NDA Maths · Teaching notes
Application of Derivatives — NDA Mathematics
Application of Derivatives is around 73 past-year NDA questions and the pay-off of Differentiation: once you can differentiate, the derivative tells you slopes, rates, where a function rises or falls, and where it peaks. Work the three notes in order — first tangents, rates of change, and small-change approximations; then monotonicity and the maxima/minima tests; then optimisation word problems. The single biggest time-saver is recognising when AM-GM beats calculus for a max/min, and the recurring trap is forgetting to check endpoints (or open-interval behaviour) when hunting the absolute extremum.
Subtopic notes
Tangents, Rates of Change & Approximations
5 PYQsThe derivative read geometrically (slope of the tangent), dynamically (a rate of change), and as a tool for estimating small changes via differentials.
Open note
Monotonicity, Maxima & Minima
38 PYQsThe sign of f′ says where a function rises or falls; the zeros of f′ are the candidates for peaks and valleys, sorted by the first- or second-derivative test, with endpoints checked for the absolute extremum.
Open note
Optimisation — Word Problems & AM-GM
30 PYQsMaximise or minimise a real quantity: model it, reduce to one variable using the constraint, then either set the derivative to zero or — often faster — apply AM-GM.
Open note
PYQ weightage by concept
9 concepts · 73 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
9 concepts · 73 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| Tangent and normal to a curve | 3 | 4% |
| Rates of change and small-change approximation | 2 | 3% |
| Concept | PYQs | Share |
|---|---|---|
| Critical points and the derivative tests | 20 | 27% |
| Increasing and decreasing intervals | 11 | 15% |
| Greatest and least value on an interval | 4 | 5% |
| Conditions for no extremum / counting extrema | 3 | 4% |
| Concept | PYQs | Share |
|---|---|---|
| The optimisation recipe | 13 | 18% |
| Geometric maxima (area, volume, inscribed figures) | 11 | 15% |
| AM-GM: the calculus-free shortcut | 6 | 8% |
Formula & revision sheet
1 formulas · 0 gotchas across all subtopics — the exam-eve cheat-sheet
Formula & revision sheet
1 formulas · 0 gotchas across all subtopics — the exam-eve cheat-sheet