The temperature, V V\,V degrees Celsius, of a chemical reaction chamber over a period of time t t\,t minutes is modelled by the function
V(t)=∣kt−30∣−12,t≥0 V(t) = |kt - 30| - 12, \quad t \ge 0 V(t)=∣kt−30∣−12,t≥0where k k\,k is a positive constant.
The graph of y=V(t)y = V(t)y=V(t) intersects the vertical axis at the point C C\,C and has a minimum point at MMM.
(i) Write down the V V\,V coordinate of CCC. (ii) Find, in terms of kkk, the t t\,t coordinate of MMM.
Find, in terms of kkk, the range of values of t t\,t for which V(t)<0V(t) < 0V(t)<0.
A cooling phase is defined by the linear function L(t)=6−2tL(t) = 6 - 2tL(t)=6−2t.
Given that the line y=L(t)y = L(t)y=L(t) intersects the graph y=V(t)y = V(t)y=V(t) at two distinct points, find the range of possible values for kkk.
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.
