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Edexcel A-Level Mathematics A2 P3.6.2 Iteration and Approximate Equation Solving Questions

Practise rearranging equations into recurrence formulae, calculating iterates and reporting approximate roots to the stated precision.

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

Edexcel A-Level Mathematics A2 P3.6.2 Iteration and Approximate Equation Solving Questions 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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