INSTRUCTOR’S SOLUTION MANUAL
A SURVEY OF MATHEMATICS WITH APPLICATIONS
12TH EDITION
CHAPTER NO. 01: CRITICAL THINKING SKILLS
SECTION 1.1: INDUCTIVE AND DEDUCTIVE REASONING
1. Natural 13.
2. Divisible 14.
3. Counterexample
15.
4. Hypothesis
16.
5. Inductive
17. 9, 11, 13 (Add 2 to previous number.)
6. Deductive
18. 16, 19, 22 (Add 3 to the previous number.)
7. Deductive
19. 16, –32, 64 (Multiply previous number by –2.)
8. Inductive
20. -243, 729, -2187 (Multiply by –3.)
9. 5 × 5 = 25
1 1 1
21. , , (Increase denominator value by 1.)
5 6 7
10. 19 × 10 = 190
9 11 13
22. , , (Increase denominator and
10 12 14
11. 1 5
(1+4)
10
(4+6)
10
(4+6)
5
(1+4)
1
numerator values by 2.)
12. 100,000 = 10 5
23. 34, 55, 89 (Each number in the sequence is the sum of the previous two numbers.)
24. 76, 123, 199 (Each number in the sequence is the sum of the previous two numbers.)
25. The product of two odd numbers is an odd number.
26. The product of an even number and an odd number is an even number.
27. The sum of two even numbers is an even number
28. The sum of two odd numbers is an even number.
,29. a) Answers will vary.
b) Products involving 10 and natural numbers will have a ones digit 0.
30. a) Answers will vary.
b) The sum of the digits is 9.
c) The sum of the digits in the product when a one- or two-digit number is multiplied by 9 is divisible by 9.
31. a) 36, 49, 64
b) Square the numbers 6, 7, 8, 9 and 10.
c) 8 × 8 = 64, 9 × 9 = 81; 72 is not a square number since it falls between the two square numbers 64 and
81.
32. a) 28 and 36
b) To find the 7th triangular number, add 7 to the 6th triangular number.
To find the 8th triangular number, add 8 to the 7th triangular number.
To find the 9th triangular number, add 9 to the 8th triangular number.
To find the 10th triangular number, add 10 to the 9th triangular number.
To find the 11th triangular number, add 11 to the 10th triangular number.
c) 36 + 9 = 45, 45 + 10 = 55, 55 + 11 = 66; 66 + 12 = 78; 72 is not a triangular number since it falls
between the consecutive triangular numbers 66 and 78.
33. Blue: 1, 5, 7, 10, 12; Purple: 2, 4, 6, 9, 11; Yellow: 3, 8
34. a) 19 (Each new row has two additional triangles.)
b) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100
35. a) $3700
b) We are using observation of specific cases to make a prediction.
36. a) $415
b) We are using observation of specific cases to make a prediction.
,37. a) You should obtain the original number.
b) You should obtain the original number.
c) Conjecture: The result is always the original number.
38. a) You should obtain twice the original number.
b) You should obtain twice the original number.
c) Conjecture: The result is always twice the original number.
39. a) You should obtain the number 5.
b) You should obtain the number 5.
c) Conjecture: The result is always the number 5.
40. a) You should obtain the number 8.
b) You should obtain the number 8.
c) Conjecture: The result is always the number 8.
3𝑛𝑛+6 3𝑛𝑛 6
41. 𝑛𝑛 → 3𝑛𝑛 → 3𝑛𝑛 + 6 → = + = 𝑛𝑛 + 2 → 𝑛𝑛 + 2 − 2 = 𝑛𝑛
3 3 3
4𝑛𝑛+6 4𝑛𝑛 6
42. 𝑛𝑛 → 4𝑛𝑛 → 4𝑛𝑛 + 6 → = + = 2𝑛𝑛 + 3 → 2𝑛𝑛 + 3 − 3 = 2𝑛𝑛
2 2 2
2𝑛𝑛+10 2𝑛𝑛 10
43. 𝑛𝑛 → 𝑛𝑛 + 1 → 𝑛𝑛 + (𝑛𝑛 + 1) = 2𝑛𝑛 + 1 → 2𝑛𝑛 + 1 + 9 = 2𝑛𝑛 + 10 → = + = 𝑛𝑛 + 5 → 𝑛𝑛 + 5 − 𝑛𝑛 =
2 2 2
5
2𝑛𝑛+16 2𝑛𝑛 16
44. 𝑛𝑛 → 𝑛𝑛 + 5 → 𝑛𝑛 + (𝑛𝑛 + 5) = 2𝑛𝑛 + 5 → 2𝑛𝑛 + 5 + 11 = 2𝑛𝑛 + 16 → = + = 𝑛𝑛 + 8 → 𝑛𝑛 + 8 −
2 2 2
𝑛𝑛 = 8
45. 3 × 5 = 15 is a counterexample.
46. 10 + 11 + 12 = 33, which is not a three-digit number.
5
47. Two is a counting number. The sum of 2 and 3 is 5. Five divided by two is , which is not an even number.
2
48. 900 is a three-digit number. The product of 900 and 900 is 810,000, which is not a five-digit number.
49. One and two are counting numbers. The difference of 1 and 2 is 1 − 2 = −1, which is not a counting number.
, 50. The sum of the odd numbers 1 and 5 is 6, which is not divisible by 4.
51. a) The sum of the measures of the interior angles should be 180°.
b) Yes, the sum of the measures of the interior angles should be 180°.
c) Conjecture: The sum of the measures of the interior angles of a triangle is 180°.
52. a) The sum of the measures of the interior angles should be 360°.
b) Yes, the sum of the measures of the interior angles should be 360°.
c) Conjecture: The sum of the measures of the interior angles of a quadrilateral is 360°.
53. Inductive reasoning: a general conclusion is obtained from observation of specific cases.
54. Inductive reasoning: a general conclusion is obtained from observation of specific cases.
55. 129; The numbers in the positions of each inner 4 × 4 square is determined as follows.
𝑎𝑎 𝑏𝑏
𝑐𝑐 𝑎𝑎 + 𝑏𝑏 + 𝑐𝑐
56. 1881, 8008, 8118 (They look the same when looked at in a mirror.)
57. c
SECTION 1.2: ESTIMATION TECHNIQUES
Answers in this section will vary depending on how you round your numbers. The answers may differ from the
answers in the back of the textbook. However, your answers should be something near the answers given. All
answers are approximate.)
1. Estimation 5. 197,500 ÷ 4.063 ≈ 200,000 ÷ 4.000 =
50,000
2. Equal
1,032,645 1,000,000
3. 39.7 + 60.3 + 18 + 1.8 6. ≈ = 20
49,827 50,000
≈ 40 + 60 + 20 + 0 = 120
7. 1776 × 0.0098 ≈ 1800 × 0.01 = 18
4. 86 + 47.2 + 289.8 + 532.4 + 12.8
8. 0.63 × 1523 ≈ 0.6 × 1500 = 900
≈ 90 + 50 + 290 + 530 + 10 = 970
A SURVEY OF MATHEMATICS WITH APPLICATIONS
12TH EDITION
CHAPTER NO. 01: CRITICAL THINKING SKILLS
SECTION 1.1: INDUCTIVE AND DEDUCTIVE REASONING
1. Natural 13.
2. Divisible 14.
3. Counterexample
15.
4. Hypothesis
16.
5. Inductive
17. 9, 11, 13 (Add 2 to previous number.)
6. Deductive
18. 16, 19, 22 (Add 3 to the previous number.)
7. Deductive
19. 16, –32, 64 (Multiply previous number by –2.)
8. Inductive
20. -243, 729, -2187 (Multiply by –3.)
9. 5 × 5 = 25
1 1 1
21. , , (Increase denominator value by 1.)
5 6 7
10. 19 × 10 = 190
9 11 13
22. , , (Increase denominator and
10 12 14
11. 1 5
(1+4)
10
(4+6)
10
(4+6)
5
(1+4)
1
numerator values by 2.)
12. 100,000 = 10 5
23. 34, 55, 89 (Each number in the sequence is the sum of the previous two numbers.)
24. 76, 123, 199 (Each number in the sequence is the sum of the previous two numbers.)
25. The product of two odd numbers is an odd number.
26. The product of an even number and an odd number is an even number.
27. The sum of two even numbers is an even number
28. The sum of two odd numbers is an even number.
,29. a) Answers will vary.
b) Products involving 10 and natural numbers will have a ones digit 0.
30. a) Answers will vary.
b) The sum of the digits is 9.
c) The sum of the digits in the product when a one- or two-digit number is multiplied by 9 is divisible by 9.
31. a) 36, 49, 64
b) Square the numbers 6, 7, 8, 9 and 10.
c) 8 × 8 = 64, 9 × 9 = 81; 72 is not a square number since it falls between the two square numbers 64 and
81.
32. a) 28 and 36
b) To find the 7th triangular number, add 7 to the 6th triangular number.
To find the 8th triangular number, add 8 to the 7th triangular number.
To find the 9th triangular number, add 9 to the 8th triangular number.
To find the 10th triangular number, add 10 to the 9th triangular number.
To find the 11th triangular number, add 11 to the 10th triangular number.
c) 36 + 9 = 45, 45 + 10 = 55, 55 + 11 = 66; 66 + 12 = 78; 72 is not a triangular number since it falls
between the consecutive triangular numbers 66 and 78.
33. Blue: 1, 5, 7, 10, 12; Purple: 2, 4, 6, 9, 11; Yellow: 3, 8
34. a) 19 (Each new row has two additional triangles.)
b) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100
35. a) $3700
b) We are using observation of specific cases to make a prediction.
36. a) $415
b) We are using observation of specific cases to make a prediction.
,37. a) You should obtain the original number.
b) You should obtain the original number.
c) Conjecture: The result is always the original number.
38. a) You should obtain twice the original number.
b) You should obtain twice the original number.
c) Conjecture: The result is always twice the original number.
39. a) You should obtain the number 5.
b) You should obtain the number 5.
c) Conjecture: The result is always the number 5.
40. a) You should obtain the number 8.
b) You should obtain the number 8.
c) Conjecture: The result is always the number 8.
3𝑛𝑛+6 3𝑛𝑛 6
41. 𝑛𝑛 → 3𝑛𝑛 → 3𝑛𝑛 + 6 → = + = 𝑛𝑛 + 2 → 𝑛𝑛 + 2 − 2 = 𝑛𝑛
3 3 3
4𝑛𝑛+6 4𝑛𝑛 6
42. 𝑛𝑛 → 4𝑛𝑛 → 4𝑛𝑛 + 6 → = + = 2𝑛𝑛 + 3 → 2𝑛𝑛 + 3 − 3 = 2𝑛𝑛
2 2 2
2𝑛𝑛+10 2𝑛𝑛 10
43. 𝑛𝑛 → 𝑛𝑛 + 1 → 𝑛𝑛 + (𝑛𝑛 + 1) = 2𝑛𝑛 + 1 → 2𝑛𝑛 + 1 + 9 = 2𝑛𝑛 + 10 → = + = 𝑛𝑛 + 5 → 𝑛𝑛 + 5 − 𝑛𝑛 =
2 2 2
5
2𝑛𝑛+16 2𝑛𝑛 16
44. 𝑛𝑛 → 𝑛𝑛 + 5 → 𝑛𝑛 + (𝑛𝑛 + 5) = 2𝑛𝑛 + 5 → 2𝑛𝑛 + 5 + 11 = 2𝑛𝑛 + 16 → = + = 𝑛𝑛 + 8 → 𝑛𝑛 + 8 −
2 2 2
𝑛𝑛 = 8
45. 3 × 5 = 15 is a counterexample.
46. 10 + 11 + 12 = 33, which is not a three-digit number.
5
47. Two is a counting number. The sum of 2 and 3 is 5. Five divided by two is , which is not an even number.
2
48. 900 is a three-digit number. The product of 900 and 900 is 810,000, which is not a five-digit number.
49. One and two are counting numbers. The difference of 1 and 2 is 1 − 2 = −1, which is not a counting number.
, 50. The sum of the odd numbers 1 and 5 is 6, which is not divisible by 4.
51. a) The sum of the measures of the interior angles should be 180°.
b) Yes, the sum of the measures of the interior angles should be 180°.
c) Conjecture: The sum of the measures of the interior angles of a triangle is 180°.
52. a) The sum of the measures of the interior angles should be 360°.
b) Yes, the sum of the measures of the interior angles should be 360°.
c) Conjecture: The sum of the measures of the interior angles of a quadrilateral is 360°.
53. Inductive reasoning: a general conclusion is obtained from observation of specific cases.
54. Inductive reasoning: a general conclusion is obtained from observation of specific cases.
55. 129; The numbers in the positions of each inner 4 × 4 square is determined as follows.
𝑎𝑎 𝑏𝑏
𝑐𝑐 𝑎𝑎 + 𝑏𝑏 + 𝑐𝑐
56. 1881, 8008, 8118 (They look the same when looked at in a mirror.)
57. c
SECTION 1.2: ESTIMATION TECHNIQUES
Answers in this section will vary depending on how you round your numbers. The answers may differ from the
answers in the back of the textbook. However, your answers should be something near the answers given. All
answers are approximate.)
1. Estimation 5. 197,500 ÷ 4.063 ≈ 200,000 ÷ 4.000 =
50,000
2. Equal
1,032,645 1,000,000
3. 39.7 + 60.3 + 18 + 1.8 6. ≈ = 20
49,827 50,000
≈ 40 + 60 + 20 + 0 = 120
7. 1776 × 0.0098 ≈ 1800 × 0.01 = 18
4. 86 + 47.2 + 289.8 + 532.4 + 12.8
8. 0.63 × 1523 ≈ 0.6 × 1500 = 900
≈ 90 + 50 + 290 + 530 + 10 = 970
