Selected Mathematical Formulas

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Arithmetic Operations
Factoring Out Constant
Multiplication/Division

of Fraction by a

Constant
Addition of Fractions
Subtraction of Fractions
Miscelaneous

Relationships
Powers and Exponents
Multiplication
Division
Power to a Power
Zero Power
a ≠ 0
Power of a Product
Power of a Quotient
Negative Exponents
Fractional Exponent
Radicals
nth Root
nth Root of a Product
nth Root of a Quotient
Root of a Root
Root of a Power
(if n is odd)

(if n is even)
Properties of Inequalities
Properties of Absolute Value
Definition
NonNegativity
Reflective Symmetry of Graph
Multiplicativeness
Preservation of Division
b ≠ 0
Triangle Inequality
Reverse Triangle Inequality
Distance Formula
Distance Between Points
(x1,y1) & (x2,y2)
Complex Numbers
Definition
Square and Square Root
Addition of Complex Numbers
Subtraction of Complex Numbers
Multiplication of Complex Numbers
Multiplication by Complex Conjugate
Complex Modulus
Complex Conjugate
Properties of Logarithms
Definition
Natural Log
Common Log
Log of b
Log of 1
Log bx
Log of Exponent
Log of Product
Log of Quotient
Domain of Log Function
Polynomials
Difference of Two Squares
Perfect Square
Two Binomials
Perfect Cube
Sum of 2 Cubes
Difference of 2 Cubes
Difference of 2 Even Powers
Quadratic Equation
a ≠ 0
Quadratic Formula
Number & Types of Roots
of Quadratic Formula


Square Root Property
Cubic Equation
Cubic Formula
Roots
Discriminant
D > 0
D = 0
D < 0
Linear Functions
Constant Function
Slope-Intercept Form
Slope
Point-Slope Form
Parabola/Quadratic Functions
Parabola with Vertex at (h,k)
Opens Up if a > 0, Down if a < 0
Parabola
Opens Up if a > 0, Down if a < 0

Vertex
Parabola
Opens Right if a > 0, Left if a < 0

Vertex
Circle
Circle
w/radius = r and Vertex at (h,k)
Ellipse
Ellipse w/Center at (h,k)
Vertices 'a' units r/l & 'b' units u/d from center
Hyperbola
Hyperbola w/Center at (h,k)
Opens Left/Right, Vertices at 'a' units L/R of center. Asymptotes with Slope ± b/a
Hyperbola w/Center at (h,k)
Opens Up/Down, Vertices at 'b' units U/D of center. Asymptotes with Slope ± b/a
Sequences and Series
nth Term of Arithmatic Sequence
Sum of First n Terms of
Arithmatic Sequence

given a1, an and n

given a1, d and n
nth Term of Geometric Sequence
Sum of First n Terms of
Geometric Sequence









































Rectangles
Area
Perimeter
Triangles
Area
Perimeter
Circles
Area
Circumference
Rectangular Solids
Volume
Surface Area
Cylinders
Volume
Surface Area
Spheres
Volume
Surface Area
Polygons
Area
Perimeter
Cones
Volume
Surface Area









































Pythagorean Theorem
Sine
Cosine
Tangent
Cosecant
Secant
Cotangent
Law of Sines
Law of Cosines
Standard Angles
0 °
30 °
45 °
60 °
90 °









































Derivatives
Chain Rule
xn
ex
Natural Log
Sine
Cosine
Integrals
xn
ex
1/x
Cosine
Sine









































Central Tendancy
Sample Mean
Population Mean
Geometric Mean
Sample Standard Deviation
Population Standard Deviation
Sample Variance
Population Variance
Sample Mean for
a Frequency Distribution
Sample Standard Deviation for
a Frequency Distribution
Sample Coefficient of Variation
Median
Odd number of values

Even number of values
Mode
RangeHighest - Lowest value
Normal Distribution
Standard z Value
Probability
Probability of "A"
Probability of Compliment of "A"
Multiplication rule for
Independant Events
General Multiplication Rules
Addition Rule for
Mutually Exclusive Events
General Addition Rule
Permutations
Combinations
Factorial
Mean of
Discrete Probability Distribution
Standard Deviation of
Discrete Probability Distribution
Binomial Distribution
Binomial Probability Distribution
Mean for a
binomial distribution
Standard deviation for a
binomial distribution
Confidence Intervals
Confidence Interval for a mean
(Large Samples)

(Small Samples)
Confidence interval for a proportion
(where np > 5 and nq > 5)
Sample Size
Sample Size for Estimating Means
Sample Size for
Estimating Proportions

with preliminary estimate for p

without preliminary estimate for p
Regression and Correlation
Sum of the Squares
Least Squares Line
Standard Error of Estimate
Pearson Product-Moment
Correlation Coefficient
Coefficient of Determination
Confidence Interval for y
Spearman Rank
Correlation Coefficient