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1.3 Functions

1.3 Functions

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Question 82

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

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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