A signal processor monitors the power P P\,P in milliwatts of an oscillating beam over time t t\,t milliseconds. The power output is modeled by the function
P(t)=30−5∣4−t∣,t≥0 P(t) = 30 - 5|4 - t|, \quad t \ge 0 P(t)=30−5∣4−t∣,t≥0Determine the value of PP(2)PP(2)PP(2).
Solve the equation P(t)=5tP(t) = 5tP(t)=5t.
Given that the equation P(t)=kP(t) = kP(t)=k has exactly two roots, state the range of possible values for the constant kkk.
The power signal is adjusted such that the new power output Q(t)Q(t)Q(t) is given by Q(t)=aP(t−b)Q(t) = aP(t - b)Q(t)=aP(t−b). The maximum power of the new signal is 6 mW and occurs at t=12t = 12t=12. Find the value of the constants a a\,a and bbb.
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.
