AQA C3 2009 January — Question 1 4 marks

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2009
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNumerical integration
TypeSimpson's rule application
DifficultyModerate -0.3 This is a straightforward application of Simpson's rule with clearly specified parameters (5 ordinates, 4 strips). Students must calculate ordinates at x = 1, 3, 5, 7, 9, apply the standard Simpson's formula with appropriate weightings, and round correctly. While it requires careful arithmetic with surds, it involves no conceptual difficulty or problem-solving—just direct execution of a memorized numerical method.
Spec1.09f Trapezium rule: numerical integration
1 Use Simpson's rule with 5 ordinates (4 strips) to find an approximation to \(\int _ { 1 } ^ { 9 } \frac { 1 } { 1 + \sqrt { x } } \mathrm {~d} x\), giving your answer to three significant figures.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(x\) values: 1, 3, 5, 7, 9 with \(y\) values: 0.5, 0.366(0), 0.309(0), 0.274(3), 0.25B1 \(x\) values and no extra values
4+ correct \(y\) valuesB1 or \(\frac{1}{1+\sqrt{3}}\) etc
\(\frac{1}{3} \times 2 \times \left[(0.5+0.25) + 4(0.3660+0.2743) + 2(0.3090)\right]\)M1 Correct application of Simpson's rule for their \(x\) values (\(x\) odd)
\(= 2.62\)A1 CSO, must be 3sf
Total: 4 marks
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $x$ values: 1, 3, 5, 7, 9 with $y$ values: 0.5, 0.366(0), 0.309(0), 0.274(3), 0.25 | B1 | $x$ values and no extra values |
| 4+ correct $y$ values | B1 | or $\frac{1}{1+\sqrt{3}}$ etc |
| $\frac{1}{3} \times 2 \times \left[(0.5+0.25) + 4(0.3660+0.2743) + 2(0.3090)\right]$ | M1 | Correct application of Simpson's rule for their $x$ values ($x$ odd) |
| $= 2.62$ | A1 | CSO, must be 3sf |

**Total: 4 marks**

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1 Use Simpson's rule with 5 ordinates (4 strips) to find an approximation to $\int _ { 1 } ^ { 9 } \frac { 1 } { 1 + \sqrt { x } } \mathrm {~d} x$, giving your answer to three significant figures.

\hfill \mbox{\textit{AQA C3 2009 Q1 [4]}}
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