| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch rational function from transformation |
| Difficulty | Moderate -0.3 This is a straightforward C1 transformation and algebraic question. Part (i) requires a standard horizontal translation of 1/x. Part (ii) is simple equation solving. Part (iii) involves forming and solving a quadratic, which is routine for C1, though presenting answers in surd form adds minor complexity. Overall slightly easier than average due to standard techniques throughout. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02q Use intersection points: of graphs to solve equations1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| 6 | ii |
| iii | correct graph with clear |
| Answer | Marks |
|---|---|
| position of points shown | G2 |
| Answer | Marks |
|---|---|
| B1 | G1 for one branch correct; condone |
| Answer | Marks |
|---|---|
| = x if unlabelled | 3 |
Question 6:
6 | ii
iii | correct graph with clear
asymptote x = 2 (though need not
be marked)
(0, − ½ ) shown
11/5 or 2.2 o.e. isw
1
x=
x−2
x(x − 2) = 1 o.e.
x2 − 2x − 1 [= 0]; ft their equiv
eqn
attempt at quadratic formula
1 ±√2 cao
position of points shown | G2
G1
2
M1
M1
M1
M1
A1
B1 | G1 for one branch correct; condone
(0, − ½ ) not shown
SC1 for both sections of graph
shifted two to left
allow seen calculated
M1 for correct first step
or equivs with ys
or (x − 1)2 − 1 = 1 o.e.
or (x − 1) = ±√2 (condone one error)
on their curve with y = x (line drawn
or y = x indicated by both coords);
condone intent of diagonal line with
gradient approx 1through origin as y
= x if unlabelled | 3
2
6\begin{enumerate}[label=(\roman*)]
\item \includegraphics{figure_1}
Fig. 10 shows a sketch of the graph of $y = \frac{1}{x}$.
Sketch the graph of $y = \frac{1}{x-2}$, showing clearly the coordinates of any points where it crosses the axes. [3]
\item Find the value of $x$ for which $\frac{1}{x-2} = 5$. [2]
\item Find the $x$-coordinates of the points of intersection of the graphs of $y = x$ and $y = \frac{1}{x-2}$. Give your answers in the form $a \pm \sqrt{b}$.
Show the position of these points on your graph in part (i). [6]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q6 [11]}}