2 Mid-Chapter Quiz

Do you know HOW?

Use inductive reasoning to describe the pattern of each sequence. Then find the next two terms.

1. 1, 12, 123, 1234,…
2. 3, 4.5, 6.75, 10.125,…
3. 2, 3, 5, 7, 11, 13,…

Draw the next figure in each sequence.

Find a counterexample for the conjecture.

6. Three coplanar lines always make a triangle.
7. All balls are spheres.
8. When it rains, it pours.

Identify the hypothesis and the conclusion of the conditional statements.

9. If the traffic light is red, then you must stop.
10. If x > 5 , x greater than , 5 comma  then x 2 > 25 . x squared , greater than 25 .
11. If you leave your house, then you must lock the door.

Rewrite the statements as conditional statements.

12. Roses are beautiful flowers.
13. Apples grow on trees.
14. Quadrilaterals have four sides.
15. The world's largest trees are giant sequoias.

For Exercises 16–19, write the converse, inverse, and contrapositive of each conditional statement. Determine the truth value of each statement. If it is false, provide a counterexample.

16. If a figure is a circle with radius r, then its circumference is 2 π r . 2 pi r .
17. If an integer ends with 0, then it is divisible by 2.
18. If you win the league championship game, then you win the league trophy.
19. If a triangle has one right angle, then the other two angles are complementary.
20. Write the two conditionals that make up this biconditional: An angle is an acute angle if and only if its measure is between 0 and 90.

For Exercises 21–23, rewrite the definition as a biconditional.

21. Points that lie on the same line are collinear.
22. Figures with three sides are triangles.
23. The moon is the largest satellite of Earth.
24. Which of the following is a good definition?
    1. Grass is green.
    2. Dinosaurs are extinct.
    3. A pound weighs less than a kilogram.
    4. A yard is a unit of measure exactly 3 ft long.

Do you UNDERSTAND?

25. Open-Ended Describe a situation where you used a pattern to reach a conjecture.
26. How does the word induce relate to the term inductive reasoning?

27. Error Analysis Why is the following not a good definition? How could you improve it?

    Rain is water.

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