Pre-Calculus & Calculus Mastery Hub
Grade 12 closes the K–12 path: advanced function analysis, polar & parametric forms, vectors, matrices, limits, derivatives, integrals, and differential equations.
Grade 12 · Pre-Calculus & Calculus
Curriculum Chapters
Advanced Function Analysis
Domain, range, intercepts and asymptotes, function composition and decomposition, piecewise models, sketching from features, and mixed equations and inequalities.
Polar & Parametric Equations
Convert points and equations between rectangular and polar form, graph polar curves, and write and graph parametric curves with orientation.
Vectors
Add, subtract, and scale vectors, find magnitude and direction, and use the dot product to find the angle between two vectors.
Matrices
Add, subtract, and multiply matrices, find the determinant and inverse of a 2×2 matrix, and solve a linear system with Ax = b.
Limits & Continuity
Estimate limits from tables and graphs, evaluate limits analytically and at infinity, classify discontinuities, and apply the intermediate-value theorem.
The Derivative — Tangent Lines
Watch secant lines become tangent lines, build the limit definition of the derivative, and write the equation of a tangent line.
The Derivative — Rules
Master the power, product, quotient, and chain rules and differentiate polynomial, rational, radical, exponential, logarithmic, and trig functions.
Applications of the Derivative
Find increasing/decreasing intervals, extrema, concavity, and inflection points, solve optimization and related-rates problems, and apply the mean-value theorem.
The Integral
Estimate definite integrals with Riemann sums, apply the fundamental theorem of calculus, and evaluate integrals by antidifferentiation and u-substitution.
Applications of Integration
Find area between curves, volumes of solids of revolution and known cross-sections, the average value of a function, and total displacement and distance.
Differential Equations
Explore slope fields, sketch solution curves, and solve separable differential equations.
Distributions & Inference
Expected value and variance, binomial and normal distributions, confidence intervals for a proportion, and one-sample hypothesis tests.
About this page
About Grade 12 Mathematics
Grade 12 Mathematics on Scholi is organised chapter by chapter. Each chapter opens as an interactive lesson with a visualizer, a cheat sheet of the rules and worked examples, and a practice set arranged in easy, medium and hard tiers.