IBDP · Maths AA SL
Calculus
AA SL Topic 5: Calculus
40 min readStandard~27–30% of AA SL assessment — the single largest topic, examined in every Paper 1 and Paper 2
Calculus in AA SL is really three ideas stacked on top of each other: what happens as you get infinitely close to a point (limits), how fast something is changing at an instant (differentiation), and how much has accumulated over an interval (integration). Every exam question is testing whether you can move fluently between a graph, its gradient function, and the area under it — get that translation solid and the algebra becomes routine.
Overview
Why calculus behaves the way it does
- Limits are the foundation everything else is built on — you can't rigorously define a derivative (instantaneous rate of change) or a definite integral (exact area) without first agreeing what it means to get 'infinitely close' to a value.
- Differentiation answers 'how fast right now?' — it turns a position/quantity function into a gradient function.
- Integration answers 'how much in total?' — it turns a rate function back into an accumulated quantity, and is the exact reverse process of differentiation.
- Differential equations (HL only) go the other way again: you're given a relationship between a rate and the quantity itself, and have to reconstruct the original function.
The shape of the chapter
Command terms that decide your method in calculus questions
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Show that | Derive the given result using clearly shown algebraic/calculus steps — the answer is given, so marks are for the working, not the number. | AO2 | Every line of algebra must follow logically; skipping the factorising/rationalising step loses the method mark even if your final line matches the given answer. |
| Hence | You must use the result just found in the previous part — a completely fresh method scores zero even if numerically correct. | AO2 | Reference the earlier result explicitly in your working, e.g. 'using part (a), ...'. |
| Hence or otherwise | Using the previous result is recommended but a different valid method is also accepted. | AO2 | Any correct method earns full marks, but the 'hence' route is usually far faster. |
| Deduce | State a conclusion that follows directly from work already shown, with brief justification. | AO3 | A bare answer with no reference to the preceding limit/derivative loses the justification mark. |
| Determine / Justify | Calculate a definite answer or give a reasoned argument, showing the method used. | AO2/AO3 | A correct answer with no supporting reasoning typically earns only partial credit on 'justify' parts. |
Key point
'Show that' and 'hence' questions are the exam telling you exactly which method to use. Skip the shown step or ignore the 'hence' link and you lose method marks even with a fully correct final answer.
Overview