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1.1 Algebra and functions

1.1 Algebra and functions

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Question 131

A chemical engineer models the rate of heat loss H(T)H(T)H(T), in kilowatts per degree Celsius, from a specific pressurized vessel using the formula

H(T)=2T2−3T−7T−4,T>4 H(T) = \frac{2T^2 - 3T - 7}{T - 4}, \quad T > 4 H(T)=T−42T2−3T−7​,T>4

where TTT is the temperature of the vessel in degrees Celsius.

a.

Write H(T)H(T)H(T) in the form

AT+B+CT−4 AT + B + \frac{C}{T - 4} AT+B+T−4C​

where AAA, BBB, and CCC are integers to be found.

[3]
b.

Hence use algebraic integration to show that the total heat loss between temperature T=5T = 5T=5 and T=7T = 7T=7, given by ∫57H(T) dT\int_{5}^{7} H(T) \, dT∫57​H(T)dT, is equal to

α+βln⁡3 \alpha + \beta \ln 3 α+βln3

where α\alphaα and β\betaβ are integers to be found.

[4]
Markscheme

1.1 Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.1 Algebra and functions

306 exam-style questions on CCEA A Level Maths 1.1 Algebra and functions, covering 1.1.1 Algebra and functions, 1.1.2 Algebra and functions, 1.1.3 Algebra and functions, 1.1.4 Algebra and functions, 1.1.5 Algebra and functions, 1.1.6 Algebra and functions, 1.1.7 Algebra and functions, 1.1.8 Algebra and functions, 1.1.9 Algebra and functions, 1.1.10 Algebra and functions, 1.1.11 Algebra and functions, 1.1.12 Algebra and functions, 1.1.13 Algebra and functions, and 1.1.14 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.

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