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Pearson Edexcel IAL Mathematics P3.6.2 Iteration & approximate equation solving

Practise using recurrence formulae to approximate equation roots, rearrange equations and report iterates to stated accuracy.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • substitute x_n into a given recurrence to calculate x_2, x_3 or x_4 accurately
  • rearrange f(x)=0 into x=g(x) before applying the iterative formula
  • use successive iterates to give an approximate root to the required decimal places

P3.6.2 - Iteration and approximate equation solving question 1

[Maximum number: 5]
Figure 1

Figure 1

Figure 1 shows a sketch of part of the curve with equation

y=6ln⁡(2x+3)−12x2+4x>−32y=6 \ln (2 x+3)-\frac{1}{2} x^{2}+4 \quad x>-\frac{3}{2}

The curve cuts the negative x-axis at the point P, as shown in Figure 1.

Question (a)

(a)

find, to 4 decimal places, the value of x2x_{2}

[ 2 ]

Question (b)

(b)

find, by continued iteration, the x coordinate of Q. Give your answer to 4 decimal places.

The curve has a maximum turning point at M, as shown in Figure 1.

[ 3 ]
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