the following expressions is equivalentto 521362xyz ?A.233xyzB.256xyzC.3256xyzD.3456xyzE.2511xyz5. If A = 2460− and B = 2460−−, then A – B = ?A.0000B.1001C.0800−D.4012 0−−E.4812 0−6. Listed below are 5 functions, each denoted g(x) and each involving a real number constantc > 1. If f (x) = 2x, which of these 5 functions yields the greatest value for f (g(x)), for allx > 1 ?A. g(x) = cxB. g(x) = cxC. g(x) = xcD. g(x) = x – cE. g(x) = logcx7. If the function f satisfies the equation f(x + y) = f(x) + f(y) for every pair of real numbers xand y, what are the possible values of f(0) ?A. Any real numberB. Any positive real numberC. 0 and 1 onlyD. 1 onlyE. 0 onlyCollege Algebra Placement Test Sample Items© 2004 ACT, Inc. All rights reserved.38. The imaginary number i is defined such that i2 = –1. What does i + i2 + i3 + L + i 23 equal?A. iB. –iC. –1D. 0E. 19. In an arithmetic series, the terms of the series are equally spread out. For example, in1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is3, the last term is 136, and the sum is 1,390, what are the first 3 terms?A. 3, 10, 17B. 3, 23, 43C. 3, 3613, 70D. 3, 6912, 136E. 3, 139, 1,251College Algebra Placement Test Sample Items© 2004 ACT, Inc. All rights reserved.4Correct Answers for Sample College Algebra ItemsItem # Correct Answer Content Category1 C Arithmetic and