IGCSE Maths Calculus Notes
Calculus on IGCSE (Edexcel Higher) introduces differentiation to find gradients of curves, turning points and rates of change.
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.
- 1Differentiate term by term: dy/dx = 6x + 4.
- 2Substitute x = 2: 6(2) + 4.
- 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
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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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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