> Friday 22 October 2021 – Afternoon A Level Further Mathematics B (MEI) Y434/01 Numerical Methods

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Answer all the questions. 1 (a) (i) Determine the relative error when • 1.414214 is used to approximate 2, • 1.4142142 is used to approximate 2. [3] (ii) Write down the relationship between yo... ur answers to part (a)(i). [1] (b) Fig. 1 shows some spreadsheet output.  A B C 1 2 1.414214 2 Fig. 1 The formula in cell B1 is = SQRT(A1) and the formula in cell C1 is = B1^2 . Ben evaluates 1.4142142 on his calculator and obtains 2.000001238. He states that this shows that the value displayed in cell C1 is wrong. Explain whether Ben is correct. [1] 2 The table shows some values of x and the associated values of f( ) x . x 1 2 3 4 5 f(x) ‒0.65 ‒0.35 1.77 5.71 11.47 (a) Complete the difference table in the Printed Answer Booklet. [2] (b) Explain why the data may be interpolated by a polynomial of degree 2. [1] (c) Use Newton’s forward difference interpolation formula to obtain a polynomial of degree 2 for the data. [3]4 © OCR 2021 Y434/01 Oct21 3 The method of False Position is used to find a sequence of approximations to the root of an equation. The spreadsheet output showing these approximations, together with some further analysis, is shown below.  C D E F G H I J 4 a f( ) a b f( ) b xnew f( ) xnew difference ratio 5 1 ‒1.8248 2 17.2899 1.09547 ‒1.80507 6 1.09547 ‒1.80507 2 17.2899 1.18097 ‒1.75418 0.08551 7 1.18097 ‒1.75418 2 17.2899 1.25641 ‒1.66246 0.07544 0.88229 8 1.25641 ‒1.66246 2 17.2899 1.32164 ‒1.52781 0.06523 0.86458 9 1.32164 ‒1.52781 2 17.2899 1.37672 ‒1.35706 0.05508 0.84439 10 1.37672 ‒1.35706 2 17.2899 1.42208 ‒1.1642 0.04536 0.8236 11 1.42208 ‒1.1642 2 17.2899 1.45853 ‒0.96616 0.03646 0.80376 12 1.45853 ‒0.96616 2 17.2899 1.48719 ‒0.77825 0.02866 0.78598 13 1.48719 ‒0.77825 2 17.2899 14 The formula in cell D5 is = - SINH( ) C C 5 5 ^ ^ 2 3 2 - . (a) Write down the equation which is being solved. [1] The formula in cell C6 is = IF(H510,G5,C5) [Show More]

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