Chapter 17: Further Core Pure 2: Modelling with Differential Equations

A-level Further MathsFurther Core Pure4 topicsHigher

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Further Core Pure 2: Numerical Methods Long-Answer Questions

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4 questions24 marks36 min

standard / hard / synoptic

6 marksfindstandardEdexcel

FCP17-1: x_{n+1} = x_n - (x_n^2 - 2)/(2x_n). Find iteration for

\sqrt{2}

for Newton-Raphson and numerical solution of equations. Show the method clearly by using substitute

f(x) = x^{2} - 2 into Newton-Raphson

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6 marksshow thatstandardEdexcel

FCP17-2 verification: show that the printed answer is valid by applying substitute

f(x) = x^{2} - 2 into Newton-Raphson

. Include a check using x_{n+1} = x_n - (x_n^2 - 2)/(2x_n).

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6 marksprovehardEdexcel

FCP17-3 proof: starting with x_{n+1} = x_n - (x_n^2 - 2)/(2x_n), prove iteration for

\sqrt{2}

for Newton-Raphson and numerical solution of equations; give restrictions.

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6 markshencesynopticEdexcel

Using FCP17-4's earlier result iteration for

\sqrt{2}

, hence solve the linked problem in Newton-Raphson and numerical solution of equations and state whether the answer is exact or rounded.

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16. Further Core Pure 2: Methods in Differential Equations

End of Further Core Pure

Key learning objectives

Understand the key principles behind Further Core Pure 2: Modelling with Differential Equations.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.