Place value, the four operations, factors and multiples: the foundation for all later math.

Understand, compare and compute with fractions and decimals, and connect them to percents.

Units and conversions, shapes and their properties, perimeter, area, volume and simple graphs.

Proportional reasoning for real life: ratios, unit rates, percents, discounts and interest.

Integers, exponents, expressions, equations and inequalities: everything you need before Algebra I.

Angles, area, volume, surface area, the Pythagorean theorem and transformations.

Describe and display data, measure center and spread, and calculate simple probabilities.

Linear equations and functions, systems, polynomials, factoring, quadratics and exponential models.

Proofs, congruence, similarity, right triangles, circles, polygons, solids and coordinate geometry.

Functions, complex numbers, polynomials, rational and radical functions, logarithms and sequences.

The unit circle, trig functions and graphs, identities, equations, laws of sines and cosines, and vectors.

A deep review of functions, exponentials, trigonometry, conics, vectors, matrices and limits before calculus.

AP-level statistics: distributions, regression, study design, probability, random variables and inference.

The math of money: interest, saving, investing, loans, credit and budgeting.

Limits, continuity, differentiation rules, applications of derivatives and an introduction to integrals.

Integration techniques and applications, sequences and series, power series and polar/parametric calculus.

Vectors and 3D space, partial derivatives, optimization, multiple integrals and vector calculus.

Linear systems, matrices, vector spaces, eigenvalues, orthogonality and the SVD.

First- and second-order ODEs, modeling, Laplace transforms, systems and series solutions.

Logic, proofs, sets, counting, recurrences, graph theory and number theory for computer science.

Axiomatic probability, discrete and continuous random variables, joint distributions and limit theorems.

Divisibility, primes, congruences and classic theorems of elementary number theory.

The rigorous foundations of calculus: completeness, sequences, continuity, differentiation and integration.

Groups, homomorphisms, rings and fields: the structures behind algebra.