Quantitative Reasoning

P(E) individual outcomes are equally likely

# of outcomes / total number of possible outcomes

sum of the interior angle of a polygon

(n-2)180 n is number of sides

area of a trapezoid

1/2 (sum of the lengths of the bases) (heights)

working rate problems

1/hours for comp a + 1/hrs for comp b = 1/ both hours

Ratio 30-60-90

1: root 3 : 2

Ratio 45-45-90

1:1:root 2

circumference or a circle

2 pi r

surface area of a right circular cylinder

2(pi*(r^2))+ 2*pi*r*h

Most common prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

degrees of a circle

360 degrees

0!

=1

Parallelogram

A quadrilateral with two pairs of parallel sides opposite sides & Angles congruent

Working around the average formula

Average = Total (sum of all results)/number of results

Odd * Even

Even

Odd - Odd

Even

Dividing Fractions

Invert (reciprocal) the second fraction and multiply

Mutually Exclusive P(E and F) P(E or F)

P(E and F) = 0 P(E or F) = P(E) + P(F)

independent variable P(E and F) P(E or F)

P(E and F) = P(E)P(F) P(E or F) = P(E) - P(F) - P(E)P(F)

Probability that E or F occurs

P(E) - P(F) - P(E and F)

Sets/Venn Diagram

Total people = (X-z) + (Y-z) + z (those with x and y) when given two venn diagrams make a table to make the totals add up

volume of a cylinder

V=πr²h

permutation

a selection of a group of objects in which order is important To figure out the number of combinations n!/k!(n-k)! n: number of them picked k: number of options

Right Triangle Side length

a^2 + b^2 = c^2

quadrilateral

both pairs of opposite sides are parallel opposite sides of a parallelogram also have equal length B*H

Standard Deviation

differences between the numbers and the mean, square the differences, find the average of the squared difference

Even - Odd

odd

Odd * Odd

odd

area of a circle

pi r^2

Union of A and B

set of all elements that are in a or in b or in both

Intersection of A and B

the set of all elements that are in both A and B (if they have no elements then they are mutually exclusive)

triangle sides

the sum of the lengths of any two of the sides is greater than the length of the third side

average speed of a car

total miles traveled / total hours

Quadratic Formula

x = -b ± √(b² - 4ac)/2a ax^2 + bx + c = 0 helpful for finding the factors in a equation