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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 48

The rate of change of the temperature of a kettle of water (yyy) after it boils is directly proportional to the difference between the temperature of the water and the room temperature (20∘C20^{\circ}\text{C}20∘C).

a.

Write down a differential equation for this relationship

[3]
b.

Show that y=20+Aekty = 20 + Ae^{kt}y=20+Aekt where A A\,A and k k\,k are constants

[4]
c.

Given that the initial temperature is 100∘C100^{\circ}\text{C}100∘C write down the value of AAA.

[1]
d.

After 8 minutes the temperature is 60∘C60^{\circ}\text{C}60∘C show that k=−18ln⁡2\displaystyle k = -\frac{1}{8} \ln 2k=−81​ln2

[3]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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