Math: Grades 9–12
High school math in bite-size courses, from linear equations through calculus. Each course is one focused topic; master it, then move to the next.
Algebra 1
Equations, lines and functions: the foundation for everything after.
- Functions & Transformations
Function notation, domain and range, and how shifting, stretching and reflecting a graph changes its equation.
- Polynomials & Factoring
Add, subtract and multiply polynomials, then factor them: common factors, trinomials, difference of squares and grouping.
After Exponents & Radicals
- Systems of Equations
Solve two equations at once by graphing, substitution and elimination, and model problems with systems of inequalities.
Geometry
Shapes, proof and measurement.
- Triangle Congruence
Prove triangles congruent with SSS, SAS, ASA, AAS and HL, and use congruence to prove properties of triangles and quadrilaterals.
After Logic & Proof
Trigonometry
Triangles and circles, then trig as functions.
- Laws of Sines & Cosines
Solve any triangle, not just right triangles, and find the area of a triangle from two sides and an angle.
- The Unit Circle & Radians
Radian measure, the unit circle, and the trigonometric functions of any angle.
After Functions & Transformations, Right Triangle Trigonometry
- Trig Identities & Equations
Pythagorean, sum and difference, and double-angle identities, and solving trigonometric equations.
After Graphs of Trig Functions
Algebra 2
Polynomial, rational, exponential and logarithmic functions.
- Complex Numbers
The imaginary unit, arithmetic with complex numbers, and complex solutions to quadratic equations.
- Logarithms
Logarithms as inverses of exponentials, the laws of logarithms, and solving exponential and logarithmic equations.
After Exponential Functions
- Polynomial Functions
Polynomial division, the remainder and factor theorems, finding zeros, and end behavior of polynomial graphs.
- Radical Functions & Equations
Rational exponents, graphs of square-root and cube-root functions, and solving radical equations (and spotting extraneous solutions).
- Sequences & Series
Arithmetic and geometric sequences, sigma notation, and finite and infinite geometric series.
After Exponential Functions
- Rational Functions
Simplify and operate on rational expressions, solve rational equations, and graph functions with asymptotes and holes.
After Polynomial Functions
Precalculus
Conics, vectors, matrices and polar coordinates.
- Matrices
Matrix operations, determinants and inverses, and solving systems of equations with matrices.
After Systems of Equations
- Polar & Parametric Equations
Polar coordinates and graphs, parametric equations, and the polar form of complex numbers.
After Graphs of Trig Functions, Vectors
Probability & Statistics
Data, chance and inference. Can be taken alongside the algebra track.
Calculus
Limits, derivatives, integrals and series (AP Calculus AB and BC scope).
- Limits & Continuity
What a limit is, how to evaluate one, limits at infinity, and what it means for a function to be continuous.
After Graphs of Trig Functions, Logarithms, Rational Functions
- Derivatives
The derivative as a rate of change and slope, and the power, product, quotient and chain rules.
After Limits & Continuity
- Applications of Derivatives
Related rates, optimization, curve sketching, and the mean value theorem.
After Derivatives
- Integrals & the Fundamental Theorem
Riemann sums, definite and indefinite integrals, u-substitution, and the fundamental theorem of calculus.
After Derivatives
- Applications of Integrals
Area between curves, volumes of revolution, average value, and accumulation problems.
- Infinite Series
Convergence tests, power series, and Taylor and Maclaurin series.
After Integrals & the Fundamental Theorem, Sequences & Series
- Integration Techniques
Integration by parts, partial fractions, trigonometric integrals, and improper integrals.
After Integrals & the Fundamental Theorem, Trig Identities & Equations
- Differential Equations
Slope fields, separable differential equations, and exponential and logistic growth models.
After Integration Techniques