IB Math AI SL Unit 5: Calculus

IB Maths AI SL 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.

• Differentiation Rules questions28 questions · 3 worked examples
• Integration questions35 questions · 3 worked examples
• Limits, Derivatives & Rates of Change questions23 questions · 3 worked examples
• Optimisation questions15 questions · 3 worked examples
• Tangents & Normals questions28 questions · 5 worked examples

Learn it first: AI SL Unit 5 notes

• Optimisation
• Using the CG50 or TI-Nspire for calculus

Where marks go in AI SL Unit 5

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

• Calculus: not differentiating, f(a) for f′(a), and the derivative as a rate. Gradient at a point = f′(a). Normal gradient = −1/f′(a). Finish with the equation y − y₁ = m(x − x₁). A derivative value is an instantaneous rate with units "per …". When integrating, add C and find it.
• Trapezoidal rule and integrals: heights, strip width and dx. h = (b − a)/n where n is the number of strips. The formula uses the y-values: ends once, middle values twice. Write ∫ f(x) dx with its limits and dx.
• Interpreting in context: parameters, derivatives and justifications. Name the quantity and its units: "0.35 is the cost in dollars per extra kilometre". Base every justification on a calculated value from the question.

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 SL past papers page.

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