IB Math AA HL Unit 5: Calculus

IB Maths AA 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 questions43 questions · 3 worked examples
• Advanced Integration questions52 questions · 3 worked examples
• Differential Equations and Maclaurin questions62 questions · 3 worked examples
• First Principles questions30 questions · 3 worked examples

Learn it first: AA HL Unit 5 notes

• Differentiation
• Integration by parts and cyclic integrals
• Maclaurin series and approximations
• Differential equations
• Volumes of revolution and improper integrals

Where marks go in AA HL Unit 5

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

• Arithmetic with limits, fractions and simultaneous equations on Paper 1. Write F(upper) − F(lower) with each value in brackets before simplifying. Keep fractions as fractions. Check a simultaneous-equation solution by substituting back.
• "Hence", "deduce" and "exact": using the wrong method. "Hence" = use what you just found. "Deduce" = a short argument from earlier results. "Exact" = surds, π, ln, fractions; a decimal from the GDC scores nothing.
• Volumes of revolution and areas: wrong axis, missing π or square, wrong limits. About the y-axis: V = π∫ x² dy, so rewrite x² in terms of y and use y-limits. Sketch the region first, then evaluate on the GDC unless an exact answer is required.

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

FAQ

Also for AA HL: common exam mistakes · syllabus checklist