Grade 12: Math
Start with a unit whose prerequisites fit. Work through the lessons, use the study guide to review, and try the new cases before continuing.
- Unit 1 · 4 lessons
Precalculus: Composition and Inverse Functions
Function operations must respect input order and domain. A composition feeds one output into another function, while an inverse reverses a one-to-one relationship and exchanges the original domain and range.
Before you begin: Evaluate functions; solve linear equations; interpret square-root domains and restricted quadratic inputs.
- Unit 2 · 4 lessons
Precalculus: Radians and the Unit Circle
Radians measure an angle by arc length relative to radius. On the unit circle, cosine and sine are horizontal and vertical coordinates, so quadrant signs and special triangles support exact values beyond acute angles.
Before you begin: Use fractions of π; know right-triangle sine and cosine; read signed Cartesian coordinates.
- Unit 3 · 4 lessons
Precalculus: Trigonometric Identities and Equations
An identity holds for all inputs in its domain, while an equation asks for particular angle solutions. Algebraic identities, angle formulas and geometric laws must retain signs, intervals and their defining conditions.
Before you begin: Use unit-circle values; solve equations involving squares; distinguish degrees from radians.
- Unit 4 · 4 lessons
Interpret and Construct Periodic Models
Read, build, shift, and solve levels of supplied cosine functions over stated intervals.
Before you begin: Substitute into a function and solve a simple equation. · Read radians with π and use the cosine values supplied in each activity.
- Unit 5 · 4 lessons
Precalculus: Vectors and Parametric Lines
Vectors represent directed quantities through components, while parametric equations describe coordinates using a shared parameter. Component arithmetic, magnitude and dot product answer different questions and therefore produce different kinds of results.
Before you begin: Add signed coordinates; evaluate square roots; substitute one expression into another.
- Unit 6 · 4 lessons
Precalculus: Matrices and Linear Systems
Matrices organize linear operations and systems through rows and columns. Multiplication uses row-column products, a determinant tests two-dimensional invertibility, and valid row operations preserve a system’s solution set when applied to every entry.
Before you begin: Evaluate dot products; solve linear systems; multiply signed numbers.
- Unit 7 · 4 lessons
Introductory Calculus: Limits and Continuity
A limit describes nearby approach behavior rather than necessarily a function’s value at the point. One-sided agreement, removable holes and continuity connect algebraic simplification with precise statements about a function’s local behavior.
Before you begin: Factor quadratics; evaluate rational functions; distinguish excluded inputs from nearby allowed inputs.
- Unit 8 · 4 lessons
Introductory Calculus: Derivatives and Local Lines
A derivative measures instantaneous rate through a limiting difference quotient. Differentiation rules summarize that process for suitable functions, while a tangent line uses the derivative slope and the function’s actual point to model local behavior.
Before you begin: Evaluate limits of simple expressions; expand squared binomials; use point-slope form.
- Unit 9 · 4 lessons
Introductory Calculus: Integrals and Accumulation
Integration connects signed accumulation with limiting sums. Rectangle models approximate that accumulation, antiderivatives evaluate suitable definite integrals, and the Fundamental Theorem links an accumulation function’s derivative to its continuous integrand.
Before you begin: Compute rectangle area; differentiate simple polynomials; understand interval endpoints and signed outputs.
Check what you can explain
The subject test uses additional supplied cases across these units. Its feedback links back to the relevant lessons. Use it to plan practice; a score on these questions is not a school grade or proof of complete subject mastery.
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