IB Math AA SL · Topic 1
Number and algebra
The algebraic backbone of the course. Sequences and series model growth, exponents and logarithms let you solve for an unknown power, and simple proof and the binomial theorem turn algebra into argument. A large share of it is examined with no calculator, so exact working is the point.
What the syllabus covers
Nine assessed sections, SL 1.1 to 1.9 — from standard form to proof and the binomial theorem.
How it is examined
The same topic is examined twice, in two styles: exact and by hand on Paper 1, with technology and a real-world context on Paper 2.
Paper 1 allows no calculator, so it asks for exact answers — a logarithm left as ln 5 or log₂ 7, a surd, a fraction — and for algebra you can do by hand: laws of exponents and logarithms, the general term of a binomial expansion, the sum to infinity.
Paper 2 allows technology and turns the same skills into contexts — compound interest over years, depreciation, a sequence modelling a real quantity. The guide says financial questions may require technology, and the marks go to the setup around it: which values you entered and what the output means.
Unless a question says otherwise, answers are given exactly or correct to three significant figures, so rounding is itself assessed. Carry unrounded values through a multi-step chain and round once, at the end.
Simple proof (SL 1.6) is marked step by step. A 'show that' gives you the destination, so the credit is in every visible line of algebra that reaches it — not in the final line, which was handed to you.
A sum to infinity (SL 1.8) exists only when |r| < 1. Questions that ask whether it exists, or for the range of r that makes it exist, are testing that condition directly.
In the binomial theorem (SL 1.9) the working follows the general term: choose the power of each part, then the coefficient — Pascal's triangle for small n, the nCr function beyond that.
A marked question, mark by mark
A sum-to-infinity question where the right number is not enough: the condition that makes it exist is a mark of its own.
Practise the algebra with fresh numbers every time
From SL 1.1 standard form to SL 1.9 binomial expansions, each generated exercise is written in the style of Paper 1 (exact, no calculator) or Paper 2 (technology) as the question demands — and comes back mark by mark, with a reason for each.
Start your trialNew to the codes? M1, A1, R1 explained →
Sum to infinity · SL 1.8
Seed 3K29
A geometric series has first term 12 and common ratio 1/3.
- (a)Find the sum to infinity of the series.
- (b)Explain why the sum to infinity exists.
Your work
S∞ = u₁ / (1 − r)
= 12 / (1 − 1/3) = 18
The terms get smaller, so it converges.
Marks awarded
- M1Mark awarded. Correct formula with u₁ = 12 and r = 1/3 substituted.
- A1Mark awarded. S∞ = 18.
- R1Mark not awarded. 'The terms get smaller' is not the condition: |r| = 1/3 < 1 was never stated.
Where marks are actually lost
In this topic the algebra is usually right. The marks go in what surrounds it: rounding, form and justification.
Rounding in the middle of a multi-step chain, then using the rounded value.
CostThe final answer drifts out of three significant figures and the accuracy mark goes, even though every method line was correct.
Giving a calculator decimal where an exact answer was asked for.
Cost'ln 5' and '1.609…' are not the same answer on an exact-value question; the method mark survives, the answer mark does not.
Working backwards from the result in a proof — manipulating both sides until they match.
CostA proof has to run from one side to the other. Assuming what you are asked to show earns the method marks of neither side.
Applying S∞ = u₁ / (1 − r) without checking |r| < 1.
CostWhen a question asks whether the sum exists, the check is the reasoning mark — and a value of r outside the range makes the whole answer meaningless.
Other Math AA SL topics
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