Free IB Maths AA SL and AI SL lesson: Key features of graphs & intersections with technology
A ready-to-teach IB Maths AA SL and AI SL lesson on Key features of graphs & intersections with technology: editable slides and teacher notes, free; a printable worksheet in 3 levels with answers for school plans. About 55 minutes.
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One lesson for AA SL and AI SL
Key features of graphs & intersections with technology is taught in IB Maths AA SL and IB Maths AI SL, with the same key ideas. Choose your course above the download button: each version's slides use that course's own worked example, questions and practice link.
- AA SL (Unit 2 · Functions)
- AI SL (Unit 2 · Functions)
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, 19 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
- Functions: domain and range
Key ideas on the slides
- A function assigns exactly one output to each input; a vertical line meets its graph at most once.
- The domain is the set of allowed inputs; exclude values giving division by zero, the square root of a negative, or the log of a non-positive number.
- The range is the set of outputs: sketch the graph over the domain and read the y-values.
- Write domains and ranges with inequalities or intervals: x ≥ 2, 0 < y ≤ 5, {x: x ≠ 3}.
By the end of the lesson, students should be able to answer a question like: f(x) = 3/(x − 2) + 1, x ≠ 2. Write down the range of f and solve f(x) = 4.
Key vocabulary
- domain: The set of input values.
- range: The set of output values.
- one-to-one: Each output comes from exactly one input.
- many-to-one: Some outputs come from more than one input.
Common mistakes this lesson tackles
- Giving the range in terms of x.
- Leaving out an end point or using < instead of ≤.
- Forgetting a restriction such as x > 0 for ln x.
The worked example
Consider f(x) = 5 − x² and g(x) = e^(0.5x). Use your GDC to find the x-coordinates of their intersections to 3 s.f.
- Access the GDC graph menu and input Y1 = 5 − x², Y2 = e^(0.5x).
- Set V-Window to a standard range (e.g. −4 ≤ x ≤ 4) and draw.
- Use G-Solv → ISCT to find the first intersection: x = −2.14 (3 s.f.).
- Navigate right for the second: x = 1.83 (3 s.f.).
Tip: Always check your V-Window if intersections are not visible. Never try to solve mixed exponential-polynomial equations algebraically.
Calculator tips
- Graph the function over its domain and use trace/min/max to see the range.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Function notation, domain & range and Applications: compound interest & depreciation |
| 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 your course's practice questions:
- IB Maths AA SL Unit 2: Graphing Functions practice questions
- IB Maths AI SL Unit 2: Graphing Linear, Quadratic, Exponential and Logarithmic 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 SL Unit 2: Graphing Functions practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.