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GCSE (1 – 9)
Iteration
Name: ___________________________
Instructions
- Use black ink or ball-point pen.
- Answer all questions.
- Answer the questions in the spaces provided - there may be more space than you need.
- Diagrams are NOT accurately drawn, unless otherwise indicated.
- You must show all your working out.
Information
- The marks for each question are shown in brackets - use this as a guide as to how much time to spend on each question.
Advice
- Read each question carefully before you start to answer it.
- Keep an eye on the time.
- Try to answer every question.
- Check your answers if you have time at the end
- The equation x^3 + 7 x − 2 = 55 has a solution between 3 and 4.
Use trial and improvement to find this solution. Give your answer to 1 decimal place.
- Use trial and improvement to solve x^3 + 5 x = 70
Give your answer to 1 decimal place.
xn + 1 =√( x n )+ 10 and x 1 = 3
- An approximate solution to an equation is found using this iterative process:
a) Work out the values of x (^) 2 and x 3
b) Work out the solution to 3 decimal places
U n + 1 = U n
2
−8U n + 17
- A sequence is defined by the term-to-term rule:
a) Given that U 1 =4, find U (^) 2 and U (^) 3
b) Given instead that U 1 =2, find U (^) 2 ,U (^) 3 and U (^) 100
(c) Starting with x 0 =0, use the iteration formula xn + 1 =
x^3 n 4
twice, to find an estimate to the solution of x^3 + 4 x = 1
7.(a) Show that the equation x^3 + 4 x = 1 has a solution between x = 0 and x = 1
(b) Show that the equation x^3 + 4 x = 1 can be rearranged
to give x =
x^3 4
