IB Maths Revision

Discrete Mathematics

Number theory, graph theory and recurrence relations.

Discrete Mathematics 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

Planar graphCan be drawn without edge crossings.
FaceRegion bounded by edges (incl. outer face).
Euler's formulaV - E + F = 2 for connected planar graphs.
K5Complete graph on 5 vertices, non-planar.
K3,3Complete bipartite 3+3, non-planar.
KuratowskiNon-planar iff contains K5 or K3,3 subdivision.
Dividesa | b means b = ka for some integer k.
gcdGreatest common divisor of a and b.
Euclidean algorithmgcd(a, b) = gcd(b, a mod b).
Bezoutgcd(a, b) = sa + tb for some integers s, t.
Linear recurrencea_n = c_1 a_(n-1) + c_2 a_(n-2).
Characteristic eqnx^2 = c_1 x + c_2 gives general solution.
GraphSet of vertices joined by edges.
DegreeNumber of edges incident to a vertex.

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.
Which is greater, −5 or −2?✗ −5 is greater because 5 > 2.   ✓ −2 is greater.

Practise Discrete Mathematics — 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

Number & AlgebraFunctionsGeometry & TrigonometryVectorsCalculusStatistics & Probability

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