The Grade 12 Mathematics curriculum is the gateway to tertiary studies in science, engineering, and commerce. For the Class of 2026, success in the National Senior Certificate (NSC) requires a high level of abstract thinking and problem-solving, specifically in Differential Calculus, Euclidean Geometry, and Analytical Geometry.
This guide outlines the 2026 Mathematics Annual Teaching Plan (ATP), providing a structured weekly roadmap to help learners and teachers navigate the syllabus from sequences and series to probability.
Mathematics Grade 12 ATP 2026
The curriculum is rigorously divided into two papers: Paper 1 (Algebra/Calculus) and Paper 2 (Geometry/Stats). Concepts from Grades 10 and 11 (such as Exponents and basic Trigonometry) are foundational and integrated throughout.
Term 1: Algebra, Functions & Trigonometry
Focus: The first term covers the heavy algebraic topics of Paper 1 and introduces the advanced Trigonometry required for Paper 2.
- Weeks 1–2: Patterns, Sequences & Series
- Arithmetic and Geometric sequences and series.
- Convergence and Sum to Infinity (Geometric).
- Sigma notation ($\sum$) and its applications.
- Weeks 3–4: Functions & Inverses
- Concept of an inverse function ($f^{-1}$).
- Restricting domains to ensure functions are one-to-one.
- Graphs of Exponential ($y=a^x$) and Logarithmic ($y=\log_x$) functions.
- Weeks 5–6: Finance, Growth & Decay
- Future Value ($F$) and Present Value ($P$) annuities.
- Calculations involving loan repayments, sinking funds, and the time period ($n$) using logarithms.
- Weeks 7–10: Trigonometry
- Compound Angles: $\cos(\alpha \pm \beta)$, $\sin(\alpha \pm \beta)$.
- Double Angles: $\cos 2\alpha$, $\sin 2\alpha$.
- Solving trigonometric equations and proving identities.
- 2D and 3D problems: Using the Sine, Cosine, and Area rules in three dimensions.
Term 1 Assessments
- Task 1: Investigation or Project (e.g., Series or Functions).
- Task 2: Control Test (Minimum 50 Marks).
Term 2: Calculus & Analytical Geometry
Focus: The second term introduces the major new topic for Grade 12—Calculus—and advances coordinate geometry.
- Weeks 1–2: Polynomials
- The Remainder and Factor Theorems.
- Factorising cubic polynomials ($ax^3 + bx^2 + cx + d$).
- Weeks 3–6: Differential Calculus
- Limits: Understanding the concept of a limit ($\lim_{h \to 0}$).
- Differentiation: First principles ($f'(x) = \lim_{h \to 0} \frac{f(x+h) – f(x)}{h}$) and using rules (Power rule).
- Graphs: Drawing cubic functions (intercepts, stationary points, points of inflection).
* **Optimization:** Practical applications (e.g., maximizing area or minimizing cost).
- Weeks 7–9: Analytical Geometry
- Circles: Equation of a circle with center $(a;b)$: $(x-a)^2 + (y-b)^2 = r^2$.
- Tangents: Determining the equation of a tangent to a circle.
Term 2 Assessments
- Task 3: June Examination (Paper 1 & Paper 2) – 150 Marks each.
Term 3: Euclidean Geometry, Statistics & Probability
Focus: The third term deals with visual reasoning in Geometry and data analysis in Statistics.
- Weeks 1–4: Euclidean Geometry
- Proportionality: The Proportionality Theorem in triangles (lines parallel to one side).
- Similarity: Equiangular triangles and similarity proofs ($\Delta ABC ||| \Delta DEF$).
- Pythagoras: Proofs involving similar triangles.
- Weeks 5–7: Statistics
- Bivariate Data: Scatter plots, correlation, and the line of best fit (Least Squares Regression).
- Regression: Using the calculator to find $A$ and $B$ in $y = A + Bx$ and the correlation coefficient ($r$).
- Normality: The Normal Distribution curve.
- Weeks 8–9: Probability
- Counting Principles: Fundamental Counting Principle (FCP) and Factorial notation ($n!$).
- Arrangements with constraints (e.g., items grouped together).
Term 3 Assessments
- Task 4: Test (Minimum 50 Marks).
- Task 5: Trial / Preparatory Examination (Paper 1 & Paper 2).
Term 4: Final Assessment
Focus: The final term is dedicated to revision and the external NSC examination.
- Weeks 1–3: Revision of Past Papers (Papers 1 & 2).
- Final Assessment:NSC Final Examinations.
- Paper 1 (150 Marks): Algebra, Equations, Inequalities, Patterns, Functions, Calculus, Finance, Probability, Counting.
- Paper 2 (150 Marks): Statistics, Analytical Geometry, Trigonometry, Euclidean Geometry.
FAQ: Mathematics Grade 12
Q: What is the difference between Paper 1 and Paper 2?
A:
- Paper 1 focuses on Algebra, Calculus, and Functions. It is often considered the “calculation” paper.
- Paper 2 focuses on Geometry, Trigonometry, and Statistics. It involves more “visual” reasoning and proofs.
Q: How many marks is the Geometry section worth?
A:
Euclidean Geometry is a major component of Paper 2, usually accounting for 50 marks ($\pm$ 33% of the paper). This includes Grade 11 circle geometry and Grade 12 similarity/proportion.
Q: Is “Counting Principles” in Paper 1 or Paper 2?
A:
Counting Principles and Probability are examined in Paper 1.