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Differential Equations
Quick questions on Modelling with differential equations explained: H2 Further Mathematics
6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is translating a rate description into an equation?Show answer
The phrase "the rate of change of " is . Build the right-hand side from the description:
What is not interpreting the answer?Show answer
Modelling questions reward a sentence explaining the long-term behaviour or the meaning of a constant, not just the algebra.
What is units and context?Show answer
Keep track of units and check the answer is physically reasonable (a positive time, a mass between and the initial value).
What is q1?Show answer
Write a differential equation for a quantity decaying at a rate proportional to itself. [1 mark]
What is q2?Show answer
For , what is the long-term value of ? [1 mark]
What is q3?Show answer
A model gives . State the initial value and the limiting value. [2 marks]
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