Applications & Interpretation HL · Topic 5 · Calculus

IB Math AI HL Differentiation Worksheet (with full solutions)

The core rules of differentiation and their first uses: gradients, tangents and increasing/decreasing functions.

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

22pages
120marks
3difficulty levels
Yessolutions included
T5Calculus

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What this AI HL differentiation worksheet covers

The core rules of differentiation and their first uses: gradients, tangents and increasing/decreasing functions. The questions follow the order of the AI 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.

Power rule, including negative and fractional indices
Gradient at a point and the equation of a tangent
Increasing and decreasing intervals
Simple stationary points
Exam tip for this topic. Rewrite roots and fractions as powers before differentiating; most errors happen in that first line.

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 Calculus

✓ = solutions included

The same topic for other courses

Questions

Is this AI HL differentiation 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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