Transcription
ER SCORE GUARANTEEDPERT Math Readiness2013
PERT Math Practice Guideyour math practice and success answerTable of ContentsPERT Math Overview & Success . iPERT Math Practice Test . 1Additional PERT Math Practice Questions . . 4Answer key and Prescription Guide . 5Step-by-step Solution Guide . 6Answer Key & Solution Guide forAdditional PERT Math Practice Questions . . 11PERT Math Study Guide . 13Topics, Guidelines, Rules & Exercise Sets .13Additional Math Resources .19Answer Key for PERT Math Study Guide . 21PERT Math Readiness - www.theperttest.com
PERT Math OverviewThe math subtest of the Postsecondary Education Readiness Test (PERT or P.E.R.T.) has 30 multiple choicequestions. The test is computer adaptive, meaning that the computer program chooses your next questionbased on your previous answer. Students are not allowed to go back after answering a question. Studentscannot use a calculator for most questions on this test - an on-screen pop-up calculator is made availablefor a few questions. Test questions on the math subtest range from basic algebra through college-level algebra.There is no time limit for completing the math subtest; however, students should schedule at least 2 hours tosuccessfully complete this part of the test. Below are sample questions you can expect to see on the PERT.Here’s a multiple-choice format of a basic algebra question:Evaluate:2 xy 3 x2 11ifx 4and y 5 .a. 139b. 99c. 19d. 469SOLUTION:To evaluate2 xy 3 x2 11, replace x with -4 and y with 5 and use the order of operations, G E MD AS, to simplify.2 4 5 3 4 1122 4 5 3 16 11substitutioncomputed exponentmultiplication performed 40 48 11add because all numbers are negatives 99Answer: choice b.Here’s a harder question taken from intermediate algebra:Find the standard form of the equation of a line withslope -3 and passing through the point 2 , 4 .a. 4 y 3 x 2b. 2 x 4 y 3c.d.y 3 x 63 x y 2SOLUTION:To find the equation of this line, use the point-slope formulaas the point 2 ,4 y y 1 m x x 1 then, convert the equation into standard form with m 3 and x 1y1 Ax By C . substitute -3 and (-2, 4) into formulay 4 3 x 2 y 4 3 x 2 distribute -3 to (x 2)y 4 3 x 63 x y 6 43 x y 2double negatives move -3x and -4 to opposite sides (moving to opposite side means changing to opposite sign)combine -6 4 on right sideAnswer: choice d.PERT Math Readiness - www.theperttest.com
Upon completion of the test, students are awarded a score between 50 to 150 points. A high score on thePERT math subtest is 114 points or higher – this is the score range that shows college and career readiness.High school students with a high score on the math subtest will not need to do remediation during their senioryear. College students with a high score on the math subtest will be allowed to register for college-level mathcourses and do not need to do remediation (MAT0018, MAT0028 or any MAT0 course) at the start of theircollege education. Note: Check with your school or college for their updated PERT testing policy on the numberof times students can take and retake the PERT test.How to Use this GuideProvided below is a self-paced, guided practice designed for students to achieve success on the math section ofthe PERT test. To gain the most from this practice, we recommend following each outlined step carefully andcompletely. Work through the outlined parts: PART I, PART II AND PART III as follows: PART I – Take the PERT Math Practice Test, and the Additional PERT Math Practice Questionson pages 1 – 4. If there are questions you are not familiar with, skip them and carefully check solution guide. PART II – Check answers and see prescription guide for PERT Math Practice Test, page 5.Carefully go over all questions using the step-by-step solution and explanation guide, pages 6 – 10*Pay careful attention to questions you skipped or missed!Continue checking answers and solution guide for Additional PERT Math Practice Questions PART III – Use the PERT Math Study Guide, pages 13 – 21, to review guidelines/rulesand practice more PERT math questions. Take your test! You will need to schedule at least two hours to successfully complete themath section of the PERT.PERT Math Readiness - www.theperttest.com
PART IPERT MATHPRACTICE TEST&ADDITIONAL PERT MATHPRACTICE QUESTIONSPERT Math Readiness - www.theperttest.com
PERT Math Practice TestDIRECTIONS: Select the correct answer choice for each question. Upon completion, check the answer key andfollow prescription given on page 5 to strengthen areas where questions were missed/skipped.Do not guess on this practice test; skip questions you are not familiar with and follow directions for these questionsgiven in the prescription guide. Do not use a calculator while working on these practice questions – NO CALCULATORS.ALLOWED ON THE PERT – an on-screen pop-up calculator is available for a few questions.1.Topic: Order of Operations2.Simplify: 18 8 2 5 4 23.Evaluate: 2 xy 3 xy 7 if x 4 and y 5 .b. 18a. 147b. 133c. 81d.c.d. 1653 73Topic: Simplifying Algebraic Expressions4.Solve for y: 4 y 5 y 3 24 x 30b.8 x 30a.c.8 x 42d. 8 x 54c.Topic: Solving Equations6.a.1 .4b.5c. 2d.0 .3Topic: Solving Proportionsx 4x25b.2d.21959a. 4 y 12 3 xb. y c. y 3 x 8d. y 434x 3Topic: Solving InequalitiesFind all solutions of 5 2 x 7 6 .35a. x 39. 5Solve the formula 3 x 4 y 12 , for y.8. Topic: Solving Formulas0 . 2 2 x 1 0 . 2 x 0 . 08Solve the equation:233Topic: Solving Equationsa.Solve for x:7.2a. 10Simplify: 6 4 3 2 x 5 4 x 5.Topic: Evaluating Algebraic Expressionsa. x 5b. x 6c. x 10d. x 2Topic: Solving Word Problem SituationsSet up the equation that can be used to solve thefollowing: “Eight less than the square of a numberis the same as adding the number and four. ”Use x to represent the unknown number.b. x 3c. x 310.d. x 3Topic: Solving Word Problem SituationsThe perimeter of a rectangular swimming pool is30 meters. The width of the pool is 3 meters lessthan its length; find the width of this swimming pool.a. 8 x 2 x 4b. x 2 8 x 4a. 10 metersb.c. 2 x 8 x 4d. 8 2 x x 4c.d.6 meters9 meters3 meters1PERT Math Readiness - www.theperttest.com
11.Topic: Scientific Notation12.Topic: Simplifying Exponent ExpressionsSimplify: 8 x yWrite the number 34,120,000 using scientificnotation.4a.a.3 . 412 10b.7c. 34 . 12 10 713.217.c.d. 34 . 12 10 69 x y 12 xy214. 7b. 74 48 x y 1048 xy5 48 xd.4y43Topic: Subtracting polynomialsSubtract: 7 x 3 6 x 2 2 x 5 x 2 8 x 3 3 xy3 xya. 6 x 9 yb. 3 x 4 yc. 3 x 4 y 1d. 3 x2 4 y xyTopic: Multiplying Polynomials16.a. 7 x 3 11 x 2 6 x 3b. 3 xc. 7 x 3 11 x 2 10 x 3d. 4 x 3 10 x 3Topic: Multiplying PolynomialsMultiply: 2 m 5 n 4 m n Multiply: 4 na. 8 m 2 5 n 2b. 8 m 2 18 mn 5 n 2a. 16 n 2 9b. 16 n 2 24 n 9c. 8 m 2 5 n 2d. 8 m 2 18 mn 5 n 2c. 16 n 2 9d. 8 n 2 6Topic: Multiplying Polynomials18.Find the product for 2 k 2 6 k 9 k 3 a. 2 k 3 12 k 2 9 k 27b. 2 k 3 9 k 27c.d. 2 k 3 9 k 2 9 k 2719. 6 xy 7Topic: Dividing polynomialsDivide:15.3 . 412 104 48 x y32k3 12 k2 27 k 27Topic: Factoring 5 2c. 3 x 5 3 x 5 b. 3 x 5 2Topic: FactoringFactor completely: 4 x 2 16a. 2 x 4 2 x 4 c. 4 x 2 x 2 20.b. 2 x 4 x 4 d. 2 x 4 x 4 Topic: FactoringFactor completely: 4 x 3 12 x 2 x 3Factor completely: 9 x 2 30 x 25a. 3 x 3 2d. 9 x 5 x 5 a. x 3 4 x2 1 c. 4 x 3 4 x 2 1 b.4xd. x2 x 3 3 2 x 1 22PERT Math Readiness - www.theperttest.com
21.23.Topic: Factoring22.What is one factor of the trinomial 3 x 2 2 x 8 ?What is one solution of 4 a 2 20 a 0 ?a. x 2b. 3 x 2a. a 20b. a 5c. x 8d. 3 x 4c. a 4d. a 5Topic: Solving Quadratic Equations24.a. x 12 or 2b. x 6 or 4c. x 6 or 4d. x 2 or 12Topic: Simplifying Radicals8Simplify:4a. 3 a b3c. 3 a b27.27 a b3a.26.232d. 3 a b 3 a b3Topic: Solving System of Two Equations28.2 4x 4x2 5x 64x 4b.2x 2x 3x 2d.3x 3Topic: Multiplying RadicalsMultiply:232b. 3 a b 3 a bx5x 6c.73b3Topic: Simplifying Rational Expressions (Fractions)Simplify:Solve the equation: x 2 10 x 24 025.Topic: Solving Quadratic Equations 6 4 6 4 a. -10b.20c. 22d.6 16Topic: Finding Intercepts of a LineSolve the system of two equations for y:29.Find the x-intercept for the graph 4 x 3 y 12x y 82x y 10a. y 4b. y 6c. y 4d. y 2Topic: Finding the slope of a Line30.Find the slope, m, of the line passing through thepoints 4 , 3 and 0 , 2 a. m c.m 423b. m 8d. m 14a. 4 , 3 b. 3, 0 c. 0 , 3 d. 3, 4 Topic: Finding the Equation of LinesFind the standard form of the equation of a linethat passes through the points 1 , 3 and 2 , 5 .a. y 4 x 3c. y 43x 1b. 2 x 3 y 11d.2 x 3y 43PERT Math Readiness - www.theperttest.com
Additional PERT Math Practice QuestionsDIRECTIONS: Select the correct answer choice for each question below and check answer key and solution guideon page 11.Note: Do not use a calculator. Calculators cannot be used on most questions on the math section of the PERT test .1.Topic: Order of OperationsSimplify:3.2 3 7 22. 5 3 1 Topic: Solving EquationsSolve for x:2a. 208b. 110c. 48d. 0Topic: Solving Inequalities4.5.c. 10b.c.4d. –6b.c. 6 feetd. 20 feet6.9.b.2 x 14d.2x 5a. 6 x 13 6 x 21Topic: Operations with Polynomials8.3614 m n35 mn14 mny3 64b.3 y 12c.y3 48 y 64d.y3 12 y2 48 y 64Topic: Solving Quadratic Equations2355n2m3write answer using positive exponents.b.d.662m n352m5n53Topic: Factoring Polynomials 5 x 5 x 5 a. xy 5 x 5 b.c. xy 5 x 5 d. prime (cannot be factored)10.y x2Topic: Finding Slope of a LineFind the slope of the line: 3 x 2 y 4Solve: y 2 5 y 6a. m c. y 2 or 358Factor completely: x 2 y 5 xy 5 x 25a.a. y 1 or 69 feetTopic: Exponent Rules4 2 x 3 6 x 17Multiply: y 4 3a. 14 feetc.7.3a.Simplify:a.2d. 2 y 8Topic: Simplifying Algebraic ExpressionsSimplify: 2 1 A 20-ft piece of board is cut into two pieces such thatthe second piece is 2 feet more than twice the first.piece; find the length of the longer piece of board.b. 8 y 2c. 15 y 15 x3Topic: Solving Word Problem SituationsSolve the inequality: 3 y 5 3a. 2 y 85b. y 2 or 3d.2b. m 3c. m 2332d. m 34PERT Math Readiness - www.theperttest.com
PART IIANSWER KEYS&SOLUTION GUIDESPERT MATHSTUDY GUIDEPERT Math Readiness - www.theperttest.com
PERT Math Practice Test - Answer Key and Prescription GuidePrescription GuideAnswer KeyAnswer1) Review each missed question using the Solution Guide starting on page 6.2) Review the suggested topic(s) using the PERT Math Study Guide starting on page 13.1.b.Review topics 1 & 2 – signed numbers & order of operations, then practice questions in exercise set2.a.Review topics 1, 2 & 3 – signed numbers, order of operations & evaluating algebraic expression, thenpractice questions in each exercise set.3.d.Review topics 1, 2 & 3 – signed numbers, order of operations & simplifying algebraic expression, thenpractice questions in each exercise set4.c.Review topic 4 – solving equations, then practice questions in exercise set5.a.Review topic 4 – solving equations, then practice questions in exercise set6.d.Review topic 4 – solving formulas, then practice questions in exercise set7.c.Review topic 4 – solving proportions, then practice questions in exercise set8.b.Review topic 4 – solving inequalities, then practice questions in exercise set9.b.Review topic 12 – solving word problem situations, also see keyword guide on page 18, then practicequestions in exercise set.10.c.Review topic 12 – solving word problem situations, also see keyword guide on page 18, then practicequestions in exercise set.11.c.Review topic 5 – scientific notation, then practice questions in exercise set12.a.Review topic 5 – simplifying exponent expressions, then practice questions in exercise set13.c.Review topic 6 – dividing polynomials, then practice questions in exercise set14.a.Review topic 6 – adding/subtracting polynomials, then practice questions in exercise set15.b.Review topic 6 – multiplying polynomials, then practice questions in exercise set16.b.Review topic 6 – multiplying polynomials, then practice questions in exercise set17.b.Review topic 6 – multiplying polynomials, then practice questions in exercise set18.c.Review topic 7 – general factoring strategy, GCF & DoS, then practice questions in each exercise set19.a.Review topic 7 – perfect square trinomial (PsT), then practice questions in exercise set20.a.Review topic 7 – factor by grouping, then practice questions in exercise set21.d.Review topic 7 – factoring ax trinomials, then practice questions in exercise set22.b.Review top
PERT Math Practice Test . 1 Additional PERT Math Practice Questions . successfully complete this part of the test. Below are sample questions you can expect to see on the PERT. Here’s a multiple-choice format of a basic algebra question: Evaluate: 2xy 3x 2 11 if x 4 and y 5. a. 139 b. 99 c. 19 d. 469 SOLUTION: To evaluate 2xy 3x 2 11, replace x with -4 and y with 5 and use the order of .
