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

What are Interior Angles:

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

What are 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.

What are Adjacent Interior Angles:

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

Where Remote Interior Angles are located:

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 have ___ angles?

They have equal angles

When triangles are similar:

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

Where the hypotenuse is located:

Longest side, directly opposite right angle

Triangle Angle Sum Theorem:

All angles in a triangle are equal to 180°. Thus, if 2 angles are equal, the third will also be equal.

What is the Sin of an angle?

The Sin is the opposite side, over the hypotenuse. Remember SOH, where S=sin, O=opposite, and H=hypotenuse

What is the Cosine of an angle?

Cosine is the adjacent side over the hypotenuse. Remember CAH, where C=cosine, A=adjacent, and H=hypotenuse.

What is the Tan of an angle?

Tangent is the opposite side over the adjacent side. Remember TOA, where T=tangent, O=opposite and A=adjacent

What is the relationship between sin and cosine?

Sin of θ = Cos(90° - θ)

What is an Arc Length?

It is the distance between two points on a curve

What are vertical angles?

They are pairs of opposite angles formed by two intersecting lines

What is a central angle?

An angle with its vertex at the center point of the circle, its sides (arms) are two radii which intersect the circles circumference.

How many degrees are in a circle?

360 degrees

How many radians of arc are in a circle?

There are 2π radians

How many degrees are in 1 radian

180/π degrees = 1 radian

How many radians are in 1 degree

π/180 radians = 1 degree