Further numerical methods questions

Practice questions covering further numerical methods from this specification. Attempt the questions below; real-paper references for this topic are being imported.

Questions to attempt

6 questions on Further numerical methods, each with its mark scheme and worked method. Reveal the answer when you have had a go.

FP1-6.1 · Numerical solution of first order and second order differential equations.
Q1
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
1.
For $\dfrac{\mathrm{d}y}{\mathrm{d}x}=x^2-y$ it is given that $y(1)=0.5$ and $y(1.1)=0.55$ . Use the approximation $\left(\dfrac{\mathrm{d}y}{\mathrm{d}x}\right)_n\approx\dfrac{y_{n+1}-y_{n-1}}{2h}$ with $h=0.1$ to estimate $y(1.2)$ .
(5)
(Total for Question 1 is 5 marks)
FP1-6.1 · Numerical solution of first order and second order differential equations.
Q2
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
2.
Given $\dfrac{\mathrm{d}y}{\mathrm{d}x}=x+y$ with $y=1$ at $x=0$ , use the approximation $\left(\dfrac{\mathrm{d}y}{\mathrm{d}x}\right)_n\approx\dfrac{y_{n+1}-y_n}{h}$ with $h=0.1$ to estimate $y$ at $x=0.1$ and at $x=0.2$ .
(4)
(Total for Question 2 is 4 marks)
FP1-6.1 · Numerical solution of first order and second order differential equations.
Q3
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
3.
Given $\dfrac{\mathrm{d}y}{\mathrm{d}x}=x+y^2$ with $y=0.5$ at $x=0$ , use the forward-difference approximation with $h=0.05$ to estimate $y(0.1)$ , giving your answer to $4$ decimal places.
(6)
(Total for Question 3 is 6 marks)
FP1-6.2 · Simpson's rule.
Q4
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
4.
Use Simpson's rule with four strips to estimate $\displaystyle\int_0^1\mathrm{e}^{-x^2}\,\mathrm{d}x$ , giving your answer to $6$ decimal places.
(5)
(Total for Question 4 is 5 marks)
FP1-6.2 · Simpson's rule.
Q5
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
5.
Use Simpson's rule with four strips to estimate $\displaystyle\int_0^1\sqrt{1+x^3}\,\mathrm{d}x$ , giving your answer to $4$ decimal places.
(4)
(Total for Question 5 is 4 marks)
FP1-6.2 · Simpson's rule.
Q6
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
6.
Show that Simpson's rule is exact for $\displaystyle\int_0^{2h}x^3\,\mathrm{d}x$ .
(5)
(Total for Question 6 is 5 marks)

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Printable question pack — FP1-6 Further numerical methods (Further Pure 1)All 20 questions across 2 specification points — 14 more than the 6 above — with the full mark scheme. Guest accessible · browser print.

FP1-6 Further numerical methods (Further Pure 1) revision notes

Real-paper references

Real-paper references for this module are being imported — the questions above are the site's own, exam-faithful, marked.

Reference rows contain series, paper, question number, marks and classification metadata only. Pearson's question papers open on Pearson's own website.

Questions to attempt

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