The altitude of a specialized drone AAA, in meters, relative to a reference platform is modeled by the function A(t)=1.5∣t−6∣−12A(t) = 1.5|t - 6| - 12A(t)=1.5∣t−6∣−12, where t∈Rt \in \mathbb{R}t∈R represents the time in seconds since a tracking sensor was activated.
State the coordinates of the vertex P P\,P of the graph of y=A(t)y = A(t)y=A(t).
Calculate the value of the composite function AA(2)AA(2)AA(2).
Determine the set of values of t t\,t for which 1.5∣t−6∣−12<2t−31.5|t - 6| - 12 < 2t - 31.5∣t−6∣−12<2t−3.
Solve the equation A(∣t∣)=0A(|t|) = 0A(∣t∣)=0.
471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.