A **monomial** contains one term, a **binomial** contains two terms, and a **polynomial** contains more than two terms. **Linear** expressions have no exponents. A **quadratic** expression contains variables that are squared (raised to the exponent of 2).

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A **monomial** contains one term, a **binomial** contains two terms, and a **polynomial** contains more than two terms. **Linear** expressions have no exponents. A **quadratic** expression contains variables that are squared (raised to the exponent of 2).

You can only add or subtract monomials that have the same variable and the same exponent. However, you can multiply and divide monomials with unlike terms.

To multiply binomials, use the FOIL method. FOIL stands for **F**irst, **O**utside, **I**nside, **L**ast and refers to the position of each term in the parentheses.

To factor a quadratic expression, apply the FOIL (**F**irst, **O**utside, **I**nside, **L**ast) method in reverse.

An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, **P**arentheses, **E**xponents, **M**ultiplication/**D**ivision, **A**ddition/**S**ubtraction.)

When presented with two equations with two variables, evaluate the first equation in terms of the variable you're not solving for then insert that value into the second equation. For example, if you have x and y as variables and you're solving for x, evaluate one equation in terms of y and insert that value into the second equation then solve it for x.

When solving quadratic equations, if the equation is not set equal to zero, first manipulate the equation so that it is set equal to zero: ax^{2} + bx + c = 0. Then, factor the quadratic and, because it's set to zero, you know that one of the factors must equal zero for the equation to equal zero. Finding the value that will make each factor, i.e. (x + ?), equal to zero will give you the possible value(s) of x.

Solving equations with an inequality (<, >) uses the same process as solving equations with an equal sign. Isolate the variable that you're solving for on one wide of the equation and put everything else on the other side. The only difference is that your answer will be expressed as an inequality (x > 5) and not as an equality (x = 5).

A line segment is a portion of a line with a measurable length. The **midpoint** of a line segment is the point exactly halfway between the endpoints. The midpoint **bisects** (cuts in half) the line segment.

A right angle measures 90 degrees and is the intersection of two **perpendicular** lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

An acute angle measures less than 90°. An obtuse angle measures more than 90°.

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are **supplementary** (they add up to 180°) and angles across from either other are **vertical** (they're equal).

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A **transversal** occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called **interior** angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called **corresponding** angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The **perimeter** of a triangle is equal to the sum of the lengths of its three sides, the **height** of a triangle is equal to the length from the **base** to the opposite **vertex** (angle) and the **area** equals one-half triangle base x height: a = ½ base x height.

An **isosceles** triangle has two sides of equal length. An **equilateral** triangle has three sides of equal length. In a **right** triangle, two sides meet at a right angle.

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the **hypotenuse** squared (c^{2}) is equal to the sum of the two perpendicular sides squared (a^{2} + b^{2}): c^{2 }= a^{2} + b^{2} or, solved for c, \(c = \sqrt{a + b}\)

A quadrilateral is a shape with four sides. The **perimeter** of a quadrilateral is the sum of the lengths of its four sides (a + b + c + d).

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A **square** is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s^{2}).

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

A rhombus has four equal-length sides with opposite sides parallel to each other. The perimiter is the sum of the lengths of all sides (a + b + c + d) or, because all sides are the same length, 4 x length of one side (4s).

A trapezoid is a quadrilateral with one set of parallel sides. The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height. In this diagram, that becomes ½(b + d)(h).

A circle is a figure in which each point around its perimeter is an equal distance from the center. The **radius** of a circle is the distance between the center and any point along its perimeter (AC, CB, CD). A **chord** is a line segment that connects any two points along its perimeter (AB, AD, BD). The **diameter** of a circle is the length of a chord that passes through the center of the circle (AB) and equals twice the circle's radius (2r).

The **circumference** of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The **area** of a circle is π x (radius)^{2} : a = π r^{2}.

A cube is a rectangular solid box with a height (h), length (l), and width (w). The **volume** is h x l x w and the **surface area** is 2lw x 2wh + 2lh.

A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The **volume** of a cylinder is π r^{2}h and the **surface area** is 2(π r^{2}) + 2π rh.

The coordinate grid is composed of a horizontal **x-axis** and a vertical **y-axis**. The center of the grid, where the x-axis and y-axis meet, is called the **origin**.

A line on the coordinate grid can be defined by a slope-intercept equation: **y = mx + b**. For a given value of x, the value of y can be determined given the **slope** (m) and **y-intercept** (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.