The strength of a signal SSS detected by a proximity sensor is modeled by the function S=13.5−∣1.5p−6∣S = 13.5 - |1.5p - 6|S=13.5−∣1.5p−6∣ where ppp is the position of an object on a linear track. Sketch the graph of SSS against ppp, marking the coordinates of the vertex and any points where the graph intersects the coordinate axes.
The sensor triggers an alarm when the signal strength is strictly less than 9 units. Solve the inequality 13.5−∣1.5p−6∣<913.5 - |1.5p - 6| < 913.5−∣1.5p−6∣<9 to find the range of values for ppp for which the alarm is active.
Practise Edexcel A Level Maths 2.7 Solving Modulus Problems with exam-style questions for A Level Maths. 32 questions, matched to the Edexcel A Level Maths (9MA0) 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.