A laboratory tracks the pressure variance VVV, in kilopascals, within a reaction vessel. The variance is modelled by the function V(t)=(t+2)(t−4)(2t−5)V(t) = (t+2)(t-4)(2t-5)V(t)=(t+2)(t−4)(2t−5), where t t\,t is the time in minutes relative to a baseline event.
A secondary model is defined as g(t)=12V(t−3)+k\displaystyle g(t) = \frac{1}{2}V(t - 3) + kg(t)=21V(t−3)+k. Given that the graph of y=g(t)y = g(t)y=g(t) passes through the point (3,14)(3, 14)(3,14), determine the value of the constant kkk.
The pressure variance model is shifted horizontally such that h(t)=V(t+m)h(t) = V(t + m)h(t)=V(t+m). Given that the graph of y=h(t)y = h(t)y=h(t) passes through the origin (0,0)(0,0)(0,0), find all possible values of the constant mmm.
Find V′(t)V'(t)V′(t).
Determine the set of values of t t\,t for which the rate of change of the pressure variance is less than -6.
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.
