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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 321

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

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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