Formulas & Concepts

The trapezoid area formula finds the area of a four-sided shape with one pair of parallel sides. Use A = ½(a + b)h, where a and b are the parallel sides and h is the height.

The area of a circle is πr², where r is the radius. Learn the formula, what each part means, and how to find the area from the radius or diameter.

The diameter of a circle is the longest distance across it, passing through the center — equal to twice the radius. Learn the definition and how to find it from radius or circumference.

A 30-60-90 triangle is a special right triangle with fixed side ratios 1 : √3 : 2. Learn the ratio, why it holds, and how to find every side from just one.

The hypotenuse is the longest side of a right triangle, opposite the right angle. Learn the definition and how to find it with the Pythagorean theorem.

An acute angle measures less than 90 degrees. Learn the definition, how acute angles compare to right and obtuse angles, and how they appear in triangles.

A right triangle has exactly one 90-degree angle. Learn the definition, the names of its sides (legs and hypotenuse), and the Pythagorean theorem that defines its side lengths.

Point-slope form — y − y₁ = m(x − x₁) — writes a line from a single point and the slope. Learn the formula, when to use it, and how to convert it to slope-intercept form.

Slope-intercept form — y = mx + b — reads off a line's slope and y-intercept at a glance. Learn what m and b mean and how to convert from point-slope form.

A coefficient is the number multiplying a variable in a term — like 7 in 7x. Learn the definition, how to spot coefficients, and how to combine like terms.

The binomial theorem expands (a + b)ⁿ into a sum of terms without multiplying step by step. Learn the formula, the binomial coefficients, and the link to Pascal's triangle.

The density formula is ρ = m / V — mass divided by volume. Learn what density measures, the three forms of the formula, and a worked example.

Partial fraction decomposition splits a complex rational expression into a sum of simpler fractions. Learn what it does, the steps to perform it, and why it is useful for integration.

An integer is a whole number with no fractional part — positive, negative, or zero. Learn the definition, the set of integers, and how they differ from other number types.

An irrational number cannot be written as a simple fraction — its decimal goes on forever without repeating. Learn the definition, examples like π and √2, and how they differ from rationals.

The median is the middle value of an ordered data set — a measure of center that ignores extreme values. Learn how to find it and when it beats the mean.

A derivative measures a function's instantaneous rate of change — the slope of its tangent line. Learn the concept, notation, and the core rules for computing one.

An integral accumulates a quantity over an interval — geometrically, the signed area under a curve. Learn the concept, notation, and how integrals reverse derivatives.

A Venn diagram uses overlapping circles to visualize how sets relate — what they share, what is unique to each, and how they combine. Learn the parts of a Venn diagram and how to read one.

Interval notation is a compact way to write ranges of numbers using parentheses and brackets. Learn what ( ), [ ], and combinations mean, and when to use each.

The domain of a function is the set of valid inputs (x-values); the range is the set of outputs (y-values) it produces. Learn how to find each and what to exclude.