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1.11 H: Integration

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Question 1

The rate of change of the temperature of a heated metal rod (TTT) in a laboratory setting is directly proportional to the difference between the temperature of the rod and the constant room temperature (15∘C15^{\circ}\text{C}15∘C).

a.

Write down a differential equation for this relationship.

[2]
b.

Show that T=15+AektT = 15 + Ae^{kt}T=15+Aekt where A A\,A and k k\,k are constants.

[4]
c.

Given that the initial temperature of the rod is 115∘C115^{\circ}\text{C}115∘C, write down the value of AAA.

[1]
d.

After 10 minutes, the temperature of the rod is 65∘C65^{\circ}\text{C}65∘C. Show that k=−110ln⁡2\displaystyle k = -\frac{1}{10} \ln 2k=−101​ln2.

[3]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank