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3.1 Algebra and functions (A-level only)

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Question 32

A sensor's output voltage VVV, in volts, is modeled by the function V(p)=7+3ln⁡p, p>0V(p) = 7 + 3\ln p, \, p > 0V(p)=7+3lnp,p>0, where p p\,p is the internal pressure in kilopascals. The pressure is controlled by a mechanical setting x x\,x such that p(x)=12x−63x+1\displaystyle p(x) = \frac{12x - 6}{3x + 1}p(x)=3x+112x−6​ for x>0.5x > 0.5x>0.5.

a.

Find V−1(13)V^{-1}(13)V−1(13).

[2]
b.

Use differentiation to prove that p p\,p is an increasing function for x>0.5x > 0.5x>0.5.

[3]
c.

Find p−1(x)p^{-1}(x)p−1(x).

[3]
d.

Determine the range of the composite function VpVpVp.

[3]
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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