2.1.1 Using Inductive Reasoning to Make Conjectures − Worksheet

Example 1: Find the next item in each pattern. 1. March, May, July, ... 2.

1 3

2 4

3 5

3.

,

,

,

,

,

, …

Example 2: Complete each conjecture. 4. The product of two even numbers is ? .

5. A rule in terms of n for the sum of the first n odd positive integers is ? .

Example 3: 6. A laboratory culture contains 150 bacteria. After twenty minutes, the culture contains 300 bacteria. After one hour, the culture contains 1200 bacteria. Make a conjecture about the rate at which the bacteria increases.

Example 4: Show that each conjecture is false by finding a counterexample. 7. President

Age at Inauguration

Washington T. Roosevelt Truman Kennedy Clinton

57 42 60 43 46

Kennedy is the youngest U.S. president to be inaugurated.

8. Three points on a plane always form a triangle.

9. For any real number x , if x 2 ≥ 1, then x ≥ 1.

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