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3.2 Algebra and Functions (A-level only)

3.2 Algebra and Functions (A-level only)

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Question 119

A chemical reaction's yield Y Y\,Y is modeled as a function of the applied pressure xxx (in atmospheres) by the function:

Y(x)=4x+12x−2,x>2 Y(x) = \frac{4x + 12}{x - 2}, \quad x > 2 Y(x)=x−24x+12​,x>2
a.

Find an expression for the inverse function Y−1(x)Y^{-1}(x)Y−1(x).

[3]
b.

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

YY(x)=ax+bcx+d YY(x) = \frac{ax + b}{cx + d} YY(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 Q(6,9)Q(6, 9)Q(6,9) lies on the curve with equation y=Y(x)y = Y(x)y=Y(x).

Find the coordinates of the point to which Q Q\,Q is mapped under the transformation to the curve with equation y=5Y(4x)−8y = 5Y(4x) - 8y=5Y(4x)−8.

[3]
Markscheme

3.2 Algebra and Functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.2 Algebra and Functions (A-level only)

216 exam-style questions on WJEC A Level Maths 3.2 Algebra and Functions (A-level only), covering 3.2.1 Algebra and Functions (A-level only), 3.2.2 Algebra and Functions (A-level only), 3.2.3 Algebra and Functions (A-level only), 3.2.4 Algebra and Functions (A-level only), 3.2.5 Algebra and Functions (A-level only), 3.2.6 Algebra and Functions (A-level only), and 3.2 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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