Matric Maths Master Pack

Grade 12 Mathematics

🎓 Grade 12 (NSC / IEB)⏱ 42 hours of content📄 PDF workbook🎥 Video lessons📱 Phone / laptop

A complete Grade 12 Mathematics program built around the CAPS curriculum. You will master Functions, Calculus, Trigonometry, Analytical Geometry, Sequences & Series, Financial Maths, Statistics and Probability. Every topic is taught the same way top-scoring learners study: short theory, worked example, then guided practice with fully-solved memos so you never get stuck.

What's inside this pack

✓120-page PDF study guide
✓10 years of past papers + memos
✓8 hours of video lessons
✓Formula sheet & quick-revision cards
✓Bonus: exam-day strategy guide

Sample lessons — read before you buy

4 previews

1Lesson 1 — Functions & Inverses

A function f is a rule that assigns to every input x exactly one output f(x). The inverse f⁻¹ swaps the roles of x and y. Given f(x) = 2x + 3, we find the inverse by writing y = 2x + 3, swapping to x = 2y + 3, then solving: y = (x − 3)/2. So f⁻¹(x) = (x − 3)/2. On a graph, f and f⁻¹ are always reflections in the line y = x. Common exam trap: the inverse of y = x² is NOT a function unless the domain is restricted.

2Lesson 2 — Differential Calculus from First Principles

The derivative f'(x) measures the instantaneous rate of change. From first principles: f'(x) = lim (h→0) [f(x+h) − f(x)] / h. Example — differentiate f(x) = x²: f'(x) = lim (h→0) [(x+h)² − x²]/h = lim (h→0) [2xh + h²]/h = 2x. On the exam the 'first principles' question is worth 4 marks and the h in the denominator must cancel before you substitute h = 0.

3Lesson 3 — Trig Identities & Reduction

Memorise the three anchor identities: sin²θ + cos²θ = 1, tan θ = sinθ/cosθ, and the co-function pair sin(90°−θ) = cosθ. Reduction formulae simplify angles into the first quadrant using CAST. Example: cos(180° + θ) sits in Q3 where cos is negative, so cos(180° + θ) = −cosθ. Whenever you see 360°k, drop it — trig functions are periodic.

4Lesson 4 — Financial Maths: Loans & Annuities

For a loan repaid in equal instalments, use the present-value annuity formula: PV = x · [1 − (1+i)⁻ⁿ] / i. A R500 000 home loan at 10.5% p.a. compounded monthly (i = 0.105/12) over 20 years (n = 240) gives monthly repayment x ≈ R4 993. Always convert the annual rate to a monthly rate before substituting.

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