| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Sketch reciprocal function graphs |
| Difficulty | Moderate -0.8 Part (a) is a standard bookwork sketch of cosec x on a restricted domain, requiring only recall of the reciprocal relationship with sin x. Part (b) applies the mid-ordinate rule mechanically with given strip count—straightforward numerical method application with calculator work. Both parts are routine exercises with no problem-solving or insight required, making this easier than average. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.09f Trapezium rule: numerical integration |
| Answer | Marks | Guidance |
|---|---|---|
| [Graph showing correct shape with vertex at approximately (π/2, 1)] | M1 | Correct shape |
| A1 | Vertex | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| x | y | |
| 0.15 | 6.692 | |
| 0.25 | 4.042 | |
| 0.35 | 2.916 | |
| 0.45 | 2.299 | |
| \(\int = 0.1 \times \sum y\) (\(\sum y = 15.949\)) | B1 | correct \(h\) used correctly |
| \(= 1.59\) | A1 |
### 6(a)
[Graph showing correct shape with vertex at approximately (π/2, 1)] | M1 | Correct shape |
| A1 | Vertex | **Total: 2**
### 6(b)
| x | y |
|---|---|
| 0.15 | 6.692 |
| 0.25 | 4.042 |
| 0.35 | 2.916 |
| 0.45 | 2.299 | | M1 B1 | Correct $x$ values / ≥ 3 correct $y$ values |
$\int = 0.1 \times \sum y$ ($\sum y = 15.949$) | B1 | correct $h$ used correctly |
$= 1.59$ | A1 | | **Total: 4**6
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve with equation $y = \operatorname { cosec } x$ for $0 < x < \pi$.
\item Use the mid-ordinate rule with four strips to find an estimate for $\int _ { 0.1 } ^ { 0.5 } \operatorname { cosec } x \mathrm {~d} x$, giving your answer to three significant figures.
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2008 Q6 [6]}}