Exercise 1 — Cambridge IGCSE 0580 Mar 2025 Paper 22 Q22
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Cambridge IGCSE·Mathematics 0580·Extended
Calculus
Key knowledge — Functions And Graphs
Formulas & equations
Gradient of a straight line: m = (y₂−y₁) ÷ (x₂−x₁)Equation of a line: y = mx + cGradient of tangent ≈ Δy/Δx over a very small interval (numerical differentiation)Area under a curve ≈ sum of trapezium areasFor f(x): f⁻¹(x) is the inverse (reflect in y = x); fg(x) means f(g(x))
Key facts & rules
- y = mx + c: m is gradient, c is y-intercept.
- Parallel lines have the same gradient.
- Perpendicular lines: m₁ × m₂ = −1.
- To find the gradient at a point on a curve: draw a tangent and calculate its gradient.
- Transformations of y = f(x): y = f(x) + a shifts up by a; y = f(x+a) shifts left by a; y = af(x) stretches vertically; y = f(ax) stretches horizontally.
- Key graphs to know: y = x², y = x³, y = 1/x, y = aˣ, y = sin x, y = cos x, y = tan x.
IGCSE Functions and Graphs — Calculus Practice Extended
7 Cambridge IGCSE 0580 questions on calculus at the Extended tier — each with its full mark scheme. For the Core tier on the same skill, click here.
How to approach calculus — open the study guide
Calculus on IGCSE 0580
Practice with past paper questions on calculus at the Extended tier.
Practice exercises
Exercise 2 — Cambridge IGCSE 0580 Jun 2024 Paper 41 Q8
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Exercise 3 — Cambridge IGCSE 0580 Jun 2025 Paper 21 Q22
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Exercise 4 — Cambridge IGCSE 0580 Jun 2025 Paper 22 Q21
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Exercise 5 — Cambridge IGCSE 0580 Jun 2025 Paper 23 Q21
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Exercise 6 — Cambridge IGCSE 0580 Nov 2024 Paper 42 Q10
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Exercise 7 — Cambridge IGCSE 0580 Nov 2024 Paper 43 Q10
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