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.
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.