IB Math AI HL Unit 5: Calculus

IB Maths AI HL Unit 5: Calculus, topic by topic

Each topic in this unit has a free page with step-by-step worked examples and the key formulas, then exam-style questions with mark schemes.

• Advanced Differentiation and Related Rates questions40 questions · 2 worked examples
• Advanced Integration and Kinematics questions31 questions · 3 worked examples
• Differential Equations and Eulers Method questions52 questions · 2 worked examples
• Phase Portraits questions14 questions · 3 worked examples
• The Second Derivative and Concavity questions17 questions · 3 worked examples

Learn it first: AI HL Unit 5 notes

• Differentiation
• Integration
• Differential equations
• Slope fields and qualitative DE analysis
• Optimisation in context

Where marks go in AI HL Unit 5

From the IB subject reports we summarise on AI HL Examiner Insights, in our own words:

• Volumes of revolution: about the y-axis, π, squaring, limits. About the y-axis: V = π∫ x² dy, with x² written in terms of y and y-limits. Sketch the solid, then evaluate on the GDC (or set up an equation with an unknown limit and solve it on the GDC).
• Derivatives in context: not differentiating, gradient and angle, rates. Normal: differentiate, evaluate, take −1/m. An angle between two lines: θ = |arctan m₁ − arctan m₂|. Point of inflection: f″ = 0 with a sign change. A derivative value is a rate at an instant, with units.
• Euler's method: formula copied, not applied, and GDC variables. Write the recurrence in the question's variables (xₙ₊₁ = xₙ + h, yₙ₊₁ = yₙ + h × f(xₙ, yₙ)), show the first step with numbers, then give the final value from the GDC table.

The questions here are original, written in the style of IB papers with IB-style mark schemes; for real papers see the IB Maths AI HL past papers page.

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