Differentiation — IGCSE Mathematics - Additional (0606) questions by topic
Differentiation questions cover finding unknown coefficients in a polynomial using a given derivative value and a known factor, finding a rate of change of a sphere's surface area given the rate of change of its volume, and using calculus to approximate a small change in y as x increases slightly. Find, show, state, calculate and determine are the top command words, with related-rates questions requiring you to connect two different derivatives correctly.
This page draws on 9 real questions worth between 3 and 10 marks, all from 2025 papers. Related-rates and small-change problems depend on setting up the right chain of derivatives before substituting values, so submit your workings for instant marking to catch a misapplied chain rule or wrong substitution point early.
May–June 2025, Paper 11
A curve has equation y = ((x^2 − 1)/(x^2 + 1))^4. Show that dy/dx can be written as A x (x^2 − 1)^3 / (x^2 + 1)^5, where A is a positive integer to be found.
Answer this question and get it marked →May–June 2025, Paper 12
The polynomial p is such that p(x) = 3x^3 - 7x^2 + ax + b, where a and b are integers. It is given that p'(-1) = 21 and that x - 2 is a factor of p(x). Find the values of a and b.
Answer this question and get it marked →It is given that y = ln(3x^2 + 16) / (x + 2). Find dy/dx when x = 0. Give your answer in the form ln(p), where p is a constant.
Answer this question and get it marked →May–June 2025, Paper 13
The normal to the curve y = 4 / x^2 + ax + 7 at the point where x = 2 has equation x + 4y = b. Find the values of a and b.
Answer this question and get it marked →May–June 2025, Paper 21
Given that y = x^2 tan(x/2), use calculus to find the approximate change in y as x increases from π/3 to π/3 + h, where h is small.
Answer this question and get it marked →May–June 2025, Paper 22
Given that y = 4 sin 2x cos 2x, find the value of dy/dx when x = pi/6.
Answer this question and get it marked →The volume, V, of a sphere is increasing at the constant rate of 2pi cm^3 s^-1. Find the rate of change of the surface area, S, of this sphere when the volume of the sphere is…
Answer this question and get it marked →May–June 2025, Paper 23
Given that y = (4x^3 − 5) / x^2, show that dy/dx can be written as 2(2x^3 + 5) / x^3.
Answer this question and get it marked →It is given that y = e^(3x+2) tan x. Use calculus to find the approximate change in y as x increases from 0.1 to 0.1 + h, where h is small.
Answer this question and get it marked →