AQA C2 2008 January — Question 4 4 marks

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2008
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNumerical integration
TypeTrapezium rule with stated number of strips
DifficultyModerate -0.8 This is a straightforward application of the trapezium rule with clear parameters given (four ordinates, three strips). It requires only substitution into the standard formula with function values that are easy to calculate using a calculator. No problem-solving or conceptual understanding beyond the basic trapezium rule procedure is needed.
Spec1.09f Trapezium rule: numerical integration
4 Use the trapezium rule with four ordinates (three strips) to find an approximate value for $$\int _ { 0 } ^ { 3 } \sqrt { x ^ { 2 } + 3 } d x$$ giving your answer to three decimal places.
Question 4:
AnswerMarks Guidance
WorkingMark Guidance
\(h = 1\)B1 PI
\(I \approx \frac{h}{2}\{\ldots\}\)M1 OE summing of areas of the three 'trapezia'
\(\{\ldots\} = f(0)+f(3)+2[f(1)+f(2)]\) \(= \sqrt{3}+\sqrt{12}+2[\sqrt{4}+\sqrt{7}]\)A1 (\(\sum\)trap\(=1.866.+2.3228.+3.0549\))
\(= \frac{1}{2}[14.4876\ldots] = 7.2438\ldots = 7.244\)A1 CAO Must be 3dp — Total: 4 
## Question 4:
| Working | Mark | Guidance |
|---------|------|----------|
| $h = 1$ | B1 | PI |
| $I \approx \frac{h}{2}\{\ldots\}$ | M1 | OE summing of areas of the three 'trapezia' |
| $\{\ldots\} = f(0)+f(3)+2[f(1)+f(2)]$ $= \sqrt{3}+\sqrt{12}+2[\sqrt{4}+\sqrt{7}]$ | A1 | ($\sum$trap$=1.866.+2.3228.+3.0549$) |
| $= \frac{1}{2}[14.4876\ldots] = 7.2438\ldots = 7.244$ | A1 | CAO Must be 3dp — **Total: 4** |

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4 Use the trapezium rule with four ordinates (three strips) to find an approximate value for

$$\int _ { 0 } ^ { 3 } \sqrt { x ^ { 2 } + 3 } d x$$

giving your answer to three decimal places.

\hfill \mbox{\textit{AQA C2 2008 Q4 [4]}}
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