Free IB Maths AA HL lesson: Definite integrals & area between curves
A ready-to-teach IB Maths AA HL lesson on Definite integrals & area between curves (Unit 5 · Calculus): editable slides and teacher notes, free; a printable worksheet in 3 levels with answers for school plans. About 55 minutes.
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What's inside
- Slides (PowerPoint, editable) · freeabout 12 slides: do now, objectives, key ideas, a worked example step by step, “your turn”, practice QR code, exit ticket
- Teacher notes (PDF) · freelesson plan with timings, common mistakes, homework links
- Worksheet (PDF) · school plans6 questions, 30 marks: Fluency, Reasoning, Exam-style. Included with school plans and the teacher trial.
- Answers (PDF) · school plansthe answer to every worksheet question, from its mark scheme. Included with school plans and the teacher trial.
Learning objectives
- Definite Integrals, Area Under a Curve & Between Curves
- Areas: The Area Between a Curve and the y-axis
- Rotation About the x-axis
- Rotation About the y-axis
Key vocabulary
- definite integral: An integral with limits; its value is a number.
- limits: The values a and b between which you integrate.
- area: Always positive, even when the integral is negative.
- bounded region: A region enclosed by curves and/or lines.
- point of intersection: Where two curves meet; gives the limits.
Common mistakes this lesson tackles
- 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.
- 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.
- Integrating across a root and letting positive and negative parts cancel.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Antiderivatives (integration) and Optimisation in context |
| 5–8 min | Share the learning objective and success criteria |
| 8–20 min | Teach: the worked example, step by step; students copy the method |
| 20–25 min | Your turn: 1 mini-whiteboard question; check every board before moving on |
| 25–42 min | Practise: the worksheet (6 questions in 3 levels, with school plans and the teacher trial) or the topic's practice questions online; move up a level after two right in a row |
| 42–47 min | Plenary: 1-question exit ticket; collect it to plan the next lesson |
For students: practise this topic
The worksheet's QR code opens the IB Maths AA HL Unit 5: Definite Integrals practice questions.
What schools get
- Set this lesson as homework, marked by AI against the mark scheme, with every result in your markbook (school Pro plan).
- This lesson's worksheet in three levels, with its answers, ready to print.
- Support, Core and Stretch versions and A/B copies of the worksheet from the full question bank, in the worksheet builder.
- Create lesson: this lesson rebuilt for your class's next scheme-of-work lesson, from the full bank.
School licences from €490 a year. Try everything free for 30 days as a teacher: no card.
Questions teachers ask
Is this lesson free?
The slides and the teacher notes are free to download with a free IB Math Revision teacher account (sign in with Google, Microsoft or email); no card. The printable worksheet in three levels and its answers are included with school plans and the free 30-day teacher trial.
Can I edit the slides?
Yes. The slides are an ordinary PowerPoint file: change, add or delete anything. They also open in Google Slides and Keynote. The logo and web address sit on the slide master, so your edits do not move them.
What do students use for homework?
The practice slide's QR code and web address take students to the IB Maths AA HL Unit 5: Definite Integrals practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.