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Edexcel A-Level Mathematics A2 P3.1 Algebra and Functions Questions

Practise manipulating rational functions, inverses, modulus graphs and combined transformations, with coordinates, ranges and constants to determine.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • simplify rational expressions by factorising, dividing and cancelling to reach a required form
  • find inverses, composite functions and ranges while respecting domains and asymptotes
  • track graph features under modulus and transformation equations, including mapped points

Covered syllabus points

P3.1.1 - Simplification of rational Denominators of rationalP3.1.2 - Definition of a functionP3.1.3 - modulus functionP3.1.4 - Combined transformations of functions

Question 1

[Maximum number: 6]

The function f is defined by

f(x)=5xx2+7x+12+5xx+4,x>0f(x)=\frac{5x}{x^2+7x+12}+\frac{5x}{x+4},\qquad x>0

Question (a)

(a)

Show that f(x)=5xx+3f(x)=\frac{5x}{x+3}.

[ 3 ]

Question (b)

(b)

Find f−1f^{-1}.

[ 3 ]

Question 2

[Maximum number: 12]

Figure 1 shows a sketch of part of the graph with equation y=f(x), where

f(x)=∣3x−13∣+5,x∈Rf(x)=|3x-13|+5,\qquad x\in\mathbb{R}

The vertex of the graph is at point P, as shown in Figure 1.

Figure 1

Figure 1

Question (a)

(a)

State the coordinates of P.

[ 2 ]

Question (b)

(b)

State the range of f.

[ 2 ]

Question (c)

(c)

Find the value of ff(4).

[ 2 ]

Question (d)

(d)

Solve, using algebra and showing your working,

16-2x>|3x-13|+5
[ 4 ]

Question (e)

(e)

The graph with equation y=f(x) is transformed onto the graph with equation y=af(x+b).
The vertex of the graph with equation y=af(x+b) is (4,20).

Given that a and b are constants, find the value of a and the value of b.

[ 2 ]
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