Important Formulas

(under construction)

Part I: Algebra

1) Slopes and equations of a line:

a. Slope-intercept form: y = mx b

b. Two lines are parallel if their slopes are the same.

c. Two lines are perpendicular if their slopes are negative reciprocal of each other.

2) Distance and midpoint formulas:

a. Midpoint formula:

b. Distance between two points:

c. Distance from a point to a line Ax By C = 0 is given by:

3) Divisibility Test:

· A number is divisible by 2 if and only if its last digit is 0, 2, 4, 6, or 8.

· A number is divisible by 5 if and only if its last digit is 0 or 5.

· A number is divisible by 10 if and only if the last digit is 0.

· A number is divisible by 4 if and only if the number represented by its last two digits is divisible by 4.

· A number is divisible by 8 if and only if the number represented by its last three digits is divisible by 8.

· A number is divisible by 3 if and only if the sum of its digits is divisible 3.

· A number is divisible by 9 if and only if the sum of its digits is divisible 9.

· A number is divisible by 11 if and only if the difference between the sum of the odd numbered digits (1st, 3rd, 5th...) and the sum of the even numbered digits (2nd, 4th...) is divisible by 11. (Note that: 0 is divisible by 11)

4) Remainder Theorem: The remainder when p(x) is divided by (x – a) is f(a)

5) Factoring techniques:

a. Difference of two squares:

b. Difference of two cubes:

c. Sum of two cubes:

6) Quadratic Equation:

a. Quadratic Formula:

b. If are two solutions, then

7) Properties of Logarithms:

8) Arithmetic sequence:

9) Geometric Sequence:

Part II: Trigonomotry

1) Sine/Cosine of special angles

2) Basic trig identities:

3) Double-angle identities:

4) Sum-to-product:

5) Law of Sine: or

6) Law of Cosine:

7) Area of a triangle: where

Part III: Geometry

1) Area: triangle, square, trapezoid, circle, etc.

2) Volume:

a. Rectangular box: V = length x width x height

b. Cylinder:

c. Cone:

d. Sphere: