A laser displacement sensor is calibrated to measure the surface profile of a machined groove. The vertical height y y\,y relative to a datum, at a horizontal distance x x\,x from the start of the sensor's path, is modelled using two related functions.
Given that k k\,k and m m\,m are positive constants with k>mk > mk>m,
Sketch, on separate diagrams, the graph with equation
(i) y=∣3x−k∣y = |3x - k|y=∣3x−k∣
(ii) y=∣3x−k∣−my = |3x - k| - my=∣3x−k∣−m
Show on each sketch
Solve the equation
∣3x−k∣−m=7x |3x - k| - m = 7x ∣3x−k∣−m=7xgiving any solution for x x\,x in terms of k k\,k and mmm.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.