The Academy · Grade 12 · Mathematics
Grade 12 Mathematics
Pre-Calculus. A senior year built around one idea: a function is a rule that pairs each input with exactly one output. Across 36 weeks you build that idea up through polynomials, rational functions, exponentials, logarithms, trigonometry, and sequences - the language calculus speaks. Every check is tap-only on phone or tablet; nothing to type.
Functions, Transformations, and the Standard Library
- Week 1 - What a function is. Notation f(x). Domain and range. Piecewise. Reading from a graph.
- Week 2 - Transformations: shifts, stretches, reflections. Even and odd. Vertex form.
- Week 3 - Composition (f composed with g) and inverse functions.
- Week 4 - Linear functions. Quadratics in standard, factored, and vertex form.
- Week 5 - Polynomials: degree, end behavior, synthetic division, the factor theorem.
- Week 6 - Rational functions: vertical and horizontal asymptotes, holes, slant asymptotes.
- Week 7 - Exponential functions: b^x, the natural base e, growth and decay.
- Week 8 - Logarithms as inverses of exponentials. Properties of logs.
- Week 9 - Exponential and logarithmic applications. Quarter 1 synthesis at 85% mastery.
Trigonometry
- Angles, radians, and the unit circle.
- Sine, cosine, tangent as functions.
- Graphs of trig functions. Amplitude, period, phase shift.
- Trig identities and equations.
- Inverse trig functions.
Analytic Geometry and Vectors
- Conic sections: parabolas, ellipses, hyperbolas.
- Parametric equations and polar coordinates.
- Vectors in two and three dimensions.
- Matrices and systems of equations.
Sequences, Series, and a Bridge to Calculus
- Arithmetic and geometric sequences and series.
- Mathematical induction.
- The binomial theorem.
- Limits, intuitively. A first look at instantaneous rate of change.
- Year synthesis - one interactive sequence reviewing the whole year (no paper).
Self-paced and self-checked. Every activity in every lesson is auto-graded by the runner; there is no human grader and no AI grader. Mastery is reached when you can do the tap-mechanics for a week reliably. Move at your own speed.
See something off? Report it. Resolutions are tracked on Corrections.