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3.8 Numerical Methods (A-level only)

3.8 Numerical Methods (A-level only)

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Question 24

g(x)=2x3−6x2+3g(x) = 2x^3 - 6x^2 + 3g(x)=2x3−6x2+3

a.

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

[3]
b.

Show that the equation g(x)=0g(x) = 0g(x)=0 can be written in the form x=36−2x\displaystyle x = \sqrt{\frac{3}{6-2x}}x=6−2x3​​

[3]
c.

Use the iteration formula xn+1=36−2xn\displaystyle x_{n+1} = \sqrt{\frac{3}{6-2x_n}}xn+1​=6−2xn​3​​ with x0=0.8x_0 = 0.8x0​=0.8 to find, to 3 decimal places, the values of x1x_1x1​, x2 x_2\,x2​ and x3x_3x3​.

[3]
d.

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

[3]
Markscheme

3.8 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.8 Numerical Methods (A-level only)

129 exam-style questions on WJEC A Level Maths 3.8 Numerical Methods (A-level only), covering 3.8.1 Numerical Methods (A-level only), 3.8.2 Numerical Methods (A-level only), 3.8.3 Numerical Methods (A-level only), 3.8.4 Numerical Methods (A-level only), and 3.8.5 Numerical Methods (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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