Math 1 Formulas
Interval Notation
( 1 , 5 ) ↔ 1 < x < 5 [ 1 , 5 ] ↔ 1 ≤ x ≤ 5
Exponents
(-any number)² ≠ -any number² any number⁰ = 1 any number⁻³ = 1 — 4³ yⁿ x yˣ = yⁿ⁺ˣ (yⁿ)ˣ = ⁿ×ˣ yˣ — = xˣ⁻ⁿ yⁿ (yz)ⁿ = yⁿ x zⁿ
Surface Area of Triangular Prisms
Break the prism into 5 pieces, using the sides as the separate parts, Find the area of each side, and add them all together.
Surface Area of Rectangular Prisms
SA = 2lw + 2lh + 2hw
Surface Area of Rectangular Pyramids
SA = B + 1/2 Pl (P.S. P = Perimeter of the base. l = Slant height. B = Area of base.)
Surface Area of Triangular Pyramids
SA = B + 1/2 Pl (P.S. P = Perimeter of the base. l = Slant height. B = Area of base.)
Inequalities
Solve like a normal equation. Remember to change the direction of your sign when you multiply or divide by a negative number.
Volume of Rectangular Pyramids
V = Bh —— 3
Volume of Triangular Pyramids
V = Bh —— 6
Volume of Rectangular Prisms
V = lwh
Volume of Triangular Prisms
V = lwh —— 2
Equations of Lines
m = slope y = mx + b : Slope Intersept y - y₁ = m ( x - x₁ ) : Point Slope
Mean
the average value of a set of numbers. / add all numbers and divide by the number of values in the data set.
Median
the middle value. / list all numbers in a data set from least to greatest and find the center number. if there are two in the middle, add and divide by two.
Undefined
when a fraction has a denominator of zero.
Slope
x = abscissa, y = ordinate m = Vertical Change .... Rise ...... y₂ - y₁ ————————— = ——— = ———— Horizontal Change .... Run ......... x₂ - x₁
Domain
x values
Quadratic Equation
x² - 5x + 6 = 0 Set = 0 ( x - 3 ) ( x - 2 ) = 0 Factor x = 3 ; x = 2 Find Roots
Systems of equations
y - 2x = 1 OR y + 2x = 9 Linear: substitute; add to eliminate one variable or graph. y = x² - x - 6 OR y = 2x - 2 Linear Quadratic: substitute or graph. For inequality systems, graph.
Parabola
y = ax² + bx + c Axis of symmetry : x = -b —— 2a Roots : where the graph crosses the x-axis
Direct Variation
y = kx where k = constant of variation k = y ÷ x
Range
y values / difference between the largest number in a data set and the smallest.
Mean Absolute Deviation (MAD)
Find the mean of the given data set, Subtract the mean from each given number in the data set, make all new numbers positive, and find the mean of the new set of numbers.
Factor
Look for a GCF (greatest common factor) Factor binomial or trinomial.
Vertical Angles
Opposite equal angles create a "V" shape.
PEMDAS
P = Parentheses E = Exponents M = Multiply D = Divide A = Add S = Subtract Used in any equation.
Parallel and Perpendicular
Parallel : slopes are equal Perpendicular : slopes are negative reciprocals (flip over and negate)
Function
Passes the vertical line test. A set of ordered pairs in which each x element has only one y element associated with it. f(x) = 3x + 4 f(3) = 3 x 3 + 4 = 13
Factorial
Any number with an exclamation mark in front of it is a factorial. To solve, you follow this procedure: 0! = 1 1! = 1 2! = 2 x 1 = 2 3! = 3 x 2 x 1 = 6
Area of Semicircles
A = 1/2 (πr^2)
Area of Triangles
A = 1/2bh OR A = bh/2
Area of Trapezoids
A = 1/2h (b1 + b2)
Area of Parallelograms
A = bh OR A = lw
Area of Circles
A = πr^2
Perimeter
Add all sides.
Solving Equations
Add of subtract first then multiply or divide.
Circumference
C = 2πr OR C = πd
Properties of Real Numbers
Commutative : a + b = b + a ~ ab = ba Associative : a + ( b + c ) = ( a + b ) + c ~ a ( bc ) = ( ab ) c Distributive : a ( b + c ) = ab + ac Identity : a + 0 = a ~ a x 1 = a Inverse : a + ( -a ) = 0 ~ a x ( 1 / a ) = 1 Zero : a x 0 = 0
Degree
Degree of monomial = sum of exponents 4x³ is of degree 3 x²y³ is of degree 5
FOIL
F = First O = Outer I = Inner L = Last Used to distribute Binomials.
Scientific Notation
The first number must be 1 ≤ n ≤ 10.
Mode
The number that occurs the most in a data set.
Supplementary Angles
Two angles that add up to give you 180º.
Complementary Angles
Two angles that add up to give you 90º.
