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1.5 B: Algebra and functions

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Question 282
a.

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.

[4]
b.

The sensor triggers an alarm when the signal strength is strictly less than 9 units. Solve the inequality

13.5−∣1.5p−6∣<9 13.5 - |1.5p - 6| < 9 13.5−∣1.5p−6∣<9

to find the range of values for ppp for which the alarm is active.

[3]

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

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.

Question bank