Free IB Maths AA HL lesson: Amplitude, period, phase shift of sin/cos
A ready-to-teach IB Maths AA HL lesson on Amplitude, period, phase shift of sin/cos (Unit 3 · Geometry & Trigonometry): 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, 34 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
- Trigonometric graphs: amplitude, period and phase shift
Key ideas on the slides
- For y = asin(b(x − c)) + d: amplitude |a|, period 2π/b (or 360°/b), horizontal shift c, principal axis y = d.
- Maximum value d + |a|; minimum value d − |a|.
- y = tan x has period π and vertical asymptotes at x = π/2 + nπ.
- Read parameters from a graph: d = (max + min)/2, a = (max − min)/2, period = distance between two maxima.
By the end of the lesson, students should be able to answer a question like: Find the period and amplitude of the function y = -3cos(2x - π).
Key vocabulary
- amplitude: Half the distance between the maximum and minimum values.
- period: The horizontal length of one complete cycle.
- principal axis: The horizontal line y = d midway between maximum and minimum.
- phase shift: The horizontal translation of the graph.
Common mistakes this lesson tackles
- Giving the period as b instead of 2π/b.
- Using the full height (max − min) as the amplitude.
- Shifting the wrong way for sin(x − c).
Calculator tips
- Plot in the right angle mode and use max/min to check the parameters.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Solving trig equations and Compound-angle & double-angle identities |
| 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 3: Trigonometric 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 3: Trigonometric Functions practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.