Blitzer, Thinking Mathematically, 8e Chapter 1 Test Item File SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find a counterexample to show that the statement is false. 1) No women have sat on the bench of the U.S. Supreme Court. Objective: (1.1) Understand and Use Inductive Reasoning
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 2) If a number is multiplied by itself, the result is greater than 0. A) The number is 0.
B) The number is 0.1.
C) The number is 1.
D) The number is
Objective: (1.1) Understand and Use Inductive Reasoning
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) All U.S. presidents have been one-term presidents. Objective: (1.1) Understand and Use Inductive Reasoning
4) All actors are Academy Award winners. Objective: (1.1) Understand and Use Inductive Reasoning
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify a pattern in the list of numbers. Then use this pattern to find the next number. 5) 2, 9, 16, 23, 30, ___ A) 37 B) 32 C) 44
D) 36
Objective: (1.1) Understand and Use Inductive Reasoning
6) 1, 12, 1, 18, 1, 24, 1, _____ A) 36
B) 30
C) 1
D) 32
C) 0
D) 2
C) -3,375
D) 3,375
C) -1/32
D) -1/64
Objective: (1.1) Understand and Use Inductive Reasoning
7) 31, 26, 21, 16, 11 A) 6
B) 5
Objective: (1.1) Understand and Use Inductive Reasoning
8) 3, -15, 75, -375, 1,875 A) 9,375
B) -9,375
Objective: (1.1) Understand and Use Inductive Reasoning
9) 1, -
1 1 1 1 , ,- , 8 16 2 4
A) 1/32
B) 1/64
Objective: (1.1) Understand and Use Inductive Reasoning
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1 . 2
10) 1, 5, 2, 10, 4, 20 A) 30
B) 8
C) 6
D) 40
Objective: (1.1) Understand and Use Inductive Reasoning
Identify a pattern in the sequence of figures. Then use the pattern to find the next figure in the sequence. 11)
A)
________________ C)
B)
Objective: (1.1) Understand and Use Inductive Reasoning
12)
A)
B)
C)
D)
Objective: (1.1) Understand and Use Inductive Reasoning
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D)
The problem describes procedures that are to be applied to numbers. Repeat the procedure for four numbers of your choice. Write a conjecture that relates the result of the process to the original number selected. 13) Select a number. Multiply the number by 16. Add 16 to the product. Divide this sum by 8. Subtract 2 from the quotient. A) The result is one more than the original number. B) The result is one more than double the original number. C) The result is double the original number. D) The result is the original number. Objective: (1.1) Understand and Use Inductive Reasoning
Use inductive reasoning to predict the next line in the pattern. Then perform the arithmetic to determine whether your conjecture is correct. 14) 60 - 9 = 51 600 - 89 = 511 6,000 - 789 = 5,211
A) 60,000 - 6,789 = 593,211 C) 60,000 - 6,789 = 53,211
B) 6,000 - 6,789 = 53,211 D) 600,000 - 6,789 = 53,211
Objective: (1.1) Understand and Use Inductive Reasoning
15) 96 - 94 + 92 - 90 = 97 - 95 + 93 - 91 106 - 104 + 102 - 100 = 107 - 105 + 103 - 101 A) 116 + 114 - 112 - 110 = 117 + 115 - 113 + 111 C) 116 - 114 - 112 + 110 = 117 - 115 + 113 - 111
B) 116 + 114 - 112 + 110 = 117 + 115 - 113 + 111 D) 116 - 114 + 112 - 110 = 117 - 115 + 113 - 111
Objective: (1.1) Understand and Use Inductive Reasoning
16) 2 x 4 = 3 × 5 - 7 4 x 6 = 5 × 7 - 11 A) 6 × 8 = 7 × 9 + 13
B) 6 × 8 = 7 × 9 - 13
C) 6 × 8 = 7 × 9 - 15
D) 6 × 8 = 9 × 11 - 15
Objective: (1.1) Understand and Use Inductive Reasoning
17) 3 × 3 = 9 33 × 33 = 1,089 333 × 333 = 110,889 A) 3,333 × 3,333 = 112,889 C) 3,333 × 3,333 = 111,889
B) 3,333 × 3,333 = 11,108,889 D) 333 × 3,333 = 11,108,889
Objective: (1.1) Understand and Use Inductive Reasoning
18) 20 × 21 = 22 × 23 - (20 + 21 + 22 + 23) 21 × 22 = 23 × 24 - (21 + 22 + 23 + 24) A) 23 × 24 = 25 × 26 - (23 + 24 + 25 + 26) C) 23 × 24 = 25 × 26 - (22 + 21 + 20 + 19)
B) 22 × 23 = 24 × 25 - (20 + 21 + 22 + 23 + 24 + 25) D) 22 × 23 = 24 × 25 - (22 + 23 + 24 + 25)
Objective: (1.1) Understand and Use Inductive Reasoning
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19) (1 × 9) - 9 = 0 (21 × 9) - 9 = 180 (321 × 9) - 9 = 2,880 A) (4321 × 9) - 9 = 3,879 C) (4321 × 9) - 9 = 28,880
B) (4321 × 9) - 9 = 38,880 D) (432 × 9) - 9 = 38,880
Objective: (1.1) Understand and Use Inductive Reasoning
20) (4 × 1) × (2 × 1) = 8 (4 × 10) × (2 × 2) = 160 (4 × 100) × (2 × 3) = 2,400 A) (4 × 1000) × (2 × 4) = 36,000 C) (4 × 1000) × (2 × 4) = 32,000
B) (4 × 1000) × (2 × 4) = 28,000 D) (4 × 1000) × (2 × 4) = 3,200
Objective: (1.1) Understand and Use Inductive Reasoning
21) 37,037 × 3 = 111,111 37,037 × 6 = 222,222 37,037 × 9 = 333,333 37,037 × 12 = 444,444 A) 111,111 × 15 = 1,666,665 C) 37,037 × 18 = 666,666
B) 37,037 × 13 = 481,481 D) 37,037 × 15 = 555,555
Objective: (1.1) Understand and Use Inductive Reasoning
1 1 1 = 13 2 3
22)
1 1 1 1 + = 13 9 2 9 1 1 1 1 1 = 1+ + 27 3 9 27 2 1 1 1 1 1 1 = 1+ + + 81 3 9 27 81 2
A)
1 1 1 1 1 1 1 = 1+ + + + 729 3 9 27 81 729 2
B)
1 1 1 1 1 1 1 = 1+ + + + 243 3 9 27 81 243 3
C)
1 1 1 1 1 1 1 + + + + = 1243 3 9 27 81 243 2
D)
1 1 1 1 1 1 1 + + + + = 1162 3 9 27 81 162 2
Objective: (1.1) Understand and Use Inductive Reasoning
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23)
8(5) = 10(5 - 1) 8(5) + 8(25) = 10(25 - 1) 8(5) + 8(25) + 8(125) = 10(125 - 1) 8(5) + 8(25) + 8(125) + 8(625) = 10(625 - 1)
A) 8(5) + 8(25) + 8(125) + 8(625) + 8(3125) = 8(3125 - 1) B) 8(5) + 8(25) + 8(125) + 8(625) + 8(1250) = 10(1250 - 1) C) 8(5) + 8(25) + 8(125) + 8(625) + 8(5000) = 10(5000 - 1) D) 8(5) + 8(25) + 8(125) + 8(625) + 8(3125) = 10(3125 - 1) Objective: (1.1) Understand and Use Inductive Reasoning
The following table relates an adult's body weight, in pounds, to his or her dosage of a certain medication, in milligrams. 24) Weight 100 125 150 175 200 225 Dosage 20 25 30 a. Use inductive reasoning to fill in the missing portions of the table. b. What would be the dosage of a person who weighs 375 pounds?
A) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 95 115
B) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 39 40
b. 80 mg
b. 70 mg
C) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 35 35
D) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 40 45
b. 65 mg
b. 75 mg
Objective: (1.1) Understand and Use Inductive Reasoning
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem using inductive reasoning. 25) Write the next three "square" figurate numbers.
Objective: (1.1) Understand and Use Inductive Reasoning
26) Write the next three "triangular" figurate numbers.
Objective: (1.1) Understand and Use Inductive Reasoning
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which reasoning process is shown in the following example? 27) We examine the genetic blueprints of 100 people. No two individuals from this group of people have identical genetic blueprints. We conclude that for all people, no two people have identical genetic blueprints. A) reasoning by counterexample B) deductive reasoning C) theoretical reasoning D) inductive reasoning Objective: (1.1) Understand and Use Deductive Reasoning
28) If Mary goes to the mall, she gets ice cream. Mary did not get ice cream. We conclude Mary did not go to the mall. A) inductive reasoning B) reasoning by counterexample C) theoretical reasoning D) deductive reasoning Objective: (1.1) Understand and Use Deductive Reasoning
The problem describes procedures that are to be applied to numbers. Represent the original number as n and use deductive reasoning to prove a conjecture that relates the result of the process to the number n. 29) Select a number. Multiply the number by 24. Add 24 to the product. Divide this sum by 12. Subtract two from the quotient. 24n + 24 24n + 24 - 2 = 2n + 2 - 2 = 2n -2=n+1-2=n-1 A) B) 12 24
C)
24n + 24 -1=n+1-1=n 24
D)
24n + 12 - 2 = 2n + 1 - 2 = 2n - 1 12
Objective: (1.1) Understand and Use Deductive Reasoning
Solve the problem. 30) Study the pattern, or trend, shown by the data. Then select the expression that best describes the number of tickets sold, in thousands, n years after Year 1.
A) 2.5 - 0.2n
B) 2.5 - 1.02n
C) 2.5 + 0.2n
D) 2.5 + 1.02n
Objective: (1.1) Understand and Use Deductive Reasoning
Round the number to the given place value. 31) In the past year, a company spent $693,749,312 on advertising. Round the advertising figure to the nearest hundred thousand. A) $693,800,000 B) $700,000,000 C) $693,700,000 D) $600,000,000 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
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