IB Maths Revision

Number & Algebra

Sequences and series, exponents and logarithms, the binomial theorem and complex numbers.

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

ExpressionsCombinations of numbers, letters and operations.
Expanding bracketsMultiplying out, e.g. 3(x+2) = 3x+6.
FactorisingWriting an expression as a product of factors.
Indices lawsRules for powers, e.g. xᵃ × xᵇ = xᵃ⁺ᵇ.
SubstitutionReplacing letters with numbers to evaluate.
SimplifyingCollecting like terms.
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.

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 17 games in the Subjects Arcade →

More IB Maths topics

FunctionsGeometry & TrigonometryVectorsCalculusStatistics & ProbabilityDiscrete Mathematics

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