Number and Algebra
SL 1.1-1.9
This topic is where your GDC becomes a genuine tool, not a crutch — the exam wants you to set up the right equation from a word problem and then interpret what the calculator spits out. Examiners mark the modelling step (spotting growth vs decay, identifying , , or ) far more heavily than the button-pressing. Every worked example below is built from real exam phrasing — value depreciating, populations growing, isotopes decaying — because that's exactly how this content is tested.
Overview
Number and Algebra in AI SL is really five toolkits stitched together: exponential/log models for growth and decay, the binomial expansion for powers of brackets, and two families of sequences (arithmetic and geometric) that underpin financial maths. Polynomials and rational functions round it off by giving you the algebraic machinery — factorising, solving, sketching — that every other topic (calculus, statistics, financial models) leans on.
- Exponential/log questions almost always come as a real-world context (car value, bacteria, radioactive decay) — the skill tested is translating words into or .
- Binomial theorem is a single formula from the data booklet, applied to find one term or one coefficient — never the whole expansion by hand.
- Arithmetic and geometric sequences share the same four unknowns (, or , , ) — most marks are lost mixing up which formula belongs to which sequence.
- Polynomials and rational functions test factor theorem, remainder theorem and asymptote behaviour, usually GDC-assisted for finding roots.
The shape of the chapter
Command terms you'll actually see here
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| State | Give the answer with no working needed — usually reading a value straight off the model. | AO1 | 1 mark for the correct value; no method needed but wrong rounding still loses the mark. |
| Calculate | Obtain a numerical answer showing the working or GDC steps used. | AO2 | Method mark for correct substitution, answer mark for final value to required accuracy. |
| Determine | Find a value from given information, often requiring an equation to be solved. | AO2 | Marks split between setting up the equation and solving it correctly. |
| Show that | Prove a given result using algebra — the answer is given, so every line of working must be explicit. | AO2 | No marks for just stating the given answer; each algebraic step must be shown. |
Key point
Overview