ACCUPLACER Sample Questions for Students

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1 ACCUPLACER Sample Questions for Students College Algebra Study Guide LCC Student Success Center Sam Jack Academic Coordinator Cathy Hyten SSS Program Assistant 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:

2 8. 0x 6 + 8x 4 = x 9x 4x 4 5x 4 + 4x 5x + x 9. 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? On Monday, it took Helen hours to do a page of science homework exercises. The next day she did the same number of exercises in hours. If her average rate on Monday was p exercises per hour, what was her average rate the next day, in terms of p? (p + ) exercises per hour (p ) exercises per hour p exercises per hour p exercises per hour College-Level Mathematics There are 0 questions administered on the College- Level Mathematics test, divided into the following content areas: Algebraic operations. Topics include simplifying rational algebraic expressions, factoring and expanding polynomials, and manipulating roots and exponents. Solutions of equations and inequalities. Topics include solving linear and quadratic equations and inequalities, systems of equations and other algebraic equations. Coordinate geometry. Topics include plane geometry, the coordinate plane, straight lines, conics, sets of points in the plane, and algebraic function graphs. Functions. Topics include polynomial, algebraic, exponential, and logarithmic functions. Trigonometry. Topics include trigonometric functions. Applications and other topics. Topics include complex numbers, series and sequences, determinants, permutations and combinations, factorials, and word problems. College-Level Mathematics Sample Questions For each of the questions below, choose the best answer from the five choices given. You may use the paper you received as scratch paper.. 5 = 5 06 The College Board. ACCUPLACER SAMPLE QUESTIONS

3 a b and x +. If a = b, then x = b a b a ab a b ab ab a b. If x x + = 0, then ( x ) = The graph of which of the following equations is a straight line parallel to the graph of y = x? 4x y = 4 x y = x y = 4 x + y = x y = 4 5. An equation of the line that contains the origin and the point (, ) is y = x y = x y = x y = x + y = x 6. An apartment building contains units consisting of one- and two-bedroom apartments that rent for $60 and $450 per month, respectively. When all units are rented, the total monthly rental is $4,950. What is the number of two-bedroom apartments? If the two square regions in the figures below have the respective areas indicated in square yards, how many yards of fencing are needed to enclose the two regions? (Assume the regions are fenced separately.) If log 0 x =, then x = 0, x 9. Iff (x) = x + and g(x) =, then f (g(x)) = x x 4x + 4x + x 5x + (x + )(x ) 0. If θ is an acute angle and sin θ =, then cos θ = 0. 5y(y ) + (y ) = (5y + ) (y + ) (5y + ) (y ) (5y ) (y + ) (5y ) (y ) 0y (y ) 06 The College Board. ACCUPLACER SAMPLE QUESTIONS

4 . For what real numbers x is the value of x 6x + 9 negative? < x < x < or x > x = or x = 0 < x < 6 For no real numbers x. A root of x 5x = 0 is In the xy-plane, the graph of y = x and the circle with center (0, ) and radius have how many points of intersection? 5. None One Two Three More than three (0, r) (s, 0) y 0 x If an equation of the linear function in the figure above is y = mx + b, then m = r s r s rs r s 6. One ordering of the letters T, U, V, and W from left to right is UTVW. What is the total number of orderings of these letters from left to right, including UTVW? If f (x) = x and f is the inverse of f, what is the value of f ()? 8. The sequence {a n } is defined by a o = and a n + = a n + for n = 0,,,.... What is the value of a? From 5 employees at a company, a group of employees will be chosen to work on a project. How many different groups of employees can be chosen? If and a < b, which of the following must be true? f (a) + f (b) = f (x) = ( ) x f (a) + = f (b) f (a) = f (b) f (a) < f (b) f (a) > f (b) 06 The College Board. ACCUPLACER SAMPLE QUESTIONS

5 Answer Key COLLEGE-LEVEL MATHEMATICS QUESTION NUMBER CORRECT ANSWER C E E 4 C 5 A 6 E C 8 B 9 A 0 D B E E 4 C 5 B 6 E E 8 E 9 D 0 E ESL READING SKILLS QUESTION NUMBER CORRECT ANSWER C D A 4 A 5 D 6 C A 8 B 9 D 0 A 06 The College Board. ACCUPLACER SAMPLE QUESTIONS