Analysis & Approaches HL · Topic 5 · Calculus

IB Math AA HL Applications of Integration Worksheet (with full solutions)

Areas between curves, volumes of revolution and the link between displacement, velocity and acceleration.

26 pages · 120 marks · with full solutions · free PDF for IB Mathematics: Analysis and Approaches HL students.

26pages
120marks
3difficulty levels
Yessolutions included
T5Calculus

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What this AA HL applications of integration worksheet covers

Areas between curves, volumes of revolution and the link between displacement, velocity and acceleration. The questions follow the order of the AA HL syllabus for Topic 5 (Calculus) and are graded in three bands — routine practice, exam-standard, and the harder multi-step questions that separate a 6 from a 7.

Area between a curve and the x-axis, including regions below the axis
Area between two curves
Volumes of revolution about the x-axis (and y-axis at HL)
Definite integrals from a GDC with correct notation
Exam tip for this topic. Sketch the region first; an area that crosses the axis must be split or the integrals cancel.

Preview

How to use it

  1. Do the first band without the AA HL formula booklet, then check which formulas you had to look up — those are the ones to memorise.
  2. Time the second band at roughly 1.2 minutes per mark, the pace of Paper 1 and Paper 2.
  3. Mark the third band against the solutions and rewrite every question you lost marks on from a blank page.

More AA HL worksheets on Calculus

✓ = solutions included

Questions

Is this AA HL applications of integration worksheet free?

Yes — download the PDF with no sign-up. It is one of over 130 free IB Math worksheets on this site, written to match the current syllabus.

Does it come with answers?

Yes, full worked solutions are included at the end of the PDF.

Which IB course is it for?

IB Mathematics: Analysis and Approaches HL. The same topic is also available for the other courses where it is on the syllabus — see the links above.

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