Act Math Rules/formulas

Front 1

Least Common Multiple (LCM)

Back 1

- The lowest number that is a multiple of two other numbers

(Ex. the LCM of 8 and 3 is 24)

Front 2

Greatest Common Factor (GCF)

Back 2

- The biggest number that is a factor of two other numbers

(Ex. the GCF of 14 and 21 is 7)

Front 3

Ratios

Back 3

- Ratios compare one quantity to another

(Ex. the ratio of boys to girls in a class with 10 boys and 15 girls is 10:15, or 2:3)

- Ratios can also be set up as fractions (10/15; 2/3)

Front 4

X^a = 1

Back 4

a = 0

Front 5

X^a = X

Back 5

a = 1

Front 6

X^a = square root of X

Back 6

a = 1/2

Front 7

X^a = 1/X

Back 7

a = -1

Front 8

Absolute Value

Back 8

- The absolute value of a number is the "positive value" of that number; to simplify an expression within an absolute value sign, treat it just like you would an expression in parentheses

-3 |-6 + 7| = -3

Front 9

Mode

Back 9

- The number(s) in a set that appear(s) most frequently

(Ex. the modes of the set {1, 3, 3, 4, 6, 7, 8, 8} are 3 and 8; the set {1, 3, 4, 6, 7, 8} has no mode)

Front 10

Median

Back 10

- The middle number of a set when the numbers are arranged in either ascending or descending order

(Ex. the median of the set {1, 3, 4, 6, 7, 8} is 5 (halfway between 4 and 6))

Front 11

Average (Arithmetic Mean)

Back 11

- The average of a set is the sum of the numbers in the set divided by the count of all the numbers in the set

(Ex. the average of the set {1, 3, 4, 6, 7, 8} is 4.83 (1+3+4+6+7+8 divided by 6))

Front 12

Range

Back 12

1. The difference between the biggest and the smallest number in the set

(Ex. the range of the set {1, 3, 4, 6, 7, 8} is 7)

2. All of the y-values for which a function is defined

(Ex. the range of the function y = x^2 is "y is greater than or equal to 0")

Front 13

Domain

Back 13

- All of the x-values for which a function is defined

(Ex. the domain of the function y = 1/x is "x > 0 < x")

Front 14

Probability

Back 14

- Probability of an even happening = # of ways the event can happen / # of possible outcomes

- To find the probability of TWO events happening, multiply the probabilities of each individual event happening TOGETHER

Front 15

Percent Increase or Decrease

Back 15

- % increase or decrease = change / original #

Front 16

"Is Over Of" Rule

Back 16

- The number next to the "is" should go in the numerator and the number next to the "of" should go in the denominator.

(Ex. to answer the question "9 is what percent of 12?" set up the following equation: 9/12 = .75 OR 75%

Front 17

Inequalities

Back 17

- Inequalities can be solved like equations, but if you multiply or divide both sides by a negative number, you must switch the direction of the inequality sign

(Ex. 4 - 3x < -23

-3x < -27

x > 9)

Front 18

Quadratic Equation

Front 19

Factoring Quadratic Equations

Front 20

Function Notation

Back 20

- To evaluate a function for a particular value of x, simply substitute that value everywhere you see an x

(Ex. f(x) = x^2 + 6x + 3

f(1) = (1)^2 + 6(1) + 3

f(1) = 1 + 6+ 3

f(1) = 10)

Front 21

Complex Numbers

Back 21

- i is defined as the square root of -1

- i^2 = 1

- treat complex numbers just like variables

(Ex. (i + 2)^2

i^2 + 4i + 4

-1 + 4i + 4

4i + 3)

Front 22

Logs

Back 22

- loga x = y ---> a^y = x

(Ex. loga25 = 2

a^2 = 25

a = 5)

Front 23

Matrices

Front 24

Midpoint Formula

Back 24

((x1 + x2) / 2, (y1 + y2) / 2)

Front 25

Distance Formula

Front 26

Slope Formula

Back 26

(y2 - y1) / (x2 - x1)

"Rise over Run"

Front 27

Y-Intercept Form

Back 27

y = mx + b

Front 28

Point-Slope Form

Back 28

y - y1 = m (x - x1)

Front 29

Area of a Circle

Front 30

Circumference of a Circle

Front 31

Arc Area of a Circle

Front 32

Arc Length of a Circle

Front 33

Equation of a Circle

Back 33

(x - a)^2 + (y - b)^2 = r^2

where (a, b) is the center and r is the radius

Front 34

Sum of the Interior Angles of a Polygon

Back 34

180 (n - 2)

where n is the number of sides of the polygon

Front 35

Pythagorean Theorem

Back 35

a^2 + b^2 = c^2

Front 36

Area of a Triangle

Back 36

A = (1/2)b * h

Front 37

30 - 60 - 90 Triangle

Front 38

45 - 45 - 90 Triangle

Front 39

Area of a Rectangle

Back 39

A = l * w

Front 40

Volume of a Cylinder

Front 41

Volume of a Rectangular Prism

Back 41

V = l * w * h

Front 42

SOHCAHTOA

Back 42

- sin(x) = opposite / hypotenuse

- cos(x) = adjacent / hypotenuse

- tan(x) = adjacent / opposite

Front 43

cotangent(x)

Back 43

1/tan(x)

Front 44

secant(x)

Back 44

1/cos(x)

Front 45

cosecant(x)

Back 45

1/sin(x)

Front 46

sin^2(x) + cos^2(x) = ?

Back 46

1