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IGCSE Maths Calculus Notes

Calculus on IGCSE (Edexcel Higher) introduces differentiation to find gradients of curves, turning points and rates of change.

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Key concepts

Differentiation
Finding dy/dx, the gradient function of a curve, from its equation.
Gradient at a point
Substitute the x-value into dy/dx to get the gradient there.
Turning points
Set dy/dx = 0 and solve to find maximum and minimum points.

Key formulas

Power rule

if y = xⁿ then dy/dx = n·xⁿ⁻¹

Stationary points

set dy/dx = 0

Solve for x to locate maxima and minima.

Worked example

Differentiate y = 3x² + 4x and find the gradient at x = 2.

  1. 1Differentiate term by term: dy/dx = 6x + 4.
  2. 2Substitute x = 2: 6(2) + 4.
  3. 3Calculate the gradient.

Answer: dy/dx = 6x + 4; gradient at x = 2 is 16

Common mistakes

✗ Forgetting to reduce the power by one.

✓ Multiply by the power, then subtract 1 from it.

✗ Differentiating a constant to something non-zero.

✓ The derivative of a constant is 0.

✗ Not solving dy/dx = 0 for turning points.

✓ Stationary points occur where the gradient is zero.

Quick check

Try these, then reveal the answers.

Differentiate y = x³.Reveal answer

3x²

Differentiate y = 5x.Reveal answer

5

Where is the turning point of y = x² − 4x?Reveal answer

x = 2

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Exam tips

  • Rewrite terms as powers of x before differentiating.
  • For turning points, differentiate, set to zero, solve, then find the y-value.
  • Use a second derivative or a sign check to classify maximum vs minimum.

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AlgebraFunctions (f(x))

Key terms explained

Short, exam-ready definitions with a formula, a worked example and an examiner tip.

What is differentiation?What is gradient?Full glossary

Frequently asked questions

Is calculus on all IGCSE Maths courses?+

Differentiation appears on Edexcel IGCSE Higher tier; check your specification, as Cambridge IGCSE Maths does not include it.

What does dy/dx represent?+

It is the gradient function — the rate at which y changes with x at any point on the curve.

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