The Grade 12 Technical Mathematics curriculum is designed to support students in technical fields by bridging abstract mathematical concepts with practical applications. Unlike standard Mathematics, this subject includes Complex Numbers, Integration, and practical Mensuration suited for engineering and trade contexts.
This guide outlines the 2026 Technical Mathematics Annual Teaching Plan (ATP), providing a structured weekly roadmap to help learners and teachers navigate the syllabus from differential calculus to Euclidean geometry.
Technical Mathematics Grade 12 ATP 2026
The curriculum is divided into four terms, with a strong emphasis on Calculus (Differentiation and Integration) and applied Geometry.
Term 1: Complex Numbers, Polynomials & Calculus
Focus: The first term introduces non-real numbers and the fundamental concepts of calculus (limits and derivatives).
- Weeks 1–3: Complex Numbers
- Definition: Defining complex numbers $\mathbb{C}$, where $z = a + bi$1.
- Operations: Simplifying imaginary numbers through addition, subtraction, multiplication, and division2.
- Representation: Using the Argand diagram and finding the Argument of $z$3.
- Forms: Converting between rectangular and polar (trigonometric) forms and solving equations with complex numbers4.
- Weeks 4–6: Analytical Geometry
- Circles: Determining the equation of a circle $x^2 + y^2 = r^2$ and tangents to circles5555.
- Ellipses: Plotting graphs of ellipses in the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$6.
- Weeks 7–8: Polynomials
- Theorems: Defining and applying the Remainder Theorem and Factor Theorem for third-degree polynomials7777.
- Factorising: Factorising cubic polynomials using inspection or long division8888.
- Weeks 9–11: Differential Calculus
- Limits: Intuitive understanding of limits and average gradient ($m = \frac{f(x+h)-f(x)}{h}$)9.
- Derivatives: Using first principles ($f'(x) = \lim_{h \to 0} \dots$) and differentiation rules ($\frac{d}{dx} (ax^n) = anx^{n-1}$)10101010.
- Graphs: Sketching cubic functions using stationary points and intercepts11.
- Optimization: Solving practical problems involving rates of change and motion12.
Term 1 Assessments
- PAT 1: Practical Assessment Task.
- Test: Control Test covering Term 1 content13.
Term 2: Integration, Trigonometry & Geometry
Focus: The second term covers the reverse of differentiation (Integration) and advances in 2D geometry.
- Weeks 1–3: Integration
- Concept: Integration as the converse of differentiation14.
- Functions: Integrating standard forms like $k$, $x^n$, and exponential functions ($ka^{nx}$)15.
- Area: Using integration to determine the magnitude of an area bounded by a curve and the x-axis16.
- Weeks 4–6: Trigonometry
- Revision: Right-angled triangles and basic ratios17.
- Rules: Applying the Sine, Cosine, and Area rules to solve problems in 2 dimensions18.
- Weeks 7–9: Euclidean Geometry
- Similarity: Theorems regarding equiangular triangles and triangles with proportional sides19.
- Proportionality: The theorem stating a line drawn parallel to one side of a triangle divides the other two sides proportionally20.
Term 2 Assessments
- PAT 2: Practical Assessment Task.
- Assignment.
- June Examination: Covering work from Grade 10, 11, and Term 1 & 221.
Term 3: Advanced Trigonometry & Trial Exams
Focus: The third term is dedicated to solving complex 3D problems and preparing for the final exams.
- Weeks 1–3: Trigonometry (3D)
- Solving problems in 2 and 3 dimensions.
- Note: Measurements must always be given for angles and lengths of sides22.
- Weeks 4–11: Consolidation & Trials
- Intensive revision and writing of the Trial Examinations (Paper 1 and Paper 2)23.
Term 3 Assessments
- PAT 3: Final Practical Assessment Task.
- Trial Examination: Papers 1 & 2.
Term 4: Final Assessment
Focus: The final term is dedicated to revision and the external NSC examination.
- Weeks 1–2: Revision of Algebra, Calculus, and Geometry.
- Final Assessment: NSC Final Examinations24.
Exam Structure: Paper 1 vs. Paper 2
It is critical to know the weighting of topics for your final revision:
| Paper 1 (150 Marks) | Marks | Paper 2 (150 Marks) | Marks |
| Algebra (Exponents, Logs, Equations) | $50 \pm 3$ | Analytical Geometry | $25 \pm 3$ |
| Functions & Graphs | $35 \pm 3$ | Trigonometry | $50 \pm 3$ |
| Finance, Growth & Decay | $15 \pm 3$ | Euclidean Geometry | $40 \pm 3$ |
| Differential Calculus & Integration | $50 \pm 3$ | Mensuration & Circles | $35 \pm 3$ |
| Total | 150 | Total | 150 |
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FAQ: Technical Mathematics Grade 12
Q: What is the difference between Technical Maths and Pure Maths?
A:
Technical Maths includes Integration (calculating areas under curves), Complex Numbers (imaginary numbers), and focuses heavily on practical applications like Mensuration (gears, angular movement). It does not include Probability or Statistics.
Q: Is Integration examined in Paper 1 or Paper 2?
A:
Integration is examined in Paper 1, combined with Differential Calculus. Together they count for approx. 50 marks26.
Q: Do I need to know circle geometry proofs?
A:
You need to apply theorems (like proportionality and similarity) and solve problems, but the ATP specifically notes for polynomials that “No proofs are required”27. Check your specific exam guidelines for geometry proofs.