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1.2 Algebra and Functions

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Question 163

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

1.2 Algebra and Functions Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra and Functions

566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.

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