| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Complete table then apply trapezium rule |
| Difficulty | Easy -1.2 This is a straightforward C2 question requiring only calculator work to complete a table and mechanical application of the trapezium rule formula. No conceptual understanding of integration is needed, just arithmetic and formula substitution, making it easier than average. |
| Spec | 1.09f Trapezium rule: numerical integration |
| \(x\) | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 |
| \(y\) | 1 | 1.65 | 5 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(2.35, \quad 3.13, \quad 4.01\) | B1 B1 (2) | One or two correct: B1 B0; All correct: B1 B1. If part (a) is blank or answers crossed out with no replacement, send to Review as 'out of clip' |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{1}{2} \times 0.2\) ... | B1 | Or equivalent numerical value |
| \(k\{(1+5) + 2(1.65 + p + q + r)\}\), \(k\) constant, \(k \neq 0\) | M1 A1 | See notes below |
| \(= 2.828\) | A1 (4) | awrt 2.83, allowed even after minor slips in values. Fractional answer \(\frac{707}{250}\) also acceptable |
# Question 1:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2.35, \quad 3.13, \quad 4.01$ | B1 B1 (2) | One or two correct: B1 B0; All correct: B1 B1. If part (a) is blank or answers crossed out with no replacement, send to Review as 'out of clip' |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{1}{2} \times 0.2$ ... | B1 | Or equivalent numerical value |
| $k\{(1+5) + 2(1.65 + p + q + r)\}$, $k$ constant, $k \neq 0$ | M1 A1 | See notes below |
| $= 2.828$ | A1 (4) | awrt 2.83, allowed even after minor slips in values. Fractional answer $\frac{707}{250}$ also acceptable |
**Notes:**
- $p, q, r$ are positive numbers, none equal to: $1, 5, 1.65, 0.2, 0.4, 0.6$ or $0.8$
- M1 A1: $k\{(1+5) + 2(1.65 + p + q + r)\}$
- M1 A0: $k\{(1+5) + 2(1.65 + p + q)\}$ or $k\{(1+5) + 2(p+q+r)\}$
- M0 A0: $k\{(1+5) + 2(1.65 + p + q + r + \text{other value(s)})\}$
- Omitting one value from second bracket treated as a slip; M mark allowed
- Separate trapezia method may be used and marked equivalently
- Answers with no working score no marks
---1.
$$y = 3 ^ { x } + 2 x$$
\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
$x$ & 0 & 0.2 & 0.4 & 0.6 & 0.8 & 1 \\
\hline
$y$ & 1 & 1.65 & & & & 5 \\
\hline
\end{tabular}
\end{center}
\item Use the trapezium rule, with all the values of $y$ from your table, to find an approximate value for $\int _ { 0 } ^ { 1 } \left( 3 ^ { x } + 2 x \right) d x$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2010 Q1 [6]}}