| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Line intersecting reciprocal curve |
| Difficulty | Moderate -0.3 This is a straightforward simultaneous equations question requiring students to equate the expressions, form a quadratic equation (2x + 4 = 2/x leads to 2x² + 4x - 2 = 0), and solve using the quadratic formula. The sketching in part (a) is routine. While it involves multiple steps, all techniques are standard AS-level procedures with no novel insight required, making it slightly easier than average. |
| Spec | 1.02m Graphs of functions: difference between plotting and sketching1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02q Use intersection points: of graphs to solve equations |
| Answer | Marks | Guidance |
|---|---|---|
| Correct line beyond the axes | B1 | correct line beyond the axes |
| Correct shaped curve approaching axes, not touching, in quadrant 1 and 3, beyond points of intersections | B1 | Check second graph page |
| Answer | Marks | Guidance |
|---|---|---|
| \(2x + 4 = \frac{2}{x}\) | B1 | |
| \(2x^2 + 4x - 2 = 0\) oe | M1 | Some rearrangement to form quadratic, allow sign errors; SC Exact answers only, no working B0M1M1A1A1 |
| \((x+1)^2 - 1 - 1 = 0\) or \(\frac{-2 \pm \sqrt{2^2 - 4\times1\times(-1)}}{2\times1}\) oe | M1 | condone calculator; SC decimal values only — no working: \(-2.414\), \(0.414\) then B0M1M1A0A0 |
| \(-1 \pm \sqrt{2}\) | A1 | for either root, exact answer only |
| \([x=]-1-\sqrt{2}\) or \([x=]-1+\sqrt{2}\) | A1 | both roots correct; isw when roots found |
## Question 7(a):
Correct line beyond the axes | **B1** | correct line beyond the axes
Correct shaped curve approaching axes, not touching, in quadrant 1 and 3, beyond points of intersections | **B1** | Check second graph page
## Question 7(b):
$2x + 4 = \frac{2}{x}$ | **B1** |
$2x^2 + 4x - 2 = 0$ oe | **M1** | Some rearrangement to form quadratic, allow sign errors; SC Exact answers only, no working B0M1M1A1A1
$(x+1)^2 - 1 - 1 = 0$ or $\frac{-2 \pm \sqrt{2^2 - 4\times1\times(-1)}}{2\times1}$ oe | **M1** | condone calculator; SC decimal values only — no working: $-2.414$, $0.414$ then B0M1M1A0A0
$-1 \pm \sqrt{2}$ | **A1** | for either root, exact answer only
$[x=]-1-\sqrt{2}$ or $[x=]-1+\sqrt{2}$ | **A1** | both roots correct; isw when roots found
---7
\begin{enumerate}[label=(\alph*)]
\item On the pair of axes in the Printed Answer Booklet, sketch the graphs of
\begin{itemize}
\item $y = 2 x + 4$
\item $\mathrm { y } = \frac { 2 } { \mathrm { x } }$
\item Determine the $x$-coordinates of the points of intersection of the line $y = 2 x + 4$ and the curve $\mathrm { y } = \frac { 2 } { \mathrm { x } }$, giving your answers in an exact form.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2022 Q7 [7]}}