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# FTCE Middle Grades Math: Mathematical Reasoning Chapter Exam

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### Page 1

#### Question 1 1. Triangles have 180 degrees in total, and squares are two triangles put together. What can you say about the total degrees of a square?

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

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Question 3
3.
If the following two propositions are true, which is a true statement?

Theresa loves dogs.

Spot is a dog.

#### Question 4 4. Which is the correct definition of a disjunction?

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Question 5
5.
Which is a correct logical conjunction formed with the following phrases?

Drew likes roses.

Drew loves lilies.

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#### Question 6 6. Which is the correct definition of a conjunction?

#### Question 7 7. A statement can be determined to be which of the following through a direct proof?

#### Question 8 8. 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 9 9. Which of the following occurs with a direct proof?

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

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#### Question 11 11. What single word best describes Negation logic?

#### Question 12 12. Which logic connective has a symbol that looks like an upside down V (or a tepee that traps things inside)?

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Question 13
13.
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 14 14. 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 15 15. Which of the following is a conditional statement?

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Question 16
16.
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 17 17. Which of the following statements are true?

#### Question 18 18. If we wanted to use an indirect proof to prove that the integer 77 is odd, what would our initial assumption be?

#### 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'?

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Question 21
21.
p: The pond is not frozen over.

q: The fish are not jumping.

For the combination p AND (NOT q), for which truth values of p and q is the combination true?

#### Question 22 22. The converse of a logical statement is found by doing what?

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Question 23
23.
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 24 24. Which of these is always logically equivalent to the inverse?

#### Question 25 25. 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?

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#### Question 26 26. If you are starting with what you know about a large population and coming to a conclusion about a specific scenario, then which type of reasoning are you using?

#### Question 27 27. 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?

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Question 28
28.
Which of the following is a logic proposition?

A: Sam only eats square foods

B: Once upon a time

C: Circles roll

####
Question 29
29.
Which is a correct logical disjunction formed with the following phrases?

Algebra is easy.

Geometry is a breeze.

#### Question 30 30. All of the following statements could be proven with a direct proof EXCEPT:

#### 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!