← Our pedagogy
How we teach Additional Mathematics
Sec 3–4
Additional Mathematics punishes memorising more than any other subject. Every topic is built on understanding.
1 · Understand the concept, never just memorise it
Additional Mathematics moves fast and builds on itself, so gaps snowball. We make each idea intuitive before the algebra, so the rules make sense and are never just remembered.
How we explain it, simply
- Differentiation“How steep a hill is exactly where you are standing.”
- Logarithms“The answer to: how many of this number, multiplied together, make that one? Three 2s make 8, so the log of 8 to base 2 is 3.”
- Discriminant“It tells you whether a line misses, touches or cuts a curve before you draw anything.”
2 · Know every type of question before the exam
Additional Mathematics papers return to the same families of questions. Students learn to recognise each one and the framework to solve it.
The question types we prepare for
- Quadratics and the discriminant: where a line meets a curve
- Surds, indices and logarithms
- Polynomials, the remainder and factor theorems, partial fractions
- Binomial expansion
- Trigonometric identities, proofs and equations
- Coordinate geometry, including circles
- Linear law
- Differentiation: gradients, rates of change, stationary points, maximum and minimum
- Integration and area under a curve
3 · Find the reason behind every mistake
Most errors in Additional Mathematics come from one misunderstood rule. We find it and fix it at the root.
Mistakes, and the real reason behind them
- Wrote log(a + b) = log a + log bThe real reason: Treats log like a bracket that can be shared out, not as an operation with its own laws.
- Stuck halfway through a trigonometric proofThe real reason: Doesn’t yet look at the other side to decide which identity to aim for.
- Found the stationary point but lost marksThe real reason: Didn’t show whether it is a maximum or minimum, which the question type always needs.