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.
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.
