The concentration C C\,C of a catalyst in a chemical reaction vessel, measured in mg/L, is modelled by the equation
C=1005(3t−k),t>k3 C = \frac{100}{5(3t - k)}, \quad t > \frac{k}{3} C=5(3t−k)100,t>3kwhere t t\,t is the time in seconds since the start of the reaction, k k\,k is a positive constant, and k≠3k \neq 3k=3.
Find dCdt\displaystyle \frac{dC}{dt}dtdC, giving your answer in simplest form in terms of kkk.
The rate of change of the concentration at time t=1t = 1t=1 is -15 mg/L/s.
Find the two possible values of kkk.
Given also that k<3k < 3k<3,
find the equation of the normal to the curve of C C\,C against t t\,t at the point where t=1t = 1t=1, writing your answer in the form at+bC+c=0at + bC + c = 0at+bC+c=0, where a,b a, b\,a,b and c c\,c are integers to be found.
Show, using algebraic integration, that
∫131005(3t−k) dt=λln2 \int_{1}^{3} \frac{100}{5(3t - k)} \, dt = \lambda \ln 2 ∫135(3t−k)100dt=λln2where λ \lambda\,λ is a constant to be found.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) 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.
