CHAPTER 1 Review Exercises 35 Important Facts and Concepts Examples and Discussion Section 1.1 The natural numbers or counting numbers are 1, 2, 3, 4, . . . . A conjecture is a prediction based on specific observations. A counterexample is a special case that satisfies all the conditions of a conjecture but proves the conjecture false. Inductive reasoning is the process of reasoning to a general conclusion through observations of specific cases. Deductive reasoning is the process of reasoning to a specific conclusion from a general statement. Examples 1, 2, 4, 5, pages 2–5 Example 4, page 4 Discussion page 5 Examples 1– 4, pages 2– 4 Example 5, page 5 Section 1.2 Estimation is the process of arriving at an approximate answer to a question. Examples 1–7, pages 10 –14 Section 1.3 Guidelines for Problem Solving 1. Understand the problem. 2. Devise a plan to solve the problem. 3. Carry out the plan. 4. Check the results. Discussion page 22 Examples 1–7, pages 21–28 Summary CHAPTER 1 1.1 In Exercises 1–8, use inductive reasoning to predict the next three numbers or figures in the pattern. 1. 3, 8, 13, 18, … 23, 28, 33 2. 28, 25, 22, 19, … 16, 13, 10 3. 4, 8, 16, 32, − − … 64, 128, 256 − 4. 5, 7, 10, 14, 19, … 25, 32, 40 5. 25, 24, 22, 19, 15, … 10, 4, 3− 6. 6, 3, , , 3 2 3 4 … 3 8 , 3 16 , 3 32 7. , , , , . . . * 8. , , , , , . . . * Review Exercises CHAPTER 1 9. Pattern Examine the following grid for a pattern and then select the answer which completes the pattern. (Hint: Think about rotating groups of four squares at a time.) a) b) c) d) (c) *See Instructor Answer Appendix
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