Introduction to Algebra

Question 1

Define:

Variable

Answer 1

A letter or symbol that represents a value that can change like time, temperature, or age.

Question 2

Define:

Constant

Answer 2

A value that cannot change.

Question 3

Define:

Numerical expression

Answer 3

May contain ONLY constants and operations.

Question 4

Define:

Algebraic expression

Answer 4

May contain variables, constants, and operations.

Question 5

Define:

Absolute value

Answer 5

The distance from a number to zero on a number line.

Find the absolute value of the following:
* |-31|
* |7|
* |-47|
* |12|

Question 6

Define:

Opposite / Additive inverses

Answer 6

The numbers are opposite if their sum is zero

Question 7

Define:

Undefined

Answer 7

Any number divided by zero is undefined.

Question 8

Define:

Reciprocals / Multiplicative Inverses

Answer 8

Two numbers are reciprocals if their product is 1. These two numbers are also called multiplicative inverses.

Question 9

Define:

Power

Answer 9

An expression of an exponent.

An exponent is a repeated multiplcation. Power refers to how many times a number is multiplied by itself.

Question 10

Define:

Square root

Answer 10

A number that is multiplied by itself to form a product.

Question 11

Define:

Perfect square

Answer 11

A number whose positive square root is a whole number.

(example: 1, 4, 9, 16, and 25)

Question 12

Define:

Real numbers

Answer 12

All numbers that can be represented on a number line.

Contains natural numbers, whole numbers, integers, and rational numbers.

Question 13

Define:

Natural numbers

Answer 13

The counting numbers.

(does not include zero or negative numbers)

Question 14

Define:

Whole numbers

Answer 14

Natural numbers with the addition of zero.

Question 15

Define:

Integers

Answer 15

Whole numbers and their opposites.

(includes positive and negative whole values)

Question 16

Define:

Rational numbers

Answer 16

Numbers that can be expressed as a fraction.

or in the form of ʸ⁄ₓ where x ≠ 0, where x and y are integer values

Question 17

Define:

Irrational numbers

Answer 17

These numbers cannot be expressed as fractions.

These numbers include square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat.

Question 18

Define:

Order of operations

Answer 18

When the expression contains more than one operation symbol, the order of operations tells you which operation to perform first.

PEMDAS

• Parenthesis
• Exponents
• Multiplication/Division
• Addition/Subtractions

Question 19

Define:

Commutative Property

Answer 19

You can add numbers in any order and multiply numbers in any order in the expression.

a+b = b+a

Question 20

Define:

Associative Property

Answer 20

When you are only adding or only multiplying in part of an expression, you can group any of the numbers together.

(a+b)+c = a+(b+c)

Question 21

Define:

Distributive Property

Answer 21

Can help evaluate expressions with parenthesis.

a(b+c) = ab+ac

Question 22

Define:

Quadrant

Answer 22

There are four quadrants separated by the axis line.

They are referred to as Quadrant I, II, III, and IV.

Question 23

Define:

Ordered pair

Answer 23

Has an x-coordinate and a y-coordinate and is written in parenthesis separated by a comma.

**(x,y) **