Free IB Maths AA HL lesson: Polynomial division
A ready-to-teach IB Maths AA HL lesson on Polynomial division (Unit 2 · Functions): 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, 23 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
- Algebraic division, factor and remainder theorems
Key ideas on the slides
- Factor theorem: (x − a) is a factor of f(x) if and only if f(a) = 0; for (ax − b), test f(b/a).
- Remainder theorem: the remainder when f(x) is divided by (x − a) is f(a).
- To factorise a cubic: find a root by testing factors of the constant term, divide (long division or comparing coefficients), then factorise the quadratic.
- f(x) = (x − a)q(x) + r: the quotient q(x) has degree one less than f.
By the end of the lesson, students should be able to answer a question like: Divide 2x^3 - x + 4 by x + 2 to find the remainder.
Key vocabulary
- factor: An expression that divides exactly, leaving no remainder.
- remainder: What is left over after division.
- quotient: The result of the division (without the remainder).
Common mistakes this lesson tackles
- Complex numbers and polynomials: conjugate roots, all the roots, general solutions. A real polynomial with root a + bi also has a − bi. Build the quadratic factor (z − (a + bi))(z − (a − bi)) = z² − 2az + a² + b² and divide, or use sum/product with every root.
- Using f(a) for the divisor (x + a) instead of f(−a).
- Leaving out a missing power in long division instead of writing it as 0x².
- Saying "is a factor" without showing f(a) = 0 and concluding.
Calculator tips
- A table of values finds roots quickly; the polynomial solver checks the factorisation.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Logarithmic graphs & solving log equations and Exponential graphs & modelling |
| 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 2: Polynomials and Rational Functions practice questions.
What schools get
- Set this lesson as homework, marked by AI against the mark scheme, with every result in your markbook (with a School 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 2: Polynomials and Rational Functions practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.