IB DP Mathematics: Command terms

IB Diploma Programme Mathematics (Analysis and Approaches, Applications and Interpretation) uses the standard IB command terms. Mathematics emphasises Calculate, Show, Prove, Derive and Find. Clear working and correct notation are essential.

Key command terms for Mathematics

Command term	What to do	Common mistake
State	Give value or expression	Showing working when not asked
Write	Give equation or expression	Incomplete
Write down	Give without working	Showing unnecessary working
Find	Obtain answer; show relevant working	No working
Calculate	Numerical answer; show stages	No working; wrong precision
Show	Prove with full working	Skipping steps
Prove	Logical argument; each step justified	Assuming what we prove
Derive	Obtain from given/known results	Stating without derivation
Determine	Obtain the only possible answer	Multiple answers
Sketch	Approximate graph; key features	Precise plot when sketch asked
Draw	Accurate graph/diagram	Unlabelled
Solve	Find value(s) satisfying equation	Incomplete solution
Verify	Check by substitution	Proving
Hence	Use previous result	Starting from scratch
Hence or otherwise	Use previous result or different method	Ignoring “hence”

Tips for Mathematics exams

1. Show working—marks for method even if answer wrong
2. Hence—must use the previous part
3. Prove—show each step; no gaps
4. Sketch— intercepts, asymptotes, shape; not plot every point
5. Precision—round to required accuracy (e.g. 3 significant figures)
6. Notation—use correct symbols (e.g. ∈, ⊆, ⇒)
7. Past papers—check mark schemes for alternative methods

How Tutopiya helps

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Based on IB Diploma Programme Mathematics subject guides. Check the guide for subject-specific command terms.