Learn math in order

How PEMDAS really works: why multiplication and division tie, how to handle exponents, negatives and fraction bars, and worked examples with answers.

A complete fraction refresher: simplifying, common denominators, mixed numbers, multiplying, dividing, comparing and converting, with worked problems.

The three kinds of percent problem, percent increase and decrease, discounts and tax, undoing a percent change, and simple and compound interest.

Ratios, unit rates and proportions explained: simplifying ratios, cross-multiplying, scale drawings, unit conversion, and direct and inverse variation.

The product, quotient, power, zero, negative and fractional exponent rules, how to combine them, scientific notation, and the mistakes that cost points.

Simplify square roots and cube roots, add and multiply radicals, rationalize denominators, convert to fractional exponents, and solve radical equations.

Solve any linear equation: one-step and multi-step, variables on both sides, fractions and decimals, no-solution cases, and word problems, with worked examples.

Solve and graph inequalities: when to flip the sign, compound "and" and "or" inequalities, absolute value inequalities, and interval notation.

Find slope from two points, write a line in slope-intercept, point-slope or standard form, and handle parallel and perpendicular lines, with worked examples.

Solve systems of two linear equations by substitution, elimination or graphing, spot no-solution and infinite-solution systems, and set up word problems.

A reliable order for factoring: greatest common factor, trinomials, the ac method, difference of squares, cubes and grouping, with worked examples and practice.

Three methods for solving any quadratic equation, with fully worked examples, how to choose the fastest method, what the discriminant tells you, and the mistakes that cost the most points.

What a function is, how to read f(x), find domain and range, compose two functions, find an inverse, and shift a graph, with worked examples and practice.

How f(x) + k, f(x − h), −f(x), f(−x) and a·f(x) move a graph, why horizontal shifts look backwards, and how to combine transformations in order.

Exponential growth and decay explained: the formula y = a(1 + r)^t, growth vs decay factors, compound interest, half-life, and linear vs exponential.

What a logarithm means, the product, quotient, power and change-of-base rules, and how to solve exponential and log equations, with growth examples.

The nth-term and sum formulas for arithmetic and geometric sequences, how to tell them apart, infinite geometric series, and worked examples.

Every common area, surface area and volume formula in one place, plus composite shapes, unit conversions, scaling, and real-world problems with full solutions.

Use a² + b² = c² to find a missing side, test whether a triangle is right, find distances on a graph, and recognize triples and special right triangles.

Every circle formula you need: circumference, area, arc length, sector area in degrees and radians, inscribed angles, and the equation (x − h)² + (y − k)² = r².

How sine, cosine and tangent work in a right triangle, how to find a missing side or angle, angles of elevation, exact values, and complementary angles.

Learn the unit circle: radians, the first-quadrant values, reference angles, signs in each quadrant, tangent, coterminal angles and the Pythagorean identity.

How to find the mean, median, mode, range, quartiles and standard deviation, when each is the right summary, and how changing data affects them.

Probability basics: complements, the addition and multiplication rules, conditional probability in two-way tables, counting and expected value.

The counting principle, factorials, permutations vs combinations with nPr and nCr, repeated letters, and probability with combinations, with worked examples.

What a limit means, how to evaluate one by substitution, factoring and rationalizing, one-sided limits, limits at infinity, and continuity, with examples.

What a derivative measures, the limit definition, the power, product, quotient and chain rules, tangent lines and motion problems, with worked examples.

What an integral means, the basic integration rules, definite integrals and area, the Fundamental Theorem of Calculus, and u-substitution, with examples.

How the digital SAT Math section works, the four content areas and what each covers, timing, the built-in calculator, sample questions and an 8-week study plan.

The ACT Math format after the 2025 update, the topics it tests, what it covers that the SAT does not, a pacing plan, and a four-week study schedule.