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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 47

A civil engineer is modeling the optimal depth ddd, in metres, of a high-capacity drainage channel. The relationship between the depth and the surrounding soil pressure leads to the equation:

d3+50d=800 d^3 + 50d = 800 d3+50d=800
a.

Show that the equation has a root α\alphaα in the interval [7,8][7, 8][7,8].

[2]
b.

Using the iteration formula

dn+1=800−50dn3withd1=7.5 d_{n+1} = \sqrt[3]{800 - 50d_n} \quad \text{with} \quad d_1 = 7.5 dn+1​=3800−50dn​​withd1​=7.5

(i) Calculate the value of d2d_2d2​, giving your answer to 4 decimal places. (ii) Determine the value of α\alphaα, corrected to 4 decimal places, through repeated iteration.

[3]
Markscheme

1.10 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.10 Numerical Methods (A-level only)

137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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