Chapter 1

Question 1

Define equation.

Answer 1

Mathematical statement only true for some values of x.

Question 2

Define identity.

Answer 2

Mathematical statement true for all values of x.

Question 3

Give an example of congruent expressions.

Answer 3

x^2+9 ≡ (x+3)(x-3)

Question 4

Define polynomial.

Answer 4

Sum of terms with non-negative integer powers of x.

Question 5

Define coefficient.

Answer 5

Constant in front of variable.

Question 6

Define integer.

Answer 6

Whole number.

Question 7

Define function.

Answer 7

Rule for changing an input into an output.

Question 8

⇒

Answer 8

x implies y

Question 9

<–

Answer 9

y implies x

Question 10

⇔

Answer 10

x is true if and only if y is true.

Question 11

∴

Answer 11

Therefore

Question 12

Write a<x<b and other variants in set notation.

Question 13

Write a<b and a<x<b in interval notation.

Question 14

How does disproof by counter example work?

Answer 14

Find an example to disproof something.

Question 15

Write an odd and an even number for some integer n.

Answer 15

2n+1
2n

Question 16

What do these symbols mean?

N.
Z.
Q.
R.
Irrational.

Answer 16

Natural numbers (pos whole).
Integers (whole and 0).
Rational numbers.
Real numbers.
Irrational numbers.

Question 17

Prove that 89 is prime and a whole number squared and divided by 3 will only have a remainder of 0 or 1.

Answer 17

Notebook.

Question 18

What is proof by exhaustion?

Answer 18

Checking all possibilities.