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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 20

The depth of a straight drainage channel is modelled by

d(x)=4−x2d(x)=4-x^2d(x)=4−x2, 0≤x≤20\leq x\leq20≤x≤2,

where x x\,x and d d\,d are measured in metres across half of the channel. Eight equal-width rectangles are used to bound the cross-sectional area under this curve.

a.

Explain which endpoints give the upper rectangle sum.

[2]
b.

Calculate lower and upper bounds for the cross-sectional area.

[4]
c.

The channel is 10 m long and its cross-section is assumed constant. State corresponding bounds for the volume represented by the model.

[2]
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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