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

1. Theorem – An “important” true mathematical statement.
2. Tautology – A proposition that is always false.
3. Lemma – A theorem that is needed as a stepping stone to prove a greater theorem.
4. Axiom – An elementary mathematical truth that is assumed self-evident and not in need of proof.
5. Contradiction – A proposition that is always false.
6. 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.

1. n is odd: n = 2k + 1 for some integer k
2. n is rational: n = a/b for some integers a and b, b doesn’t equal 0.
3. 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