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.
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.
