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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 6

The interval 0≤x≤4 0\leq x\leq4\,0≤x≤4 is divided into n n\,n equal strips to bound the area under y=xy=\sqrt{x}y=x​ using left- and right-endpoint rectangles.

a.

For n=4n=4n=4, find exact lower and upper bounds for the area.

[4]
b.

Show that, for general nnn, the difference between the upper and lower bounds is 8n\displaystyle \frac{8}{n}n8​.

[2]
c.

Determine the least value of n n\,n for which the difference is less than 0.1.

[1]
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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