IB Maths Optimisation Problems: FAQs on Concept, Exams & Technique

Optimisation problems ask you to find the maximum or minimum value of a quantity — area, volume, cost, profit — by writing it as a function of one variable, differentiating, and setting the derivative to zero. They're examined in Paper 1 (non-calculator, AA only) and Paper 2 (calculator) as both short-answer questions and full HL-style problems worth 6-10 marks.

Optimisation is formally taught in the Calculus topic, but it reappears in Applications & Interpretation as a modelling skill — sometimes using a GDC to find a maximum/minimum on a graph rather than differentiating by hand. In HL AA, it can also link to related rates and second-derivative tests within the same question.

SL optimisation questions usually involve a single differentiation step with a straightforward constraint — think a cylinder's surface area given fixed volume. HL questions add extra layers: implicit differentiation, parametric functions, or a second-derivative justification, and they're more likely to appear combined with kinematics or related rates in Paper 2.

Start by identifying the quantity to optimise and writing it as a function of two variables. Use the given constraint to eliminate one variable, differentiate the resulting single-variable function, set it to zero, solve for the variable, then check it's a maximum or minimum before answering in context with correct units.

The single most common mistake I see in fifteen years of marking mocks is forgetting to eliminate the second variable before differentiating — students try to differentiate a function with both r and h still in it. Second most common: finding f'(x) = 0 but never checking whether it's actually a maximum or minimum.

Both are accepted by IB examiners — a nature table (checking the sign of f' either side of the critical point) or the second derivative test ($f^{\prime \prime }(x)>0$ for a minimum, $f^{\prime \prime }(x)<0$ for a maximum) both earn full marks, provided the justification is written out, not just implied.

Yes — in Paper 2 you can graph the function directly and use your GDC's built-in maximum/minimum feature to find the answer numerically, without showing algebraic differentiation. This is standard practice for Applications & Interpretation and perfectly acceptable in AA Paper 2 too, as long as you state the equation you graphed.

Optimisation isn't conceptually hard — the calculus itself is often SL-level differentiation — but it's a topic where marks get lost through setup errors, not calculation errors. Students who are comfortable differentiating routinely stumble on turning a word problem or diagram into the right equation in the first place.

No single topic guarantees a grade boundary, but Calculus (which includes optimisation) makes up roughly 30% of the AA syllabus content and around 27% in AI, so it's a heavily weighted area across both papers. Missing optimisation technique alone could easily cost 6-10 marks in a single exam sitting.

Work through past paper questions by topic rather than by full paper, so you build pattern recognition for how constraints get disguised in word problems. Time yourself on the setup step alone first, then the full solve — most students need more setup practice than differentiation practice.

You don't need to know the maths to help — the most useful thing a parent can do is make sure your child is working through past-paper questions regularly, not just re-reading notes. Ask them to explain their working out loud; if they can't, that's usually a sign the concept isn't fully understood yet.

Look for resources organised by exact sub-topic rather than generic textbooks — past-paper questions grouped specifically under optimisation, with full mark schemes, let your child see exactly where marks are lost. RevisionPrep's Revision Notes and Topical Worksheets for DP Mathematics are built around this exact structure for AA and AI, SL and HL.