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Math Equations
Term | Definition |
---|---|
Area of a trapezoid | A = (1/2)(b + B)h |
Distance formula (for finding diagonals, corner-to-corner distance, distance between points) | d = SQRT ((a-b)^2 + (c-d)^2 + ...) |
Volume of a cone | V = 1/3 pi (r^2) h |
Volume of a pyramid | V = 1/3 Bh |
Volume of a sphere | V = 4/3 pi r^3 |
SA of a sphere | SA = 4 pi r^2 |
Number of diagonals | n(n-3)/2 |
Sum of interior angles of a polygon | 180(n-2) |
Number of sides of a polygon | Total degrees/180 + 2 |
Degree measure of an interior angle | 180(n-2)/n 180 - (360/n) |
30-60-90 Triangle Values | 1/2, SQRT(3)/2, SQRT(3) - Use left hand |
45-45-90 Triangle Values | SQRT(2)/2 (both x and y), 1 - use left hand |
Z-Score | Z = (actual score - mean) / standard deviation |
Probability of independent events | P(A and B) = P(A)*P(B) |
Probability of dependent events (without replacement) | P(A and B) = P(A)*P(B:A) |
Probability of non-mutually exclusive events | P(A or B) = P(A) + P(B) - P(both) |
Probability of mutually exclusive events | P(A or B) = P(A) + P(B) |
Complimentary angles Supplementary angles | add to 90 add to 180 |
Arithmetic Mean | Add and divide by number of terms |
Geometric Mean | Multiply numbers and find square root OR Square root numbers and multiply |
Discriminant | b^2 - 4ac |
Determinant | multiply top left and bottom right, then subtract the product of top right and bottom left |
How to find the vertex of a parabola | -b/2a, then plug in to find y find the derivative, then plug x value in to find y |
reference angles | first quadrant angles that are equivalent to given angle always made with the nearest x axis |
co-terminal angles | angles that are either +/- 360 degrees or 2pi radians from a given angle |
period of a sine/cosine function period of a tangent function | 2pi/b pi/b |
How to identify characteristics of a trig function (amplitude, period, phase shift, vertical shift) | amplitude: coefficient of the entire function period: either 2pi or pi divided by the coefficient of x phase shift: horizontal shift inside parentheses vertical shift: vertical translation outside of parentheses |
square root of the variance of a set of data | standard deviation |
finding equation of a tangent line | find derivative, then find slope at the point, then use point-slope form |
Derivative rules | power rule, chain rule, product rule most common |
Percents in a normal curve | 1 sd away: 68% 2 sd away: 95% 3 sd away: 99.7% |