A specialized hydraulic piston's displacement DDD (in mm) relative to a benchmark is modeled by the equation:
D(t)=25∣5t+8∣−6,t∈R D(t) = \frac{2}{5}|5t + 8| - 6, \quad t \in \mathbb{R} D(t)=52∣5t+8∣−6,t∈Rwhere t t\,t is the time in seconds.
State the coordinates of the vertex, VVV, of the graph of y=D(t)y = D(t)y=D(t).
Using algebra, determine the set of values of t t\,t for which
D(t)>2−15t D(t) > 2 - \frac{1}{5}t D(t)>2−51tSketch the graph with equation y=∣D(t)∣y = |D(t)|y=∣D(t)∣, stating the coordinates of the local maximum point and each local minimum point.
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.
