Algebra I Chapter 1 - 5 Study Set

What are the next two terms of 2, 6, 18, ...

54 and 162 Multiply previous term by 3

Terminating Decimal

A decimal number that ends.

Repeating Decimal

A decimal number that has digits that repeat forever.

set-builder notation

A notation used to describe the elements of a set

Perfect Square

A number made by squaring a whole number.

Irrational Numbers

A number that can NOT be expressed as a ratio of two integers or as a repeating or terminating decimal. Examples include: PI or any square root that is not a perfect square number.

Rational Numbers

A number that can be expressed as a ratio (fraction) examples include-terminating and repeating decimals

Base of an Exponent

A number that is raised to a power.

Squared Number

A number with an exponent 2.

Cubed Number

A number with an exponent 3.

rate of change

A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

inequality

A statement that compares two quantities using <, >, ≤,≥, or ≠

vertical line test

A test used to determine whether a relation is a function by checking if a vertical line touches 2 or more points on the graph of a relation

Real Numbers

All the numbers on the number line ( including fractions, decimals, rational and irrational )

Integers

Positive or Negative whole numbers

Combine Like Terms

To simplify an expression by adding and subtracting terms with the same variable(s) and exponent(s).

compound inequality

Two inequalities that are combined into one statement by the word "and" or "or"

inverse operations

Two operations that undo each other

arithmetic sequence

a sequence in which each term is found by adding, subtracting, multiplying, or dividing to find the next term

term

a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs.

constant

a term that has no variable factor

independent variable

a variable (often denoted by x ) whose variation does not depend on that of another.

dependent variable

a variable (often denoted by y ) whose value depends on that of another.

y = |x|

absolute value function

Subtraction Inverse

addition

equivalent expression

algebraic expressions that have the same value

function notation

an equation in the form of 'f(x)=' to show the output value of a function, f, for an input value x

function rule

an equation that describes a function

Proportion

an equation that states 2 ratios are equal

solution of an inequality

any value that makes the inequality true

Multi - Step Equation

get the variable by itself by undoing the problem, reverse the order of operations, get the variables on one side of equal sign and numbers on the opposite side

at least

greater than or equal to

Solve: 5x + 2 = 1/2 (10x + 4)

identity

Similar Figures

same shape but not the same size, help you measure real-world distances indirectly

graph of a linear function

straight line

Addition Inverse

subtraction

like terms

terms with the same variable(s) that are raised to the same power

absolute value

the distance a number is from zero on the number line

Range of a function

Complete set of all dependent variables (y-values)

function

a relation in which each element of the domain is paired with exactly one element of the range

Perfect Cube

The result of using a whole number in a multiplication three times.

2 step Equation

get the variable by itself by undoing the problem, reverse the order of operations

What are the next two terms of 0.5, 0.25, 0.125, ...

0.0625 and 0.03125 Divide by two

Division Property of Inequalities

If each side of a true inequality is divided by the same positive number, the resulting inequality is also true. a < b a/c < b/c watch out if you divide by a negative, you must flip the inequality sign the opposite direction

Addition Property of Equality

If you add the same number to each side of an equation, the two sides remain equal. a = b a+c = b+c

addition property of inequality

If you add the same number to each side of an inequality, the inequality remains true. a < b a+c < b+c

Division Property of Equality

If you divide each side of an equation by the same nonzero number, the two sides remain equal. a = b a/c = b/c

Multiplication Property of Equality

If you multiply each side of an equation by the same nonzero number, the two sides remain equal. a = b a*c = b*c

Subtraction Property of Equality

If you subtract the same number from each side of an equation, the two sides remain equal. a = b a-c = b-c

subtraction property of inequality

If you subtract the same number from each side of an inequality, the inequality remains true. a < b a-c < b-c

Round a Number

Means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use.

Square Root

One of two equal factors of a number

Relative Error

Ratio of the absolute vale of the difference of a measured (estimated) value and an actual value compared to the actual value

slope

Rise over run

Exponent

Tells you how many times the base number is multiplied to itself.

intersection

The overlapping of two graphs of a compound inequality

table, graph, chart

Visual or graphic that shows lots of information using lines, labels and numbers

multiplication property of inequality

When you multiply each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true. a < b a*c < b*c watch out if you multiply by a negative, you must flip the inequality sign the opposite direction

linear function

a function in which the graph of the solutions forms a line

nonlinear function

a function with a graph that is not a straight line

variable

a letter that represents an unknown number

algebraic expression

a mathematical phrase that includes one or more variables.

inequality

a mathematical sentence that compares the values of two expressions

equation

a mathematical sentence that uses an equal sign

Identity

both sides of equal sign are same

Ratio

compares two numbers by division

Domain

complete set of all independent variables (x-values)

recursive formula

defines the terms in a sequence by relating each term to the ones before it

output

dependent variable

explicit formula

expresses the nth term of a sequence in terms of n

1 step Equation

get the variable by itself by undoing the problem - addition - you subtract - subtraction - you add - multiplication - you divide - division - you multiply

Input

independent variable

A linear function is a function that _____________ a line

is

Solve: 2(x - 4) = 4x - (2x + 4)

no solution

No Solution

no solution works

y = x^2

parabola

Percent Change

ratio of the amount of change to the original amount - amount of increase - new amount is greater than original amount - amount of decrease - new amount is less than the original amount

whole number

the nonnegative integers

coefficient

the number in front of the variable that the variable is multiplied by

multiplication inverse

the number that, when multiplied by a given number, results in a product of one; reciprocal

distributive property

this allows you to multiply a number outside of a grouping symbol by all numbers that are inside of the grouping symbol; Example: 3(x+2) = 3x + 6

simplify

to reduce an expression to its simplest form.

evaluate

to substitute a given number for each variable and then solve.

Solve: - 14 = -5 + 3x

x = - 3

Solve: -7x = 28

x = - 4

Solve: 27 + x = 46

x = 19

Solve: x + 5(x-1) = 7

x = 2

Solve: 3(x-5) = 2(x+5)

x = 25

Solve: - 5 + x = 21

x = 26

Solve: 5(2x - 3) = 15

x = 3

Solve: 3x - 4 = 11

x = 5

Solve: x/7 = 12

x = 84

slope-intercept form

y=mx+b, where m is the slope and b is the y-intercept of the line.

Percent Proportions

you can represent "a is p percent of b" using the percent proportion

What is the domain of {(2,3), (4,5), (5, 6), (6,6)}?

{2, 4, 5, 6}

What is the range of {(2,3), (4,5), (5, 6), (6,6)}?

{3, 5, 6}

no more than

≤ less than or equal to