The strength of a radio signal SSS, measured in microvolts, is modelled by the function
S(t)=32∣2t−10∣+4,t⩾0 S(t) = \frac{3}{2}|2t - 10| + 4, \quad t \geqslant 0 S(t)=23∣2t−10∣+4,t⩾0where t t\,t is the time in seconds after a broadcast begins. The minimum signal strength occurs at point VVV.
Determine the coordinates of VVV.
Solve the equation S(t)=t+7S(t) = t + 7S(t)=t+7.
An interference signal is modelled by the equation
S(t)=mt+1 S(t) = mt + 1 S(t)=mt+1where m m\,m is a constant. Given that the broadcast signal and the interference signal have equal strength at exactly two distinct times,
find the range of possible values for mmm.
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.
