| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Complete table then apply trapezium rule |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring only routine application of calculator skills and the trapezium rule formula. Part (a) involves simple substitution into a given function, and part (b) applies a standard numerical integration method with no conceptual challenges or problem-solving required. |
| Spec | 1.09f Trapezium rule: numerical integration |
| \(x\) | 1 | 1.4 | 1.8 | 2.2 | 2.6 | 3 |
| \(y\) | 3 | 3.47 | 4.39 |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(3.84,\ 4.14,\ 4.58\) | B1 B1 | Any one correct: B1 B0; all three correct: B1 B1 |
| Total: [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(\frac{1}{2}\times0.4,\ \{(3+4.58)+2(3.47+3.84+4.14+4.39)\}\) | B1, M1 A1ft | B1 for using 0.2 or \(\frac{0.4}{2}\) as \(\frac{1}{2}h\); M1: first bracket = first plus last values, second bracket includes no additional values |
| \(= 7.852\) (awrt 7.9) | A1 | Final A1 must be correct, no follow through |
| Total: [4] |
## Question 3:
### Part (a):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $3.84,\ 4.14,\ 4.58$ | B1 B1 | Any one correct: B1 B0; all three correct: B1 B1 |
| **Total: [2]** | | |
### Part (b):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $\frac{1}{2}\times0.4,\ \{(3+4.58)+2(3.47+3.84+4.14+4.39)\}$ | B1, M1 A1ft | B1 for using 0.2 or $\frac{0.4}{2}$ as $\frac{1}{2}h$; M1: first bracket = first plus last values, second bracket includes no additional values |
| $= 7.852$ (awrt 7.9) | A1 | Final A1 must be correct, no follow through |
| **Total: [4]** | | |
---3. $y = \sqrt { } \left( 10 x - x ^ { 2 } \right)$.
\begin{enumerate}[label=(\alph*)]
\item Complete the table below, giving the values of $y$ to 2 decimal places.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
$x$ & 1 & 1.4 & 1.8 & 2.2 & 2.6 & 3 \\
\hline
$y$ & 3 & 3.47 & & & 4.39 & \\
\hline
\end{tabular}
\end{center}
\item Use the trapezium rule, with all the values of $y$ from your table, to find an approximation for the value of $\int _ { 1 } ^ { 3 } \sqrt { } \left( 10 x - x ^ { 2 } \right) \mathrm { d } x$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2009 Q3 [6]}}