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.
566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.