Algebra Review

Possible Phrases for Subtraction

Difference, less than, minus, decreased by, subtracted from

Possible Phrases for Addition

Plus, sum, increased by, more than, total

Possible Phrases for Division

Quotient, divided by, half, separated into, over

Possible Phrases for Multiplication

Product, times, twice, thrice, double, triple, of

Possible Phrases for Greater Than/Greater than or equal to

At least, no less than, minimum

Possible Phrases for Less Than/Less than or equal to

At most, no more than, maximum

Variable

A letter or symbol to represent a number operation

Verbal Equations

An expression containing numbers, variables, and operations, but written with words instead of numbers and symbols.

Algebraic Equations

An expression containing, numbers, variables, and operations

Exponent

Multiplication repeated

Square Root

The perfect square in a number

Order of Operation (GEMDAS)

G-Grouping

E-Exponents

M-Multiplication

D-Division

A-Addition

S-Subtraction

Distributive Property

Distributing a number to each term inside the grouping.

Combing like terms

Like terms have the same base and the same exponent.

Commutative Property

Order of values does not matter.

Associative Property

Order of grouping does not matter.

Property of Zero

Multiplying by zero always equals zero

Inverse Property

Using the opposite/inverse to cancel out the value

Reflexive Property

A number/expression always equals itself

Symmetric Property

In an equation, the sides can be interchanged and still be true

Transitive Property

If the first expression is equal to the second, and the second is equal to the third, that means the first and third are equal.

Addition Property of Equality

A value can be added to both sides of the equation and still be equal

Subtraction Property of Equality

A value can be subtracted to both sides of the equation and still be equivalent.

Multiplication Property of Equality

A value can be multiplied to both sides of an equation and still be equal.

Division Property of Equality

Both sides can be divided by the same value of an equation and still be equivalent.

Proportion

The statement of equality between two ratios.

Absolute Value

The distance between 0 and a value

Literal Equation

An equation with multiple variables

Set Notation

Use of curly brackets {}

Set Notation, All real numbers

{variable|variable,eR}

Set Notation, No solution

{ }

Interval Notation

The range of possible solutions, using parentheses and brackets.

Interval Notation, All real numbers

(-∞,∞)

Interval Notation, No solution

There is no notation.

'And' Compound Inequalities

The solution set where the two inequalities overlap

Intersection Symbol

∩

OR inequalities

Both inequalities that the solution could possibly fit in.

Union Symbol

U

Relation

A pairing of numbers in one set, called the domain, and another set, called the range.

Function

A certain type of relation where a x coordinate does not repeat, y coordinates can though. Another way of saying this is: Each value of the domain is paired with exactly one value in the range.

X-Intercept

The point(s) where the graph passes through the x axis

Y-Intercept

The point(s) where the graph passes through the y axis.

Names for x-intercepts

Root, Solution, Zero

Function Notation

f(x)=mx+b

Domain

The x values

Range

The y values

Composite Functions

Combinations of 2 or more functions in a given order.

Replacement set

Given values that can replace the variable.

Slope

The measure of the steepness of a line.

Slope equation

y2-y1/x2-x1

Slope Intercept

y=mx+b

Point Slope

y-y1=m(x-x1)

Standard Form

Ax+By=C

Parallel Lines

Same slope, and different y intercepts

Perpendicular Lines

Opposite and reciprocal slopes

Less than/greater than to graph

Dotted line

Less than or equal to/greater than or equal to graph

Solid Line

Slope, linear equation

Use when given two points or when trying to determine rate of change

Point slope, linear equation

Use when given a rate of change (m) and a pair of related values

Slope intercept, linear equation

Use when given a rate of change (m) and a starting/initial value (b)

Standard Form

Use when working with combinations of two different items

Translation

The transformation where the geometric figure/line/coordinates slide up or down, this does not change the slope.

Reflection

A transformation where the geometric figure/line/coordinates are reflected across a line/axis for a mirrored image. The slope becomes the negative version of the original slope.

Dilation

The transformation where the geometric figure/line/coordinates is the exact same, but larger/smaller, for lines, this does not change the slope, it only changes the y-intercept.

Rotation

A transformation where the geometric figure/line/coordinates are rotated around a fixed point. For linear equations, this changes the slope.

Consistent

Has at least one solution

Inconsistent

Has no solution

Independent

Only one solution

Dependent

Infinite solutions

Elimination Method

Use this to cancel out a term, this uses addition/subtraction. If no terms have the same coefficient, multiply either one of the equations to have the same coefficient.

Substitution Method

This is where we know what one of the variables represents, substitute that variable with its equivalent and solve from there.

Exponential Law: Adding/Subtracting

Combine Like Terms, do not change the exponent

Exponential Law: Multiplication

Add the exponents

Exponential Law: Power

Multiply the exponents.

Exponential Law: Quotient

Subtract the exponents.

Exponential Law: Negative Exponent

Then it becomes a fraction, with the positive exponent in the denominator.

Exponential Law: Zero Exponent

Anything with the power of 0 is equal to 1.

Scientific Notation

A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10.

Radicand

The expression inside the radical sign

Simplifying Radicals: Addition/Subtraction

With already simplified radicals combine the like radicals.

Simplifying Radicals: Multiplication

Multiply the radicand.

Rationalizing the Denominator

Multiply the denominator with an equivalent '1'.

Extraneous Values

Values that work for a certain form of the equation, but do not satisfy the original equation.

Pythagorean Theorem

a²+b²=c²

Monomial

A real number, variable, or a product of a real number

Binomial

The sum/difference of two monomials

Trinomial

The sum/difference of three monomials

Polynomial

The sum/difference of 4 or more monomials

Constant

Degree of 0

Linear

Degree of 1

Quadratic

Degree of 2

Cubic

Degree of 3

Quartic

Degree of 4

Degree of Monomial

The sum of the exponents of all the variables. Zero has no degree.

Degree of Polynomial

The highest degree monomial in the polynomial.

Standard Form (Polynomials)

The degree of it's monomial terms decreasing left to right.

GCF (Greatest Common Factor)

The largest factor that divides two (or more) numbers

Perfect Square Trinomial

a2+2ab+b2=(a+b)(a+b)=(a+b)²

a2-2ab+b2=(a-b)(a-b)=(a-b)²

Zero Property

If a product is equal to 0, one or more of the terms must equal to 0.

Difference of Squares

a²-b²=(a+b)(a-b)