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1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

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Question 23

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.

Let α \alpha\,α be the root of g(x)=0g(x) = 0g(x)=0 between 0.8 and 0.9. Show that α=36−2α\displaystyle \alpha = \sqrt{\frac{3}{6-2\alpha}}α=6−2α3​​.

[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

1.9 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9 Numerical Methods (A-level only)

125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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