IB Maths: Number & Algebra Revision

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Does multiplying always make a number bigger?

Number & Algebra is a core part of IB Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.

Key concepts

Indices lawsRules for powers, e.g. xᵃ × xᵇ = xᵃ⁺ᵇ.

Polar formz = r(cos θ + i sin θ).

Exponential formz = r e^(iθ), via Euler's formula.

De Moivre(cos θ + i sin θ)^n = cos(nθ) + i sin(nθ).

Multiplicationz1 z2 = r1 r2 e^(i(θ1+θ2)).

Divisionz1 / z2 = (r1/r2) e^(i(θ1-θ2)).

Modulus times|z1 z2| = |z1| × |z2|.

Root of unityComplex z with z^n = 1.

Primitive rootω = e^(2πi/n), generates all n roots.

Learn Number & Algebra step by step

Free interactive mini-lessons: short screens, worked examples and quick checks. Pick your exam board to open its course map, then tap L on this topic:

IB Mathematics: Analysis & Approaches · HL IB Mathematics: Analysis & Approaches · SL IB Mathematics: Applications & Interpretation · HL IB Mathematics: Applications & Interpretation · SL

Common mistakes to avoid

Questions where students often pick the tempting wrong answer — make sure you know the right one:

Does multiplying always make a number bigger?✗ Yes, multiplication always increases a number. ✓ No — multiplying by a number between 0 and 1 makes it smaller.

How do you decide the order of operations?✗ Always strictly left to right. ✓ Brackets, indices, then ×/÷, then +/− (BIDMAS).

Practise Number & Algebra — free games

Test yourself with these quick revision games for this topic:

▶ Two Truths, One Lie ▶ Reveal Race ▶ Connections Grid ▶ Falling Words ▶ Word Web

See all 22 games in the Revision Arcade →

Number & Algebra

Key concepts

Common mistakes to avoid

Practise Number & Algebra — free games

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