Question 2 - A-Level Maths

AQA C2 2007 January — Question 2 4 marks

Exam Board	AQA
Module	C2 (Core Mathematics 2)
Year	2007
Session	January
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Numerical integration
Type	Trapezium rule with stated number of strips
Difficulty	Moderate -0.8 This is a straightforward application of the trapezium rule with clear parameters given (four ordinates, three strips). Students only need to evaluate the function at four points, apply the standard trapezium rule formula, and round. It requires basic recall and arithmetic with no problem-solving or conceptual challenges, making it easier than average.
Spec	1.09f Trapezium rule: numerical integration

2 Use the trapezium rule with four ordinates (three strips) to find an approximate value for $$\int _ { 0 } ^ { 3 } \sqrt { 2 ^ { x } } \mathrm {~d} x$$ giving your answer to three decimal places.

Show mark scheme Show mark scheme source

Answer	Marks	Guidance
$\{p = \} 2$	B1	Condone '$64 = 8^2$'
$\{q = \} -2$	B1ft	Ft on '$-p$' if $q$ not correct
$\{r = \} 0.5$	B1	Condone '$\sqrt{8} = 8^{0.5}$'
$\frac{8^y}{8^{0.5}} = 8^{-6-0.5} = 8^{-2}$ OE	M1	Using parts (a) & valid index law to stage $8^y = 8^p$ (PI)
$\Rightarrow x - 0.5 = -2 \Rightarrow x = -1.5$	A1ft	Ft on c's ($q + r$) if not correct
(Accept correct answer without working)
(M1 A1)
ALT: $\log8^x = \log x$, $x\log 8 = \log x$; $x = -1.5$
Total: 5

| $\{p = \} 2$ | B1 | Condone '$64 = 8^2$' |
| $\{q = \} -2$ | B1ft | Ft on '$-p$' if $q$ not correct |
| $\{r = \} 0.5$ | B1 | Condone '$\sqrt{8} = 8^{0.5}$' |
| $\frac{8^y}{8^{0.5}} = 8^{-6-0.5} = 8^{-2}$ OE | M1 | Using parts (a) & valid index law to stage $8^y = 8^p$ (PI) |
| $\Rightarrow x - 0.5 = -2 \Rightarrow x = -1.5$ | A1ft | Ft on c's ($q + r$) if not correct |
| | | (Accept correct answer without working) |
| | | (M1 A1) |
| ALT: $\log8^x = \log x$, $x\log 8 = \log x$; $x = -1.5$ | | |
| | **Total: 5** | |

---

Show LaTeX source

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

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

giving your answer to three decimal places.

\hfill \mbox{\textit{AQA C2 2007 Q2 [4]}}

This paper (9 questions)

View full paper

Q1 5 Q2 4 Q3 5 Q4 8 Q5 7 Q6 16 Q7 7 Q8 12 Q9 11

Answer	Marks	Guidance
\(\{p = \} 2\)	B1	Condone '\(64 = 8^2\)'
\(\{q = \} -2\)	B1ft	Ft on '\(-p\)' if \(q\) not correct
\(\{r = \} 0.5\)	B1	Condone '\(\sqrt{8} = 8^{0.5}\)'
\(\frac{8^y}{8^{0.5}} = 8^{-6-0.5} = 8^{-2}\) OE	M1	Using parts (a) & valid index law to stage \(8^y = 8^p\) (PI)
\(\Rightarrow x - 0.5 = -2 \Rightarrow x = -1.5\)	A1ft	Ft on c's (\(q + r\)) if not correct
(Accept correct answer without working)
(M1 A1)
ALT: \(\log8^x = \log x\), \(x\log 8 = \log x\); \(x = -1.5\)
Total: 5