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ACCUPLACER® Sample Questions Math Sample Questionsfor forStudents Students (ANSWER KEYS ARE FOUND AT THE END OF THIS DOCUMENT) © 2012 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College Board. All other products and services may be trademarks of their respective owners. Visit the College Board on the Web: www.collegeboard.org. CAMOSUN COLLEGE ASSESSMENT CENTRE Sample Questions - Fundamental Math Levels 1-6 Fundamental Math This local test is designed for those who have less than completed academic Grade 9 math. The actual test could include as many as 39 questions or as few as 5 depending on how you answer. The sample test has a total of 20 multiple choice questions. For practice you may also want to try the math sample questions following this set, if the material looks familiar to you. 1. The number 3 781 265 in words is: A. three billion, seven hundred eighty-one million, two hundred sixty-five B. three million, seven thousand eighty-one hundred, two hundred sixty-five C. three million, seven hundred eighty-one thousand, two hundred sixty-five D. three billion, seven hundred eighty-one thousand, two hundred sixty-five E. three million, seven thousand eighty-one, two hundred sixty-five 2. Add: 547 + 38 A. 575 B. 585 C. 827 D. 927 E. none of these 6. Divide: 2754 ÷ 6 A. 359 B. 458 C. 459 D. 4059 E. none of these 3. Add: 349 + 54 A. 303 B. 393 C. 403 D. 889 E. none of these 7. Round 4.657 to the nearest hundredth. A. 4.65 B. 4.66 C. 4.76 D. 5.66 E. none of these 4. Subtract: 674 − 58 A. 114 B. 616 C. 624 D. 626 E. none of these 8. Add: 43.84 + 7.5 A. 41.34 B. 44.59 C. 50.34 D. 51.34 E. none of these 5. Multiply: 67 × 54 A. 3298 B. 3518 C. 3598 D. 3618 E. none of these 9. Subtract: 7.84 − 5.3 A. 0.254 B. 0.731 C. 2.54 D. 7.31 E. none of these 2 SAMPLE QUESTIONS 16. Subtract: 34 − 23 5 A. 12 B. 6 12 C. 21 D. 9 4 E. none of these 10. Subtract: 5.236 – 2.19 A. 3.046 B. 3.146 C. 3.166 D. 5.017 E. none of these 11. Multiply: 0.52 × 2.3 A. 0.260 B. 1.196 C. 2.60 D. 11.96 E. none of these 9 − 3 17. Subtract: 410 10 9 A. 1 10 B. 46 20 6 C. 4 20 D. 4 3 5 E. none of these 12. Multiply: 2.5 × 3.2 A. 1.25 B. 7.00 C. 8.00 D. 80.0 E. none of these 18. Multiply: 78 ˟ 45 A. 35 B. 7 10 C. 35 40 C. 35 32 E. none of these 13. Divide: 4.32 ÷ 0.8 A. 0.185 B. 0.54 C. 4.14 D. 5.4 E. none of these 14. Write 3 45 as an improper fraction. A. 12 5 19 B. 5 C. 32 5 34 D. 5 E. none of these 19. Divide: 34 ÷ 23 A. 12 B. 9 12 C. 89 C. 1 18 E. none of these 15. Add: 2 25 + 12 3 A. 2 10 B. 2 37 C. 2 12 9 D. 2 10 E. none of these 7 ÷3 20. Divide: 10 4 21 A. 40 B. 21 30 C. 14 15 D. 30 28 E. none of these END OF FUNDAMENTAL MATH SAMPLE QUESTIONS 3 SAMPLE QUESTIONS Arithmetic Arithmetic Sample Questions This test measures your ability to perform basic arithmetic operations and to solve problems that involve fundamental arithmetic concepts. There are 17 questions on the Arithmetic tests, divided into three types. For each of the questions below, choose the best answer from the four choices given. You may use the paper you received as scratch paper. 1. 2.75 + .003 + .158 = A. 4.36 B. 2.911 C. 0.436 D. 2.938 • Operationswithwholenumbersandfractions: Topics included in this category are addition, subtraction, multiplication, division, recognizing equivalent fractions and mixed numbers, and estimating. 2. 7.86 × 4.6 = A. 36.156 B. 36.216 C. 351.56 D. 361.56 • Operationswithdecimalsandpercents:Topics include addition, subtraction, multiplication, and division with decimals. Percent problems, recognition of decimals, fraction and percent equivalencies, and problems involving estimation are also given. 3. 7 20 A. B. C. D. • Applicationsandproblemsolving:Topicsinclude rate, percent and measurement problems; simple geometry problems; and distribution of a quantity into its fractional parts. = 0.035 0.858 0.35 3.5 4. Which of the following is the least? A. 0.105 B. 0.501 C. 0.015 D. 0.15 5. All of the following are ways to write 25 percent of N EXCEPT A. 0.25 N B. 25N 100 C. 1 4 N D. 25 N 6. Which of the following is closest to 27.8 × 9.6? A. 280 B. 300 C. 2,800 D. 3,000 7. A soccer team played 160 games and won 65 percent of them. How many games did it win? A. 94 B. 104 C. 114 D. 124 © 2012 The College CollegeBoard. Board. 4 8 ACCUPLACER SAMPLE QUESTIONS QUESTIONS ACCUPLACER SAMPLE 8. Three people who work full-time are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full-time. If one of the people is budgeted for one-half of his time to the project and a second person for one-third of her time, what part of the third worker’s time should be budgeted to this project? A. 13 B. C. D. 14. 46.2 × 10−2 = A. B. C. D. 3 1 ÷ = n, then n is between 2 4 A. 1 and 3 B. 3 and 5 C. 5 and 7 D. 7 and 9 3 5 1 6 1 8 15. If 9. 32 is 40 percent of what number? A. 12.8 B. 128 C. 80 D. 800 1 16. What is 12% of 120? A. 10 B. 14.4 C. 18.4 D. 28.8 2 10. 3 3 – 2 5 = A. B. C. D. 17. A box in a college bookstore contains books, and each book in the box is a history book, an English book or a science book. If one-third of these books are history books and one-sixth are English books, what fraction of the books are science books? 1 12 1 15 14 15 1 1 15 A. 1 3 B. 1 2 2 C. 3 D. 3 4 11. 2 1 + 4 2 = 2 3 A. 6 1 6 5 6 1 C. 7 6 B. 6 18. The measures of two angles of a triangle are 35° and 45°. What is the measure of the third angle of the triangle? A. 95° B. 100° C. 105° D. 110° 5 D. 7 6 12. What is A. B. C. D. 12 13 14 15 0.0462 0.462 4.62 462 1,345 rounded to the nearest integer? 99 13. Three of four numbers have a sum of 22. If the average of the four numbers is 8, what is the fourth number? A. 4 B. 6 C. 8 D. 10 © 2012 The College CollegeBoard. Board. 5 9 ACCUPLACER SAMPLE QUESTIONS QUESTIONS ACCUPLACER SAMPLE Elementary Algebra Sample Questions Elementary Algebra For each of the questions below, choose the best answer from the four choices given. You may use the paper you Sample Questions 1 2 19. Erica bought 3 yards of fabric. If she uses of the fabric 2 3 tomakeacurtain,howmuchwillshehaveleft? 1 2 19. Erica yd. 3 2 yards of fabric. If she uses 3 of the fabric A. 1bought 6 tomakeacurtain,howmuchwillshehaveleft? B. 1 yd. 3 A. 1 yd. 1 C. 16 yd. 6 B. 1 yd. 1 D. 32 yd. 13 C. 1 yd. 20. Jen wants 6 to tile the floor of her kitchen. The floor is rectangular and measures 12 feet by 8 feet. If it costs $2.50 1 2 yd. D. square per foot for the materials, what is the total cost of the 3 for tiling the kitchen floor? materials 20. Jen wants A. $160 to tile the floor of her kitchen. The floor is rectangular B. $200 and measures 12 feet by 8 feet. If it costs $2.50 per C.square $220 foot for the materials, what is the total cost of the materials D. $240for tiling the kitchen floor? A. $160 B. $200 ENDC.OF$220 ARITHMETIC SAMPLE QUESTIONS D. $240 received as scratch paper. For each of the questions below, choose the best answer 1. If A represents the number of apples purchased at 15 cents from theand four choices given. You may use thepurchased paper you each, B represents the number of bananas at 10 cents each, which of the following represents the total received as scratch paper. value of the purchases in cents? 1. IfA. A represents the number of apples purchased at 15 cents A+B each, and B represents the number of bananas purchased B. 25(A + B) atC. 10 cents each, which of the following represents the total 10A + 15B value of the purchases in cents? D. 15A + 10B A. A + B 2. √B. 2 × 25(A √ 15 =+? B) A. 10A 17 + 15B C. B. 15A 30 + 10B D. C. √ 30 2. √ D. 2× √ √ 15 17 = ? A. 17 3. What is the value of the expression 2x2 + 3xy – 4y2 when x = B. 30 2 C. and√y30 = - 4? A. √ -80 D. 17 B. 80 3. What is the value of the expression 2x2 + 3xy – 4y2 when x = C. -32 2 D. and y32= - 4? A. -80 4. Inthefigurebelow,bothcircleshavethesamecenter,and B. 80 the C. radius -32 of the larger circle is R. If the radius of the smaller circle D. is 323 units less than R, which of the following represents the area of the shaded region? 4. Inthefigurebelow,bothcircleshavethesamecenter,and A. πR 2 the radius of the larger circle is 2R. If the radius of the smaller B. π(R – 3) circle is 3 units lessC.thanπRR,2 –which π × 32of the following represents the area of the shaded region? 2 D. πR – π(R - 3)2 A. πR 2 B. π(R – 3)2 C. πR 2 – π × 32 5. (3x – 2y)2 = D. πR 2 – π(R - 3)2 A. 9x2 – 4y2 B. 9x2 + 4y2 C. 9x22+ 4y2 – 6xy 5. (3x 2y)2 +=4y2 – 12xy D.– 9x A. 9x2 – 4y2 2 + 4y2x2 –2 x – 6 = 6. IfB. x >9x 2, then x –4 2 C. 9x + 4y2 – 6xy x–3 A. 9x22 + 4y2 – 12xy D. Elementary Algebra A total of 12 questions of three types are administered in this test. Elementary Algebra • Thefirsttypeinvolvesoperationswithintegers A total 12 questions of three are administered andofrational numbers, andtypes includes computation in this test. with integers and negative rationals, the use of absolute values, and ordering. • Thefirsttypeinvolvesoperationswithintegers rational numbers, and includes computation • and Thesecondtypeinvolvesoperationswithalgebraic with integersusing and negative rationals, theformulas use of expressions evaluation of simple absolute values, and and expressions, andordering. adding and subtracting monomials and polynomials. Questions involve • Thesecondtypeinvolvesoperationswithalgebraic multiplying using and dividing monomials expressions evaluation of simpleand formulas polynomials, the evaluation of positive rational and expressions, and adding and subtracting roots and exponents, simplifying algebraic monomials and polynomials. Questions involve fractions, and factoring. multiplying and dividing monomials and the evaluation of positive rational • polynomials, Thethirdtypeofquestioninvolvestranslating roots and exponents, simplifying algebraicand written phrases into algebraic expressions fractions, and factoring. solving equations, inequalities, word problems, linear equations and inequalities, quadratic • Thethirdtypeofquestioninvolvestranslating equations (by factoring), and verbal problems written phrases into algebraic expressions and presented in an algebraic context. solving equations, inequalities, word problems, linear equations and inequalities, quadratic equations (by factoring), and verbal problems presented in an algebraic context. © 2012 The College CollegeBoard. Board. B. xx –– 32 6. If x > 2, then C. xx –+– 332 A. 2 D. x32 – 3 B. x – 2 C. D. 6 10 x2 – x – 6 x2 – 4 = x–3 x+2 3 2 ACCUPLACER SAMPLE QUESTIONS QUESTIONS ACCUPLACER SAMPLE 7. 4 – (-6) -5 A. B. – C. 13. For which of the following equations are x = 5 and x = –5 both solutions? = 2 5 2 5 A. x2 – x 2 − 5x − 25 = 0 B. x 2 + 25 = 0 2 0 C. x 2 + 10x − 25 = D. – 2 0 D. x 2 − 25 = 8. If 2x – 3(x + 4) = – 5, then x = A. 7 B. – 7 C. 17 D. - 17 14. If x ≠ 0, then 9. – 3(5 – 6) – 4(2 – 3) = A. – 7 B. 7 C. – 1 D. 1 A. 7x 5u B. 5u 7x C. 29u 5x u 5u u + − = x x 5x D. 31u 5x 10. Which of the following expressions is equivalent to 20 – 45 x > 16? A. x ≤ 5 B. x ≥ 5 C. x ≥ 32½ D. x ≤ 32½ 15. -2 -1 0 1 2 The solution set of which of the following inequalities is graphed on the number line above? A. B. C. D. 11. Which of the following lists of numbers is ordered from least to greatest? 1 3 2 3 A. − , − , , 3 5 3 5 3 1 3 2 B. − , − , , 5 3 5 3 1 3 3 2 C. − , − , , 3 5 5 3 3 1 2 3 D. − , − , , 5 3 3 5 2x − 4 ≥ −3 2x + 5 ≤ 6 3x − 1 ≤ 5 4x − 1 ≥ 7 16. 2x + 6y = 5 x + 3y = 2 How many solutions ( x, y ) are there to the system of equations above? A. None B. One C. Two D. More than two 12. If 5t + 2 = 6, then t = 17. Which of the following is a factor of both x 2 − x − 6 and x 2 − 5x + 6 ? A. 8 A. B. C. D. B. 5 4 C. 4 5 x x x x −3 +3 −2 +2 D. –8 © 2012 The College CollegeBoard. Board. 7 11 ACCUPLACER SAMPLE QUESTIONS QUESTIONS ACCUPLACER SAMPLE College-Level Mathematics Test 6 4 18. 10x +2 8x = 2x 12 A. 9x 4 B. 14x The College-Level Mathematics test measures your ability to solve problems that involve college-level mathematics concepts. There are six content areas measured on this test: (a) Algebraic Operations, (b) Solutions of Equations and Inequalities, (c) Coordinate Geometry, (d) Applications and other Algebra Topics, (e) Functions and (f) Trigonometry. The Algebraic Operations content area includes thesimplificationofrationalalgebraicexpressions, factoring and expanding polynomials, and manipulating roots and exponents. The Solutions of Equations and Inequalities content area includes the solution of linear and quadratic equations and inequalities, systems of equations, and other algebraic equations. The Coordinate Geometry content area presents questions involving plane geometry, the coordinate plane, straight lines, conics, sets of points in the plane, and graphs of algebraic functions. The Functions content area includes questions involving polynomial, algebraic, exponential and logarithmic functions. The Trigonometry content area includes trigonometric functions. The Applications and other Algebra Topics content area contains complex numbers, series and sequences, determinants, permutations and combinations, factorials, and word problems. A total of 20 questions are administered on this test. 4 2 C. 5x + 4x D. 5x3 + 2x 2 19. A rectangular yard has area 96 square feet. If the width of the yard is 4 feet less than the length, what is the perimeter, in feet, of the yard? A. 40 B. 44 C. 48 D. 52 20. On Monday, it took Helen 3 hours to do a page of science homework exercises. The next day she did the same number of exercises in 2 hours. If her average rate on Monday was p exercises per hour, what was her average rate the next day, in terms of p? A. 2 ( p + 1) exercises per hour B. 3 ( p − 1) exercises per hour C. 2 p exercises per hour 3 D. 3 p exercises per hour 2 END OF ELEMENTARY ALGEBRA SAMPLE QUESTIONS Sample Questions For each of the questions below, choose the best answer from the four choices given. You may use the paper you received as scratch paper. 5 3 1. 2 2 – 2 2 1 A. 2 2 B. 2 3 C. 2 2 5 D. 2 3 E. 22 © 2012 The College CollegeBoard. Board. 8 12 ACCUPLACER SAMPLE QUESTIONS QUESTIONS ACCUPLACER SAMPLE 7. Ifthetwosquareregionsinthefiguresbelowhavethe respective areas indicated in square yards, how many yards of fencing are needed to enclose the two regions? 1 2. If a ≠ b and 1xx + 1aa = 1b , then x = b A. 1 – 1aa b B. b – a 11 C. ab ab a–b a-b D. abab abab E. a – b a-b 1 2 3. If 3x2 – 2x + 7 = 0, then x – 3 = ( A. B. C. D. E. 125 5 A. B. C. D. E. ) 20 20 99 77 99 77 -9 9 88 -9 9 20 20 -9 9 4√130 20√10 24√5 100 104√5 8. If log10x = 3, then x = A. 310 B. 1,000 C. 30 10 10 3 3 3 E. 10 10 D. 4. The graph of which of the following equations is a straight line parallel to the graph of y = 2x ? A. 4x – y = 4 B. 2x – 2y = 2 C. 2x – y = 4 D. 2x + y = 2 E. x – 2y = 4 xx –_11 9. If f(x) = 2x + 1 and g(x) = , then f(g(x)) = 2 A. x xx –_ 11 B. 4x + 2 4 x+2 44xx + 22 C. –_ 1 x 1 55xx + 11 D. 2 ((2x + 1)(x )( –_1) ) E. 2 x 12 x 1 2 11 10. If θ is an acute angle and sin θ = 2 , then cos θ = 2 A. -1 B. 0 11 C. 2 2 √√3 3 D. 2 2 E. 2 5. An equation of the line that contains the origin and the point (1, 2) is A. y = 2x B. 2y = x C. y = x –1 D. y = 2x +1 y E. y2 = x – 1 2 6. An apartment building contains 12 units consisting of one- and two-bedroom apartments that rent for $360 and $450 per month, respectively. When all units are rented, the total monthly rental is $4,950. What is the number of twobedroom apartments? A. 3 B. 4 C. 5 D. 6 E. 7 11. 5y(2y – 3) + (2y – 3) = A. (5y + 1) (2y + 3) B. (5y + 1) (2y – 3) C. (5y – 1) (2y + 3) D. (5y –1) (2y – 3) E. 10y (2y – 3) 12. For what real numbers x is x2– 6x + 9 negative? A. –3 < x < 3 B. x < –3 or x > 3 C. x = –3 or x = 3 D. 0 < x < 6 E. For no real numbers x © 2012 The College CollegeBoard. Board. 9 13 ACCUPLACER SAMPLE QUESTIONS QUESTIONS ACCUPLACER SAMPLE 13. 13. 13. A root of x2 – 5x – 1 = 0 is A root of x2 – 5x – 1 = 0 is A root of x22 – 5x – 1 = 0 is 1 − 29 A. 1 − 29 A. 1 − 2 29 A. 2 One ordering of the letters T, U, V and Wfromlefttoright One ordering of the letters U, V and Wfromlefttoright is UTVW. What is the totalT, number of orderings of these One ordering of the letters U, V and Wfromlefttoright is UTVW. What is the totalT,number of orderings of these lettersfromlefttoright,includingUTVW? is UTVW. What is the total number of orderings of these lettersfromlefttoright,includingUTVW? A. 8 lettersfromlefttoright,includingUTVW? A. 12 8 B. A. 812 B. C. B. 16 12 C. 20 16 D. C. 16 D. 20 E. 24 D. E. 20 24 E. 24 1 and −1 is the inverse of f, what is the 17. If f ( x ) = 33xx − f − 17. If f ( x ) = 2 1 and f −1 is the inverse of f, what is the 17. If f ( x ) = −31x 2− 1 and f −1 is the inverse of f, what is the value of f (23) ? value of f −1 ( 3) ? value of f −1 ( 3) ? 1 A. 1 A. 13 A. 3 2 B. 32 3 B. 2 B. 3 C. 13 C. 1 C. 1 D. 2 D. 2 D. 2 E. 7 7 E. 3 E. 7 3 3 18. The sequence {an} isdefinedby a0 = 1 and 18. The sequence {an} isdefinedby a0 = 1 and 18. The sequence 1 and n = 0, 1, 2, ...a0. =What an= 2an + {2afor is the value of n} isdefinedby +1 n = 0, 1, 2, ... . an= 2 a + 2 for What is the value of +1 n an3= 2an + 2 for n = 0, 1, 2, ... . What is the value of +?1 a3 ? 8 aA. 3? A. 8 B. 10 A. 810 B. C. 16 B. C. 10 16 D. 20 C. 16 D. 20 E. 22 D. E. 20 22 E. 22 19. From 5 employees at a company, a group of 3 employees will 19. be From 5 employees at aacompany, a group ofdifferent 3 employees will chosen to work on project. How many groups 19. From 5 employees at aacompany, a group ofdifferent 3 employees will be chosen to work on project. How many groups of 3 employees can be chosen? be to work project. How many different groups of 3chosen employees canon beachosen? 3 ofA. 3 employees can be chosen? A. 53 B. A. B. 365 C. B. C. 510 6 D. C. D. 615 10 E. D. E. 10 15 E. 15 x 1 20. If f ( x ) = 1 xx and a < b, which of the following must be 20. If f ( x ) = 13 and a < b, which of the following must be true? f ( x ) = 3 and a < b, which of the following must be 20. If true? 3 true? 3 A. f ( a ) + f ( b ) = 3 A. f ( a ) + f ( b ) = 3 A. f ( a ) + 1f ( b ) = f (b) B. f ( a ) + 1 = + 13 = f (b) B. ff ( aa ) + f (b) B. f ( a ) = 3f = ( ) 3 (b) C. C. f ( a ) = f ( b ) f ( a ) = f (b) C. D. f ( a ) < f ( b ) < f (b) D. ff ( aa ) < ( ) f (b) D. E. f ( a ) > f ( b ) E. f ( a ) > f ( b ) E. f ( a ) > f ( b ) 16. 16. 16. 5 − 2 17 5 − 17 5 − 2 17 2 1 + 2 29 1 + 29 1 + 2 29 2 5 + 2 17 5 + 17 5 + 2 17 2 5 + 2 29 E. 5 + 29 E. 5 + 2 29 E. 2 2 B. B. B. C. C. C. D. D. D. In the xy -plane, the graph of y = x2 and the circle with In the xy -plane, the graph of yhow = x2many and the circle center (0,1) and radius 3 have points of with In the xy -plane, the graph of yhow = x22many and the circle center (0,1) and radius 3 have points of with intersection? center (0,1) and radius 3 have how many points of intersection? A. None intersection? A. One None B. A. B. None One C. Two B. C. One Two D. Three C. D. Two Three than three E. More D. E. Three More than three 15. E. More than three 15. 15. y 14. 14. 14. (0, r) x (s, 0) 0 Ifanequationofthelinearfunctioninthefigureaboveis yIfanequationofthelinearfunctioninthefigureaboveis = mx + b, then m = Ifanequationofthelinearfunctioninthefigureaboveis y = mx + b, then m = y = mx +r b, then m = A. − r A. − rs A. − s r B. r s B. rs B. s C. rss C. rs C. rs D. r D. r D. r E. −s E. −s E. −s END OF COLLEGE-LEVEL MATHMATICS SAMPLE QUESTIONS © The College © 2012 2012 The CollegeBoard. Board. © 2012 The College Board. © 2012 The College Board. 10 14 14 14 ACCUPLACER SAMPLE ACCUPLACER SAMPLE QUESTIONS QUESTIONS ACCUPLACER SAMPLE QUESTIONS ACCUPLACER SAMPLE QUESTIONS Math Answer Keys FUNDAMENTAL LEVELS 1-6 ARITHMETIC QUESTION NUMBER CORRECT ANSWER QUESTION NUMBER CORRECT ANSWER 1 C 1 B 2 B 2 A 3 C 3 C 4 B 4 C 5 D 5 D 6 C 6 A 7 B 7 B 8 D 8 C 9 C 9 C 10 A 10 C 11 B 11 C 12 C 12 C 13 D 13 D 14 B 14 B 15 D 15 C 16 E 16 B 17 D 17 B 18 B 18 B 19 D 19 C 20 C 20 D © 2012 The College Board. 11 ACCUPLACER SAMPLE QUESTIONS Math Answer Keys ELEMENTARY ALGEBRA COLLEGE LEVEL QUESTION NUMBER CORRECT ANSWER QUESTION NUMBER CORRECT ANSWER 1 D 1 C 2 C 2 E 3 A 3 E 4 D 4 C 5 D 5 A 6 B 6 E 7 D 7 C 8 B 8 B 9 B 9 A 10 A 10 D 11 B 11 B 12 C 12 E 13 D 13 E 14 C 14 C 15 C 15 A 16 A 16 E 17 A 17 E 18 C 18 E 19 A 19 D 20 D 20 E © 2012 The College Board. 12 ACCUPLACER SAMPLE QUESTIONS