IB Maths: Calculus Revision

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What does differentiation give you?

Calculus 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

Limitlim x→a f(x) = L if f(x) approaches L.

Derivativef'(x) = lim h→0 (f(x+h) - f(x))/h.

Power ruled/dx (x^n) = n x^(n-1).

Product rule(uv)' = u'v + uv'.

Quotient rule(u/v)' = (u'v - uv') / v^2.

Chain rule(f(g(x)))' = f'(g(x)) × g'(x).

Displacements(t) position along an axis vs time.

Velocityv = ds/dt, instantaneous rate of position.

Accelerationa = dv/dt = d^2s/dt^2.

Implicit diffDifferentiate F(x,y) = 0 treating y = y(x).

Related ratesLink dy/dt to dx/dt via dy/dx.

DistanceIntegral of |v| over time interval.

Antiderivative∫ f(x) dx = F(x) + C where F' = f.

Power integral∫ x^n dx = x^(n+1)/(n+1) + C, n ≠ -1.

Learn Calculus 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:

What does differentiation give you?✗ The area under the curve. ✓ The gradient / rate of change of a function.

What does integration find?✗ The gradient of the curve. ✓ The area under a curve (the reverse of differentiation).

Practise Calculus — 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 →

Calculus

Key concepts

Common mistakes to avoid

Practise Calculus — free games

More IB Maths topics