Formula Centre
Formula guides and key subject rules for every grade and subject, with worked examples and practice.
Compound Interest
Mathematics • Finance, Growth and Decay • Grade 12
When to use it
Use it for investments or loans where interest is earned on interest.
Worked example
R10 000 at 8% p.a. for 5 years → A = 10 000(1,08)⁵ = R14 693,28.
Common mistakes
- Using 8 instead of 0,08 for i
- Not converting to monthly periods when compounding monthly
Practice question
R25 000 is invested at 6% p.a. compounded monthly for 3 years. Calculate A.
Cosine Rule
Mathematics • Trigonometry • Grade 12
When to use it
Use it in a non-right-angled triangle when you know two sides and the included angle, or all three sides.
Worked example
b = 8, c = 6, A = 60° → a² = 64 + 36 − 48 = 52, so a ≈ 7,21 units.
Common mistakes
- Using it when the angle is not between the two known sides
- Calculator in radian mode
Practice question
In △PQR, q = 10, r = 7 and P = 45°. Calculate p.
Derivative of a Power
Mathematics • Calculus • Grade 12
When to use it
Use it to differentiate any polynomial term, then to find gradients, tangents and stationary points.
Worked example
f(x) = 4x³ ⇒ f′(x) = 12x².
Common mistakes
- Forgetting that the derivative of a constant is 0
- Subtracting 1 from the coefficient instead of the exponent
Practice question
Differentiate f(x) = 5x⁴ − 3x² + 7.
Quadratic Formula
Mathematics • Algebra and Equations • Grade 12
When to use it
Use it to solve any quadratic equation ax² + bx + c = 0, especially when the expression does not factorise.
Worked example
Solve 2x² + 3x − 2 = 0. x = [−3 ± √(9 + 16)]/4 = (−3 ± 5)/4, so x = 0,5 or x = −2.
Common mistakes
- Forgetting the ± and losing a root
- Dividing only part of the numerator by 2a
Practice question
Solve 3x² − 5x − 2 = 0 using the quadratic formula.