A-level · Differentiation

Connected rates of changeExam-style questions

Working out how fast one quantity changes from how fast another does. Why linked quantities have linked rates; the chain rule as the bridge, dV/dt = (dV/dh)(dh/dt); finding the formula that links them in one variable; differentiating before substituting; signs and units for quantities that shrink; and chains of three rates, including a point moving along a curve.

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22 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
The radius of a circular oil slick increases at a rate of $0.2\text{ m s}^{-1}$ . Find the rate at which its area is increasing at the instant when the radius is $10\text{ m}$ .
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