MATH · Grade 12 CAPS
Mathematics
CAPS Grade 12 Mathematics (Paper 1: Algebra, Calculus, Finance; Paper 2: Analytical & Euclidean Geometry, Trigonometry, Statistics)
Official DBE "Mind the Gap" Study Guides
Free downloadable Department of Basic Education self-study textbooks and literature guides.
Mind the Gap Study Guide
English
DBE Mind the Gap Study Guide: Mathematics
29.68 MB PDF
CAPS Examination Guidelines
English
DBE Official CAPS Examination Guidelines (2021): Mathematics
1.19 MB PDF
Mind the Gap Study Guide
Afrikaans
DBE Mind the Gap Study Guide: Wiskunde
23.82 MB PDF
Official CAPS Examination Structure
Standard paper durations and mark allocations prescribed by the Department of Basic Education (DBE).
Paper 1
180 mins
150 marks
150 marks, 3 hours: Algebra (25), Patterns (25), Functions (35), Financial Maths (15), Calculus (35), Probability (15)
Paper 2
180 mins
150 marks
150 marks, 3 hours: Statistics (20), Analytical Geometry (30), Trigonometry (40), Euclidean Geometry (50), Circle Theorems (10)
CAPS Topics & Exam Mark Weightings
Topic-by-topic weightings and syllabus breakdown for Grade 12.
| Paper | Term | Topic Title | Exam Weighting | Scope / Overview |
|---|---|---|---|---|
| Paper 1 | Term 1 | Algebra, Equations & Inequalities | 25 marks (~16.7%) | Quadratic equations, quadratic inequalities, simultaneous equations, laws of exponents, surds, and nature of roots. |
| Paper 1 | Term 1 | Number Patterns, Sequences & Series | 25 marks (~16.7%) | Arithmetic and geometric sequences, sigma notation, sum to infinity, quadratic patterns. |
| Paper 1 | Term 1 | Functions & Inverse Functions | 35 marks (~23.3%) | Linear, quadratic, hyperbolic and exponential functions, domain, range, asymptotes, and algebraic inverse reflections. |
| Paper 1 | Term 2 | Financial Mathematics | 15 marks (~10%) | Future and present value annuities, sinking funds, balance of loans, outstanding balances, nominal vs effective interest. |
| Paper 1 | Term 2 | Differential Calculus | 35 marks (~23.3%) | Limits, derivative from first principles, differentiation rules, tangents, cubic polynomial sketches, optimization and rates of change. |
| Paper 1 | Term 3 | Probability & Counting Principles | 15 marks (~10%) | Addition and multiplication rules, Venn diagrams, tree diagrams, contingency tables, fundamental counting principle, factorial combinations. |
| Paper 2 | Term 1 | Analytical Geometry | 30 marks (~20%) | Distance, gradient, midpoint, equation of lines, inclination, circle equations, tangents to circles, properties of chords. |
| Paper 2 | Term 2 | Trigonometry | 40 marks (~26.7%) | Compound and double angle identities, general solutions, reduction formulae, trig graphs, sine/cosine/area rules in 2D and 3D triangles. |
| Paper 2 | Term 3 | Euclidean Geometry & Circle Theorems | 50 marks (~33.3%) | Proportionality theorem, similarity of triangles, circle theorems (angles subtended by chord, cyclic quads, tangent-chord theorem). |
| Paper 2 | Term 1 | Statistics & Regression | 20 marks (~13.3%) | Histograms, ogives, five-number summary, box-and-whisker plots, variance, standard deviation, scatter plots, bivariate data, least squares regression line. |
Revision Study Notes & Worked Examples
High-yield CAPS definitions, formulas, and step-by-step worked solutions.
Functions & Inverse Functions
Inverse Functions, Parabolas & Hyperbolas
15 min read
2.1 Revision
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Functions & Inverse Functions
Inverse Functions, Parabolas & Hyperbolas
15 min read
2.2 Functions and relations
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Functions & Inverse Functions
Inverse Functions, Parabolas & Hyperbolas
15 min read
2.3 Inverse functions
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Differential Calculus
Derivative from First Principles
15 min read
Differential Calculus: First Principles & Rules
1. The First Principles Definition
The derivative \( f'(x) \) represents the instantaneous rate of change of a function. By definition:
\( f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \)
Crucial Exam Rules:
- Always state the formula first.
- Write
\lim_{h \to 0}on every single line until you actually substitute \( h = 0 \). - Factor out \( h \) in the numerator before dividing by the denominator \( h \).
Worked Example:
Find \( f'(x) \) from first principles if \( f(x) = 2x^2 - 3x \).
- \( f(x+h) = 2(x+h)^2 - 3(x+h) = 2(x^2 + 2xh + h^2) - 3x - 3h = 2x^2 + 4xh + 2h^2 - 3x - 3h \)
- \( f(x+h) - f(x) = (2x^2 + 4xh + 2h^2 - 3x - 3h) - (2x^2 - 3x) = 4xh + 2h^2 - 3h = h(4x + 2h - 3) \)
- \( f'(x) = \lim_{h \to 0} \frac{h(4x + 2h - 3)}{h} = \lim_{h \to 0} (4x + 2h - 3) = 4x - 3 \)
Examiner Tip: Always write the limit notation in every step until h is replaced by 0; forgetting lim loses 1 mark.
Differential Calculus
Rules of Differentiation & Tangents to Cubic Curves
15 min read
6.1 Limits
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Differential Calculus
Rules of Differentiation & Tangents to Cubic Curves
15 min read
6.2 Differentiation from first principles
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Differential Calculus
Rules of Differentiation & Tangents to Cubic Curves
15 min read
6.3 Rules for differentiation
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Analytical Geometry
Equation of Circles & Tangents to Circles
15 min read
7.1 Revision
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Analytical Geometry
Equation of Circles & Tangents to Circles
15 min read
7.2 Equation of a circle
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Analytical Geometry
Equation of Circles & Tangents to Circles
15 min read
7.3 Equation of a tangent to a circle
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Euclidean Geometry & Circle Theorems
Circle Theorems, Tangents & Proportionality
15 min read
8.1 Revision
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Euclidean Geometry & Circle Theorems
Circle Theorems, Tangents & Proportionality
15 min read
8.2 Ratio and proportion
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Euclidean Geometry & Circle Theorems
Circle Theorems, Tangents & Proportionality
15 min read
8.3 Polygons
Content adapted under
Creative Commons Attribution (CC-BY 4.0)
from Siyavula Open Education Grade 12 CAPS textbooks.
Examiner Tip: High-frequency exam topic in National NSC Examinations. Practice all worked examples step-by-step.
Official Past Exam Papers & Marking Guidelines (79)
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2026 Mathematics Paper 1 (May/June Eng)
Paper 1
English
2026 · May / June Mid-Year & Supplementary
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2026 Mathematics Paper 2 (May/June Eng)
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2026 · May / June Mid-Year & Supplementary
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2026 Mathematics Paper 1 (May/June Afr)
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2026 · May / June Mid-Year & Supplementary
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2026 Mathematics Paper 2 (May/June Afr)
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2026 · May / June Mid-Year & Supplementary
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2025 Mathematics Paper 1 (Nov Eng)
Paper 1
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2025 · October / November Final NSC
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2025 Mathematics Paper 2 (Nov Eng)
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2025 · October / November Final NSC
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2025 Mathematics Paper 1 (Nov Afr)
Paper 1
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2025 · October / November Final NSC
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2025 Mathematics Paper 2 (Nov Afr)
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2025 · October / November Final NSC
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2025 Mathematics Paper 1 (May/June Eng)
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2025 · May / June Mid-Year & Supplementary
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2025 Mathematics Paper 2 (May/June Eng)
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2025 · May / June Mid-Year & Supplementary
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2025 Mathematics Paper 1 (May/June Afr)
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2025 · May / June Mid-Year & Supplementary
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2025 Mathematics Paper 2 (May/June Afr)
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2025 · May / June Mid-Year & Supplementary
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2025 Mathematics Paper 1 (Sept Trial)
Paper 1
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2025 · September Preparatory / Trial Exams
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2025 Mathematics Paper 2 (Sept Trial)
Paper 2
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2025 · September Preparatory / Trial Exams
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2025 Mathematics Paper 1 (Sept Trial)
Paper 1
Afrikaans
2025 · September Preparatory / Trial Exams
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2024 Mathematics Paper 1 (NSC Nov Eng)
Paper 1
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2024 · October / November Final NSC
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2024 Mathematics Paper 2 (NSC Nov Eng)
Paper 2
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2024 · October / November Final NSC
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2024 Mathematics Paper 1 (Nov Afr)
Paper 1
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2024 · October / November Final NSC
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2024 Mathematics Paper 2 (Nov Afr)
Paper 2
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2024 · October / November Final NSC
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2024 Mathematics Paper 1 (May/June Eng)
Paper 1
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2024 · May / June Mid-Year & Supplementary
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2024 Mathematics Paper 2 (May/June Eng)
Paper 2
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2024 · May / June Mid-Year & Supplementary
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2024 Mathematics Paper 1 (May/June Afr)
Paper 1
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2024 · May / June Mid-Year & Supplementary
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2024 Mathematics Paper 2 (May/June Afr)
Paper 2
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2024 · May / June Mid-Year & Supplementary
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2024 Mathematics Paper 1 (Sept Trial)
Paper 1
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2024 · September Preparatory / Trial Exams
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2024 Mathematics Paper 2 (Sept Trial)
Paper 2
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2024 · September Preparatory / Trial Exams
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2024 Mathematics Paper 1 (Sept Trial)
Paper 1
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2024 · September Preparatory / Trial Exams
Marking Memo
2024 Mathematics Paper 2 (Sept Trial)
Paper 2
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2024 · September Preparatory / Trial Exams
2023 Mathematics Paper 1 (Nov)
Paper 1
English
2023 · October / November Final NSC
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2023 Mathematics Paper 2 (Nov)
Paper 2
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2023 · October / November Final NSC
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2023 Mathematics Paper 1 (Nov Afr)
Paper 1
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2023 · October / November Final NSC
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2023 Mathematics Paper 2 (Nov Afr)
Paper 2
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2023 · October / November Final NSC
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2023 Mathematics Paper 1 (May/June Eng)
Paper 1
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2023 · May / June Mid-Year & Supplementary
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2023 Mathematics Paper 2 (May/June Eng)
Paper 2
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2023 · May / June Mid-Year & Supplementary
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2023 Mathematics Paper 1 (May/June Afr)
Paper 1
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2023 · May / June Mid-Year & Supplementary
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2023 Mathematics Paper 2 (May/June Afr)
Paper 2
Afrikaans
2023 · May / June Mid-Year & Supplementary
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2023 Mathematics Paper 1 (Sept Trial)
Paper 1
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2023 · September Preparatory / Trial Exams
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2023 Mathematics Paper 2 (Sept Trial)
Paper 2
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2023 · September Preparatory / Trial Exams
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2023 Mathematics Paper 1 (Sept Trial)
Paper 1
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2023 · September Preparatory / Trial Exams
Marking Memo
2023 Mathematics Paper 2 (Sept Trial)
Paper 2
Afrikaans
2023 · September Preparatory / Trial Exams
2022 Mathematics Paper 1 (Nov Eng)
Paper 1
English
2022 · October / November Final NSC
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2022 Mathematics Paper 2 (Nov Eng)
Paper 2
English
2022 · October / November Final NSC
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2022 Mathematics Paper 1 (Nov Afr)
Paper 1
Afrikaans
2022 · October / November Final NSC
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2022 Mathematics Paper 2 (Nov Afr)
Paper 2
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2022 · October / November Final NSC
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2022 Mathematics Paper 1 (May/June Eng)
Paper 1
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2022 · May / June Mid-Year & Supplementary
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2022 Mathematics Paper 2 (May/June Eng)
Paper 2
English
2022 · May / June Mid-Year & Supplementary
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2022 Mathematics Paper 1 (May/June Afr)
Paper 1
Afrikaans
2022 · May / June Mid-Year & Supplementary
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2022 Mathematics Paper 2 (May/June Afr)
Paper 2
Afrikaans
2022 · May / June Mid-Year & Supplementary
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2022 Mathematics Paper 1 (Sept Trial)
Paper 1
English
2022 · September Preparatory / Trial Exams
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2022 Mathematics Paper 2 (Sept Trial)
Paper 2
English
2022 · September Preparatory / Trial Exams
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Marking Memo
2022 Mathematics Paper 1 (Sept Trial)
Paper 1
Afrikaans
2022 · September Preparatory / Trial Exams
Marking Memo
2022 Mathematics Paper 2 (Sept Trial)
Paper 2
Afrikaans
2022 · September Preparatory / Trial Exams
2021 Mathematics Paper 1 (Nov Eng)
Paper 1
English
2021 · October / November Final NSC
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2021 Mathematics Paper 2 (Nov Eng)
Paper 2
English
2021 · October / November Final NSC
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2021 Mathematics Paper 1 (Nov Afr)
Paper 1
Afrikaans
2021 · October / November Final NSC
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2021 Mathematics Paper 2 (Nov Afr)
Paper 2
Afrikaans
2021 · October / November Final NSC
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2021 Mathematics Paper 1 (May/June Eng)
Paper 1
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2021 · May / June Mid-Year & Supplementary
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2021 Mathematics Paper 2 (May/June Eng)
Paper 2
English
2021 · May / June Mid-Year & Supplementary
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2021 Mathematics Paper 1 (May/June Afr)
Paper 1
Afrikaans
2021 · May / June Mid-Year & Supplementary
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Marking Memo
2021 Mathematics Paper 2 (May/June Afr)
Paper 2
Afrikaans
2021 · May / June Mid-Year & Supplementary
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2020 Mathematics Paper 1 (Nov Eng)
Paper 1
English
2020 · October / November Final NSC
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2020 Mathematics Paper 2 (Nov Eng)
Paper 2
English
2020 · October / November Final NSC
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2020 Mathematics Paper 1 (Nov Afr)
Paper 1
Afrikaans
2020 · October / November Final NSC
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2020 Mathematics Paper 2 (Nov Afr)
Paper 2
Afrikaans
2020 · October / November Final NSC
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2019 Mathematics Paper 1 (Nov Eng)
Paper 1
English
2019 · October / November Final NSC
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2019 Mathematics Paper 2 (Nov Eng)
Paper 2
English
2019 · October / November Final NSC
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2019 Mathematics Paper 1 (Nov Afr)
Paper 1
Afrikaans
2019 · October / November Final NSC
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2019 Mathematics Paper 2 (Nov Afr)
Paper 2
Afrikaans
2019 · October / November Final NSC
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2019 Mathematics Paper 1 (May/June Eng)
Paper 1
English
2019 · May / June Mid-Year & Supplementary
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Marking Memo
2019 Mathematics Paper 2 (May/June Eng)
Paper 2
English
2019 · May / June Mid-Year & Supplementary
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2019 Mathematics Paper 1 (May/June Afr)
Paper 1
Afrikaans
2019 · May / June Mid-Year & Supplementary
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2019 Mathematics Paper 2 (May/June Afr)
Paper 2
Afrikaans
2019 · May / June Mid-Year & Supplementary
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2018 Mathematics Paper 1 (Nov Eng)
Paper 1
English
2018 · October / November Final NSC
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2018 Mathematics Paper 2 (Nov Eng)
Paper 2
English
2018 · October / November Final NSC
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2018 Mathematics Paper 1 (Nov Afr)
Paper 1
Afrikaans
2018 · October / November Final NSC
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2018 Mathematics Paper 2 (Nov Afr)
Paper 2
Afrikaans
2018 · October / November Final NSC
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2018 Mathematics Paper 1 (May/June Eng)
Paper 1
English
2018 · May / June Mid-Year & Supplementary
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2018 Mathematics Paper 2 (May/June Eng)
Paper 2
English
2018 · May / June Mid-Year & Supplementary
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+1 Answer Book / Addendum
2018 Mathematics Paper 1 (May/June Afr)
Paper 1
Afrikaans
2018 · May / June Mid-Year & Supplementary
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2018 Mathematics Paper 2 (May/June Afr)
Paper 2
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2018 · May / June Mid-Year & Supplementary
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+1 Answer Book / Addendum
Practice Quizzes for Mathematics
Topic Mastery Quiz
15 mins
Matric Mathematics Paper 1: Quick Formula & Algebra Quiz
Test your mastery of Quadratic equations, Nature of Roots, and basic limits. (Practice questions written for this platform.)