IB Maths Revision

Calculus

Limits, differentiation and integration, and differential equations.

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.

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).
If you change one side of an equation, what must you do?✗ Nothing — you can change one side only.   ✓ Do the same to the other side to keep it balanced.

Practise Calculus — free games

Test yourself with these quick revision games for this topic:

See all 17 games in the Subjects Arcade →

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