Last updated on Oct 23, 2026

Connected Rates of Change (AQA A-Level Mathematics): Quizzes

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Connected Rates of Change

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What are connected rates of change also known as?

Related rates

Which differentiation technique is used when solving related rates problems?

Implicit differentiation

What does a negative rate indicate in related rates problems?

Quantity is decreasing

If $\frac{dr}{dt} = 2$ and $r = 5$ , find $\frac{dA}{dt}$ for circle area $A = \pi r^2$ .

$20\pi$

In the conical tank, what is the relationship between $r$ and $h$ using similar triangles?

$r = \frac{h}{2}$

What is the first step in solving related rates problems?

Identify quantities involved

If $\frac{dr}{dt} = 0.2$ cm/s and $P = 2\pi r$ , what is $\frac{dP}{dt}$ ?

$0.4\pi$ cm/s

If $\frac{dA}{dt} = 20$ and $\frac{dr}{dt} = 0.2$ , find $r$ when $A = \pi r^2$ .

$\frac{50}{\pi}$

When $r = 10$ and $\frac{dr}{dt} = 0.2$ , find $\frac{dA}{dt}$ for $A = \pi r^2$ .

$4\pi$ cm²/s

If $\frac{dA}{dt} = -0.5$ and $r = 8$ for $A = \pi r^2$ , find $\frac{dr}{dt}$ .

$\frac{-1}{32\pi}$

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

Explore AQA A-Level Mathematics Exam Questions by Topics

Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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