Formula Sheet

Use when: Finding roots of a quadratic equation ax² + bx + c = 0

Use when: Determining the nature of roots of a quadratic

Use when: Finding the maximum or minimum point

Use when: Factoring a difference of two squares

Use when: Expanding a squared binomial sum

Use when: Expanding a squared binomial difference

Use when: Factoring the sum of two cubes

Use when: Factoring the difference of two cubes

Use when: Multiplying terms with the same base

Use when: Dividing terms with the same base

Use when: Raising a power to another power

Use when: Expanding or condensing log of a product

Use when: Expanding or condensing log of a quotient

Use when: Bringing exponent out of a logarithm

Use when: Converting logs to a new base

Use when: Finding the nth term of an AP

Use when: Sum of first n terms of an AP

Use when: Finding the nth term of a GP

Use when: Sum of first n terms of a GP

Use when: Sum of an infinite GP where |r| < 1

Use when: Expanding powers of binomials

Use when: Distance of complex number from origin

Use when: Relating sine and cosine of an angle

Use when: Relating tangent and secant

Use when: Relating cotangent and cosecant

Use when: Sine of sum/difference of angles

Use when: Cosine of sum/difference of angles

Use when: Tangent of sum/difference of angles

Use when: Sine of a doubled angle

Use when: Cosine of a doubled angle

Use when: Tangent of a doubled angle

Use when: Sine of a halved angle

Use when: Cosine of a halved angle

Use when: Tangent of a halved angle

Use when: Solving triangles with ASA or AAS

Use when: Solving triangles with SAS or SSS

Use when: Area given two sides and included angle

Use when: Converting sum of sines to a product

Use when: Converting sum of cosines to a product

Use when: Converting product of trig functions to a sum

Use when: Infinite series expansion of sine

Use when: Infinite series expansion of cosine

Use when: First principles derivation

Use when: Differentiating polynomials

Use when: Derivative of a product of functions

Use when: Derivative of a quotient of functions

Use when: Derivative of composite functions

Use when: Differentiating natural exponential

Use when: Differentiating natural log

Use when: Derivative of sine

Use when: Derivative of cosine

Use when: Derivative of tangent

Use when: Relating secant slope to tangent slope

Use when: Integrating polynomials (n ≠ −1)

Use when: Integral of a product of functions

Use when: Integrating inverse of x

Use when: Integrating natural exponential

Use when: Integrating sine

Use when: Integrating cosine

Use when: Finding area under a curve

Use when: Length of curve along a path

Use when: Evaluating definite integrals

Use when: Infinite series expansion of e^x

Use when: Distance between two points

Use when: Midpoint of a line segment

Use when: Point dividing a line segment in m:n ratio

Use when: Gradient of a line through two points

Use when: Equation of line given a point and slope

Use when: Equation of line given slope and y-intercept

Use when: Equation of circle centered at origin

Use when: Equation of circle centered at (h,k)

Use when: Up/Down facing parabola

Use when: Standard equation of an ellipse

Use when: Standard equation of a hyperbola

Use when: Shortest distance from point to line

Use when: Acute angle between two intersecting lines

Use when: Area using vertex coordinates

Use when: Intersection of medians

Use when: Length of a 3D vector

Use when: Algebraic definition of dot product

Use when: Geometric definition of dot product

Use when: Area of parallelogram formed by u, v

Use when: Determinant form of cross product

Use when: Vector projection

Use when: Volume of parallelepiped

Use when: Vector of length 1 in direction of u

Use when: Angles formed with axes

Use when: Work as a dot product

Use when: Average of a population

Use when: Spread of a population

Use when: Unbiased estimate of variance

Use when: Square root of variance

Use when: Standardizing normal distributions

Use when: Pearson correlation

Use when: Arrangements where order matters

Use when: Selections where order doesn't matter

Use when: Mean of a discrete random variable

Use when: Probability of exactly k successes

Use when: Updating probabilities with evidence

Use when: Joint variability of two variables

Use when: Standard deviation of sampling distribution