IBDP · Maths AI HL
Number and Algebra
AI HL Topic 1 — Number and Algebra
42 min readAdvancedLargest single strand in AI HL — appears across Paper 1 and Paper 2 almost every sitting, and underpins the financial-maths and modelling questions elsewhere on the paper.
This is the topic where IB stops asking you to do algebra and starts asking you to recognise it hiding inside a story about drugs, decibels, ants or a depreciating car. Every question in the bank below reduces to one of five patterns — exponential/log, binomial expansion, arithmetic series, geometric series, or polynomial/rational structure — and the marks are almost always won or lost on the first algebraic move, not the final answer.
Overview
What ties this topic together
- Number & Algebra is where IB AI turns real growth/decay data into equations — it's the most 'calculator + algebra' hybrid strand you'll meet.
- Every subtopic reduces to the same three-step skill: spot the pattern (add? multiply? polynomial shape?), pick the matching formula, then solve for the unknown — almost always by taking logs or factorising.
- Exam questions nearly always disguise the maths inside a context (drugs, sound, population, cars). Strip the story first, write the bare equation, then work the algebra.
The shape of the chapter
Command terms that decide how you write the answer
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Show that | Derive the given result using full algebraic steps — the answer is already known, marks are for the method. | AO2 | Zero marks for stating the given answer without working; every algebraic line earns a mark. |
| Hence | You must use the result from the previous part — an independent correct method from scratch often scores zero. | AO2/AO3 | Mark scheme explicitly ties marks to reusing part (a)'s value. |
| Determine / Find | Obtain a numerical or algebraic answer; working may still be required for method marks even with a GDC. | AO2 | A bare final answer can lose method marks if an intermediate value is needed for a later part. |
| State | One-line answer read off directly — no working expected or rewarded. | AO1 | Usually 1 mark only — don't waste time justifying it. |
| Write down | Read directly from a graph, GDC screen or given expression. | AO1 | Same weighting as State — over-explaining doesn't add marks. |
Key point
Before touching your GDC, ask: does the quantity add the same amount each step (arithmetic), multiply by the same factor (geometric/exponential), or is it a polynomial ratio? That one question tells you exactly which formula you need.
Overview