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read and understand

Identify what you know and what you want to find out.

make a plan

Decide a way to solve the problem.

solve the problem

Carry out and find the answer.

look back and check

See if your answer is reasonable and correct.

cubed

A number with an exponent of 3 is often said to be

Squared

A number with an exponent of 2 is often said to be

Addition Property of Equality

For all real numbers x, y, and z, if x = y, then x + z = y + z.

Division Property of Equality

For all real numbers x, y, and z, if x = y, and z ≠ 0, then x/z = y/z. You can divide each side of an equation by the same non-zero number and not change its truth value.

distributive property

Multiplying a sum by a number is the same as multiplying each term by the number and then adding (or subtracting ) the products.

Multiplication Property of Equality

For all real numbers x, y, and z, if x = y, then xz = yz.

Subtraction Property of Equality

For all real numbers x, y, and z, if x = y, then x - z = y - z.

Formula

An equation that relates two or more quantities

Equation

A mathematical sentence that contains an equals sign

inverse operations

operations that undo each other

Identity

The product of any number and one is that number.

reciprocal

One of two numbers whose product is 1; it is also called multiplicative inverse.

Like Terms

expressions that contain the same variables to the same power

equivalent equations

Equations that have the same solution(s).

Coefficient

the decimal part

1/aⁿ

a⁻ⁿ =

x³y²x³y⁵= x⁶y⁷

Example of the product rule for exponents

x⁸/x³ = x⁵

Example of the quotient rule for exponents

(x⁵)² = x¹⁰

Example of the power rule for exponents

Linear Equation

A polynomial equation of the first degree whose graph is a line.

Arithmetic sequence

a sequence of numbers that has a common difference between every two consecutive terms

geometric sequence

a sequence of numbers that has a common ratio between every two consecutive terms

Rate of change

A value that results from dividing the change in a function (y-values) of a variable by the change in the variable (x-values). It is another name for slope.

slope

(y₂-y₁)/(x₂-x₁)

V = s³

Volume of a cube

Volume of a Cylinder

V = pi r squared h

V = Bh

Volume of ANY prism

Markup

the amount added to the cost to determine the retail price

Discount

the amount subtracted from the cost to determine a new selling price

Linear Equation - Slope-intercept form

y = mx + b

Linear Equation - Point-slope form

y - y₁ = m (x - x₁)

Linear Equation - Standard form

Ax + By = C where A, B, and C are real numbers

Excluded value

a value for which an expression is undefined

Standard form of a polynomial is

ordering the terms from those with the highest power, to the lowest power.

Lead Coefficient

The coefficient of the leading term of a polynomial in standard form.

box-and- whisker plot

a graphic way to display the median, quartiles, and extremes of a data set on a number line to show the distribution of the data

Stem and Leaf Plot

A display where the data is organized by place value, very useful if you need to find the mean, median, or mode of the data set. The data is divided in to two parts.

Inner Quartile Ratio (IQR)

The difference between Quartile 3 and Quartile 1

parallel lines

2 lines that never cross/intersect and stay the same distance apart

results from expanding (a - b)²

Perfect Square Trinomial a² - 2ab + b²

results from expanding (a + b)²

Perfect Square Trinomial a² + 2ab + b²

Graph for a Direct Variation

This graph will be a line which must go through the origin

FOIL - First Outer Inner Last

a technique used to multiply two binomials

Graph for an Inverse Variation

This graph will be a hyperbola which has vertical and horizontal asymptotes. A hyperbola has two branches. They are mirror images of one another.

Inverse Variation

A situation when one value increases and the other value decreases. y = k/x k≠0

direct variation

A situation when one value increases as the other vaule increases or as one decreases the other decreases. y = kx k≠0

Difference of two squares a² - b²

results from expanding (a - b)(a + b)

Coinciding Lines

Given two lines with the same slope and the same y-intercepts, you know the lines are?

Intersecting lines

Two or more lines that meet at a common point.

Perpendicular lines

lines in a plane that intersect to form 4 right angles

Pythagorean Theorem

in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs

A = s²

Area of a square

A = lw

Area of a Rectangle

A = bh

Area of a Parallelogram

A = ½bh

Area of a triangle

Area of a trapezoid

A = ½h(b₁+ b₂)

skew lines

Non coplanar lines that aren't parallel or intersecting