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1.12.2 Iterative methods and Newton-Raphson (A-level only)

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Question 14

$g(x) = 2x^3 - 6x^2 + 3$

Show that $g (x)$ has a root between 0.8 and 0.9

[3]

Let $\alpha\,$ be the root of $g (x) = 0$ between 0.8 and 0.9. Show that $α=36−2α\displaystyle \alpha = \sqrt{\frac{3}{6-2\alpha}}$ .

[3]

Use the iteration formula $xn+1=36−2xn\displaystyle x_{n+1} = \sqrt{\frac{3}{6-2x_n}}$ with $x_0 = 0.8$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]

By choosing a suitable interval, prove that $α=0.832\alpha = 0.832$ to 3 decimal places

[3]

Markscheme

1.12.2 Iterative methods and Newton-Raphson (A-level only) Questions

A Level
Maths
1.12.2 Iterative methods and Newton-Raphson (A-level only)

51 exam-style questions on AQA A Level Maths 1.12.2 Iterative methods and Newton-Raphson (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.12.2 Iterative methods and Newton-Raphson (A-level only)

Question bank

1.12.2 Iterative methods and Newton-Raphson (A-level only)

Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Question 14

$g(x) = 2x^3 - 6x^2 + 3$

Show that $g (x)$ has a root between 0.8 and 0.9

[3]

Let $\alpha\,$ be the root of $g (x) = 0$ between 0.8 and 0.9. Show that $α=36−2α\displaystyle \alpha = \sqrt{\frac{3}{6-2\alpha}}$ .

[3]

Use the iteration formula $xn+1=36−2xn\displaystyle x_{n+1} = \sqrt{\frac{3}{6-2x_n}}$ with $x_0 = 0.8$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]

By choosing a suitable interval, prove that $α=0.832\alpha = 0.832$ to 3 decimal places

[3]

Markscheme

1.12.2 Iterative methods and Newton-Raphson (A-level only) Questions

A Level
Maths
1.12.2 Iterative methods and Newton-Raphson (A-level only)

51 exam-style questions on AQA A Level Maths 1.12.2 Iterative methods and Newton-Raphson (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.