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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 124

The efficiency rating of an industrial turbine, EEE, is modeled as a function of the intake pressure x x\,x by

E(x)=5x+8x−2,x>2 E(x) = \frac{5x + 8}{x - 2}, \quad x > 2 E(x)=x−25x+8​,x>2
a.

Find an expression for E−1(x)E^{-1}(x)E−1(x).

[3]
b.

Show that the composite function EE(x)EE(x)EE(x) can be written in the form

EE(x)=ax+bcx+d EE(x) = \frac{ax + b}{cx + d} EE(x)=cx+dax+b​

where a,b,c a, b, c\,a,b,c and d d\,d are integers to be found.

[4]
c.

The point P(6,9.5)P(6, 9.5)P(6,9.5) lies on the curve with equation y=E(x)y = E(x)y=E(x).

Find the coordinates of the point to which P P\,P is mapped when the curve is transformed to y=4E(0.5x)−7y = 4E(0.5x) - 7y=4E(0.5x)−7.

[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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