Free Differentiation questions for IGCSE Additional Mathematics (0606), part of Vectors & calculus. Each question has the answer and the marking points an examiner would look for.
Generate a full Differentiation worksheet →All Vectors & calculus questionsThe radius of a circle increases at 0.5 cm/s. Find the rate of increase of the area when the radius is 10 cm.
| Part | Answer and marking points | Marks |
|---|---|---|
| 31.4 cm²/s dA/dr = 2πr B1 chain rule M1 31.4 A1 | 3 |
A curve has equation y = 3x3 + 3x2 − x.
Find dydx.
Find the equation of the normal to the curve at the point where x = 3.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 9x2 + 6x − 1 Two terms correct B1 All correct B1 | 2 |
| (b) | y − 105 = −198(x − 3) gradient of tangent = 98 M1 gradient of normal = −198 M1 point (3, 105) B1 Correct equation in any form A1 | 4 |
Differentiate with respect to x: (a) (4x + 1)5; (b) x2 ln x; (c) e4xx.
| Part | Answer and marking points | Marks |
|---|---|---|
| chain/product/quotient 5(4x + 1)4 × 4 M1 20(4x + 1)4 A1 product rule M1 2x ln x + x A1 quotient rule M1 4xe4x − e4xx2 A1 | 6 |
A curve has equation y = x3 − 12x + 4.
Find the coordinates of the stationary points.
Determine the nature of each stationary point.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (2, −12) and (−2, 20) dydx = 3x2 − 12 M1 x = ±2 A1 substitute M1 (2, −12) and (−2, 20) A1 | 4 |
| (b) | minimum at x = 2, maximum at x = −2 d2ydx2 = 6x M1 both correct A1 | 2 |
The radius of a circle increases at 0.2 cm/s. Find the rate of increase of the area when the radius is 4 cm.
| Part | Answer and marking points | Marks |
|---|---|---|
| 5.03 cm²/s dA/dr = 2πr B1 chain rule M1 5.03 A1 | 3 |
A curve has equation y = 2x3 − 4x2 − x.
Find dydx.
Find the equation of the normal to the curve at the point where x = 3.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 6x2 − 8x − 1 Two terms correct B1 All correct B1 | 2 |
| (b) | y − 15 = −129(x − 3) gradient of tangent = 29 M1 gradient of normal = −129 M1 point (3, 15) B1 Correct equation in any form A1 | 4 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in