Theory Concepts

Question 1

The two main operations in mathematics are ____ and ____.

Answer 1

addition; multiplication

Question 2

When solving equations with rational components, double-check your answer in the original equation to check for ____.

Answer 2

extraneous solutions

Question 3

A bunch of things added are called ____.

Answer 3

terms

Question 4

A bunch of things multiplied are called ____.

Answer 4

factors

Question 5

In layman’s terms, the identity is what you do under a given operation to get ____.

Answer 5

yourself

Question 6

The additive identity is always ____.

Answer 6

0

Question 7

The multiplicative identity is always ____.

Answer 7

1

Question 8

Math is about “doing” and “undoing.” The mathematical word for the process of “undoing” is ____.

Answer 8

inverse

Question 9

In layman’s terms, the inverse is what you do under a given operation to get ____.

Answer 9

the identity

Question 10

Given the number 8, state its additive identity ____ and additive inverse ____

Answer 10

0; -8

Question 11

Given the number 8, state its multiplicative identity ____ and multiplicative inverse ____.

Answer 11

1; 1/8

Question 12

The identity for every function is the line: ____

Answer 12

y = x

Question 13

The graphs of a function and its inverse are ____ of each other over the line y = x.

Answer 13

mirror images

Question 14

We ____ expressions (no math verb), but we ____ equations (math verb).

Answer 14

simplify; solve

Question 15

The “mathematical” process for turning TERMS into FACTORS is called: ____

Answer 15

factoring

Question 16

Speaking of factoring, the difference of two squares factors into ____

Answer 16

conjugates

Question 17

Speaking of factoring, the sum of two squares factors into ____

Answer 17

prime

Question 18

Speaking of factoring, the sum of cubes A^3 + B^3 factors into ____

Answer 18

(A + B)(A^2 - AB + B^2)

Question 19

Speaking of factoring, the difference of cubes A^3 - B^3 factors into ____

Answer 19

(A - B)(A^2 + AB + B^2)

Question 20

Speaking of factoring, a perfect square trinomial factors into ____

Answer 20

a binomial squared

Question 21

Given the words “fish” and “frog”, form a PST: ____

Answer 21

fish^2 - 2fish * frog + frog^2

Question 22

Conjugates multiply to be ____

Answer 22

the difference of squares

Question 23

A binomial squared multiplies to be ____

Answer 23

a perfect square trinomial (PST)

Question 24

Finish this statement [formal definition]. A number is rational if it can be written as the ____ of two integers where the denominator ____

Answer 24

ratio; is not zero

Question 25

When solving an equation, if a true statement is generated at the last step, then the solution is ____.

Answer 25

all real numbers

Question 26

When solving an equation, if a false statement is generated at the last step, then the solution is ____.

Answer 26

no solution