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3.1 Algebra and functions (A-level only)

3.1 Algebra and functions (A-level only)

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Question 184

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.

[4]
b.

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

[4]
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.

[4]
Markscheme

3.1 Algebra and functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.1 Algebra and functions (A-level only)

281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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