Subject: Mathematics Grade: 12 Focus: Calculus, Euclidean Geometry, Trigonometry, and Algebra
Introduction
Grade 12 Mathematics is the most important exam of your school career. The curriculum is split into two papers.
- Paper 1 (Algebra & Calculus): Focuses on equations, sequences, and calculus.
- Paper 2 (Geometry & Trig): Focuses on space, shape, and measurement.
This guide breaks down the Exam Guidelines into manageable sections.
1. The “Major Weight” Topics
According to the guidelines, these topics carry the most marks.
A. Functions & Graphs (Paper 1 – Approx. 35 Marks)
You need to know the properties of these graphs inside out:
- Straight Line
- Parabola
- Hyperbola
- Exponential
- Inverse Functions: You must know how to find the inverse of a function (swap x and y).
- Logarithmic Function: The inverse of the exponential graph.
B. Calculus (Paper 1 – Approx. 35 Marks)
This is a new topic in Grade 12 but carries huge weight.
- First Principles: Know the formula.
- Rules of Differentiation: Power rule, constant rule, sum/difference rule.
- Cubic Graphs: Find turning points (where f'(x) = 0) and points of inflection (where f”(x) = 0).
- Optimization: Using calculus to find maximum/minimum values in real-world problems.
C. Euclidean Geometry (Paper 2 – Approx. 50 Marks)
This relies on Grade 11 theorems (Circle Geometry) plus Proportionality and Similarity.
- Ratio & Proportion: The “Proportionality Theorem” (a line parallel to one side of a triangle divides the other two sides proportionally).
- Similarity: Prove triangles are similar (AAA) to set up ratios.
D. Trigonometry (Paper 2 – Approx. 40 Marks)
- Compound & Double Angles: Expansions for Sine and Cosine.
- 2D & 3D Problems: Using the Sine, Cosine, and Area rules to solve complex triangles.
2. Exam Breakdown & Weighting
Paper 1: 3 Hours (150 Marks)
| Topic | Weighting |
|---|---|
| Algebra, Equations & Inequalities | 25 +/- 3 |
| Patterns and Sequences | 25 +/- 3 |
| Functions and Graphs | 35 +/- 3 |
| Finance, Growth & Decay | 15 +/- 3 |
| Differential Calculus | 35 +/- 3 |
| Probability | 15 +/- 3 |
Paper 2: 3 Hours (150 Marks)
| Topic | Weighting |
|---|---|
| Statistics | 20 +/- 3 |
| Analytical Geometry | 40 +/- 3 |
| Trigonometry | 40 +/- 3 |
| Euclidean Geometry | 50 +/- 3 |
3. Study Tips for Distinction
Tip 1: Master the “Information Sheet”
The exam paper includes a formula sheet (Chapter 5 of the guide).
- Don’t Memorize Formulas: Learn how to use them.
- Identify Gaps: If a formula isn’t on the sheet (e.g., some financial maths formulas), you MUST memorize it.
Tip 2: Euclidean Geometry “Acceptable Reasons”
You cannot just write any reason in a proof. You must use the standard, acceptable abbreviations listed in the guidelines (e.g., “tan chord theorem” or “opp angles cyclic quad”). Using non-standard reasons loses marks.
Tip 3: Calculator Skills (Statistics)
For Paper 2 (Statistics), learn to use your calculator’s “Stat Mode” to find the Regression Line (y = A + Bx) and Correlation Coefficient (r). This saves massive time.
Conclusion
Grade 12 Maths is a marathon, not a sprint.
- Paper 1: Focus on Calculus and Functions first—they are predictable.
- Paper 2: Practice Euclidean Geometry daily to train your eye to see the patterns.
Good luck with your Matric Finals!