A specialized sensor measures the pressure PPP, in kilopascals (kPa), within a experimental vessel. The pressure variation over time ttt, in seconds, is modeled by the function:
P(t)=2(t+2)(t−1)(t−4) P(t) = 2(t + 2)(t - 1)(t - 4) P(t)=2(t+2)(t−1)(t−4)A technician applies a vertical calibration offset to the readings. Given that the graph of the adjusted pressure y=P(t)−ky = P(t) - ky=P(t)−k passes through the point with coordinates (0,−4)(0, -4)(0,−4), find the value of the constant kkk.
The experiment is repeated with a time-delay mmm. Given that the curve with equation y=P(t+m)y = P(t + m)y=P(t+m) passes through the origin (0,0)(0, 0)(0,0), determine the three possible values of the constant mmm.
Determine an expression for P′(t)P'(t)P′(t), the rate of change of pressure with respect to time.
Hence find the set of values of ttt for which the rate of change of pressure is less than 6 kPa/s6 \text{ kPa/s}6 kPa/s.
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.
