# FTCE Middle Grades Math: Mathematical Reasoning Chapter Exam

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

####
Question 1
1.
If Jimmy does his chores, then Jimmy will get a big scoop of chocolate ice cream.

Which of the following represents the conclusion in the above conditional statement?

#### Question 2 2. Which of the following is a conditional statement?

#### Question 3 3. Which of the following is a conditional statement whose hypothesis is 'Joe has a red car' and whose conclusion is 'Billy gets to drive it'?

#### Question 4 4. Which of the following statements are true?

#### Question 5 5. If we wanted to use an indirect proof to prove that the integer 77 is odd, what would our initial assumption be?

### Page 2

#### Question 6 6. Which of the following statements are true?

#### Question 7 7. If you start with what you know about a specific scenario and generalize that information to a whole population, what type of reasoning are you using?

#### Question 8 8. Tony went swimming at a nearby lake one summer day. There were very few other swimmers there. Later, he told his friend that he had found a great new lake for swimming. He explained that it was great because no one else ever went there. What type of reasoning was Tony using?

#### Question 9 9. Using a known formula to calculate a solution to an algebra equation is an example of which type of reasoning?

####
Question 10
10.
The statement *A pet can be a quiet companion or a playmate (or both)* is an example of which logic connective.

### Page 3

#### Question 11 11. Which logic connective has a symbol that looks like an upside down V (or a tepee that traps things inside)?

#### Question 12 12. Which of the following is NOT one of the five main logic connectives?

####
Question 13
13.
Which is a correct logical disjunction formed with the following phrases?

Algebra is easy.

Geometry is a breeze.

#### Question 14 14. Which of the following connectors is the logical disjunction?

#### Question 15 15. Which of the following connectors is the logical conjunction?

### Page 4

####
Question 16
16.
Which of these is the logical contrapositive to the following statement?

*If killing in any sense is wrong, then murder is wrong.*

*If killing in any sense is wrong, then murder is wrong.*

#### Question 17 17. The converse of a logical statement is found by doing what?

####
Question 18
18.
In the following statement, which part is the hypothesis?

*If all mammals are animals, then dogs are animals.*

*If all mammals are animals, then dogs are animals.*

#### Question 19 19. What does the statement, 'We will go get ice cream if and only if you clean your room' mean?

#### Question 20 20. What is the negation of 'Triangles are not squares'?

### Page 5

####
Question 21
21.
p: The dog rolls over on command.

q: The dog gets a treat.

For the combination p AND q, for which truth values of p and q is the combination true?

#### Question 22 22. If x = 1 and y = 2, what can be said about z if z = xy?

####
Question 23
23.
If the following two propositions are true, which is a true statement?

Theresa loves dogs.

Spot is a dog.

####
Question 24
24.
If a = c and b = c, what kinds of new statements can you make?

A: If a = c and b = c, then a = b.

B: If a = 1, then b = 1.

C: If b = 2, then a = 1.

#### Question 25 25. A statement can be determined to be which of the following through a direct proof?

### Page 6

#### Question 26 26. What is the conclusion in the following statement? 'If p and q are odd integers, then pq is odd.'

#### Question 27 27. What is the hypothesis in the following statement? 'If p is an even integer and q is an odd integer, then p + q is an odd integer.'

####
Question 28
28.
If he eats a hamburger, then he will eat two bags of fries.

Which of the following represents the hypothesis in the above conditional statement?

####
Question 29
29.
If we were proving that a given line, call it *L*, is perpendicular to another line, call it *J*, using indirect proof, what would our initial assumption be?

#### Question 30 30. Most advanced mathematical proofs use which type of reasoning?

#### FTCE Middle Grades Math: Mathematical Reasoning Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!