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>4where TTT is the temperature of the vessel in degrees Celsius.
Write H(T)H(T)H(T) in the form
AT+B+CT−4 AT + B + \frac{C}{T - 4} AT+B+T−4Cwhere AAA, BBB, and CCC are integers to be found.
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∫57H(T)dT, is equal to
α+βln3 \alpha + \beta \ln 3 α+βln3where α\alphaα and β\betaβ are integers to be found.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
