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Test Bank for College Algebra Enhanced with Graphing Utilities , 7th Edition

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    T EST I TEM F ILE (D OWNLOAD O NLY ) COLLEGE ALGEBRA Enhanced with Graphing Utilities SEVENTH EDITION M ICHAEL S ULLIVAN Chicago State University

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    Ch. 0 Chapter R: Review 0.1 Real Numbers 1 Work with Sets MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 1) B ∪ C A) {1, 2, 3, 4, 5, 7, 9} B) { } C) {0} D) {1, 2, 3, 5, 7, 9} 2) A ∪ C A) {1, 2, 3, 4, 5, 8, 9} B) {4, 6, 7, 9} C) {1} D) {1, 2, 3, 5, 7, 9} 3) A ∩ B A) {2, 3, 5} B) {1, 2, 3, 5, 7, 8} C) {2, 3, 5, 7} D) {1, 2, 3, 5, 8} 4) A ∩ C A) {1} B) {1, 2, 3, 4, 5, 7, 8, 9} C) {4, 6, 7, 9} D) {1, 2, 3, 5, 7, 9} 5) (A ∩ B) ∪ C A) {1, 2, 3, 4, 5, 9} B) {1, 2, 3, 5} C) {1, 2, 3} D) {2, 3, 5} 6) (B ∪ C) ∩ A A) {1, 2, 3, 5} B) {1, 2, 3, 4, 5, 7, 9} C) { } D) {1, 2, 3} 7) B A) {0, 1, 4, 6, 8, 9} B) {1, 4, 6, 8, 9} C) {0, 1, 4, 6, 7, 8, 9} D) {0, 1, 4, 6, 9} 8) A ∪ B A) {0, 4, 6, 9} B) {4, 6, 9} C) {1, 4, 6, 8, 9} D) {1, 2, 3, 5, 7, 8} 9) A ∩ C A) {0, 2, 3, 4, 5, 6, 7, 8, 9} B) {1} C) {1, 2, 3, 4, 5, 7, 8, 9} D) {1, 2, 3, 4, 5, 6, 7, 8, 9} 10) B ∩ C A) {0, 6, 8} B) {6, 8} C) {1, 2, 3, 4, 5, 7, 9} D) { } 2 Classify Numbers MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. List all the elements of B that belong to the given set. 1) B = 7, 7, - 14, 0, 4 5 , - 5 4 , 2.5 Integers A) {7, - 14, 0} B) {7, 0} C) {7, - 14} D) {7, 0, 7} Page 1

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    2) B = 3, 5, - 18, 0, 1 3 , - 3, 1.9 Natural numbers A) {3} B) 3, 0, - 3 C) {3, 0} D) { - 18, 0, 3} 3) B = 11, 6, - 10, 0, 0 1 Real numbers A) 11, 6, - 10, 0, 0 1 B) {11, - 10, 0} C) 11, - 10, 0, 0 1 D) 11, - 10 4) B = 19, 6, - 9, 0, 0 1 , 0.83 Rational numbers A) 19, - 9, 0, 0 1 , 0.83 B) {19, 0} C) { 6} D) 6, 0 1 , 0.83 5) B = 15, 8, - 24, 0, 0 8 , 0.96 Irrational numbers A) { 8} B) { 8, 0.96} C) 8, 0 8 D) 8, 0 8 , 0.96 6) B = {20, 6, - 8, 0, 3 8 , - 8 3 , 4.4, 25 π , 0.256256256...} Integers A) {20, - 8, 0} B) {20, 0} C) {20, - 8} D) {20, 0, 6} 7) B = {7, 5, - 2, 0, 1 4 , - 4, 1.7, 5 π , 0.525525525...} Natural numbers A) {7} B) 7, 0, - 4 C) {7, 0} D) { - 2, 0, 7} 8) B = {7, 8, - 8, 0, 0 9 , 16, 0.54, - 8 π , 0.161616...} Rational numbers A) 7, - 8, 0, 0 9 , 16, 0.54, 0.161616... B) 7, - 8, 0, 0 9 , 0.54 C) 7, - 8, 0, 0 9 , 0.54, 0.161616... D) 7, - 8, 0, 0 9 , 16, 0.54, - 8 π , 0.161616... Page 2

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    9) B = {4, 8, - 18, 0, 0 3 , , 0.84, - 8 π , 0.161616...} Irrational numbers A) { 8, - 8 π } B) { 8} C) 8, 0 3 , - 8 π D) { 8, - 8 π , 0.161616...} Approximate the number rounded to three decimal places, and truncated to three decimal places. 10) 8.6586 A) 8.659 8.658 B) 8.660 8.658 C) 8.659 8.659 D) 8.658 8.659 11) 1.57142857 A) 1.571 1.571 B) 1.572 1.571 C) 1.571 1.572 D) 1.570 1.572 12) 13 9 A) 1.444 1.444 B) 1.445 1.444 C) 1.444 1.445 D) 1.445 1.445 3 Evaluate Numerical Expressions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the statement using symbols. 1) The sum of 9 and 3 is 12. A) 9 + 3 = 12 B) 9 3 = 3 C) 9 · 3 = 27 D) 9 - 3 = 6 2) The difference 70 less 14 equals 56. A) 70 - 14 = 56 B) 70 14 = 5 C) 70 + 14 = 84 D) 70 · 14 = 980 3) The product of 60 and 12 equals 720. A) 60 · 12 = 720 B) 60 12 = 5 C) 60 + 12 = 72 D) 60 - 12 = 48 4) The quotient 18 divided by 6 is 3. A) 18 6 = 3 B) 18 · 6 = 108 C) 18 + 6 = 24 D) 18 - 6 = 12 5) The sum of four times x and 5 decreased by 7 is 8. A) 4x + 5 - 7 = 8 B) 4(x + 5) - 7 = 8 C) 7 - (4x + 5) = 8 D) 4(x + 5 - 7) = 8 6) Three times the difference of x and 8 is - 10. A) 3(x - 8) = - 10 B) 3 - x - 8 = - 10 C) 3x - 8 = - 10 D) 3 + x - 8 = - 10 7) The quotient of x and the sum of 5 and x. A) x 5 + x B) x + 5 + x C) x(5 + x) D) x + 5 x Page 3

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    Evaluate the expression. 8) - 2 - 3 + 7 A) 2 B) - 12 C) 8 D) - 6 9) 9 + 2 3 A) 29 3 B) 27 3 C) 29 2 D) 27 2 10) 3 · [8(3 - 8) - 6] A) - 138 B) - 30 C) - 58 D) - 34 11) 3 · [5 + 2 · (8 + 2)] A) 75 B) 210 C) 35 D) 206 12) 9 - ( - 6 + 2 · 8 - 1) A) 0 B) 18 C) - 2 D) - 12 13) 21 36 · 4 7 A) 1 3 B) 3 C) 7 12 D) 9 7 14) 3 5 · 1 4 + 1 8 A) 9 40 B) 3 20 C) 3 40 D) 9 8 15) 1 4 · 10 - 1 5 + 7 A) 189 20 B) 93 10 C) 84 5 D) 14 5 16) 8 + 3 4 + 4 A) 11 8 B) 5 8 C) 11 0 D) 5 0 17) 8 - 2 2 - 8 A) - 1 B) 4 C) - 4 D) 6 18) 7 10 + 1 11 A) 87 110 B) 8 21 C) 4 55 D) 29 7 Page 4

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    19) 7 9 - 2 3 A) 1 9 B) 5 27 C) 5 9 D) 1 3 20) 5 6 2 7 A) 35 12 B) 12 35 C) 5 21 D) 21 5 21) 1 3 + 1 5 · 1 9 A) 16 45 B) 8 135 C) 8 5 D) 2 135 4 Work with Properties of Real Numbers MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the Distributive Property to remove the parentheses. 1) 7(x + 9) A) 7x + 63 B) 7x + 9 C) x + 63 D) 63x 2) 8x(x + 6) A) 8x 2 + 48x B) 8x 2 + 6 C) x 2 + 48x D) 48x 2 3) 2(5x + 8) A) 10x + 16 B) 7x + 10 C) 10x + 8 D) 26x 4) 4 1 2 x + 1 8 A) 2x + 1 2 B) 2x + 1 4 C) 2x + 1 8 D) 1 2 x + 1 2 5) (x - 11)(x - 2) A) x2 - 13x + 22 B) x2 + 22x - 13 C) x2 - 14x + 22 D) x2 - 13x - 13 6) (x + 3)(x - 7) A) x2 - 4x - 21 B) x2 - 21x - 4 C) x2 - 5x - 21 D) x2 - 4x - 4 7) (x + 7)(x - 7) A) x2 - 49 B) x2 - 14 C) x2 - 14x - 49 D) x2 + 14x - 49 Page 5

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    0.2 Algebra Essentials 1 Graph Inequalities MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. On the real number line, label the points with the given coordinates. 1) - 9, - 7, - 5, - 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 A) -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 B) -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 C) -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 D) -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 2) - 4.75, - 2, 0, 2.25 -5 -4 -3 -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 2 3 4 A) -5 -4 -3 -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 2 3 4 B) -5 -4 -3 -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 2 3 4 C) -5 -4 -3 -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 2 3 4 D) -5 -4 -3 -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 2 3 4 3) 13 4 , - 13 4 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 A) -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 B) -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 C) -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 D) -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 Insert < , > , or = to make the statement true. 4) - 1 8 A) < B) > C) = 5) - 1.9 3.8 A) < B) > C) = 6) - 71 - 69 A) < B) > C) = Page 6

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    7) 29 - 29 A) > B) < C) = 8) 1 3 0.33 A) > B) < C) = 9) 1.73 3 A) < B) > C) = 10) 3.14 π A) < B) > C) = Write the statement as an inequality. 11) z is positive A) z > 0 B) z < 0 C) z ≤ 0 D) z ≥ 0 12) y is greater than - 12 A) y > - 12 B) y < - 12 C) y ≥ - 12 D) y ≤ - 12 13) y is greater than or equal to 40 A) y ≥ 40 B) y > 40 C) y < 40 D) y ≤ 40 14) z is less than or equal to 2 A) z ≤ 2 B) z < 2 C) z > 2 D) z = 2 15) x is less than 6 A) x < 6 B) x > 6 C) x ≤ 6 D) x ≥ 6 Graph the numbers on the real number line. 16) x > - 5 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 A) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 B) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 C) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 D) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 Page 7

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    17) x < 4 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 A) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 B) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 C) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 D) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 18) x ≥ 4 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 A) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 B) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 C) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 D) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 Page 8

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    19) x ≤ 5 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 A) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 B) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 C) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 D) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 2 Find Distance on the Real Number Line MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given real number line to compute the distance. 1) Find d(A, B) -5 -4 -3 -2 -1 0 1 2 3 4 5 A B -5 -4 -3 -2 -1 0 1 2 3 4 5 A B A) 6 B) - 6 C) 7 D) 5 3 Evaluate Algebraic Expressions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the expression using the given values. 1) x + 13y x = 4, y = 3 A) 43 B) 7 C) 55 D) 17 2) - 4xy + 7y - 8 x = - 5, y = 1 A) 19 B) 27 C) 35 D) - 21 3) - 10x + y x = - 3, y = 3 A) 33 B) - 27 C) 0 D) - 7 4) 15x - 13y 7 x = 8, y = 5 A) 55 7 B) 107 7 C) 185 7 D) 29 7 5) 15x - 8y x + 12 x = 8, y = 4 A) 22 5 B) 1 5 C) 1 4 D) 11 2 Page 9

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    6) 5xy + 50 x x = 5, y = 7 A) 45 B) 15 C) 85 D) 10 7) x - y x = - 8, y = 7 A) 15 B) 1 C) - 15 D) - 1 8) x - y x = - 7, y = 3 A) 4 B) 10 C) - 4 D) - 10 9) 6x - 7y x = 6, y = 7 A) 13 B) 85 C) - 13 D) - 85 10) |x| x + |y| y x = 5 and y = - 3 A) 0 B) 2 C) 1 D) - 1 11) | - 8x - 10y| x = 4, y = - 1 A) 22 B) 42 C) 32 D) 48 12) 4 x + 5 y x = 5, y = - 3 A) 35 B) 5 C) - 35 D) - 5 Use the formula C = 5 9 (F - 32) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of the Fahrenheit temperature. 13) F = 32° A) 0° C B) 5° C C) - 5° C D) 10° C Express the statement as an equation involving the indicated variables. 14) The area A of a rectangle is the product of its length l and its width w. A) A = lw B) A = l + w C) A = 2(l + w) D) A = l w 15) The perimeter P of a rectangle is twice the sum of its length l and its width w. A) P = 2(l + w) B) P = l + w C) P = lw D) P = 2lw 16) The circumference C of a circle is the product of π and its diameter d. A) C = π d B) C = π d C) C = π + d D) C = 2 π d 17) The area A of a triangle is one - half the product of its base b and its height h. A) A = 1 2 bh B) A = 2bh C) A = 1 2 (b + h) D) A = bh 18) The volume V of a sphere is 4 3 times π times the cube of the radius r. A) V = 4 3 π r 3 B) V = 4 3 π r 2 C) V = 4 3 π 3 r D) V = 4 3 π r Page 10

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    19) The surface area S of a sphere is 4 times π times the square of the radius r. A) S = 4 π r 2 B) S = 4 π r C) S = 4 π r D) S = π r 2 20) The volume V of a cube is the cube of the length x of a side. A) V = x 3 B) V = 3 x C) V = 3x D) V = x 2 21) The surface area S of a cube is 6 times the square of the length x of a side. A) S = 6x 2 B) S = 6x C) S = 6 + x 2 D) S = x 2 Solve the problem. 22) The weekly production cost C of manufacturing x calendars is given by C(x) = 20 + 6x, where the variable C is in dollars. What is the cost of producing 292 calendars? A) $1772.00 B) $5846.00 C) $1752.00 D) $312.00 23) At the beginning of the month, Christopher had a balance of $208 in his checking account. During the next month, he wrote a check for $57, deposited $103, and wrote another check for $190. What was his balance at the end of the month? A) $64 B) - $64 C) - $142 D) $142 4 Determine the Domain of a Variable MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine which value(s), if any, must be excluded from the domain of the variable in the expression. 1) x 2 - 1 x A) x = 0 B) x = 1, x = - 1 C) x = 1, x = 0 D) x = - 1 2) 7x - 3 x 2 - 81 A) x = 9, x = - 9 B) x = 81 C) x = 9 D) x = 3 7 3) x 3 + 6x 4 x 2 + 49 A) x = 0, x = - 1 6 B) x = - 49 C) x = - 7 D) none 4) x 2 + 10x + 3 x 3 - 25x A) x = 5, x = - 5, x = 0 B) x = 5, x = - 5 C) x = 0 D) x = 5, x = 0 5) x x - 8 A) x = 8 B) x = - 8 C) x = 0 D) none 6) 2 x + 6 A) x = - 6 B) x = 6 C) x = 0 D) none Page 11

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    7) x - 8 x - 6 A) x = 6 B) x = - 6 C) x = 0 D) none 5 Use the Laws of Exponents MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. 1) 3 4 A) 81 B) 12 C) - 81 D) - 12 2) - 4 4 A) - 256 B) 16 C) 256 D) - 16 3) 4 - 3 A) 1 64 B) - 64 C) 64 D) 1 12 4) ( - 5) - 4 A) 1 625 B) - 625 C) 625 D) - 1 625 5) - 5 - 2 A) - 1 25 B) - 25 C) 25 D) 1 10 6) ( - 5) 3 A) - 125 B) 125 C) - 15 D) 15 7) 2 - 7 · 2 4 A) 1 8 B) 8 C) 4 D) 1 16 8) (2 - 2 ) - 1 A) 4 B) 1 4 C) 1 2 D) 2 Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 9) (5xy) 3 A) 125x 3 y 3 B) 125xy C) 5x 3 y 3 D) 1 125x 3 y 3 10) (9x 3 ) - 2 A) 1 81x 6 B) 81x 6 C) x 6 81 D) 81 x 6 Page 12

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    11) ( - 5x 3 ) - 1 A) - 1 5x 3 B) - 1 125x 3 C) 1 5x 3 D) 1 125x 3 12) (x 8 y - 1 ) 8 A) x 64 y 8 B) y 8 x 64 C) 1 x 64 y 8 D) x 64 y 8 13) (x - 4 y) 9 A) y 9 x 36 B) y 9 x 4 C) 1 x 36 y 9 D) x 36 y 9 14) x - 2 y 7 xy 9 A) 1 x 3 y 2 B) 1 xy 2 C) y 2 x 3 D) x y 2 15) x - 3 y 9 x 4 y 13 A) 1 x 7 y 4 B) x 7 y 4 C) y 4 x 7 D) x 7 y 4 16) 7x - 1 4y - 1 - 3 A) 64x 3 343y 3 B) 343x 3 64y 3 C) 64y 3 343x 3 D) 343y 3 64x 3 17) 6x - 1 7y - 1 - 2 A) 49x 2 36y 2 B) 36x 12 49y 12 C) 49y 2 36x 2 D) 36x 2 49y 2 18) (x - 6 y 8 ) - 7 z 4 A) x 42 z 4 y 56 B) y 56 z 4 x 42 C) x 42 y 56 z 4 D) y 56 x 42 z 4 19) - 8x 7 y - 2 7z 7 - 2 A) 49y 4 z 14 64x 14 B) 64x 14 49y 4 z 14 C) 49z 14 64x 14 y 4 D) 49y 4 64x 14 z 14 Page 13

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    Evaluate the expression using the given value of the variables. 20) (x + 2y)2 for x = 2, y = 2 A) 36 B) 6 C) 12 D) 16 21) 5x - 1 y 2 for x = - 1, y = - 2 A) - 20 B) - 4 5 C) - 5 4 D) - 20 22) 4x 2 - 4y 2 for x = - 3, y = 2 A) 20 B) 28 C) 52 D) - 28 23) 4x 3 + 5x 2 - 5x + 9 for x = 1 A) 13 B) 23 C) 3 D) - 5 Solve. 24) What is the value of (6666) 4 (2222) 4 ? A) 81 B) (3333) 4 C) 162 D) (2222) 4 6 Evaluate Square Roots MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. 1) 25 A) 5 B) 625 C) 1 25 D) not a real number 2) ( - 7) 2 A) 7 B) 2401 C) 1 49 D) not a real number Find the value of the expression using the given values. 3) x 2 x = - 6 A) 6 B) 2 3 C) - 6 D) - 2 3 4) ( x) 2 x = 9 A) 9 B) 81 C) 1 81 D) 1 9 5) x 2 + y 2 x = 15, y = 20 A) 25 B) 13 C) 18 D) 24 6) x 2 + y 2 x = - 5, y = 2 A) 29 B) 7 C) - 3 D) 10 7) x 2 + y 2 x = 1, y = 2 A) 3 B) - 1 C) 5 D) 1 Page 14

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    8) y x x = - 3, y = 6 A) 1 216 B) 216 C) - 216 D) - 1 216 7 Use a Calculator to Evaluate Exponents MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a calculator to evaluate the expression. Round the answer to three decimal places. 1) ( - 3.36) - 5 A) - 0.002 B) 0.002 C) - 428.249 D) 428.249 2) - ( - 4.47) 2 A) - 19.981 B) 19.981 C) - 0.050 D) 0.050 3) (1.08) - 6 A) 0.630 B) - 0.630 C) - 1.587 D) 1.587 8 Use Scientific Notation MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the number in scientific notation. 1) 6712 A) 6.712 × 10 3 B) 6.712 × 10 4 C) 6.712 × 10 - 3 D) 6.712 × 10 1 2) 237.5 A) 2.375 × 10 2 B) 2.375 × 10 - 2 C) 2.375 × 10 1 D) 2.375 × 10 - 1 3) 210.081 A) 2.10081 × 10 2 B) 2.10081 × 10 - 2 C) 2.10081 × 10 1 D) 2.10081 × 10 - 1 4) 81,000 A) 8.1 × 10 4 B) 8.1 × 10 - 4 C) 8.1 × 10 5 D) 8.1 × 10 - 5 5) 3,900,000 A) 3.9 × 10 6 B) 3.9 × 10 - 6 C) 3.9 × 10 5 D) 3.9 × 10 - 5 6) 0.000862 A) 8.62 ∘ 10 - 4 B) 8.62 × 10 4 C) 8.62 × 10 - 5 D) 8.62 × 10 - 3 7) 0.000093111 A) 9.3111 × 10 - 5 B) 9.3111 × 10 5 C) 9.3111 ± 10 - 4 D) 9.3111 × 10 4 8) 0.0000042811 A) 4.2811 × 10 - 6 B) 4.2811 × 10 6 C) 4.2811 × 10 - 5 D) 4.2811 × 10 - 7 9) 0.00000016107 A) 1.6107 × 10 - 7 B) 1.6107 × 10 7 C) 1.6107 × 10 - 6 D) 1.6107 × 10 6 Page 15

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    10) 0.0000000487015 A) 4.87015 × 10 - 8 B) 4.87015 × 10 8 C) 4.87015 × 10 - 7 D) 4.87015 × 10 - 9 11) In a certain city, the subway system carried a total of 1,840,000,000 passengers. A) 1.84 × 10 9 B) 18.4 × 10 9 C) 1.84 × 10 8 D) 1.84 × 10 10 12) A business projects next year's profits to be $884,000,000. A) 8.84 × 10 8 B) 8.84 × 10 7 C) 8.84 × 10 9 D) 8.84 × 10 - 9 13) A computer compiles a program in 0.000676 seconds. A) 6.76 × 10 - 4 B) 6.76 × 10 - 5 C) 6.76 × 10 - 6 D) 6.76 × 10 3 Write the number as a decimal. 14) 1.70 × 10 3 A) 1700 B) 17,000 C) 170 D) 51 15) 6.650 × 10 5 A) 665,000 B) 6,650,000 C) 66,500 D) 332.5 16) 6.2121 × 10 5 A) 621,210 B) 6,212,100 C) 62,121 D) 310.605 17) 9.54 × 10 - 4 A) 0.000954 B) 0.00954 C) 0.0000954 D) - 954,000 18) 7.987 × 10 - 5 A) 0.00007987 B) 0.0007987 C) 0.000007987 D) - 798,700 19) 3.974 × 10 - 6 A) 0.000003974 B) 0.00003974 C) 0.0000003974 D) - 3,974,000 20) 4.0694 × 10 - 7 A) 0.00000040694 B) 0.0000040694 C) 0.000000040694 D) - 406940,000 21) There are 2.106 × 10 6 miles of highways, roads, and streets in a certain country. A) 2,106,000 B) 21,060,000 C) 210,600 D) 210,600,000 0.3 Geometry Essentials 1 Use the Pythagorean Theorem and Its Converse MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The lengths of the legs of a right triangle are given. Find the hypotenuse. 1) a = 4, b = 3 A) 5 B) 7 C) 2 D) 25 2) a = 12, b = 16 A) 20 B) 11 C) 14 D) 19 Page 16

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    The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 3) 5, 12, 13 A) right triangle; 13 B) right triangle; 12 C) right triangle; 5 D) not right triangle 4) 2, 3, 4 A) right triangle; 4 B) right triangle; 3 C) right triangle; 2 D) not right triangle 5) 9, 12, 15 A) right triangle; 15 B) right triangle; 12 C) right triangle; 9 D) not a right triangle 6) 15, 36, 39 A) right triangle; 39 B) right triangle; 36 C) right triangle; 15 D) not a right triangle 7) 21, 72, 75 A) right triangle; 75 B) right triangle; 72 C) right triangle; 21 D) not a right triangle 8) 10, 20, 25 A) right triangle; 25 B) right triangle; 20 C) right triangle; 10 D) not a right triangle 9) 6, 8, 12 A) right triangle; 12 B) right triangle; 8 C) right triangle; 6 D) not a right triangle Solve. Use the fact that the radius of the Earth is 3960 miles and 1 mile = 5280 feet. 10) A guard tower at a state prison stands 103 feet tall. How far can a guard see from the top of the tower? Round to the nearest tenth of a mile. A) 12.4 mi B) 5600.3 mi C) 17.6 mi D) 909 mi 11) A person who is 3 feet tall is standing on the beach and looks out onto the ocean. Suddenly, a ship appears on the horizon. How far is the ship from the shore? Round to the nearest tenth of a mile. A) 2.1 mi B) 5600.3 mi C) 3 mi D) 154.2 mi 2 Know Geometry Formulas MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Find the area A of a rectangle with length 18 in and width 20 in. A) A = 360 in 2 B) A = 720 in 2 C) A = 38 in 2 D) A = 72 in 2 2) Find the area A of a rectangle with length 7.5 ft and width 10.4 ft. A) A = 78 ft 2 B) A = 156 ft 2 C) A = 17.9 ft 2 D) A = 30 ft 2 3) Find the area A of a triangle with height 3 in and base 3 in. A) A = 9 2 in 2 B) A = 9 2 in C) A = 9 in 2 D) A = 9 in Page 17

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    4) Find the area A and circumference C of a circle of radius 7 in.. Express the answer in terms of π . A) A = 49 π in. 2 ; C = 14 π in. B) A = 14 π in. 2 ; C = 14 π in. C) A = 196 π in. 2 ; C = 7 π in. D) A = 28 π in. 2 ; C = 7 π in. 5) Find the area A and circumference C of a circle of diameter 11 ft. Use 3.14 for π . Round the result to the nearest tenth. A) A = 95 ft 2 ; C = 34.5 ft B) A = 34.5 ft 2 ; C = 34.5 ft C) A = 379.9 ft 2 ; C = 17.3 ft D) A = 69.1 ft 2 ; C = 17.3 ft 6) Find the volume V of a rectangular box with length 8 yd, width 2 yd, and height 6 yd. A) V = 96 yd 3 B) V = 32 yd 3 C) V = 72 yd 3 D) V = 384 yd 3 7) Find the surface area S of a rectangular box with length 3 ft, width 2 ft, and height 4 ft. A) 52 ft2 B) 40 ft2 C) 26 ft2 D) 44 ft2 8) Find the volume V and surface area S of a sphere of radius 8 centimeters. Express the answer in terms of π . A) V = 2048 3 π cm 3 ; S = 256 π cm 2 B) V = 512 3 π cm 3 ; S = 2048 3 π cm 2 C) V = 2048 π cm 3 ; S = 16 π cm 2 D) V = 512 π cm 3 ; S = 64 π cm 2 9) Find the volume V of a sphere of radius 2 ft. Use 3.14 for π . If necessary, round the result to the nearest tenth. A) V = 33.5 ft 3 B) V = 16.7 ft 3 C) V = 18.8 ft 3 D) V = 267.9 ft 3 10) Find the volume V of a right circular cylinder with radius 7 ft and height 16 ft. Express the answer in terms of π . A) V = 784 π ft 3 B) V = 196 π ft 3 C) V = 112 π ft 3 D) V = 56 π ft 3 11) Find the surface area S of a right circular cylinder with radius 7 cm, and height 6 cm. Use 3.14 for π . Round your answer to one decimal place. A) 571.4 cm2 B) 285.7 cm2 C) 923.2 cm2 D) 439.6 cm2 12) Find the volume V of a sphere of diameter 8 yd. Use 3.14 for π . If necessary, round the result to the nearest tenth. A) V = 267.9 yd 3 B) V = 67 yd 3 C) V = 150.7 yd 3 D) V = 2143.6 yd 3 Page 18

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    13) Find the area of the shaded region. Express the answer in terms of π . 9 9 A) 81 - 81 4 π square units B) 324 - 81 π square units C) 81 - 81 2 π square units D) 81 4 π + 81 square units 14) Find the area of the shaded region. Express the answer in terms of π . 1 1 A) 1 2 π square units B) 1 4 π square units C) 1 2 square units D) 1 π square units 15) Find the area of the shaded region. Express the answer in terms of π . 2 2 A) 2 π - 4 square units B) 1 π - 4 square units C) 4 square units D) 2 π - 2 square units 16) A bicycle wheel makes 4 revolutions. Determine how far the bicycle travels in inches if the diameter of the wheel is 13 in. Use π ≈ 3.14. Round to the nearest tenth. A) 163.3 in. B) 40.8 in. C) 52 in. D) 326.6 in. 17) A rectangular patio has dimensions 10 feet by 15 feet. The patio is surrounded by a border with a uniform width of 2 feet. Find the area of the border. A) 116 ft 2 B) 54 ft 2 C) 158 ft 2 D) 84 ft 2 Page 19

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    18) A circular swimming pool, 20 feet in diameter, is enclosed by a circular deck that is 4 feet wide. What is the area of the deck? Use π = 3.1416. A) 301.6 ft 2 B) 584.3 ft 2 C) 703.7 ft 2 D) 314.2 ft 2 19) Find the perimeter. Approximate the result to the nearest tenth using 3.14 for π . 9 ft 4 ft A) 28.3 ft B) 34.6 ft C) 32.3 ft D) 38.6 ft 20) Find the area of the window. Approximate the result to the nearest tenth using 3.14 for π . 8 dm 3 dm A) 27.5 dm 2 B) 52.3 dm 2 C) 38.1 dm 2 D) 26.4 dm 2 Page 20

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    3 Understand Congruent Triangles and Similar Triangles MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The triangles are similar. Find the missing length x and the missing angles A, B, C. 1) 92° 16 28 39° 49° 14 A) x = 8 units; A = 92°; B = 39°; C = 49° B) x = 16 units; A = 39°; B = 92°; C = 49° C) x = 8 units; A = 49°; B = 39°; C = 92° D) x = 16 units; A = 92°; B = 39°; C = 49° 2) 14° 27° 30 10 20 139° A) x = 15; A = 27; B = 14; C = 139 B) x = 30; A = 14; B = 27; C = 139 C) x = 15; A = 139; B = 14; C = 27 D) x = 30; A = 27; B = 14; C = 139 Solve. If necessary, round to the nearest tenth. 3) A flagpole casts a shadow of 33 feet. Nearby, a 5 - foot tree casts a shadow of 2 feet. What is the height of the flagpole? A) 82.5 ft B) 13.2 ft C) 0.3 ft D) 330 ft 4) If a flagpole 27 feet tall casts a shadow that is 36 feet long, find the length of the shadow cast by an antenna which is 18 feet tall. A) 24 ft B) 13.5 ft C) 54 ft D) 27 ft 5) The zoo has hired a landscape architect to design the triangular lobby of the children's petting zoo. In his scale drawing, the longest side of the lobby is 6 cm. The shortest side of the lobby is 2 cm. The longest side of the actual lobby will be 49 m. How long will the shortest side of the actual lobby be? A) 16.3 m B) 0.2 m C) 147 m D) 1.5 m Page 21

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    6) If a tree 32.5 feet tall casts a shadow that is 13 feet long, find the height of a tree casting a shadow that is 25 feet long. A) 62.5 ft B) 10 ft C) 16.9 ft D) 44.5 ft 0.4 Polynomials 1 Recognize Monomials MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 1) - 18x A) Monomial; variable x; coefficient - 18; degree 1 B) Monomial, variable x; coefficient 1; degree - 18 C) Monomial,; variable x; coefficient - 18; degree 0 D) Not a monomial 2) 13x4 A) Monomial; variable x; coefficient 13; degree 4 B) Monomial; variable x; coefficient 4; degree 13 C) Monomial; variable x; coefficient 4; degree 0 D) Not a monomial 3) 7 x A) Monomial; variable x; coefficient 7; degree 1 B) Monomial; variable x; coefficient 7; degree - 1 C) Monomial; variable x; coefficient 7; degree 0 D) Not a monomial 4) - 11x - 3 A) Monomial; variable x; coefficient - 11; degree - 3 B) Monomial; variable x; coefficient 3; degree - 11 C) Monomial; variable x; coefficient - 11; degree 3 D) Not a monomial 5) - 3xy 7 A) Monomial; variables x, y; coefficient - 3; degree 8 B) Monomial; variables x, y; coefficient - 3; degree 7 C) Monomial; variables x, y; coefficient - 3; degree 1 D) Not a monomial 6) 7x 2 y 6 A) Monomial; variables x, y; coefficient 7; degree 8 B) Monomial; variables x, y; coefficient 7; degree 2 C) Monomial; variables x, y; coefficient 7; degree 6 D) Not a monomial 7) 20x y A) Monomial; variables x, y; coefficient 20; degree 1 B) Monomial; variables x, y; coefficient 20; degree - 2 C) Monomial; variables x, y; coefficient 20; degree 2 D) Not a monomial Page 22

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    8) - - 3x7 y3 A) Monomial; variables x, y; coefficient - 3; degree 7 B) Monomial; variables x, y; coefficient - 3; degree 3 C) Monomial; variables x, y; coefficient - 3; degree 4 D) Not a monomial 9) 4x 3 - 5 A) Monomial; variable x; coefficient 4; degree 3 B) Monomial; variable x; coefficient 5 ; degree 3 C) Monomial; variable x; coefficient 4; degree 1 D) Not a monomial 2 Recognize Polynomials MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Tell whether the expression is a polynomial. If it is, give its degree. 1) 7x 5 - 2 A) Polynomial; degree 5 B) Polynomial; degree 2 C) Polynomial; degree 7 D) Not a polynomial 2) 1 - 5x A) Polynomial; degree 1 B) Polynomial; degree 5 C) Polynomial; degree - 5 D) Not a polynomial 3) 18 A) Polynomial, degree 0 B) Polynomial, degree 1 C) Polynomial, degree 18 D) Not a polynomial 4) 7 π A) polynomial, degree 0 B) polynomial, degree 1 C) polynomial, degree 7 D) not a polynomial 5) 7x 5 - 2 x A) Polynomial; degree 5 B) Polynomial; degree - 1 C) Polynomial; degree 1 D) Not a polynomial 6) 14 x + 1 A) Polynomial, degree 0 B) Polynomial, degree - 1 C) Polynomial, degree 14 D) Not a Polynomial 7) - 6y 8 - 3 A) Polynomial; degree 8 B) Polynomial; degree - 6 C) Polynomial; degree 3 D) Not a polynomial 8) 8z 3 + z A) Polynomial; degree 3 B) Polynomial; degree 4 C) Polynomial; degree 1 D) Not a polynomial Page 23

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    9) - 6x6 - 18x4 - 3x2 A) Polynomial; degree 4 B) Polynomial; degree 6 C) Polynomial; degree 0 D) Not a polynomial 3 Add and Subtract Polynomials MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Add or subtract as indicated. Express the answer as a single polynomial in standard form. 1) (8x 2 + 3x - 13) + (6x + 13) A) 8x 2 + 9x B) 8x 2 + 9x - 26 C) 8x 2 + 3x + 26 D) 17x 3 2) (8x 2 - 6x - 5) + (8x 2 + 8x - 3) A) 16x 2 + 2x - 8 B) 3x 2 + 16x - 9 C) 16x 2 - 2x - 8 D) 16x 2 + 2x + 8 3) (8x2 + 14x - 6) - (3x2 + 9x - 18) A) 5x2 + 5x + 12 B) 5x2 + 17x - 24 C) 5x2 + 5x - 24 D) 5x2 + 5x - 12 4) (7x 4 - 8x 3 ) + (2x 4 - 5x 3 ) A) 9x 4 - 13x 3 B) 9x 8 - 13x 6 C) - 4x 7 D) - 4x 14 5) (17x 5 - 18x 4 ) - (9x 5 - 14x 4 ) A) 8x 5 - 4x 4 B) 8x 5 - 32x 4 C) 4x 9 D) 26x 5 - 32x 4 6) (4x 7 + 4x 6 ) + (3x 7 - 8x 6 + 2) A) 7x 7 - 4x 6 + 2 B) - 4x 7 - 4x 6 + 2x C) 2x - 4x 7 - 5x 6 D) - 2x 14 7) ( - 9x 2 - 10) - ( - x 3 + 6x 2 + 1) A) x 3 - 15x 2 - 11 B) - 8x 3 - 4x 2 - 1 C) x 3 - 3x 2 - 9 D) - 8x 3 + 6x 2 - 11 8) (9x 5 - 12x 2 - 14) - (4x 5 - 7x 2 + 6) A) 5x 5 - 5x 2 - 20 B) 5x 5 - 8x 2 - 8 C) 5x 5 - 5x 2 - 8 D) - 20x 7 9) (8x 7 + 9x 6 - 12) - ( - 11x 6 + 6x 7 - 20) A) 2x 7 + 20x 6 + 8 B) 2x 7 + 15x 6 - 32 C) 2x 7 + 20x 6 - 32 D) 30x 13 10) (6x 5 - 6x 2 - 7x) + (2x 5 - 2x 2 - 5x) A) 8x 5 - 8x 2 - 12x B) - 5x 5 + 4x 2 - 11x C) 8x - 8x 5 - 12x 2 D) - 12x 8 11) - 3(x 2 + 3x + 1) + ( - 3x 2 - x + 5) A) - 6x 2 - 10x + 2 B) 0x 2 - 10x + 2 C) - 6x 2 - 9x + 2 D) - 6x 2 - 10x + 6 12) 4( - 4x 3 + x 2 - 1) - 5(6x 3 + 2x + 2) A) - 46x 3 + 4x 2 - 10x - 14 B) - 46x 3 + 4x 2 + 10x - 14 C) - 46x 3 + x 2 - 10x - 14 D) - 46x 3 + 4x 2 - 10x + 14 Page 24

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    13) (x 2 + 1) - (9x 2 + 5) + (x 2 + x - 2) A) - 7x 2 + x - 6 B) - 9x 2 + x - 6 C) - 8x 2 + x - 6 D) - 7x 2 + 6x - 1 14) - 9(1 - y 3 ) - 3(1 + y + y 2 + y 3 ) A) 6y 3 - 3y 2 - 3y - 12 B) 6y 3 + 3y 2 - 3y + 12 C) 6y 3 - 3 - ay 2 - 3y - 12 D) - 6y 3 - 3y 2 - 3y - 12 4 Multiply Polynomials MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Perform the indicated operations. Express the answer as a single polynomial in standard form. 1) 10x( - 2x + 6) A) - 20x 2 + 60x B) 40x 2 C) - 20x 2 + 6x D) - 2x 2 + 60x 2) - 6x 4 (12x + 9) A) - 72x 5 - 54x 4 B) - 72x - 54 C) - 72x 5 + 9 D) - 126x 4 3) - 5x 3 (4x6 - 11) A) - 20x 9 + 55x 3 B) - 20x 6 + 55 C) - 20x 9 - 11 D) 35x 3 4) 3x 6 ( - 4x 5 + 12x 4 + 5) A) - 12x 11 + 36x 10 + 15x 6 B) - 12x 11 + 36x 10 C) - 12x 11 + 12x 4 + 5 D) - 12x 5 + 36x 4 + 15 5) (x - 11)(x 2 + 6x - 4) A) x 3 - 5x 2 - 70x + 44 B) x 3 + 17x 2 + 62x - 44 C) x 3 - 5x 2 - 62x - 44 D) x 3 + 17x 2 + 70x + 44 6) (10y + 11)(2y 2 - 2y - 7) A) 20y 3 + 2y 2 - 92y - 77 B) 20y 3 - 20y 2 - 70y + 11 C) 42y 2 - 42y - 147 D) 20y 3 + 42y 2 + 92y + 77 Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 7) (x + 9)(x + 3) A) x2 + 12x + 27 B) x2 + 27x + 12 C) x2 + 11x + 27 D) x2 + 12x + 12 8) ( - 2x - 11)(x + 3) A) - 2x2 - 17x - 33 B) - 2x2 - 33x - 17 C) - 2x2 - 17x - 17 D) - 2x2 - 19x - 33 9) (3x + 5)(5x + 9) A) 15x2 + 52x + 45 B) 8x2 + 52x + 45 C) 15x2 + 52x + 52 D) 8x2 + 52x + 52 10) (x - 3y)(x + 11y) A) x2 + 8xy - 33y2 B) x + 8xy - 33y C) x2 + 8xy + 8y2 D) x2 + 5xy - 33y2 Page 25

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    11) (x - 9y)(3x - 12y) A) 3x2 - 39xy + 108y2 B) x2 - 39xy + 108y2 C) 3x2 - 39xy - 39y2 D) x2 - 39xy - 39y2 12) (3x + 6y)( - 5x - 12y) A) - 15x2 - 66xy - 72y2 B) - 15x2 - 30xy - 72y2 C) - 15x2 - 36xy - 72y2 D) - 15x2 - 66xy - 66y2 5 Know Formulas for Special Products MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Multiply the polynomials. Express the answer as a single polynomial in standard form. 1) (x + 10)(x - 10) A) x2 - 100 B) x2 - 20 C) x2 - 20x - 100 D) x2 + 20x - 100 2) (10x + 13)(10x - 13) A) 100x2 - 169 B) x2 - 169 C) 100x2 - 260x - 169 D) 100x2 + 260x - 169 3) (x + 16)2 A) x2 + 32x + 256 B) x2 + 256 C) 256x2 + 32x + 256 D) x + 256 4) (x - 16)2 A) x2 - 32x + 256 B) x2 + 256 C) 256x2 - 32x + 256 D) x + 256 5) (5x + 12)2 A) 25x2 + 120x + 144 B) 25x2 + 144 C) 5x2 + 120x + 144 D) 5x2 + 144 6) (x + 9y)(x - 9y) A) x2 - 81y2 B) x2 - 18y2 C) x2 - 18xy - 81y2 D) x2 + 18xy - 81y2 7) (12y + x)(12y - x) A) 144y2 - x2 B) 24y2 - x2 C) 144y2 - 24xy - x2 D) 144y2 + 24xy - x2 8) (7x - 6)2 A) 49x2 - 84x + 36 B) 49x2 + 36 C) 7x2 - 84x + 36 D) 7x2 + 36 9) (a - b)2 A) a2 - 2ab + b2 B) a2 - ab + b2 C) a2 - 2ab - b2 D) a2 + 2ab + b2 10) (2x + 9y)2 A) 4x2 + 36xy + 81y2 B) 4x2 + 81y2 C) 2x2 + 36xy + 81y2 D) 2x2 + 81y2 11) (6x - 5y)2 A) 36x2 - 60xy + 25y2 B) 36x2 + 25y2 C) 6x2 - 60xy + 25y2 D) 6x2 + 25y2 Page 26

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    12) (x + 3)3 A) x3 + 9x2 + 27x + 27 B) x3 + 3x2 + 3x + 27 C) x3 + 9x2 + 3x + 27 D) x3 + 9x2 + 9x + 27 13) (2x + 3)3 A) 8x3 + 36x2 + 54x + 27 B) 8x3 + 36x2 + 36x + 27 C) 4x6 + 6x3 + 729 D) 4x2 + 12x + 9 6 Divide Polynomials Using Long Division MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the quotient and the remainder. 1) 18x 7 - 30x 3 divided by 6x A) 3x 6 - 5x 2 ; remainder 0 B) 18x 6 - 30x 2 ; remainder 0 C) 3x 8 - 5x 4 ; remainder 0 D) 3x 7 - 5x 3 ; remainder 0 2) 32x 2 + 20x - 13 divided by 4x A) 8x + 5; remainder - 13 B) 8x 2 + 5x - 13 4 ; remainder 0 C) 32x + 20; remainder - 13 D) 8x - 8; remainder 0 3) x2 + 8x + 12 divided by x + 6 A) x + 2; remainder 0 B) x - 6; remainder 0 C) x2 + 2; remainder 0 D) x3 - 6; remainder 0 4) 2x2 + 7x - 72 divided by x + 8 A) 2x - 9; remainder 0 B) 2x + 9; remainder 0 C) x - 9; remainder 0 D) 2x - 9; remainder 2 5) x2 + 5x - 30 divided by x + 9 A) x - 4; remainder 6 B) x - 4; remainder 0 C) x + 4; remainder 6 D) x - 6; remainder 4 6) x2 + 11x + 22 divided by x + 5 A) x + 6; remainder - 8 B) x + 6; remainder 8 C) x + 6; remainder 0 D) x + 7; remainder 0 7) 9x3 + 61x2 - 5x + 63 divided by x + 7 A) 9x2 - 2x + 9; remainder 0 B) 9x2 + 2x + 9; remainder 0 C) x2 + 3x + 4; remainder 0 D) x2 + 2x + 9; remainder 0 8) 20x3 + 41x2 - 5x - 8 divided by - 5x - 4 A) - 4x2 - 5x + 5; remainder 12 B) - 4x2 - 5x + 5; remainder 0 C) - 4x2 - 5x + 5; remainder 15 D) x2 + 5; remainder - 5 9) 5x 3 - 7x 2 + 7x - 8 divided by 5x - 2 A) x 2 - x + 1; remainder - 6 B) x 2 - x + 1; remainder 6 C) x 2 - x + 1; remainder 10 D) x 2 + x - 1; remainder - 6 Page 27

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    10) x 4 + 256 divided by x - 4 A) x 3 + 4x 2 + 16x + 64; remainder 512 B) x 3 + 4x 2 + 16x + 64; remainder 256 C) x 3 + 4x 2 + 16x + 64; remainder 0 D) x 3 - 4x 2 + 16x - 64; remainder 512 11) - 10x3 - 15x2 + 23x + 15 divided by - 2x - 5 A) 5x2 - 5x + 1; remainder 20 B) 5x2 - 5x + 1; remainder 0 C) 5x2 - 5x + 1; remainder 23 D) x2 + 1; remainder - 5 12) 9x3 + 24x2 + 3x - 13 divided by - 3x - 5 A) - 3x2 - 3x + 4; remainder 7 B) - 3x2 - 3x + 4; remainder 0 C) - 3x2 - 3x + 4; remainder 10 D) x2 + 4; remainder - 3 13) x4 + 4x2 + 5 divided by x2 + 1 A) x2 + 3; remainder 2 B) x2 + 3x + 1 2 ; remainder 0 C) x2 + 3; remainder 0 D) x2 + 3x + 1; remainder 2 14) x 4 + 256 divided by x - 4 A) x 3 + 4x 2 + 16x + 64; remainder 512 B) x 3 + 4x 2 + 16x + 64; remainder 256 C) x 3 + 4x 2 + 16x + 64; remainder 0 D) x 3 - 4x 2 + 16x - 64; remainder 512 15) x 2 - 16a 2 divided by x - 4a A) x + 4a B) x - 4a C) x 2 - 8xa D) x 2 + 8xa 7 Work with Polynomials in Two Variables MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 1) (x - 2y)(x + 9y) A) x2 + 7xy - 18y2 B) x + 7xy - 18y C) x2 + 7xy + 7y2 D) x2 + 4xy - 18y2 2) ( - 3x + 7y)( - 3x - 4y) A) 9x2 - 9xy - 28y2 B) 9x2 - 21xy - 28y2 C) 9x2 + 12xy - 28y2 D) 9x2 - 9xy - 9y2 Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 3) (x + 3y)(x - 3y) A) x 2 - 9y 2 B) x 2 - 6y 2 C) x 2 - 6xy - 9y 2 D) x 2 + 6xy - 9y 2 4) (6x + y)(6x - y) A) 36x 2 - y 2 B) 12x 2 - y 2 C) 36x 2 - 12xy - y 2 D) 36x 2 + 12xy - y 2 5) (5x + 9y)(5x - 9y) A) 25x 2 - 81y 2 B) 25x 2 - 90xy - 81y 2 C) 10x 2 - 18y 2 D) 25x 2 + 90xy - 81y 2 Page 28

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    6) (x - y) 2 A) x 2 - 2xy + y 2 B) x 2 - xy + y 2 C) x 2 - y 2 D) x 2 - 2x 2 y 2 + y 2 7) (x - 3y) 2 A) x 2 - 6xy + 9y 2 B) x 2 - 3xy + 9y 2 C) x 2 - y 2 D) x 2 + 6xy + 9y 2 8) (4x - y) 2 A) 16x 2 - 8xy + y 2 B) 16x 2 - 4xy + y 2 C) 16x 2 + y 2 D) 16x 2 - 8xy - 2y 2 9) (2x + 7y)2 A) 4x2 + 28xy + 49y2 B) 4x2 + 49y2 C) 2x2 + 28xy + 49y2 D) 2x2 + 49y2 10) (10x - 11y)2 A) 100x2 - 220xy + 121y2 B) 100x2 + 121y2 C) 10x2 - 220xy + 121y2 D) 10x2 + 121y2 0.5 Factoring Polynomials 1 Factor the Difference of Two Squares and the Sum and Difference of Two Cubes MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polynomial by removing the common monomial factor. 1) 6x - 54 A) 6(x - 9) B) 6(x + 9) C) x(x - 6) D) x(x + 6) 2) 4x2 - 8x A) 4x(x - 2) B) 4x(x + 2) C) 4(x 2 - 2x) D) 4x 2 (x - 2) Factor the difference of two squares. 3) x 2 - 9 A) (x + 3)(x - 3) B) (x + 9)(x - 9) C) (x - 3)(x - 3) D) (x 2 + 3)(x 2 - 3) 4) 100x 2 - 1 A) (10x - 1)(10x + 1) B) (10x + 1) 2 C) (10x - 1) 2 D) prime 5) 16 - x 2 A) (4 - x)(4 + x) B) (4 + x) 2 C) (4 - x) 2 D) prime 6) 9x2 - 49 A) (3x + 7)(3x - 7) B) (3x - 7)2 C) (3x + 7)2 D) (9x + 1)(x - 49) Factor the sum or difference of two cubes. 7) x 3 - 64 A) (x - 4)(x 2 + 4x + 16) B) (x + 4)(x 2 - 4x + 16) C) (x - 4)(x 2 + 16) D) (x + 64)(x 2 - 1) 8) x 3 + 27 A) (x + 3)(x 2 - 3x + 9) B) (x - 3)(x 2 + 3x + 9) C) (x + 3)(x 2 + 9) D) (x - 27)(x 2 - 1) Page 29

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