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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 52

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∈R

where t t\,t is the time in seconds.

a.

State the coordinates of the vertex, VVV, of the graph of y=D(t)y = D(t)y=D(t).

[2]
b.

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)>2−51​t
[4]
c.

Sketch 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.

[4]
Markscheme

1.5 B: Algebra and functions Questions

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

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.

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