A-LevelMathematicsNumerical methods9709/23 · May/June 2017 · Q35 Marks
By sketching a suitable pair of graphs, show that the equation x³ = 11-2x has exactly one real root.
- (i)By sketching a suitable pair of graphs, show that the equation x³ = 11-2x has exactly one real root.[2]
- (ii)Use the iterative formula x_n+1 = ³√(11-2x_n) to find the root correct to 4 significant figures. Give the result of each iteration to 6 significant figures.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [*B1] Draw sketch of y = x³ May be implied by part graph in first quadrant
- [DB1] Draw straight line with negative gradient crossing positive y-axis and indicate one intersection dep *B
- [M1] Use iterative formula correctly at least once
- [A1] Obtain final answer 1.926
- [A1] Show sufficient iterations to justify 4 sf or show sign change in interval (1.9255,1.9265)
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