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∣<9 13.5 - |1.5p - 6| < 9 13.5−∣1.5p−6∣<9to find the range of values for ppp for which the alarm is active.
566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.