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The Grade 10-12 Formula Rosetta Stone

Every formula across the CAPS syllabus — algebra to statistics. Tap or hover any variable or card below to reveal exactly what it means, and the specific mistake examiners see most often around it.

Algebra — The Quadratic Formula

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Functions

Tap any card to see the trap examiners set for each graph type.

Trigonometry — Triangle Rules

Sine, cosine, area rule, and the identity that ties them together.

\sin^2\theta + \cos^2\theta = 1

Sequences & Series

Arithmetic vs geometric — tap a card for the trap.

Financial Mathematics

Tap or hover a variable to see its meaning and trap.

A = P(1 + i)^n

Annuities — Present vs Future Value

Same-looking formulas, completely different use case. Mixing them up is one of the most common Paper 1 errors.

Present Value (loans, mortgages)

P_v = \dfrac{x\left[1 - (1+i)^{-n}\right]}{i}

Future Value (sinking funds, retirement)

F_v = \dfrac{x\left[(1+i)^n - 1\right]}{i}

⚠️ Timing warning: check whether the first payment happens in 1 month (standard) or immediately (upfront) — this shifts n by one period and is a favourite trick in exam questions.

Analytical Geometry

Points, lines, and circles on the Cartesian plane.

Euclidean Geometry — Circle Theorems

The condition attached to each theorem is the exam trap — tap to reveal it.

Calculus — First Principles

The single most common way to lose method marks on this topic.

f'(x) = \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}

⚠️ Trap: you must write

\lim_{h \to 0}

on every single line of your working until h actually cancels out — dropping it early costs you the method mark even if your final answer is correct.

Calculus — Power Rule & Stationary Points

Statistics & Probability

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Trig-specific? Try the Trigonometry Decision Tree.