(Test Bank) College Algebra

Miller, 2

Math & Statistics

Test Bank

2nd Edition

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Test Bank for College Algebra, The downloadable file consists of 588 pages, and the total size of the file is 4.83 MB. Purchase now only for highly discounted price.

Author(s): Miller

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Study Note Preview

Chapter 0Review of Prerequisites 0.1 Sets and the Real Number Line 0Concept Connections Provide the missing information. 1)A is a collection of items called elements. Answer: set Type: SA Var: 1 Objective: Concept Connections 2)W = {0, 1, 2, 3, ...} is called the set of numbers. Answer: whole Type: SA Var: 1 Objective: Concept Connections 3)N = {1, 2, 3, ...} is called the set of numbers. Answer: natural Type: SA Var: 1 Objective: Concept Connections 4)Z = {... , -3, -2, -1, 0, 1, 2, 3, ...} is called the set of . Answer: integers Type: SA Var: 1 Objective: Concept Connections 5)A set can be defined using - notation by using a description of the set. Answer: set, builder Type: SA Var: 1 Objective: Concept Connections 6)Listing elements in a set within set braces is called the method to define a set. Answer: roster Type: SA Var: 1 Objective: Concept Connections 7)Real numbers that can be expressed as a ratio of two integers are called numbers. Answer: rational Type: SA Var: 1 Objective: Concept Connections 8)An number is a real number that cannot be expressed as a ratio of two integers. Answer: irrational Type: SA Var: 1 Objective: Concept Connections Page 1(College Algebra 2e Julie Miller) (Test bank all Chapter)9) The statement x < y means that x lies to the of y on the number line. Answer: left Type: SA Var: 1 Objective: Concept Connections 10) The of x is denoted by x. Answer: absolute, value Type: SA Var: 1 Objective: Concept Connections 11) Write an absolute value expression to represent the distance between a and b on the number line: . Answer: a - b or b - a Type: SA Var: 1 Objective: Concept Connections 12) Given the expression bn, the value of b is called the and n is called the . Answer: base, exponent or power Type: SA Var: 1 Objective: Concept Connections 13) The symbol x represents the principal root of x. Answer: square Type: SA Var: 1 Objective: Concept Connections 14) The expression 0 5 equals , whereas 5 0 is . Answer: 0, undefined Type: SA Var: 1 Objective: Concept Connections 1Identify Subsets of the Set of Real Numbers Determine whether the statement is true or false. 1) 3 N A) True B) False Answer: A Type: BI Var: 10 Objective: Identify Subsets of the Set of Real Numbers 2) 7.5 ∉ Z A) True B) False Answer: A Type: BI Var: 50+ Objective: Identify Subsets of the Set of Real Numbers Page 23) 6 ∈ N A) False B) True Answer: B Type: BI Var: 20 Objective: Identify Subsets of the Set of Real Numbers 4) 0.15 ∈ Z A) False B) True Answer: A Type: BI Var: 36 Objective: Identify Subsets of the Set of Real Numbers 2Use Inequality Symbols and Interval Notation Write the statement as an inequality. 1) u is at least 10. A) u < 10 B) u ≤ 10 C) u > 10 D) u ≥ 10 Answer: D Type: BI Var: 10 Objective: Use Inequality Symbols and Interval Notation 2) The quantity ( t + 4) exceeds 31. A) t + 4 ≤ 31 B) t + 4 < 31 C) t + 4 ≥ 31 D) t + 4 > 31 Answer: D Type: BI Var: 50+ Objective: Use Inequality Symbols and Interval Notation Determine whether the statement is true or false. 3) 13 < - 13 A) True B) False Answer: B Type: BI Var: 18 Objective: Use Inequality Symbols and Interval Notation 4) -3.51 > -3.51 A) False B) True Answer: A Type: BI Var: 50+ Objective: Use Inequality Symbols and Interval Notation Express the set in interval notation. 5) -3 A) [-3, ∞] B) [-3, ∞) C) (- ∞, -3) D) (-3, ∞) Answer: D Type: BI Var: 40 Objective: Use Inequality Symbols and Interval Notation Page 36) 9 A) [- ∞, 9] B) (- ∞, 9] C) (- ∞, 9) D) (9, ∞) Answer: B Type: BI Var: 40 Objective: Use Inequality Symbols and Interval Notation 7) -9 -7 A) (-9, ∞) B) (-9,-7] C) (- ∞, -9) D) [-9, -7] Answer: D Type: BI Var: 36 Objective: Use Inequality Symbols and Interval Notation 8) 6 7 A) [6, 7] B) [6, 7) C) (6, 7] D) (- ∞, 6) Answer: B Type: BI Var: 36 Objective: Use Inequality Symbols and Interval Notation 9) 3 9 A) [3,9] B) (3, 9] C) [3, 9) D) (- ∞, 3) Answer: B Type: BI Var: 36 Objective: Use Inequality Symbols and Interval Notation Graph the set and express it in interval notation. 10) {x | x > 5} Answer: (5, ∞) Type: SA Var: 1 Objective: Use Inequality Symbols and Interval Notation 11) {x | x < –1} Answer: (– ∞, –1] Type: SA Var: 1 Objective: Use Inequality Symbols and Interval Notation Page 4Write the subset of real numbers in set-builder notation. 12) (-4, 4] A) {x -4 < x ≤ 4} B) { x -4 ≤ x < 4} C) { x -4 ≤ x ≤ 4} D) { x -4 < x < 4} Answer: A Type: BI Var: 50+ Objective: Use Inequality Symbols and Interval Notation For the following exercise, interval notation is given for several sets of real nu mbers. Graph the set and write the corresponding set-builder notation. 13) (- ∞, 1.1 A) -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 x | x < 1.1 B) -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 x | x > 1.1 C) -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 x | x ≤ 1.1 D) -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 x | x ≥ 1.1 Answer: C Type: BI Var: 50+ Objective: Use Inequality Symbols and Interval Notation Page 53Find the Union and Intersection of Sets List the elements of . 1) A = {-29, 14, 13, -20, 11, -2} and B = {-27, -10, 13, 11} A) {13} B) { } C) {13, 11} D) {-29, 14, 13, -20, 11, -2, -27, -10} Answer: C Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets Determine the intersection X ∩ Y. Express the answer in interval notation. 2) X = {x x ≥ 18 } and Y = {x x < 11 } A) (- ∞, 11] ∪ (18, ∞) B) [11, 18) C) (11, 18] D) { } Answer: D Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets Determine the union X ∪ Y. Express the answer in interval notation. 3) X = { x x > 14 } and Y = { x x ≤ 11 } A) (11, 14] B) [11, 14) C) (- ∞, 11] ∪ (14,∞) D) { } Answer: C Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets 4) X = { x x > -9 } and Y = { x x ≤ 16 } A) All real numbers B) { } C) (16, -9] D) (- ∞, 16] ∪ (-9,∞) Answer: A Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets Determine the intersection X ∩ Y. Express the answer in interval notation. 5) X = {x x ≥ -2 } and Y = {x x < -6 } A) { } B) [-6, -2) C) (- ∞, -6] ∪ (-2, ∞) D) (-6, -2] Answer: A Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets Page 64Evaluate Absolute Value Expressions Simplify by writing the expression without absolute value bars. 1) 1 A) 1 B) -1 Answer: A Type: BI Var: 20 Objective: Evaluate Absolute Value Expressions 2) w - 2 for w < 2 A) w - 2 B) - w + 2 C) - w - 2 D) w + 2 Answer: B Type: BI Var: 20 Objective: Evaluate Absolute Value Expressions 3) x + 7 for x ≥ -7 A) - x +7 B) - x - 7 C) x - 7 D) x + 7 Answer: D Type: BI Var: 17 Objective: Evaluate Absolute Value Expressions 4) 15 - z 15 - z for z < 15 A) 15 B) 1 C) -1 D) -15 Answer: B Type: BI Var: 18 Objective: Evaluate Absolute Value Expressions 5Use Absolute Value to Represent Distance Write an absolute value expression to represent the distance between th e two points on the number line and simplify. 1) -3 and 2 A) -3 - 2 ; 5 B) -3 + 2 ; 1 C) -3 - 2 ; -5 D) -3 - 2 ; -1 Answer: A Type: BI Var: 50+ Objective: Use Absolute Value to Represent Distance 6Apply the Order of Operations Evaluate the expression. 1) (-11)2 A) -9 B) -121 C) -22 D) 121 Answer: D Type: BI Var: 10 Objective: Apply the Order of Operations Page 7Evaluate the root without using a calculator or note that root is not a real number. 2) 364 A) 4 B) 5 C) -4 D) Not a real number Answer: A Type: BI Var: 5 Objective: Apply the Order of Operations 3) 3-125 A) –5 B) 6 C) 5 D) Not a real number Answer: A Type: BI Var: 1 Objective: Apply the Order of Operations 7Simplify Algebraic Expressions Apply the associative property of addition. 1) (r + 3) + 7 A) r + 3 B) r + 7 C) r + 10 D) r +4 Answer: C Type: BI Var: 24 Objective: Simplify Algebraic Expressions Apply the associative property of multiplication. 2) - 5 11 - 11 5p A) -5 p B) p C) -55 p D) 6p Answer: B Type: BI Var: 20 Objective: Simplify Algebraic Expressions Apply the commutative property of multiplication. 3) w · 5 6 A) - 5 6w B) w · 6 5C) 6 5w D) 5 6w Answer: D Type: BI Var: 18 Objective: Simplify Algebraic Expressions Clear parentheses and combine like terms. 4) -11 z3 - 8z3 - z3 Answer: -20 z3 Type: SA Var: 50+ Objective: Simplify Algebraic Expressions Page 85) 3(2 x - 5) + 14 x A) 6x - 15 + 14 x B) 20 x - 5 C) 20 x - 15 D) 15 x Answer: C Type: BI Var: 40 Objective: Simplify Algebraic Expressions 6) -2 x(4 - 3 x) + 16 x2 - 7 x Answer: 22 x2 - 15 x Type: SA Var: 50+ Objective: Simplify Algebraic Expressions 7) 2[3.5(2.5 - 3 x) - x(5 + 0.5 x)] + 7.5 x2 Answer: 6.5 x2 - 31 x + 17.5 Type: SA Var: 50+ Objective: Simplify Algebraic Expressions Clear parentheses by applying the distributive property. 8) -(-4 s + 9 t + 7) A) 4s - 9 t - 7 B) -4 s - 9 t - 7 C) 4 s + 9 t + 7 D) 4 s - 9 t + 7 Answer: A Type: BI Var: 50+ Objective: Simplify Algebraic Expressions 9) 4(4s - 4)- 1(8 t - 2 u) A) 16 s - 4 - 8 t - 2 u B) 16 s - 4 - 8 t + 2 u C) 16 s - 16 - 8 t - 2 u D) 16 s - 16 - 8 t + 2 u Answer: D Type: BI Var: 50+ Objective: Simplify Algebraic Expressions Page 98Write Algebraic Models Solve the problem. 1) A new diet program guarantees you will lose 1.6 lb per week. A male with a starting w eight of 220 lb is modeled by W = 220 - 1.6 t where t is the number of weeks after starting the diet. Use the model to determine the male's weight after 19 weeks. 2 4 6 8 10 12 14 16 18 250 200 150 100 50 t (weeks) W (lb) 2 4 6 8 10 12 14 16 18 250 200 150 100 50 t (weeks) W (lb) A) 170.6 lb B) 189.6 lb C) 218.4 lb D) 208.6 lb Answer: B Type: BI Var: 50+ Objective: Write Algebraic Models 2) A tool rental store charges a flat fee of $6.50 to rent a chain saw, and $3.75 for each day, incl uding the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days. A) y = 6.50 x + 3.75 B) y = 3.75( x + 6.50) C) y = 3.75 x + 6.50 D) y = 3.75 x - 6.50 Answer: C Type: BI Var: 50+ Objective: Write Algebraic Models 3) A tool rental store charges a flat fee of $8.50 to rent a chain saw, and $4.00 for each day, incl uding the first. Use a linear equation to find the cost of renting the saw for one week. A) $32.50 B) $36.50 C) $12.50 D) $28.00 Answer: B Type: BI Var: 50+ Objective: Write Algebraic Models 4) A tool rental store charges a flat fee of $9.00 to rent a chain saw, and $4.00 for each day, incl uding the first. If you need to rent the saw and absolutely refuse to spend more than $49.00, what's the maximum number of days you can keep the saw? A) 7 days B) 5 days C) 14 days D) 10 days Answer: D Type: BI Var: 50+ Objective: Write Algebraic Models Page 10 5) The width of a rectangle is 2 ft less than 4 times the length. Write a model for the width W in terms of the length L. A) W = 2L - 4 B) W = 2L + 4 C) W = 4L + 2 D) W = 4L - 2 Answer: D Type: BI Var: 15 Objective: Write Algebraic Models 9Mixed Exercises Evaluate the expression for the given values of the variables. 1) -q 4t for q = -3, t = 2 A) 3 8B) - 3 2C) - 3 8D) - 1 8 Answer: A Type: BI Var: 50+ Objective: Mixed Exercises 2) Under selected conditions, a sports car gets 14 mpg in city driving and 19 mpg for highway dr iving. The model G = 1 14 c + 1 19 h represents the amount of gasoline used (in gal) for c miles driven in the city and h miles driven on the highway. Determine the amount of gas required to drive 98 mi in the city and 399 mi on the highway. A) 37 gal B) 28 gal C) 33 gal D) 34 gal Answer: B Type: BI Var: 50+ Objective: Mixed Exercises 10 Expanding Your Skills Write the set as a single interval. 1) -∞, 5 ∩ -6, 8 ∩ [1,6] A) 1 , 5 B) 1, 6 C) -6 , 5 D) -∞, 8 Answer: A Type: BI Var: 5 Objective: Expanding Your Skills 2) -∞, 7 ∪ 12, ∞∩10 , 15 A) 10 , 15 B) 10 , ∞ C) -∞, 15 D) 12, 15 Answer: D Type: BI Var: 16 Objective: Expanding Your Skills Page 11 11 Technology Connections Solve the problem. 1) If n > 0, then 9 n - 9n = A) n B) 9n C) 0 D) 1 Answer: C Type: BI Var: 8 Objective: Technology Connections 2) If z > 0, then 5 z + 5z = A) 10 z B) 5z C) 0 D) 1 Answer: A Type: BI Var: 8 Objective: Technology Connections 0.2 Integer Exponents and Scientific Notation 0Concept Connections Provide the missing information. 1) For a nonzero real number b, the value of b0 = . Answer: 1 Type: SA Var: 1 Objective: Concept Connections 2) For a nonzero real number b, the value b□ = 1 bn. Answer: - n Type: SA Var: 1 Objective: Concept Connections 3) A number expressed in the form a × 10 n, where 1 ≤ a < 10 and n is an integer is said to be written in notation. Answer: scientific Type: SA Var: 1 Objective: Concept Connections 4) From the properties of exponents, bmbn = b□. Answer: m + n Type: SA Var: 1 Objective: Concept Connections 5) If b ≠ 0, then bm bn = b□. Answer: m - n Type: SA Var: 1 Objective: Concept Connections Page 12 6) From the properties of exponents, bmn = b□. Answer: m · n Type: SA Var: 1 Objective: Concept Connections 1Simplify Expressions with Zero and Negative Exponen ts Simplify. 1) 19 90 A) 1 B) 19 9C) 0 D) 1 9 Answer: A Type: BI Var: 50+ Objective: Simplify Expressions with Zero and Negative Exponen ts 2) 4-2 A) 1 16 B) 2 C) -16 D) -8 Answer: A Type: BI Var: 14 Objective: Simplify Expressions with Zero and Negative Exponen ts 3) 4 5-3 A) 1 2B) - 12 5C) 125 64 D) - 64 125 Answer: C Type: BI Var: 33 Objective: Simplify Expressions with Zero and Negative Exponen ts 4) 4x - 4 A) 1 256 x 4 B) 1 4x 4 C) 256 x 4 D) 4 x 4 Answer: D Type: BI Var: 27 Objective: Simplify Expressions with Zero and Negative Exponen ts Page 13 5) 6p - 3r 6 q -9 A) 6q 9r 6 p 3 B) 6q 9 p 3r 6 C) 6p 3r 6q 9D) 6p 3r 6 q 9 Answer: A Type: BI Var: 50+ Objective: Simplify Expressions with Zero and Negative Exponen ts 2Apply Properties of Exponents Simplify the expression. Write your answer with positive exponents only. 1) 64 · 67 A) 6-3 B) 611 C) 36 11 D) 628 Answer: B Type: BI Var: 1 Objective: Apply Properties of Exponents 2) 18 12 18 5 A) 18 17 B) 18 7C) 18 12 - 18 5D) 18 12/5 Answer: B Type: BI Var: 19 Objective: Apply Properties of Exponents 3) (x9)4 A) x36 B) x5C) x6,561 D) x13 Answer: A Type: BI Var: 25 Objective: Apply Properties of Exponents 4) z2y3 y-3 z6 A) 1 z4 B) y6 z4 C) z4y3D) 1 z4y6 Answer: B Type: BI Var: 44 Objective: Apply Properties of Exponents 5) (-2 a2b4c4)3 Answer: -8 a6b12 c12 Type: SA Var: 50+ Objective: Apply Properties of Exponents Page 14 6) 2x-4 y4 5x5y-5 -3 Answer: 125 x27 8y27 Type: SA Var: 50+ Objective: Apply Properties of Exponents 7) (t3z) 2(3 t-2 z4)-2 A) z7t 9B) t10 9z6 C) 1 81 t4z20 D) 9z10 t Answer: B Type: BI Var: 1 Objective: Apply Properties of Exponents 8) 1 10 x 2y -5-2 20 x -23 y 12 -1 A) 2 x27 y22 B) x19 5y22 C) 5y 2 x 19 D) x27 2y2 Answer: C Type: BI Var: 50+ Objective: Apply Properties of Exponents 9) (4vw-3x2)2 (2 v3w2x-2)4 · (- v3w2x-4)-3 A) x24 v23 w8 B) - x24 v19 w20 C) x16 v19 w8 D) - 4x16 v23 w20 Answer: B Type: BI Var: 50+ Objective: Apply Properties of Exponents 3Apply Scientific Notation Write the number in scientific notation. 1) 528,000,000 Answer: 5.28 × 10 8 Type: SA Var: 50+ Objective: Apply Scientific Notation 2) 0.00000063 A) 63 × 10 -8 B) 6.3 × 10 -7 C) 0.63 × 10 -6 D) 6.3 × 10 7 Answer: B Type: BI Var: 1 Objective: Apply Scientific Notation Page 15