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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.
