The signal strength SSS, measured in decibels (dB), of a satellite passing directly over a ground station is modeled by the function
S(t)=24−4∣5−t∣,t≥0 S(t) = 24 - 4|5 - t|, \quad t \ge 0 S(t)=24−4∣5−t∣,t≥0where t t\,t is the time in minutes since the signal was first detected.
Find the value of SS(8)SS(8)SS(8).
Solve the equation S(t)=2tS(t) = 2tS(t)=2t.
Given that the equation S(t)=kS(t) = kS(t)=k has exactly two distinct solutions for ttt, determine the range of possible values for the constant kkk.
A calibration adjustment transforms the signal graph into the graph with equation y=pS(t−q)y = pS(t - q)y=pS(t−q). The vertex of this transformed graph is at (1,12)(1, 12)(1,12). Find the value of the constants p p\,p and qqq.
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.