Sample Questions from TCC Mathematics Assessment Test

Sample Questions from TCC MathematicsAssessment TestIf you have had a course in General Math, then you mayhave success with the following types of questionsSkills Covered in COMPASS Pre AlgebraBasic operations with whole numbersBasic operations with fractionsBasic operations with decimalsExponentsRatios and proportionsPercentagesConversions between fractions and decimals andpercentsMultiples and factors of whole numbersAbsolute values of numbersOrder concepts (greater than; less than)Estimation skillsNumber theoryCounting problems and simple probability(Averages: Means, Medians, and Modes)1. What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2?A.437D. 554B. 6E.465C.647

(Basic Operations with Decimals)2. Ben is making wooden toys for the next arts and crafts sale.Each toy costs Ben $1.80 to make. If he sells the toys for $3.00each, how many will he have to sell to make a profit of exactly$36.00 ?A. 12 D. 60B. 20 E. 108C. 30(Basic Operations with Fractions)3. How many yards of material from a 24-yard length of clothremain after 3 pieces, each12 yards long, are removed?413 yards long, and 5 pieces, each2A.12 D.41104B.14 E.45106C.546

(Percentages)4. Phillip charged $400 worth of goods on his credit card. On hisfirst bill, he was not charged any interest, and he made apayment of $20. He then charged another $18 worth of goods.On his second bill a month later, he was charged 2% interest onhis entire unpaid balance. How much interest was Phillipcharged on his second bill?A. $8.76 D. $7.24B. $7.96 E. $6.63C. $7.60Answers:1. C 2. C 3. A 4. BIf you have had a course in Algebra 1, Geometry and/orAlgebra 2, then you may have success with the followingtypes of questions.Skills Covered in COMPASS AlgebraElementary Algebra SkillsSubstituting values in algebraic equationsSetting up equations for given situationsBasic operations with polynomialsFactoring polynomialsSolving polynomial equations by factoringFormula manipulation and field axiomsLinear equations in one variableExponentsLinear inequalities in one variable.

Intermediate Algebra SkillsRational expressionsExponentsSystems of linear equations in 2 variablesQuadratic formulasAbsolute value equations and inequalitiesCoordinate Geometry and Graphing SkillsLinear equations in 2 variablesDistance formulas in the planeGraphing conics (circle, parabola, etc.)Graphing relations in the planeGraphing systems of equations and functionsMidpoint formulas(Elementary Algebra: Linear Equations in One Variable)1. A student has earned scores of 87, 81, and 88 on the first 3 of4 tests. If the student wants an average (arithmetic mean) ofexactly 87, what score must she earn on the fourth test?A. 85 D. 92B. 86 E. 93C. 87

(Elementary Algebra: Basic Operations with Polynomials)2. Which of the following expressions represents the product of3 less than twice x and 2 more than the quantity 3 times x ?A. − 6x 2 + 25x+ 6 D. 6x2 − 5x− 6B. 6x 2 + 5x+ 6 E. 6x2 −13x− 6C. 6x2 − 5x+ 6(Elementary Algebra: Substituting Values into AlgebraicExpressions)3. If x = –1 and y = 2, what is the value of the expression2x 3 − 3xy?A 8 D. -4B. 4 E. -8C. -1(Elementary Algebra: Factoring Polynomials)4. For all x, 12x 2 – 40x – 32 = ?A. (3x – 8)(4x +4) D. 4(x – 4)(3x + 2)B. 4(3x – 2)(x + 4) E. (4x – 4)(3x – 8)

C. (4x – 4)(3x + 8)(Elementary Algebra: Solving Polynomial Equations byFactoring)5. What is the sum of the solutions of the equation3x 2 + 11x = 4?A.13D.2− 33B.C.23 E.31−31− 43

(Elementary Algebra: Linear Equations in One Variable)6. If 3x – 7 = 4, then x = ?A.4 − 734D. + 734B. 3(7− 4)E. − 73C.4 + 73(Elementary Algebra: Factoring Polynomials)7. Which of the following belong to the set of factors of thepolynomial 3x 3 + 9x 2 – 30x ?I. xII. x + 2III. x + 5A.B.C.D.E.I onlyII onlyI and II onlyI and III onlyI, II and III

(Intermediate Algebra: Rational Expressions)2r − 5r+ 68. For all r 2,= ?2r − 4A.r − 3r + 2D.r + 3r − 2B.r − 2r + 2E.r + 3r + 2C.r − 2r + 3(Intermediate Algebra: Rational Expressions)9. If ( x ≠ 2) and3 x2 + kx + 4= 3x2,x − 2− then k = ?A. 8 D. -2B. -3 E. -8C. 3

(Coordinate Geometry: Linear Equations in Two Variables)10. What is the equation of the line that contains the points with(x, y) coordinates (–3, 7) and (5, –1) ?A. y = 3x− 2 D.3 11y = − x +2 4B. y = x + 10E. y = −x+ 41C. y = − x + 83(Coordinate Geometry and Graphing Skills: Linear Equation inTwo Variables)11. Which of the following equations generates the data in thefollowing table:X 1 2 3 4 5Y -1 -4 -7 -10 -13A. y = - 3x + 2 D.1x − y = 02B. y = x – 2 E. x = 3y – 6C. x = -y

Answers:1. D 2. D 3. B 4. D 5. D 6. C7. D 8. A 9. E 10. E 11. A____________________________________________________If you have had a course in Algebra 2 and/or MathAnalysis, you may have success with the following kindsof questions.Skills tested in the College Algebra portion ofCOMPASS are:FunctionsExponentsComplex numbersArithmetic and geometric sequences and seriesFactorialsMatrices (basic operations, equations, and determinants)Systems of linear equations in three or more variablesLogic and proof techniquesRoots of polynomials(Complex Numbers)( ) i1. For i = − 1 , if 3 i 2 + 5i= x + 6 , then x = ?A. –15 D. 15iB. 5 E. 27iC. 5i

(Functions)( ) 0f2. If f 4 = and f ( 6 ) = 6 , which of the following could( x)represent ?2 3A. x − 4D. x + 632B. x + 2E. 3x−12C. x − 2Answers1. A 2. EIf you have had a course in Math Analysis with Trigonometry,then you may have success with the following types ofquestions.Skills covered in the Trigonometry portion ofCOMPASS are:Trigonometric functions and identitiesRight-triangle trigonometryTrigonometric equations and inequalitiesGraphs of trigonometric functionsSpecial angles (multiples of 30 and 45 degrees)Polar coordinates

(Trigonometric Functions and Identities)21−cos 01. Which of the following is equivalent to2cos 0?A.sec 2 0D. sin 2 01−csc 2 2− E. sin 0B. ( 0) 1C. tan 2 0(Right-Triangle Trigonometry)2. From a point on the ground the angle of elevation to a ledge ona building is 27 o , and the distance to the base of the building is45 meters. How many meters high is the ledge?A.450sin 27B.450tan 270C. 45sin 27D.045cos 27E.045 tan 27

Answers:1. C 2. ESelect practice items for COMPASS/ESL used withpermission of ACT, Inc.