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.
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.