# Grade 12 Mathematics Notes > CAPS-aligned Grade 12 Mathematics revision notes, broken down topic by topic with worked examples, diagrams, and key definitions. - Page: https://www.hlayiso.com/grade-12/mathematics/notes Breadcrumbs: [Home](https://www.hlayiso.com/) › [Grade 12](https://www.hlayiso.com/grade-12) › [Mathematics](https://www.hlayiso.com/grade-12/mathematics) › [Notes](https://www.hlayiso.com/grade-12/mathematics/notes) ## Topics Each section has a free preview; the full notes are in the free Hlayiso account. ### Exponents and Surds - [Exponents and Surds notes](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds) - [The Number System](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds/the-number-system) - [Working with Irrational Numbers](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds/working-with-irrational-numbers) - [Exponents](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds/exponents) - [Exponential Equations](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds/exponential-equations) - [Equations with Rational Exponents](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds/equations-with-rational-exponents) - [Exam-Type Examples](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds/exam-type-examples) ### Algebraic expressions, equations and inequalities - [Algebraic expressions, equations and inequalities notes](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities) - [Algebraic Expressions](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/algebraic-expressions) - [Addition and Subtraction](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/addition-and-subtraction) - [Multiplication and Division](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/multiplication-and-division) - [Factorising](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/factorising) - [Notes on Factorising a Trinomial](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/notes-on-factorising-a-trinomial) - [Quadratic Equations](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/quadratic-equations) - [Quadratic Inequalities](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/quadratic-inequalities) - [Simultaneous Equations](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/simultaneous-equations) - [The Nature of the Roots](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/the-nature-of-the-roots) ### Number patterns - [Number patterns notes](https://www.hlayiso.com/grade-12/mathematics/notes/number-patterns) - [Number Patterns](https://www.hlayiso.com/grade-12/mathematics/notes/number-patterns/number-patterns) - [Arithmetic Sequences](https://www.hlayiso.com/grade-12/mathematics/notes/number-patterns/arithmetic-sequences) - [Quadratic Sequences](https://www.hlayiso.com/grade-12/mathematics/notes/number-patterns/quadratic-sequences) - [Geometric Sequences](https://www.hlayiso.com/grade-12/mathematics/notes/number-patterns/geometric-sequences) - [Arithmetic and Geometric Series](https://www.hlayiso.com/grade-12/mathematics/notes/number-patterns/arithmetic-and-geometric-series) ### Functions and graphs - [Functions and graphs notes](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs) - [What is a Function?](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/what-is-a-function) - [Function Notation](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/function-notation) - [The Basic Functions, Formulas and Graphs](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/the-basic-functions-formulas-and-graphs) - [Inverse Functions](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/inverse-functions) - [The Logarithmic Function](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/the-logarithmic-function) ### Trig Functions - [Trig Functions notes](https://www.hlayiso.com/grade-12/mathematics/notes/trig-functions) - [Graphs of Trigonometric Functions](https://www.hlayiso.com/grade-12/mathematics/notes/trig-functions/graphs-of-trigonometric-functions) - [Effect of a: Amplitude](https://www.hlayiso.com/grade-12/mathematics/notes/trig-functions/effect-of-a-amplitude) - [Effect of q: Vertical Shift](https://www.hlayiso.com/grade-12/mathematics/notes/trig-functions/effect-of-q-vertical-shift) - [Effect of b: Period](https://www.hlayiso.com/grade-12/mathematics/notes/trig-functions/effect-of-b-period) - [Effect of p: Horizontal Shift](https://www.hlayiso.com/grade-12/mathematics/notes/trig-functions/effect-of-p-horizontal-shift) ### Finance, growth and decay - [Finance, growth and decay notes](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay) - [Revision: Simple and Compound Interest](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay/revision-simple-and-compound-interest) - [Calculating the Value of P, i and n](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay/calculating-the-value-of-p-i-and-n) - [Simple and Compound Decay Formulae](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay/simple-and-compound-decay-formulae) - [Nominal and Effective Interest Rates](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay/nominal-and-effective-interest-rates) - [Investments with Time and Interest Rate Changes](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay/investments-with-time-and-interest-rate-changes) - [Annuities](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay/annuities) ### Differential Calculus - [Differential Calculus notes](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus) - [Average Gradient](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/average-gradient) - [Average Rate of Change](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/average-rate-of-change) - [The Derivative of a Function at a Point](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/the-derivative-of-a-function-at-a-point) - [Uses of the Derivative](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/uses-of-the-derivative) - [Drawing the Graph of a Cubic Polynomial](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/drawing-the-graph-of-a-cubic-polynomial) ### Counting principle and probability - [Counting principle and probability notes](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability) - [Revision](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/revision) - [Theoretical Probability and Relative Frequency](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/theoretical-probability-and-relative-frequency) - [Venn Diagrams](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/venn-diagrams) - [Mutually Exclusive Events](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/mutually-exclusive-events) - [Complementary Events](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/complementary-events) - [Events Which Are Not Mutually Exclusive](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/events-which-are-not-mutually-exclusive) - [Summary of Symbols and Sets Used in Probability](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/summary-of-symbols-and-sets-used-in-probability) - [Tree Diagrams and Contingency Tables](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/tree-diagrams-and-contingency-tables) - [Contingency Tables](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/contingency-tables) - [Counting Principles](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/counting-principles) - [Use of Counting Principles in Probability](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability/use-of-counting-principles-in-probability) ### Analytical Geometry - [Analytical Geometry notes](https://www.hlayiso.com/grade-12/mathematics/notes/analytical-geometry) - [Revise: Analytical Geometry](https://www.hlayiso.com/grade-12/mathematics/notes/analytical-geometry/revise-analytical-geometry) - [The Equation of a Line](https://www.hlayiso.com/grade-12/mathematics/notes/analytical-geometry/the-equation-of-a-line) - [The Inclination of a Line](https://www.hlayiso.com/grade-12/mathematics/notes/analytical-geometry/the-inclination-of-a-line) - [Circles in Analytical Geometry](https://www.hlayiso.com/grade-12/mathematics/notes/analytical-geometry/circles-in-analytical-geometry) ### Trigonometry - [Trigonometry notes](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry) - [Revise: Trig Ratios](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/revise-trig-ratios) - [Trig Ratios in All Quadrants](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/trig-ratios-in-all-quadrants) - [Solving Triangles with Trig](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/solving-triangles-with-trig) - [Using a Calculator](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/using-a-calculator) - [Special Angles](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/special-angles) - [Using Reduction Formulae](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/using-reduction-formulae) - [Trigonometric Identities](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/trigonometric-identities) - [More Trig Identities](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/more-trig-identities) - [Solving Trigonometric Equations](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/solving-trigonometric-equations) - [More Solving Trig Equations](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/more-solving-trig-equations) - [Compound & Double Angle Identities](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/compound-and-double-angle-identities) - [Determining x Undefined](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry/determining-x-undefined) ### Trigonometry: Sine, Cosine and Area Rules - [Trigonometry: Sine, Cosine and Area Rules notes](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry-sine-cosine-and-area-rules) - [Right-angled Triangles](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry-sine-cosine-and-area-rules/right-angled-triangles) - [The Area Rule](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry-sine-cosine-and-area-rules/the-area-rule) - [The Sine Rule](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry-sine-cosine-and-area-rules/the-sine-rule) - [The Cosine Rule](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry-sine-cosine-and-area-rules/the-cosine-rule) - [Solving Problems in Two and Three Dimensions](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry-sine-cosine-and-area-rules/solving-problems-in-two-and-three-dimensions) ### Euclidean Geometry - [Euclidean Geometry notes](https://www.hlayiso.com/grade-12/mathematics/notes/euclidean-geometry) - [Revise: Proportion and Area of Triangles](https://www.hlayiso.com/grade-12/mathematics/notes/euclidean-geometry/revise-proportion-and-area-of-triangles) - [Proportion Theorems](https://www.hlayiso.com/grade-12/mathematics/notes/euclidean-geometry/proportion-theorems) - [Similar Polygons](https://www.hlayiso.com/grade-12/mathematics/notes/euclidean-geometry/similar-polygons) ### Statistics - [Statistics notes](https://www.hlayiso.com/grade-12/mathematics/notes/statistics) - [Bar Graphs and Frequency Tables](https://www.hlayiso.com/grade-12/mathematics/notes/statistics/bar-graphs-and-frequency-tables) - [Measures of Central Tendency](https://www.hlayiso.com/grade-12/mathematics/notes/statistics/measures-of-central-tendency) - [Measures of Dispersion (or Spread)](https://www.hlayiso.com/grade-12/mathematics/notes/statistics/measures-of-dispersion-or-spread) - [Five Number Summary and Box and Whisker Plot](https://www.hlayiso.com/grade-12/mathematics/notes/statistics/five-number-summary-and-box-and-whisker-plot) - [Histograms and Frequency Polygons](https://www.hlayiso.com/grade-12/mathematics/notes/statistics/histograms-and-frequency-polygons) - [Cumulative Frequency Tables and Graphs (Ogives)](https://www.hlayiso.com/grade-12/mathematics/notes/statistics/cumulative-frequency-tables-and-graphs-ogives) - [Variance and Standard Deviation](https://www.hlayiso.com/grade-12/mathematics/notes/statistics/variance-and-standard-deviation) - [Bivariate Data and the Scatter Plot](https://www.hlayiso.com/grade-12/mathematics/notes/statistics/bivariate-data-and-the-scatter-plot) - [The Linear Regression Line](https://www.hlayiso.com/grade-12/mathematics/notes/statistics/the-linear-regression-line) ## Frequently asked questions ### Are the Grade 12 Mathematics notes free? Each Grade 12 Mathematics note section has a free preview on Hlayiso. Create a free Hlayiso account to read the full notes on the web or in the app; the free plan has daily limits. ### Are the notes aligned with CAPS and the ATP? Yes. All Grade 12 Mathematics notes are written against the official CAPS curriculum and ATP so you only study what’s examinable. --- Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. When citing, link the page URL above, not a PDF or /api/ URL.