SAT Math

Polynomial Remainder Theorem:

When f(x) is divided by x-a, using polynomial long division, f(a) will be equal to the remainder

Asymptotes:

Lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique, depending on the behavior of the function.

End Behaviours of a Graph:

In the term axⁿ; If a > 0, then y approaches positive infinity as x increases. If a < 0, then y approaches negative infinity as x increases. If n is even, then the ends of the graph point in the same direction. If n is odd, then the ends point in different directions.

Undefined Terms:

In f(x) = 1/x-2, f(2) will be undefined as 2 - 2 = 0, and division with 0 is undefined.

Property of Exponents:

(b^m)ⁿ = b^{m x n.}

Simplifying Algebraic Questions:

For these equations factor out the top and bottom. Then cancel out common factors. This will not work however, if x is equal to 0, or, if the denominator is equal to 0.

Volume of a Cone and Cylinder:

Cylinder: πhr²

Cone:1/3(πhr²)

Volume of a Rectangular Pyramid:

V= 1/3(lwh)

Area and Circumference of a Circle:

Area = (π)r²

Circumference = 2(π)r

Interior Angles:

There are three of these within a triangle. They are always equal to 180°

Exterior Angles:

Formed when one of the lines of the triangle is extended. It will be situated outside of the triangle. It forms a straight line with one of the interior angles.

Adjacent Interior Angles:

They share a side with the Exterior Angle. Together, they make a straight line (180°)

Remote Interior Angles:

They are the two angles furthest away from the Exterior Angle.

Exterior Angle Theorem:

The measure of the Exterior Angle of a triangle, is equal to the sum of the measures of the two Remote Interior Angles.

Similar Triangles 1:

They have equal angles

Similar Triangles 2:

Same shape, but necessarily aren’t the same size; they will have the same angle measures, but usually not the same side lengths