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.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.