Applications & Interpretation HL · Topic 3 · Geometry & Trigonometry

IB Math AI HL 3D Geometry Worksheet (with full solutions)

Distances, angles and volumes in three dimensions — the standard AI toolkit for pyramids, cones, spheres and composite solids.

23 pages · 120 marks · with full solutions · free PDF for IB Mathematics: Applications and Interpretation HL students.

23pages
120marks
3difficulty levels
Yessolutions included
T3Geometry & Trigonometry

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What this AI HL 3d geometry worksheet covers

Distances, angles and volumes in three dimensions — the standard AI toolkit for pyramids, cones, spheres and composite solids. The questions follow the order of the AI HL syllabus for Topic 3 (Geometry & Trigonometry) and are graded in three bands — routine practice, exam-standard, and the harder multi-step questions that separate a 6 from a 7.

Distance between two points and the midpoint in 3D
Angle between a line and a plane using right-angled triangles
Surface area and volume of pyramids, cones, spheres and hemispheres
Composite solids and unit conversion
Exam tip for this topic. Draw the right-angled triangle inside the solid before touching the calculator — most lost marks come from using the wrong triangle, not the wrong formula.

Preview

How to use it

  1. Do the first band without the AI 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 AI HL worksheets on Geometry & Trigonometry

✓ = solutions included

Questions

Is this AI HL 3d geometry 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: Applications and Interpretation 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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