Selected Mathematical Formulas

Algebra | ||

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 | ||

n^{th} Root | ||

n^{th} Root of a Product | ||

n^{th} 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 (x _{1},y_{1}) & (x_{2},y_{2}) | ||

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 b^{x} | ||

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 | ||

n^{th} Term of Arithmatic Sequence | ||

Sum of First n Terms of Arithmatic Sequence | given a _{1}, a_{n} and n | |

given a _{1}, d and n | ||

n^{th} Term of Geometric Sequence | ||

Sum of First n Terms of Geometric Sequence | ||

First n Terms of Fibonacci Sequence |

Geometry | |

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 |

Trigonometry | |

Pythagorean Theorem | |

Sine | |

Cosine | |

Tangent | |

Cosecant | |

Secant | |

Cotangent | |

Law of Sines | |

Law of Cosines | |

Standard Angles | |

0 ° | |

30 ° | |

45 ° | |

60 ° | |

90 ° |

Calculus | |

Derivatives | |

Chain Rule | |

x^{n} | |

e^{x} | |

Natural Log | |

Sine | |

Cosine | |

Integrals | |

x^{n} | |

e^{x} | |

1/x | |

Cosine | |

Sine |

Statistics | |

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 | |

Range | Highest - 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 |