Patterns and Inductive Reasoning Homework Review

Make a conjecture for the following. Show/explain your work.

8. the sum of the first 100 positive odd numbers.

Make a conjecture for the following. Show/explain your work.

9. the sum of the first 100 positive even numbers.

Make a conjecture for the following. Show/explain your work.

10. the sum of two odd numbers

Make a conjecture for the following. Show/explain your work.

11. the product of two even numbers

Find one counterexample to show that each conjecture is false.

12. ∠A and ∠B are supplementary, so one of the angles is acute.

Find one counterexample to show that each conjecture is false.

13. The sum of two numbers is greater than either number.

Find one counterexample to show that each conjecture is false.

14. The product of two positive numbers is greater than either number

15. Error analysis: For each of the past three years, Jared has grown 2 inches every year. He is now 16 years old and is 5 feet 10 inches tall. He figures that when he is 24 years old he will be 7 feet 2 inches tall. What would you tell Jared about his conjecture?

16. Sue is working out and running a mile each day. She started out running a mile in 10 minutes, but each week for three weeks she has shaved a whole minute off of her time. Make a conjecture for how long it will take her to run a mile after three more weeks.

How do you feel about your conjecture?

Find one counterexample to show that each conjecture is false.

12. ∠A and ∠B are supplementary, so one of the angles is acute.