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Raising a negative number to a power

Factoring ax²+bx+c

Factoring by grouping

Canceling out opposites

When raising a negative number to a power always put the nega…

If both terms are opposite signs they can be crossed out and…

Raising a negative number to a power

When raising a negative number to a power always put the nega…

Factoring ax²+bx+c

Raising a negative number to a power

Factoring ax²+bx+c

Factoring by grouping

Canceling out opposites

When raising a negative number to a power always put the nega…

If both terms are opposite signs they can be crossed out and…

Raising a negative number to a power

When raising a negative number to a power always put the nega…

Factoring ax²+bx+c

equation

formula

set

elements

statement that says two mathematical expressions are true

an equation that uses variables to express a relationship bet…

a collection of elements

objects in a set

equation

statement that says two mathematical expressions are true

formula

an equation that uses variables to express a relationship bet…

Complex Numbers

Real Numbers

Imaginary Numbers

Rational Numbers

Have the form a + bi where a and b are real and i = √-1 (e.g.…

Have points on the number line (e.g., 3, -17.4, √5, π, 4/3)

Square roots of negative numbers, have NO points on the numbe…

Can be expressed exactly as a ratio of two integers (e.g., 4/…

Complex Numbers

Have the form a + bi where a and b are real and i = √-1 (e.g.…

Real Numbers

Have points on the number line (e.g., 3, -17.4, √5, π, 4/3)

In ∆EFG, e = 4.56, E = 43°, and G = 57…

Designed by Maya Lin, the Vietnam Vete…

In ∆QRS, q = 15, r = 28, and Q = 43.6°…

In ∆XYZ, x = 23.5, y = 9.8, and X = 39…

43°, 80°, 57°, 4.56, 6.58, 5.61 ... (8.1)

2961.4 in., 2960.2 in.... (8.1)

No solution.... (8.1)

39.7°, 15.4°, 124.9°, 23.5, 9.8, 30.2... (8.1)

In ∆EFG, e = 4.56, E = 43°, and G = 57…

43°, 80°, 57°, 4.56, 6.58, 5.61 ... (8.1)

Designed by Maya Lin, the Vietnam Vete…

2961.4 in., 2960.2 in.... (8.1)

Multiplying Algebraic Fractions

Dividing Algebraic Fractions

Adding/Subtracting Algebraic Fractions

Rule of -1

1) Factor... 2) Reduce

1) Flip divisor... 2) Factor... 3) Reduce

1) Find common denominator... 2) Add/Subtract numerators ONLY.... 3…

Puts equation into a solvable form... 1-x²... -1(x²-1)... -1(x-1)(x-1)

Multiplying Algebraic Fractions

1) Factor... 2) Reduce

Dividing Algebraic Fractions

1) Flip divisor... 2) Factor... 3) Reduce

opposite leg

adjacent leg

SOHCAHTOA

sine (SIN)

the leg located opposite an angle of reference in a right tri…

the leg located next to an angle of reference in a right tria…

a mnemonic (memory) device that is used to remember the 3 bas…

opposite/hypotenuse

opposite leg

the leg located opposite an angle of reference in a right tri…

adjacent leg

the leg located next to an angle of reference in a right tria…

Raising a negative number to a power

Factoring ax²+bx+c

Factoring by grouping

Canceling out opposites

When raising a negative number to a power always put the nega…

If both terms are opposite signs they can be crossed out and…

Raising a negative number to a power

When raising a negative number to a power always put the nega…

Factoring ax²+bx+c

absolute value

absolute value

amplitude

angle of depression

the distance a number lies from 0 on a number line

the piecewise function that returns x if x is not negative an…

the absolute value of the difference between the maximum valu…

the angle by which an observer must lower one's line of sight…

absolute value

the distance a number lies from 0 on a number line

absolute value

the piecewise function that returns x if x is not negative an…

natural numbers

whole numbers

opposite or additive inverse

integers

The set of numbers 1, 2, 3, 4, ... Also called counting numbe…

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

equal distance but on opposite sides of zero... a + (-a) = 0... Ev…

Positive and Negative Whole Numbers and 0. Examples: .... -3,…

natural numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbe…

whole numbers

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

a symbol or group of symbols used to r…

the number represented by the expressi…

a sentence formed by placing equals si…

a sentence formed by placing an inequa…

numerical expression

value of a numerical expression

equation

inequality

a symbol or group of symbols used to r…

numerical expression

the number represented by the expressi…

value of a numerical expression

Column Matrix

Dilation

Element

Equal Matrix

A matrix that has only one column.

A transformation in which a geometric figure is enlarged or r…

Each value in a matrix.

Two matrices that have the same dimensions and each element o…

Column Matrix

A matrix that has only one column.

Dilation

A transformation in which a geometric figure is enlarged or r…

Function

Function Notation

What are the 3 ways to show functions?

What is point-slope form?

An equation or rule where there is only one output for every…

y=f(x)

Graph, Table, Words

y=m(x-x1)-y1

Function

An equation or rule where there is only one output for every…

Function Notation

y=f(x)

set

set example

real numbers

real numbers example

a group of object (numbers) a set can be infinite (having an…

~0 and 3~ is the set containing 0 and 3

the set of all numbers that exist on a number line

3, -5, 2.42, square root of a number

set

a group of object (numbers) a set can be infinite (having an…

set example

~0 and 3~ is the set containing 0 and 3

Raising a negative number to a power

Factoring ax²+bx+c

Factoring by grouping

Canceling out opposites

When raising a negative number to a power always put the nega…

If both terms are opposite signs they can be crossed out and…

Raising a negative number to a power

When raising a negative number to a power always put the nega…

Factoring ax²+bx+c

Raising a negative number to a power

Factoring ax²+bx+c

Factoring by grouping

Canceling out opposites

When raising a negative number to a power always put the nega…

If both terms are opposite signs they can be crossed out and…

Raising a negative number to a power

When raising a negative number to a power always put the nega…

Factoring ax²+bx+c

Raising a negative number to a power

Factoring ax²+bx+c

Factoring by grouping

Canceling out opposites

When raising a negative number to a power always put the nega…

If both terms are opposite signs they can be crossed out and…

Raising a negative number to a power

When raising a negative number to a power always put the nega…

Factoring ax²+bx+c

Law of Sines

Law of Cosines

Trigonometric Identities

Trigonometric Ratios

Formula that relates the sines of angles to the lengths of th…

Formula that relates the lengths of sides to the cosines of t…

Trig equation that is true for all values of the variable

Relationship between the sides of a right triangle, can be re…

Law of Sines

Formula that relates the sines of angles to the lengths of th…

Law of Cosines

Formula that relates the lengths of sides to the cosines of t…

Algebraic Expression

Associative property of Addition

Associative property of Multiplication

Base

Constants and variables combined using addition, subtraction,…

The sum of 3 numbers may be grouped differently without affec…

The product of 3 numbers may be grouped differently without a…

In exponential notation, the expression that is being multipl…

Algebraic Expression

Constants and variables combined using addition, subtraction,…

Associative property of Addition

The sum of 3 numbers may be grouped differently without affec…

Square root on bottom domain

One to one function

Parentheses and Bracket

Square root on top

Set expression greater than 0

For every y element of range, corresponds to only one x eleme…

Not included ... Included... Infinity always parentheses ... Greater a…

Numerator greater than or equal to 0... Denominator not equal to 0

Square root on bottom domain

Set expression greater than 0

One to one function

For every y element of range, corresponds to only one x eleme…

Quadratic Equation

Sum of the roots of a Quadratic

Product of the roots of a Quadratic

Quadratic Formula

an equation of the form ax² + bx + c = 0, where a ≠ 0

-b/a

c/a

Quadratic Equation

an equation of the form ax² + bx + c = 0, where a ≠ 0

Sum of the roots of a Quadratic

-b/a

sin(θ) cos(θ) tan(θ) csc(θ) sec(θ) cot…

sin(30°, 45°, 60°)... cos(30°, 45°, 60°)…

Conversion to radians

Conversion to degrees

o/h, a/h, o/a, h/o, h/a, a/o (y/r, x/r, y/x, r/y, r/x, x/y)

1/2, √2/2, √3/2... √3/2, √2/2, 1/2... √3/3, 1, √3... π/6, π/4, π/3

π/180

180/π

sin(θ) cos(θ) tan(θ) csc(θ) sec(θ) cot…

o/h, a/h, o/a, h/o, h/a, a/o (y/r, x/r, y/x, r/y, r/x, x/y)

sin(30°, 45°, 60°)... cos(30°, 45°, 60°)…

1/2, √2/2, √3/2... √3/2, √2/2, 1/2... √3/3, 1, √3... π/6, π/4, π/3

Variable

numerical expression

Algebraic expression

Input

A symbol usually a letter that represents one or more numbers…

A mathematical phrase that contains numbers and operations sy…

A mathematical phrase that contains one or more variables... 3n…

X variable

Variable

A symbol usually a letter that represents one or more numbers…

numerical expression

A mathematical phrase that contains numbers and operations sy…

Sine Formula

Cosine Formula

Tangent Formula

Cosecant Formula

sin x = Opposite Side/Hypotenuse

cos x = Adjacent Side/Hypotenuse

tan x = Opposite Side/Adjacent Side

csc x = Hypotenuse/Opposite Side

Sine Formula

sin x = Opposite Side/Hypotenuse

Cosine Formula

cos x = Adjacent Side/Hypotenuse

Discrete function

Continuos function

Interval notation

Set notation

The graph of this function consists of seperate points

The graph of this function is unbroken.

Notation Used for domain and range in a continuos function

Notation Used for domain and range in a discrete function

Discrete function

The graph of this function consists of seperate points

Continuos function

The graph of this function is unbroken.

domain

solution or root of the equation

equivalent equations

Addition Property of Equality

The domain is the set of numbers that can replace the variabl…

A number from the domain that makes an equation true is a sol…

equations that have the same solution

if you add the same number to each side of an equation, the t…

domain

The domain is the set of numbers that can replace the variabl…

solution or root of the equation

A number from the domain that makes an equation true is a sol…

Degree

Slope (mx in y=mx=b)

1st Difference

2nd Difference

Highest exponent/ power

"Constant rate of change"

Linear: Degree of 1. Will find the constant on the 1st degree…

Quadratic: Degree of 2. Will find the constant on the 2nd deg…

Degree

Highest exponent/ power

Slope (mx in y=mx=b)

"Constant rate of change"

abscissa

angle of depression

angle of elevation

base of an exponential function

the distance from a point to the y-axis

the angle formed by the horizontal and the line of sight when…

the angle formed by the horizontal and the line of sight when…

the number b in the exponential function y=b^x

abscissa

the distance from a point to the y-axis

angle of depression

the angle formed by the horizontal and the line of sight when…