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IB Math AI SL · Topic 1

Number and algebra

The course's arithmetic engine. Half of this topic is modelling growth with sequences; the other half is money — compound interest, depreciation, loans and annuities — plus the approximation discipline that decides whether your final answer survives marking.

What the syllabus covers

Eight assessed sections, SL 1.1 to 1.8 — the quantitative backbone of the course, from growth models to loan mathematics.

SL 1.1Standard formOperations with numbers of the form a × 10ᵏ, where 1 ≤ a < 10 and k is an integer.
SL 1.2Arithmetic sequences and seriesnth term and partial sums from the formulae, sigma notation, and real contexts where growth is close to — but not exactly — arithmetic.
SL 1.3Geometric sequences and seriesThe same apparatus with a constant ratio: nth term, partial sums, sigma notation, and their applications.
SL 1.4Financial applicationsCompound interest and annual depreciation, read as geometric sequences in disguise.
SL 1.5Exponents and logarithmsLaws of exponents with integer exponents; logarithms in base 10 and e, evaluated numerically with technology.
SL 1.6ApproximationDecimal places and significant figures, upper and lower bounds of rounded values, percentage errors, estimation.
SL 1.7Amortization and annuitiesLoan repayments and savings plans computed with the GDC's time-value-of-money solver.
SL 1.8Solving equations with technologySystems of up to three linear equations, and polynomial equations, solved on the GDC.

How it is examined

Both papers allow a GDC, so the calculator does the arithmetic — the marks live in the setup around it.

  • Financial questions run as multi-part chains in real contexts — a loan that compounds monthly, a van that depreciates annually — with conditions buried in the wording that decide which formula applies.

  • Unless a question says otherwise, answers are given exactly or correct to three significant figures, so rounding discipline is itself assessed.

  • Every paper states it explicitly: solutions found from a GDC must be supported by suitable working. A bare number from the screen earns little on its own — naming your inputs is the evidence examiners mark against.

  • Amortization and annuities (SL 1.7) have no formula in the booklet — they are examined as GDC fluency, with marks for stating which values you entered and what the output represents.

  • Command terms set the bar: 'write down' wants an answer without working; 'find' or 'calculate' wants visible method; 'justify' and 'show that' want reasoning written out — precisely where the R1 mark lives.

  • The formula booklet supplies the arithmetic and geometric uₙ/Sₙ formulae, compound interest, and percentage error — so recall is never the skill being tested; choosing and substituting correctly is.

A marked question, mark by mark

A typical depreciation exercise, marked the way an IB examiner would mark it — including the reasoning mark most students lose.

Practise number and algebra as it is examined

AscentIQ generates a fresh exercise on any SL 1.1–1.8 skill every attempt, then marks your written solution mark by mark — so the reasoning you skipped above becomes impossible to skip.

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New to the codes? M1, A1, R1 explained →

Depreciation · SL 1.3 / 1.4

Seed 7B29

A catering company buys a delivery van for €25,000. Its value falls by 20% each year.

  1. (a)Find the value of the van after four years.
  2. (b)Justify why a geometric model is appropriate for the van's value.

Your work

V₄ = 25000 × (0.80)⁴

= 25000 × 0.4096

V₄ = €10,240

Marks awarded

  • M1Mark awarded. Correct model: multiplied by the constant ratio 0.8 four times.
  • A1Mark awarded. Correct value: €10,240.
  • R1Mark not awarded. No justification given — a constant percentage loss means a constant ratio, which is why the model is geometric.

Where marks are actually lost

Patterns seen again and again in examiner reports on this topic.

Reading past buried conditions — compounding per year versus per month, payments at the start versus the end.

CostOne missed condition sets up the wrong model, and every downstream part inherits the error.

Rounding mid-calculation instead of carrying full precision and rounding once, at the end.

CostAccuracy penalties even when the method is perfect.

Treating a repeated percentage change as arithmetic growth.

CostWithout a constant ratio there is no geometric model to award method marks against.

Quoting bare calculator output for annuities and amortization without stating what was computed.

CostExaminers cannot award what they cannot see — the setup is the evidence.