Number and Algebra
AA SL Topic 1 — Number and Algebra
This topic is the algebra toolkit you'll reach for constantly across the whole course — sequences, logs, and polynomials keep resurfacing in calculus and statistics questions too. The examiners aren't testing whether you can recite — it's in the booklet. They're testing whether you can spot which formula a wordy context needs, show the algebra chain a 'show that' demands, and keep exact values alive through a multi-step 'hence'.
Overview: What This Topic Covers
Number and Algebra at SL splits into four connected skill sets: recognising and manipulating sequences and series (arithmetic and geometric), handling polynomials and rational functions (factor/remainder theorem, asymptotes), working fluently with exponentials and logarithms as inverse operations, and expanding powers efficiently with the binomial theorem. They overlap constantly — a geometric sequence's logarithm is arithmetic (that's a real exam question), and binomial expansions get used for numerical approximation.
- Almost every formula here is in the data booklet — the skill being examined is selection and substitution, not memorisation.
- This topic shows up on both papers: Paper 1 tests clean algebraic manipulation without a GDC; Paper 2 rewards fast, correct use of the calculator for numerical roots and log/exponential solving.
- Command terms carry real weight in this topic specifically — 'show that' and 'hence' questions are where most marks are lost, not on the arithmetic itself.
The shape of the chapter
Command terms that decide your marks in this topic
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Show that | Derive a given result, displaying every algebraic line — the destination is known, the journey is marked | AO2 | Writing only the final line with no working typically scores 0/2 or 1/2 even if it matches the given answer exactly. |
| Hence | You must use the method or result just obtained — not a fresh, independent method | AO2 | Solving with the GDC from scratch instead of building on the previous part can be awarded 0 marks even with the right final answer. |
| Determine | Find a value or expression with working shown | AO1/AO2 | Bare answers with no supporting line usually lose the method mark even if correct. |
| Find | Compute a value; GDC use is normally acceptable unless 'algebraically' is specified | AO1 | If 'algebraically' or 'exact' appears, a decimal GDC answer forfeits the accuracy mark. |
| Sketch | Show general shape with key features (intercepts, asymptotes, turning points) labelled | AO3 | Missing an asymptote equation or intercept coordinate on the diagram loses marks even if the curve's shape is right. |
| Justify / Show | Give a full logical chain, not just a numeric check at one point | AO2/AO3 | Checking only one value instead of proving the general case scores partial credit at best. |
Key point
Overview