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1.9 Numerical Methods (A-level only)

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Question 20

The equation has a single solution Y=αY = \alphaY=α in the interval [2.1,2.2][2.1, 2.2][2.1,2.2].

a.

By considering a suitable change of sign, show that α\alphaα lies between 2.1 and 2.2.

[2]
b.

Show that the equation Y3−6Y+3=0Y^3 - 6Y + 3 = 0Y3−6Y+3=0 can be rearranged into the form

Y=6−3Y Y = \sqrt{6 - \frac{3}{Y}} Y=6−Y3​​
[2]
c.

Use the iterative formula

Yn+1=6−3Yn Y_{n+1} = \sqrt{6 - \frac{3}{Y_n}} Yn+1​=6−Yn​3​​

with Y1=2.1Y_1 = 2.1Y1​=2.1, to determine the values of Y2,Y3Y_2, Y_3Y2​,Y3​ and Y4Y_4Y4​, giving your answers to four decimal places.

[3]
d.

Hence, deduce an interval of width 0.001 in which α\alphaα lies.

[2]
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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