# Grade 12 Technical Mathematics Notes

> CAPS-aligned Grade 12 Technical Mathematics revision notes, broken down topic by topic with worked examples, diagrams, and key definitions.

- Page: https://www.hlayiso.com/grade-12/technical-mathematics/notes

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## Topics

Each section has a free preview; the full notes are in the free Hlayiso account.

### Complex Numbers

- [Complex Numbers notes](https://www.hlayiso.com/grade-12/technical-mathematics/notes/complex-numbers)
- [Solving Equations With Complex Numbers](https://www.hlayiso.com/grade-12/technical-mathematics/notes/complex-numbers/solving-equations-with-complex-numbers)
- [Argand Diagram Argument and Polar Form](https://www.hlayiso.com/grade-12/technical-mathematics/notes/complex-numbers/argand-diagram-argument-and-polar-form)
- [Defining and Simplifying Complex Numbers](https://www.hlayiso.com/grade-12/technical-mathematics/notes/complex-numbers/defining-and-simplifying-complex-numbers)

### Analytical Geometry

- [Analytical Geometry notes](https://www.hlayiso.com/grade-12/technical-mathematics/notes/analytical-geometry)
- [Equation of a Circle Centre at the Origin](https://www.hlayiso.com/grade-12/technical-mathematics/notes/analytical-geometry/equation-of-a-circle-centre-at-the-origin)
- [The Ellipse](https://www.hlayiso.com/grade-12/technical-mathematics/notes/analytical-geometry/the-ellipse)
- [Tangents to Circles and Points of Intersection](https://www.hlayiso.com/grade-12/technical-mathematics/notes/analytical-geometry/tangents-to-circles-and-points-of-intersection)

### Polynomials and Algebra

- [Polynomials and Algebra notes](https://www.hlayiso.com/grade-12/technical-mathematics/notes/polynomials-and-algebra)
- [Factorising Third-Degree Polynomials](https://www.hlayiso.com/grade-12/technical-mathematics/notes/polynomials-and-algebra/factorising-third-degree-polynomials)
- [Remainder Theorem and Factor Theorem](https://www.hlayiso.com/grade-12/technical-mathematics/notes/polynomials-and-algebra/remainder-theorem-and-factor-theorem)

### Differential Calculus

- [Differential Calculus notes](https://www.hlayiso.com/grade-12/technical-mathematics/notes/differential-calculus)
- [Sketching Cubic Functions and Optimisation](https://www.hlayiso.com/grade-12/technical-mathematics/notes/differential-calculus/sketching-cubic-functions-and-optimisation)
- [Limits Average Gradient and First Principles](https://www.hlayiso.com/grade-12/technical-mathematics/notes/differential-calculus/limits-average-gradient-and-first-principles)
- [Differentiation Rules and Equations of Tangents](https://www.hlayiso.com/grade-12/technical-mathematics/notes/differential-calculus/differentiation-rules-and-equations-of-tangents)

### Integration

- [Integration notes](https://www.hlayiso.com/grade-12/technical-mathematics/notes/integration)
- [Area Under Curves and Between Curves](https://www.hlayiso.com/grade-12/technical-mathematics/notes/integration/area-under-curves-and-between-curves)
- [Standard Integrals and Integrating Polynomials](https://www.hlayiso.com/grade-12/technical-mathematics/notes/integration/standard-integrals-and-integrating-polynomials)

### Trigonometry

- [Trigonometry notes](https://www.hlayiso.com/grade-12/technical-mathematics/notes/trigonometry)
- [Problems in Two and Three Dimensions](https://www.hlayiso.com/grade-12/technical-mathematics/notes/trigonometry/problems-in-two-and-three-dimensions)
- [Trigonometric Ratios and Right-Angled Triangles](https://www.hlayiso.com/grade-12/technical-mathematics/notes/trigonometry/trigonometric-ratios-and-right-angled-triangles)
- [Sine, Cosine and Area Rules](https://www.hlayiso.com/grade-12/technical-mathematics/notes/trigonometry/sine-cosine-and-area-rules)

### Euclidean Geometry

- [Euclidean Geometry notes](https://www.hlayiso.com/grade-12/technical-mathematics/notes/euclidean-geometry)
- [Proportionality Theorem and Parallel Lines](https://www.hlayiso.com/grade-12/technical-mathematics/notes/euclidean-geometry/proportionality-theorem-and-parallel-lines)
- [Similar and Congruent Triangles](https://www.hlayiso.com/grade-12/technical-mathematics/notes/euclidean-geometry/similar-and-congruent-triangles)

## Frequently asked questions

### Are the Grade 12 Technical Mathematics notes free?

Each Grade 12 Technical 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 Technical Mathematics notes are written against the official CAPS curriculum and ATP so you only study what’s examinable.

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