www.justmaths.co.uk Iteration (H) - Version 2 January 2016 Iteration (H) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. 1 (a) Show that the equation 3 + 4 = 1 has a solution between = 0 and = 1 [2] b) Show that the equation 3 + 4 = 1 can be arranged to give = 1 4 − 3 4 [1] c) Starting with 0 =0 , use the iteration formula +1 = 1 4 − 3 4 twice, to find an estimate for the solution of 3 + 4 = 1 [3] 2. An approximate solution to an equation is found using this iterative process. +1 = ( ) 3 − 3 8 and 1 = −1 a) Work out the values of 2 and 3 2 =_______________ 3 =_______________ [2] Name: Total Marks:
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Iteration (H) · Iteration (H) - Version 2 January 2016 Iteration (H) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas.
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www.justmaths.co.uk Iteration (H) - Version 2 January 2016
Iteration (H) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas.
1 (a) Show that the equation 𝑥3 + 4𝑥 = 1 has a solution between 𝑥 = 0 and 𝑥 = 1
[2]
b) Show that the equation 𝑥3 + 4𝑥 = 1 can be arranged to give 𝑥 = 14
− 𝑥3
4
[1]
c) Starting with 𝑥0 = 0 , use the iteration formula 𝑥𝑛+1 = 14
− 𝑥𝑛3
4 twice, to find an
estimate for the solution of 𝑥3 + 4𝑥 = 1
[3]
2. An approximate solution to an equation is found using this iterative process.
𝑥𝑛+1 = (𝑥𝑛)3 − 38
and 𝑥1 = −1
a) Work out the values of 𝑥2 and 𝑥3
𝑥2 =_______________
𝑥3 =_______________ [2]
Name:
Total Marks:
www.justmaths.co.uk Iteration (H) - Version 2 January 2016
b) Work out the solution to 6 decimal places.
[1]
3. a) Show that the equation 3𝑥2 – 𝑥3 + 3 = 0 can be rearranged to give
These questions have been retyped from the original sample/specimen assessment materials and whilst every effort has been made to ensure there are no errors, any that do appear are mine and not the exam board s (similarly any errors I have corrected from the originals are also my corrections and not theirs!).
Please also note that the layout in terms of fonts, answer lines and space given to each question does not reflect the actual papers to save space.
These questions have been collated by me as the basis for a GCSE working party set up by the GLOW maths hub - if you want to get involved please get in touch. The objective is to provide support to fellow teachers and to give you a flavour of how different topics “could” be examined. They should not be used to form a decision as to which board to use. There is no guarantee that a topic will or won’t appear in the “live” papers from a specific exam board or that examination of a topic will be as shown in these questions.