Higher November 2021 Paper 2 Q16
16
(a) Use the iteration formula \(x_{n + 1} = \sqrt[3]{10 - 2x_n}\) to find the values of \(x_1\), \(x_2\) and \(x_3\)
Start with \(x_0 = 2\) (3)
Start with \(x_0 = 2\) (3)
The values of \(x_1\), \(x_2\) and \(x_3\) found in part (a) are estimates of the solution of an equation of the form \(x^3 + ax + b = 0\) where \(a\) and \(b\) are integers.
(b) Find the value of \(a\) and the value of \(b\). (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(x_1 = 1.817\) \(x_2 = 1.853\) \(x_3 = 1.846\) | M1 | for a correct method to find \(x_1\) eg \(\sqrt[3]{10 - 2 \times 2}\ (= 1.8171\ldots\ldots)\) |
| M1 | (dep on M1) for substitution of \(x_1\) to give \(x_2\) and \(x_2\) to give \(x_3\) | |
| A1 | for \(x_1 = 1.81(71\ldots)\), \(x_2 = 1.85(33\ldots)\) and \(x_3 = 1.84(62.\ldots)\) |
Additional guidance
Accept an accuracy of 2dp or more rounded or truncated
| Answer | Mark | Mark scheme |
|---|---|---|
| \(a = 2\), \(b = -10\) | C1 | cao |