Edexcel GCSE Maths

Topic Questions

Iteration

1a
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2 marks

Show that the equation x cubed space plus space x space equals space 7 has a solution between 1 and 2

1b
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1 mark

Show that the equation space x to the power of 3 space end exponent plus space x space equals 7 can be rearranged to give x space equals space cube root of 7 minus x end root

1c
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3 marks

Starting with x subscript 0 space equals space 2 comma
use the iteration formula x subscript n plus 1 end subscript space equals space cube root of 7 minus x subscript n end root three times to find an estimate for a solution of  x cubed space plus space x space equals space 7

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2a
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2 marks

Show that the equation x cubed space plus space 4 x equals space 1 has a solution between x space equals space 0 and x space equals space 1

2b
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1 mark

Show that the equation x cubed space plus space 4 x equals space 1 can be arranged to give  x space equals space 1 fourth minus x cubed over 4

2c
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3 marks

Starting with space x subscript 0 space equals space 0 , use the iteration formula x subscript n plus 1 end subscript space equals space fraction numerator 1 over denominator 4 space end fraction space minus fraction numerator x subscript n superscript 3 over denominator 4 end fraction spacetwice ,
to find an estimate for the solution of  x cubed space plus space 4 x space equals 1


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3a
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2 marks

Show that the equation 3 x squared space minus space x cubed space plus space 3 space equals space 0 can be rearranged to give 

   x space equals space 3 space plus space 3 over x squared

3b
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3 marks

Using 

      x subscript n plus 1 end subscript space equals space 3 space plus space fraction numerator 3 over denominator x subscript n superscript 2 end fraction with x subscript 0 space equals space 3.2 comma

find the values of x subscript 1 space comma space x subscript 2 and x subscript 3

3c
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1 mark

Explain what the values of x subscript 1 space comma space x subscript 2 space comma space and  x subscript 3 represent.

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4a
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2 marks

A sphere has radius r cm

An approximate value of r can be found using the iterative formula

r subscript n plus 1 end subscript equals square root of 239 over r subscript n end root

The starting value is  r subscript 1 equals 7

Work out the values of  r subscript 2 and r subscript 3

r subscript 1 equals.....................
r subscript 2 equals.....................

4b
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1 mark

Continue the iteration to work out the radius to 1 decimal place.

................................................. cm

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5
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3 marks

x subscript n plus 1 end subscript equals cube root of 3 x subscript n plus 7 end root

Use a starting value of x subscript 1 space equals space 2 to work out a solution to x space equals space cube root of 3 x plus 7 end root
Give your answer to 3 decimal places.

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