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A-LevelMathematicsNumerical methods9709/33 · Oct/Nov 2024 · Q25 Marks

Let f(x) = 2x³ - 5x² +4.

  1. (a)Show that if a sequence of values given by the iterative formula xn+1=√4/(5-2xn), converges, then it converges to a root of the equation f(x) = 0.[2]
  2. (b)The equation has a root close to 1.2. Use the iterative formula from part (a) and an initial value of 1.2 to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [*B1] (a) State or imply the equation x = √4/(5-2x) and square the equation.
  2. [DB1] (a) Rearrange this with at least one intermediate step in the form 2x³ −5x² +4=0.
  3. [M1] (b) Use the iterative process correctly at least once.
  4. [A1] (b) Obtain final answer 1.28.
  5. [A1] (b) Show sufficient iterations to at least 4 dp to justify 1.28 to 2 dp or show that there is a sign change in the interval (1.275, 1.285).

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About this question

Topic
Numerical methods, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2024 Paper 3 Variant 3, question 2.

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