Matric Mathematics Study Guide 2026 | NSC Revision & Exam Prep

Quick Answer: Use this guide to revise the major Grade 12 Mathematics topics, practise with timed NSC past papers and memoranda, and focus on your weakest skills. With Paper 1 on 23 October and Paper 2 on 26 October 2026, prioritise active practice over rereading notes.

Your Complete Matric Mathematics Study Guide for 2026

The National Senior Certificate (NSC) Mathematics exam rewards clear methods, accurate working and regular practice. This guide is a revision map—not a guarantee of marks. Use your teacher’s scope, the official exam timetable, recent NSC papers and their memoranda alongside it.

Exam countdown: the 2026 NSC Mathematics Paper 1 is scheduled for Friday 23 October and Paper 2 for Monday 26 October. Confirm your own timetable and venue instructions with your school.

What the Matric Maths Exam Looks Like

Grade 12 Mathematics consists of two papers:

Paper	Duration	Marks	Key Topics
Paper 1	3 hours	150	Algebra, Sequences & Series, Functions & Graphs, Finance, Calculus, Probability
Paper 2	3 hours	150	Statistics, Analytical Geometry, Trigonometry, Euclidean Geometry

Each paper is marked out of 150. Your final Mathematics percentage is the average of both papers (plus your School-Based Assessment mark).

Paper 1 Topics: What You Must Know

1. Algebra & Equations (approx. 25 marks)

• Quadratic equations -- factorisation, completing the square, the formula
• Simultaneous equations -- linear and non-linear combinations
• Inequalities -- solving and representing on a number line
• Nature of roots -- discriminant (b2 minus 4ac), interpreting real, equal, or unreal roots
• Surds and exponents -- simplifying, rationalising denominators

Common exam trap: Always check for extraneous solutions when solving equations with fractions or surds.

2. Sequences & Series (approx. 25 marks)

• Arithmetic sequences: Tn = a + (n - 1)d; Sn = n/2 multiplied by (2a + (n - 1)d)
• Geometric sequences: Tn = ar to the power (n-1); Sn = a(r to the n minus 1) divided by (r - 1)
• Infinite geometric series: S = a divided by (1 - r) when the absolute value of r is less than 1
• Sigma notation: Reading and evaluating summation expressions

Top tip: Always identify whether a sequence is arithmetic (constant difference) or geometric (constant ratio) before applying any formula.

3. Functions & Graphs (approx. 35 marks)

Functions are the biggest section in Paper 1. Make sure you can:

• Sketch and interpret straight lines, parabolas, hyperbolas, exponentials and their inverses
• Find domain, range, intercepts, asymptotes, and turning points
• Perform transformations: f(x+a), f(x)+a, a times f(x), f(-x), -f(x)
• Determine equations from graphs using given key points
• Answer inequality questions from graphs (for example: for which x is f(x) greater than 0?)

4. Finance, Growth & Decay (approx. 15 marks)

• Simple and compound interest: A = P(1 + in) versus A = P(1 + i) to the power n
• Nominal and effective interest rates
• Annuities -- future value and present value
• Sinking funds and loan repayments

5. Calculus

• Limits -- understanding the concept; evaluating limits
• Differentiation from first principles -- f'(x) = limit as h approaches 0 of (f(x+h) minus f(x)) divided by h
• Rules of differentiation: power rule, constant rule, sum and difference rule
• Application of derivatives: gradient of tangent, increasing/decreasing intervals, concavity, optimisation
• Cubic functions: sketching, turning points, point of inflection

Worked example: differentiate and find a turning point

Question: For f(x) = x² − 4x + 3, find f′(x) and the stationary point.

1. Differentiate term by term: f′(x) = 2x − 4.
2. At a stationary point, set f′(x) = 0: 2x − 4 = 0, so x = 2.
3. Substitute into the original function: f(2) = 4 − 8 + 3 = −1.
4. The stationary point is (2, −1). Since the coefficient of x² is positive, the parabola opens upwards, so this is a minimum.

Exam check: state the derivative, show the equation you solve, and substitute into the original function to find the y-coordinate. Do not confuse f′(x) with f(x).

Try it yourself: For g(x) = x² − 6x + 5, find the derivative and stationary point before checking your work with a teacher or tutor.

6. Probability

• Venn diagrams, two-way contingency tables
• Addition rule: P(A or B) = P(A) + P(B) - P(A and B)
• Mutually exclusive and independent events
• Counting principles: fundamental counting principle, permutations, combinations

Paper 2 Topics: What You Must Know

1. Statistics (approx. 20 marks)

• Five-number summary and box-and-whisker plots
• Measures of central tendency and spread (mean, median, standard deviation)
• Histograms and frequency polygons
• Scatter plots and regression lines (least squares)
• Correlation coefficient

2. Analytical Geometry (approx. 40 marks)

• Distance, midpoint, and gradient formulae
• Equation of a straight line (gradient-intercept and two-point forms)
• Circles: equation (x minus a) squared plus (y minus b) squared = r squared; finding centre and radius
• Tangents to circles; perpendicularity condition

3. Trigonometry (approx. 50 marks)

• Definitions in all four quadrants (CAST rule)
• Reduction formulae, co-ratios, negative angles
• Identities: sin squared + cos squared = 1; tan = sin divided by cos; compound angles; double angles
• General solutions: sin theta = k, cos theta = k, tan theta = k
• 2D and 3D applications -- sine rule, cosine rule, area formula
• Graphs of sin, cos, tan and their transformations

4. Euclidean Geometry (approx. 40 marks)

• Proportionality theorem and its converse
• Similar triangles (AA, SSS, SAS)
• Riders involving circles, tangents, and chords
• Two-column proofs -- must show every reason

Key advice: Draw clear diagrams, label all given information, and state every theorem or axiom you use by name.

Final Countdown Study Plan: 12–25 October

There is not enough time to treat every topic equally. Adjust this plan to your teacher’s scope and your weakest areas. Mathematics Paper 1 is scheduled for 23 October and Paper 2 for 26 October 2026.

Date	Priority	What to do
12 Oct	Diagnose gaps	Attempt selected questions from both papers; list your three weakest topics.
13 Oct	Algebra and sequences	Practise equations, inequalities, arithmetic and geometric sequences.
14 Oct	Functions and graphs	Sketch from key features; practise domain, range, intercepts and transformations.
15 Oct	Calculus	Differentiate, find stationary points, interpret gradients and sketch cubics.
16 Oct	Finance and probability	Practise formula selection and probability questions; show every step.
17 Oct	Paper 1 practice	Write a timed paper or a substantial timed section without notes.
18 Oct	Correct mistakes	Mark your work, classify errors, then redo incorrect questions from a blank page.
19 Oct	Trigonometry	Work on identities, equations, graphs and application problems.
20 Oct	Analytical geometry	Practise gradients, equations of lines, circles and tangents.
21 Oct	Euclidean geometry and statistics	Write full reasons in proofs; revise summaries, spread and regression.
22 Oct	Paper 1 final review	Review error log and formulas; avoid an all-nighter and prepare exam materials.
23 Oct	Paper 1 exam	Follow school and exam-centre instructions; read each question carefully.
24 Oct	Paper 2 targeted revision	Focus on the two Paper 2 topics where you lose the most marks.
25 Oct	Paper 2 preparation	Do a timed mixed set, review geometry reasons and pack exam materials.
26 Oct	Paper 2 exam	Use the time available, show working and check answers where possible.

Daily routine: spend most of your study block solving questions, not rereading notes. After marking, redo missed questions without looking at the memo. Take breaks and get enough sleep.

Top Exam Strategies for Maximum Marks

Before the Exam

• Learn all formulae that are NOT provided on the formula sheet
• Practice at least 5 full past papers under timed conditions
• Mark your own papers using the memorandum -- understand why each mark is awarded
• Identify your top three weak topics and do extra practice on those

During the Exam

• Read through the whole paper first (5 minutes) -- plan your approach
• Start with questions you find easiest to build confidence
• Show all working -- method marks are available even if your final answer is wrong
• Use the formula sheet strategically -- it saves time and reduces errors
• Never leave a question blank -- attempt something for partial credit
• Allow 10 minutes at the end to check calculations

Common Mistakes to Avoid

• Dividing both sides of an equation by a variable that could equal zero
• Forgetting the plus-or-minus sign when taking a square root
• Mixing up compound angle formulae (always check your data sheet)
• Stating a theorem without specifying which angles or sides you mean in geometry proofs
• Rounding intermediate calculations -- only round your final answer

Essential Formulae Quick Reference

Topic	Formula
Quadratic formula	x = (-b plus or minus square root of (b squared - 4ac)) divided by 2a
Arithmetic Tn	a + (n - 1)d
Geometric Sn	a times (r to the n minus 1) divided by (r - 1)
Distance formula	square root of ((x2-x1) squared + (y2-y1) squared)
Midpoint	((x1+x2)/2 ; (y1+y2)/2)
Area of triangle (trig)	half ab times sin C
Cosine rule	a squared = b squared + c squared - 2bc times cos A

How AI Tutoring Accelerates Your Preparation

Every student's weak spots are different. StudyBuddy's AI tutor gives you instant, personalised explanations on any Mathematics topic -- so you can get unstuck at 11pm the night before your exam, not just during school hours.

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Keep revising while you plan: use your teacher's scope, practise with official NSC papers and memoranda, and verify funding details on the funder's own website.