Math Formulas

Triangle Sum Theorem

The sum of the three interior angles in a triangle is always 180°: ∠a + ∠b + ∠c = 180°.

Slope of a Line

The slope, m, is calculated by the formula: m = change in y / change in x = (y2 - y1) / (x2 - x1).

Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a), for equations in the form ax² + bx + c = 0.

Pythagorean Theorem

a² + b² = c², where c is the hypotenuse.

Standard Form of a Line

Ax + By = C.

Slope-Intercept Form of a Line

y = mx + b, where m = slope and b = y-intercept.

Point-Slope Form of a Line

y - y1 = m(x - x1).

Distance Formula

The distance between two points (x1, y1) and (x2, y2) is given by: d = √((x2 - x1)² + (y2 - y1)²).

Area of a Triangle

A = 1/2 b h, where b is the base and h is the height.

Midpoint Formula

The ________ M between points (x1, y1) and (x2, y2) is given by: M = ((x1 + x2)/2 , (y1 + y2)/2).

Simple Interest Formula

The _________ is calculated using: I = prt, where p = principal, r = rate, and t = time.

Distance, Rate, and Time Formula

: d = rt, where r = rate and t = time.

Order of Operations

PEMDAS: Parenthesis, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Percent Change

__ = (New Value - Old Value) / Old Value x 100.

Mean

The _______ is calculated as the sum of all data points divided by the number of data points.

Range

The ______ is the difference between the maximum and minimum values in a data set.

Mode

The _____ is the value that appears most frequently in a data set.

Median

The _______ of a data set is the middle value when the data points are arranged in order.

Perimeter

To find the ________ of any polygon, sum all of its side lengths.

Area of a Circle

πr², where r is the radius.

Circumference of a Circle

πd or 2πr.

Weight Conversion

1 pound = 16 ounces.

Weight Converson

1 ton = 2,000 pounds

Time Conversion

3600 seconds =1 hour

Time Conversion

1440 minutes = 1 day

Time Conversion

1 year (yr) =365.25 days

Linear Units

1 foot = 12 inches

Linear Unit

63,360 inches =1 mile (mi)

Linear Unit

5,280 feet = 1 mile

Linear Unit

36 inches = 1 yard

Linear Units

1 mile = 5,280 feet

Linear Units

3 feet= 1 yard (yd)

Triangle

A polygon with 3 sides whose interior angles sum to 180 degrees.

Quadrilateral

A polygon with 4 sides whose interior angles sum to 360 degrees.

Pentagon

A polygon with 5 sides whose interior angles sum to 540 degrees.

Hexagon

A polygon with 6 sides whose interior angles sum to 720 degrees.

Heptagon

A polygon with 7 sides whose interior angles sum to 900 degrees.

Octagon

A polygon with 8 sides whose interior angles sum to 1080 degrees.

Capacity Unit

1 cup = 8 fluid ounces.

Capacity Unit

1 gallon = 4 quarts

Capacity Unit

1 quart = 2 pints

Capacity Unit

1 pint = 2 cups

Multiplication Rule

The product and the quotient of one and any number is that number.

Zero Times Rule

The product of zero and any number is zero.

Zero Division Rule

Dividing zero by any non-zero number equals zero, but dividing by zero is undefined.

Square

Perimeter: P = 4s

Square

Area: A = s2

Rectangle

Perimeter: P = 2l + 2w

Recantagle

Area: A = lw

Parallelogram

Perimeter: P = 2a + 2b

Parallelogram

Area: A = bh

Trapezoid

Perimeter: P=a+b1 +c+b2

Trapezoid

Area:A=1(b1 +b2)∙h

Volume of a Cube

V = a³, where a is the length of a side of the cube

Cube

SA=6a2

Rectangle Solid

V= l x w x h

Rectangle solid

SA = 2(l x w) + 2(w x h) + 2(h x l)

Cylinder

V = πr²h, where r is the radius and h is the height.

Cylinder

SA= 2π𝑟h+2π𝑟2

Sphere

V= 4/3𝜋𝑟^3

Sphere

SA = 4πr², where r is the radius

Rectangular Pyramid

𝑉 = 1/3𝑎𝑏h

Probability Rule

For any event A, 0 ≤ P(A) ≤ 1; P(sure event) = 1, P(impossible event) = 0.

Prime Numbers

only two factors which are 1 and the number itself such as 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

Addition of Exponents

When multiplying two exponents with the same base, keep the base and add the exponents: a^m * a^n = a^(m+n).

Subtraction of Exponents

When dividing two exponents with the same base, keep the base and subtract the exponents: a^m / a^n = a^(m-n).

Angle Definition

An angle is formed by the intersection of two rays with a common endpoint.

Acute Angle

An angle that measures less than 90 degrees.

Right Angle

An angle that measures exactly 90 degrees.

Obtuse Angle

An angle that measures more than 90 degrees but less than 180 degrees.

Straight Angle

An angle that measures exactly 180 degrees.

Complementary Angles

Two angles whose sum is 90 degrees.

Supplementary Angles

Two angles whose sum is 180 degrees.

Factorial Definition

n! = n x (n-1) x (n-2) x ... x 1; 0! = 1.

Divisibility Rule for 2

A number is divisible by 2 if its last digit is even.

Divisibility Rule for 3

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

Reciprocals of Fractions

swap its numerator and denominator.

Like Terms

Terms that have the same variable raised to the same power can be combined.

Adding Polynomials

combine like terms together.

Subtracting Polynomials

Rewrite subtraction as addition by distributing the negative sign to the second polynomial.