Mathematics
Algebra and finance formulas, explained with worked examples.
Algebra
Quadratic Formula
Find the roots of any quadratic equation ax² + bx + c = 0, even when it can't be factored by inspection.
Learn more →Pythagorean Theorem
Relates the three sides of a right triangle, letting you find any one side from the other two.
Learn more →Slope-Intercept Form
The most common way to write the equation of a straight line, revealing its slope and y-intercept directly.
Learn more →Distance Formula
Calculates the straight-line distance between two points on a coordinate plane.
Learn more →Midpoint Formula
Finds the exact point halfway between two coordinates by averaging their x- and y-values.
Learn more →Finance
Simple Interest
Calculate interest earned on a principal amount at a fixed annual rate.
Learn more →Compound Interest
Calculate how an investment or loan grows when interest is calculated repeatedly on both the principal and previously earned interest.
Learn more →Calculus — Derivatives
Power Rule
The most fundamental differentiation rule — multiply by the exponent, then reduce the exponent by one.
Learn more →Product Rule
Differentiates a product of two functions — you cannot simply multiply their individual derivatives.
Learn more →Quotient Rule
Differentiates a ratio of two functions — remembered by the mnemonic "low d-high minus high d-low, over low squared."
Learn more →Chain Rule
Differentiates composite functions — functions nested inside other functions.
Learn more →Trigonometric Derivatives
The derivatives of all six trigonometric functions — sin, cos, tan, cot, sec, and csc.
Learn more →Inverse Trig Derivatives
The derivatives of the inverse trigonometric functions — arcsin, arccos, arctan, and arccot.
Learn more →Exponential & Log Derivatives
The three core derivatives involving exponential and logarithmic functions: eˣ, aˣ, and ln x.
Learn more →Calculus — Integrals
Basic Integration Rules
The essential integral formulas for constants, 1/x, eˣ, aˣ, and ln x.
Learn more →Trigonometric Integrals
The complete table of ten standard trigonometric integrals — each the reverse of a derivative rule.
Learn more →Special Integrals
Two integral forms that arise from square roots of quadratic expressions, producing inverse-trig or logarithmic results.
Learn more →Trigonometry
Sine, Cosine & Tangent
The three fundamental trigonometric ratios for right triangles, remembered with SOH-CAH-TOA.
Learn more →Law of Sines
Relates the sides of any triangle to the sines of their opposite angles — not just right triangles.
Learn more →Law of Cosines
A generalization of the Pythagorean theorem that works for any triangle, not just right triangles.
Learn more →Statistics
Mean, Median & Mode
The three measures of central tendency for a data set — mean (average), median (middle), and mode (most frequent).
Learn more →Standard Deviation
Measures how spread out data values are from the mean.
Learn more →Combinations & Permutations
Count the number of ways to choose (combinations) or arrange (permutations) items from a group.
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