Math Analysis & Approaches unit guide
Calculus
Differentiation, integration, optimisation, kinematics and - at HL - differential equations and Maclaurin series.
Calculus is the largest unit in AA and carries the most marks in both papers. It is also the unit where method marks are most generous: a question you cannot finish is still worth attempting, because stating the derivative before setting it to zero, or writing the integral before evaluating it, earns marks independently of the final answer. Students who write fluent but unstructured working leave those marks on the table even when the answer is right.
Topics in this unit
What gets examined
- Chain, product and quotient rules, including nested applications where a question chains several together.
- Finding stationary points, classifying them, and using the second derivative.
- Optimisation: forming an equation from a described situation, then differentiating it.
- Definite integration for area between curves and volumes of revolution.
- Kinematics: moving between displacement, velocity and acceleration by differentiating or integrating.
- At HL, separable differential equations, integration by parts and substitution, and Maclaurin series.
How to revise it
Show the step before the substitution
Write dy/dx = ... before setting it to zero. Write the integral with its limits before evaluating. These lines carry method marks that survive an arithmetic slip.
Practise forming the equation, not just solving it
Optimisation questions are hard at the setup, not the calculus. Drill turning a described box, field or cost into an equation in one variable, and the differentiation that follows is routine.
Keep the kinematics directions straight
Differentiate to go from displacement towards acceleration, integrate to come back. Sketching the chain in the margin takes seconds and prevents the wrong operation.
Never lose the constant of integration
Indefinite integrals need + c, and questions that give an initial condition are testing precisely whether you kept it and used it.
Where marks get lost
- Applying the chain rule but forgetting to multiply by the derivative of the inner function.
- Classifying a stationary point without checking the second derivative or a sign change.
- Forgetting to square the function in a volume of revolution.
- Giving a decimal where Paper 1 requires an exact value.
- Ignoring that speed is the magnitude of velocity when a question asks for one rather than the other.
Practise this unit
Reading about a unit only goes so far. Work through real IB-style questions on it, with mark schemes.