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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 312

The pressure PPP of a gas in a specialized containment unit is modeled as a function of its volume vvv by

P(v)=5v+4v−2,v∈R,v≠2 P(v) = \frac{5v + 4}{v - 2}, \quad v \in \mathbb{R}, v \neq 2 P(v)=v−25v+4​,v∈R,v=2

The volume VVV of the unit varies with time ttt according to the function

V(t)=9−2t2,t∈R,t≥0 V(t) = 9 - 2t^2, \quad t \in \mathbb{R}, t \ge 0 V(t)=9−2t2,t∈R,t≥0
a.

Determine the exact time ttt when the pressure reaching the unit is 3, by solving the equation P(V(t))=3P(V(t)) = 3P(V(t))=3.

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b.

Find the inverse function P−1(x)P^{-1}(x)P−1(x).

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c.

Sketch and label, on the same axes, the curve with equation y=V(x)y = V(x)y=V(x) and the curve with equation y=V−1(x)y = V^{-1}(x)y=V−1(x). Show on your sketch the coordinates of the points where each curve meets or cuts the coordinate axes.

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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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