What is covered in Grade 12 Mathematics Revision?

Comprehensive revision of all Grade 12 topics in preparation for the NSC examinations. Paper 1 and Paper 2 past paper practice.

Is Grade 12 Revision tested in Paper 1 or Paper 2?

Grade 12 Mathematics Revision is assessed in Paper 1 of the end-of-year examinations, as per the CAPS Mathematics curriculum guidelines.

When is Revision taught in Grade 12 Mathematics?

Revision is taught in Term 4 of Grade 12 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 12 Mathematics Revision on the CAPS curriculum?

Yes. Revision is part of the official CAPS Mathematics curriculum for Grade 12, Term 4 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 12 Mathematics study material free?

Yes. All chapter notes, definitions, formulas, and worked examples on MathSciBuddy are completely free to read. No account or subscription is needed to access CAPS-aligned study notes.

Grade 12 Mathematics

Grade 12 · Term 4Mathematics

Revision

A comprehensive revision of all Grade 12 Mathematics topics in preparation for the final NSC examination. We consolidate algebra, functions, calculus, statistics, probability, and analytical geometry through exam-style questions.

Week 1

Revision: Algebra, Functions & Finance

Consolidate all algebraic techniques from Grade 12
Revise function types (linear, quadratic, exponential, log, trig)
Revise financial mathematics (annuities, loan schedules)

🌍

Real-World Connection

The NSC exam tests whether you can bring together all strands of mathematics. A real engineer, accountant, or scientist rarely works on isolated problems — they combine algebra, graphs, rates of change and statistics in every project.

ℹ️ Note

Examination strategy: read every question fully before starting. For multi-part questions, check whether earlier parts can be used in later parts. Show ALL working — method marks are awarded even if the final answer is wrong.

Property / Rule

Key Identities to Memorise

Trig: $\sin(A\pm B)$ , $\cos(A\pm B)$ , $\sin2A$ , $\cos2A$ (all three forms). Calculus: power rule, second derivative test. Finance: PV and FV annuity formulas. Sequences: $T_n=a+(n-1)d$ , $T_n=ar^{n-1}$ , $S_n$ for both, $S_\infty$ .

\text{All Grade 12 formulas are on the CAPS formula sheet}

💡 Tip

Common NSC exam mistakes: (1) Not simplifying before differentiating. (2) Forgetting $\pm$ in general trig solutions. (3) Using wrong $n$ in annuity formulas (monthly vs annual). (4) Not checking validity of solutions in surd equations. (5) Incorrect quadratic inequality sign direction.

Worked Examples

Worked Example

Mixed review — NSC-style

Problem

f(x)=\frac{2}{x-1}+3

Worked Example

Calculus — combined review

Problem

g(x)=x^3-6x^2+9x-4

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge2 marks

State the general solution for

\sin\theta=\frac{1}{2}

L1 · Knowledge2 marks

Write down

S_\infty

for a geometric series with

a=18

and

r=\frac{1}{3}

L2 · Routine Procedures3 marks

Differentiate

h(x)=\frac{2x^3-4x}{x}

fully.

L2 · Routine Procedures4 marks

The fifth term of a geometric series is 48 and the third term is 12. Find the first term and common ratio.

L3 · Complex Procedures5 marks

R300 000 bond at 9.6% p.a. (monthly), repaid over 20 years. Find: (a) monthly payment; (b) total interest.

L3 · Complex Procedures4 marks

Prove

\dfrac{\cos2x}{\cos x+\sin x}=\cos x-\sin x

L4 · Problem Solving6 marks

A parabola

f(x)=ax^2+bx+c

has

x

-intercepts at

x=-2

and

x=3

, and

y

-intercept

-12

. Find

a

b

c

and hence

f(x)

L4 · Problem Solving6 marks

NSC-style: The sum of the first

n

terms of a series is

S_n=n^2+3n

. (a) Find

T_n

. (b) Determine if it is arithmetic, giving the common difference.