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PERTMATHPRACTICETESTwithanswer keyscoring guideand solution guideEXQUiSiTE Class Center, LLC - PERT Preparation and Tutoring - www.collegeblaze.com
Below is a full-length, 30-question, PERT math practice test to help you with preparing for the math section ofthe Florida PERT Placement Test. Circle the correct answer choice for each question. Upon completion of thispractice test, check the answer key and PERT scoring guide provided. The scoring guide will help youdetermine your possible score on the math section of the actual PERT placement test. There is also a solutionguide provided on pages 6 – 8.DO NOT USE A CALCULATOR WHILE WORKING ON THIS PRACTICE TEST. CALCULATORS CANNOTBE USED ON THE MATH SECTION OF THE ACTUAL PERT PLACEMENT TEST.30 PERT MATH PRACTICE QUESTIONS1. Evaluate: 2 xy 2 3xy 7 if x 4 and y 5.a. 147b. 133c.2332. Solve for y: 4 y 5 y 3 2a. 252b. 5c.2d.195d. 16533. Simplify: 6 4 3 2x 5 4x a.4 x 30b.8 x 30c.8 x 424. Solve for x: 0.2 2x 1 0.2x 0.08a.1.4b.5c. 2d.0.3d. 8 x 545. Find all solutions of 5 2 x 7 6.a. x 3b. x 36. Solve the formula 3x 4y 12 , for y.a. 4y 12 3xb. y c. x 3d. x 394c. y 3x 8d. y EXQUiSiTE Class Center, LLC - PERT Preparation and Tutoring - www.collegeblaze.com3x 341
x 4 3 x57. Solve the equation:a. x 58. Set up the equation that can be used to solvethe following: “Eight less than the square ofa number is the same as adding the numberand four.” Use x to represent the unknown number.b. x 6a. 8 x 2 x 4c. x 10b. x 2 8 x 4c. 2 x 8 x 4d. x 2d. 8 2 x x 49. The perimeter of a rectangular swimming pool is 30meters. The width of the pool is 3 meters less thanits length; find the width of this swimming pool.a. 10 metersb.9 metersc.6 metersd.3 meters a. 61.71b. 28.00c. 302.40d. 30.24 11. Simplify: 8x 4 y 3 6xy 7 a. 48 x 4y 7b. 48 x 4y 10c.d.10. Jose books for the semester cost 432.00.How much tax will he pay if the tax rateis 7%?48x5y412. Write the number 37,120,000 using scientificnotation.a. 3.712 107b. 3.712 10 7c. 37.12 10 7 48x 4d. 37.12 10 6y313. Divide:9 x 2 y 12 xy 2 3xy3xya. 6 x 9y 14. Subtract: 7x 3 6x 2 2x 5x 2 8x 3a. 7x 3 11x 2 6 x 3b. 3xb. 3x 4yc. 7x 3 11x 2 10x 3c. 3x 4y 1d. 4x 3 10x 3d. 3x 2 4y xyEXQUiSiTE Class Center, LLC - PERT Preparation and Tutoring - www.collegeblaze.com12
15. Multiply: 2m 5n 4m n 16. Multiply: 4n 3 2a. 8m2 5n2a. 16n2 9b. 8m2 18mn 5n2b. 16n2 24n 9c. 8m2 5n2c. 16n2 9d. 8m2 18mn 5n2 d. 8n2 6 17. Find the product for 2k 2 6k 9 k 3 18. Factor completely: 4x 2 16a. 2k 3 12k 2 9k 27a. 2x 4 2x 4 b. 2k 3 9k 27b. 2x 4 x 4 c. 2k 3 12k 2 27k 27c. 4 x 2 x 2 d. 2k 3 9k 2 9k 27d.19. Factor completely: 9x 2 6 x 4 2x 4 x 4 20. Factor completely: 4x 3 12x 2 x 3 x 3 4x 2 a. 3x 2 2a.b. 3x 2 2b. 4x 2 x 3 c. 3x 2 3x 2 c. 4 x 3 4x 2 1d. 9x 2 x 2 d.21. What is one factor of the trinomial 3x 2 2x 8 ? 1 x 3 2x 1 222. What is one solution of 4a2 20a 0 ?a. x 2a. a 20b. 3x 2b. a 5c. x 8c. a 4d. 3x 4d. a 5EXQUiSiTE Class Center, LLC - PERT Preparation and Tutoring - www.collegeblaze.com3
23. Solve the equation: x 2 10x 24 0a. x 12 or 224. Simplify:a.4x 45x 6b.x 2x 3x 2 4x 4x 2 5x 6b. x 6 or 4c. x 6 or 4d. x 2 or 12d.25. Simplify:23c.27a 8 b 7x 2x 326. Multiply: 6 4 6 4 a. -104a. 3a b33bb.b. 3a 2 b 3 3a 2 b20c. 22c. 3a3 b 3 3d.6 16d. 3a 2 b 3 3a 2 b27. Solve the system of two equations for y:x y 828. Find the x-intercept for the graph:4x 3y 122x y 10a. y 4a. 4, 3 b. y 6b. 3, 0 c. y 4c. 0 , 3 d. y 2d. 3, 4 29. Find the slope, m, of the line passing through thepoints 4 , 3 and 0 , 2 30. Find the standard form of the equation of a linethat passes through the points 1, 3 and 2 , 5 .a. y 4x 32a. m 3b. 2x 3y 11b. m 8c. y 4x 13c. m 4d. 2 x 3y 41d. m 4EXQUiSiTE Class Center, LLC - PERT Preparation and Tutoring - www.collegeblaze.com4
ANSWER KEY FOR PERT MATH PRACTICE he scoring guide below gives a good indication of your possible score on the actual PERT Math Test. Findthe total correct in the # correct line, then see below to find your possible PERT Math score and suggestion.SCORING GUIDE FOR PERT MATH PRACTICE TESTPASSING (CREDIT MATH) SCORE RANGE: 113 - 150Low-Range# correct0 1 2 3PossiblePERT MathScore50 - 59Suggestion45 660 - 6978970 - 79Mid-RangeHigh-Range10 11 1213 14 1516 17 1819 20 21 2223 24 25 26 27 28 29 3080 - 8990 - 99100 - 109110 - 119120 - 150Your score is in the borderline range; youmay need more preparation beforetaking the actual PERT Math test.Please take advantage of the solutionguide provided below and any otherresource(s) that will help you with yourpreparation for the test.Your score is in the high range;you may not need additionalpreparation before attemptingthe actual PERT Math test.Please review the ones, if any,you got incorrect and make noteof your mistakes.Your score is in the range that suggests you need additional preparationbefore attempting the actual PERT Math test. Please take advantage of the solution guideprovided below and any other resource(s) that will help you with your preparation for the test.EXQUiSiTE Class Center, LLC - PERT Preparation and Tutoring - www.collegeblaze.com5
PERT Math Practice Test - Solution GuideBelow is a solution guide with detailed, step-by-step explanations of answers to our PERT Math practice test.1. To evaluate 2xy2 3xy 7 , replace x with2. To solve 4 y 5 y 3 2 , remove( ), collect like terms, and use theproperties of equality to solve.-4 and y with 5 and use the order ofoperations, G E MD AS to simplify.SubstituteDo exponents2 4 5 3 4 5 72Distribute:4 y 5 y 3 2Collect like terms:2 4 25 3 4 5 7Move 6 to opposite side:Multiply next 147Choice a. 1474. To solve 0.2 2 x 1 0.2 x 0.08 , cleardecimals by multiplying by 100, thencontinue to use the properties of equalityto solve.100 0.2 2x 1 100 0.2x 100 0.08 20 2 x 1 20 x 840x 20 20x 840x 20x 8 2020 x 2820 x2814 202010x 1.4Choice a.6 4 2 x 15 2y 2 6 8 x 541.4x 4 3 , usex5cross multiplication and solve theresulting equation.7. To solve the proportionx 43 x5 2y 4 2 2y 26 8x 60Choice d. 8 x 54To solve the inequality 5 2x 7 6 ,use the properties of inequalities, , , , to solve.Move 5 and 7:6 4 6 x 15 4x Distribute -4 inside [ ]Combine like termsChoice c. y 25.Distribute 3 inside [ ]Combine like termsDivide:] tosimplify expression, then distribute – 4and continue to collect like terms. 2y 6 2 200 60 7Add/subtract3. To simplify the expression6 4 3 2 x 5 4 x , work inside [ 2x 6 5 7Simplify right side: 2 x 6Divide: 2 x 6 2 2x 36. To solve the formula (literal equation)3x 4y 12 , for y, use the propertiesof equality to isolate y.3x 4y 124y 3x 124y 3 x 12 4443y x 34Note: when dividing by a negative numberin an inequality, you must remember toreverse your inequality symbol.Choice b. x 38. To translate “eight less than the squareof a number is the same as adding thenumber and four,” change the followingphrases into math expressions.“eight less than the square of a number”translates to: x 2 8Choice d. y 3x 349. To solve this word situation, sketch adiagram, set up an equation, solve theequation and answer the question.xDiagram:(x – 3)“is the same as” translates to: 3x 5 x 4 3x 5x 203x 5x 20 2 x 20 2 2x 10Choice c. x 10“adding the number and four” translatesto: x 4Now, putting these expressions togethergives:x2 8 x 4Choice b. x 2 8 x 4Set up equation: 2 x 3 2 x 302x 6 2x 304x 6 30Solve the equation: 4x 30 64x36 44x 9Use 9 to replace x in the expression (x – 3)to get (9 – 3) 6 meters.Choice c. 6 meters6EXQUiSiTE Class Center, LLC - PERT Preparation and Tutoring - www.collegeblaze.com
10. To find the amount of tax to be paid on 432.00 at a 7% rate, multiply 432by 7%.Find 432 0.072 8 6 48x 4 x x5and7Putting these together we get: 48x5y 43 0 2 4which rewrites to48 x 5y4So the tax is 30.24.when usingChoice c.separate the expression and divideeach term as follows:29x y3xy 12 xy3xy2 3xy3xy 2 27x3 6x2 2x 5x2 8x 3Choice a. 7x3 11x2 6x 316. To multiply 4n 3 2 , use the specialproduct technique of squaring abinomial to get a Perfect SquareTrinomial (PsT), a2 2ab b2. 4n 2 4n 3 3 22 16n2 24n 9Choice b. 16n2 24n 919. To factor completely: 9x2 6x 4 , usethe Perfect Square Trinomial (PsT)method. 9x 2 3x 3x Check: 4 2 2 2 3x 2 12 x distributive property.2m 4m n 5n 4m n 8m2 2mn 20mn 5n28m2 18mn 5n2Choice b. 8m2 18mn 5n217. To find the product for 2k 2 6k 9 k 3 , use the distributive property to multiply.18. To factor 4x2 16 completely, first factorout the GCF, then factor using thedifference of squares (DoS) method. Factor out GCF: 4 x 2 42k 2 k 3 6k k 3 9 k 3 2k3 6k2 6k2 18k 9k 27 x 2 4 x 2 x 2 Factor DoS:32k 9k 27Rewrite final answer: 4 x 2 x 2 Choice c. 4 x 2 x 2 Choice b. 2k3 9k 2720. To factor 4x 3 12 x 2 x 3 , use thegrouping method of factoring. 4xGroup in pairs:3 12x 2 x 3 GCF factor each pair: 4x 2 x 3 1 x 3 4xGCF with x 3 :2 1 x 3 21. To find one factor of the trinomial3x2 2x 8 , find the master product, 3 8 24 , then find the two factorswhose product is 24 and sum 2 :- 6 and 4. Rewrite original trinomialusing the two factors – 6 and 4 to splitup the middle term.3x2 6x 4x 8Use grouping to finish factoring. 3x2Hence 9x 6x 4 is a perfect squaretrinomial (PsT), so we can factor as2 6 x 4 x 8 3x x 2 4 x 2 follows: 3x 2 2Choice a.Choice a.15. To multiply 2m 5n 4m n , use the7x3 11x2 6x 3Choice c. 3x 4y 1Thus 4n 3 3Scientific notation: 3.712 107Choice a. 3.712 107y41 7 x 6 x 2 x 1 5x 8 x 33x 4y 1248 x 514. To subtract these polynomials, use thedistributive property to remove ( ),then combine like terms. Insert 1’s infront of ( ) to help with the distribution.9x 2 y 12 xy 2 3xy,3xy13. To divideM 10n where M is a number less thanor equal to 1 and n is an integer.Note: the exponent 7 is positive because wemoved to the right, a positive direction.positive exponents.Choice d. 30.2412. To write 37,120,000 using scientificnotation, use the scientific notation form,Placing the decimal point between 3 . 7then count to the right, the number ofplaces, 7, to get to the original decimalposition.and y3 y 7 y 414 3 2 11. To simplify 8x 4y 3 6 xy 7 , use the rules of exponents. 4x2 1 x 3 3x 2 2EXQUiSiTE Class Center, LLC - PERT Preparation and Tutoring - www.collegeblaze.com x 2 3x 4 Choice d. 3x 47
23. To solve the equation x 2 10 x 24 0 ,22. To solve 4a2 20a 0 , factor the leftside of the equation, use the Zerouse the three step process outlinedFactor Property (ZFP) to set eachbelow:factor 0 and solve for both valuesof a. Zero Factor Property (ZFP) means: x 4 x 6 0If a b 0 , then a 0 or b 0.Factor:Factor:4a a 5 0Use ZFP:4a 0Solve for a:4a0 44a 0Thus one solution isChoice b.ora 5 0ora 0 5a 5root of9a bThen rewriteZero Factor Property (ZFP) means:If a b 0 , then a 0 or b 0.Choice c. x 6 or 427a8b79a8b6 3b , then take the square6Solve for x: x 4 or x 6x 2 5x 6process outlined below., use theFactor numerator: x 2 x 2 Factor denominator: x 3 x 2 Cancel common factor (x - 2) to get: x 2 x 2 x 3 x 2 x 2x 3 1a 527a8b7 , rewrite8x 4 0 or x 6 0x 2 4x 41a 525. To simplifyasUse ZFP:24. To simplify43to get 3a b .8727a b426. To multiplyspecial product method to multiply andobtain the difference of squares.2as 3a bx 2x 327. To solve the system for x, use theelimination method.x y 82 x y 10 6 3 6 4 6 4 , use theChoice d. 42 6 16 103b .Add the two equations to eliminate they variable and solve for x.3x18 33x 6Choice a. 3a4b3 3b .Choice a. 10Now replace x with 6 in the first equation,x y 8 , and solve for y.6 y 8y 8 6y 2Choice d. y 228. To find the x-intercept for the graph4x 3y 12 , replace y with 0 andsolve for x.29. To find the slope, m, of a line, use they y1formula m 2with the pointsx2 x1 4 ,Replace: 4 x 3 0 12Solve for x:4x 12 44Slope: 3 and 0 , 2 2 3 2 3 1m 0 4 0 4430. To find the equation of the line passingthrough 1, 3 and 2, 5 , find theslope, m, and use the point-slopeformula, y y1 m x x1 , to get theequation of the line.Find slope:m 5 322 2 1 33Use y y1 m x x1 with the slope andx 3one point to get: y 3 Choice b. 3, 0 .Distribute 2 3 y 3 3 x 1 3 3 y 3 2 x 1 Move 2x and -93y 9 2x 2Add numbers2x 3y 2 9Clear fractionChoice d. m 142 x 1 32x 3y 11Choice b. 2x 3y 11EXQUiSiTE Class Center, LLC - PERT Preparation and Tutoring - www.collegeblaze.com
DO NOT USE A CALCULATOR WHILE WORKING ON THIS PRACTICE TEST. CALCULATORS CANNOT BE USED ON THE MATH SECTION OF THE ACTUAL PERT PLACEMENT TEST. 30 PERT MATH PRACTICE QUESTIONS 1. Evaluate: 2xy2 3xy 7 if x 4 and y 5. a. 147 b. 133 c. 233 d. 1653 2. Solve for y: 4 y 5 y 3 2 a. 2 25 b. 5 c. 2 d. 5 19 3. Simplify: 6 3 2 5 4 x @ a. 4x 30 b. 8x 30 c.
