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A2 Unit 3 Pure Mathematics B

Quick questions on Numerical methods: iteration, Newton-Raphson and the trapezium rule - WJEC A-Level Maths

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is locating roots by change of sign?
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If ff is continuous and f(a)f(a) and f(b)f(b) have opposite signs, then f(x)=0f(x) = 0 has at least one root between aa and bb.
What is the Newton-Raphson method?
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Newton-Raphson uses the tangent at the current estimate to find the next, usually converging much faster than a simple iteration.
What is the trapezium rule?
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The trapezium rule approximates the area under a curve by dividing it into vertical strips of equal width hh and treating each strip as a trapezium.
What is q1?
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Show f(x)=x2−2f(x) = x^2 - 2 has a root between 11 and 22. [2 marks]
What is q2?
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Apply one Newton-Raphson step to f(x)=x2−5f(x) = x^2 - 5 from x0=2x_0 = 2. [3 marks]
What is q3?
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State how many ordinates are used in the trapezium rule with 55 strips. [1 mark]

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