Question 1: Match each of 1-6 with its appropriate definition from the list A-F below.

- Theorem – An “important” true mathematical statement.
- Tautology – A proposition that is always false.
- Lemma – A theorem that is needed as a stepping stone to prove a greater theorem.
- Axiom – An elementary mathematical truth that is assumed self-evident and not in need of proof.
- Contradiction – A proposition that is always false.
- Corollary – A theorem that is an immediate consequence (and perhaps special case) of another theorem.

Question 2: Write the infinite repeating decimals below as a ratio of two integers. Simplify your answer.

a) .111111111111111111 = 1/9

b) .1313131313131313 = 13/99

c) .123123123123123 = 123/999

Question 3: Before reading the answer choices A – F, write on a piece of paper each definition on your own. Then match 1 – 3 with its appropriate definition from the list A – F below.

- n is odd: n = 2k + 1 for some integer k
- n is rational: n = a/b for some integers a and b, b doesn’t equal 0.
- n is even: n = 2k for some integer k

Select all that are even numbers.

- 5
- -4 : correct answer
- 2.2
- 0 : correct answer
- 4 : correct answer

Select all that are odd numbers.

- 4
- -5 : correct answer
- 0
- 3.3
- 5 : correct answer

Select all that are rational numbers

- square root of 2
- 0 : correct answer
- .123 : correct answer
- 2/3 : correct answer
- pi

Select all that are irrational numbers

- pi : correct answer
- ln(6) : correct answer
- square root of 2 : correct answer
- 2/3
- .123123123