| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Line intersecting reciprocal curve |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic graph work and algebraic manipulation. Part (i) requires reading intersections from a graph, part (ii) is routine quadratic formula application, parts (iii) and (iv) involve simple transformations and connecting graphical/algebraic solutions. All techniques are standard with no problem-solving insight required, making it easier than average. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02q Use intersection points: of graphs to solve equations1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| 4 | ii |
| Answer | Marks |
|---|---|
| iv | y = 2x + 3 drawn on graph |
| Answer | Marks |
|---|---|
| curve and line [tolerance 1 mm] | M1 |
| Answer | Marks |
|---|---|
| 2 | 1 each; condone coords; must have |
| Answer | Marks |
|---|---|
| ignore y coords. | 3 |
Question 4:
4 | ii
iii
iv | y = 2x + 3 drawn on graph
x = 0.2 to 0.4 and − 1.7 to −1.9
1 = 2x2 + 3x
2x2 + 3x − 1 [= 0]
attempt at formula or completing
square
−3± 17
x=
4
branch through (1,3),
branch through (−1,1),approaching
y = 2 from below
−1 and ½ or ft intersection of their
curve and line [tolerance 1 mm] | M1
A2
M1
M1
M1
A2
1
1
2 | 1 each; condone coords; must have
line drawn
for multiplying by x correctly
for correctly rearranging to zero (may
be earned first) or suitable step re
completing square if they go on
ft, but no ft for factorising
A1 for one soln
and approaching y = 2 from above
and extending below x axis
1 each; may be found algebraically;
ignore y coords. | 3
5
2
2Answer the whole of this question on the insert provided.
The insert shows the graph of $y = \frac{1}{x}$, $x \neq 0$.
\begin{enumerate}[label=(\roman*)]
\item Use the graph to find approximate roots of the equation $\frac{1}{x} = 2x + 3$, showing your method clearly. [3]
\item Rearrange the equation $\frac{1}{x} = 2x + 3$ to form a quadratic equation. Solve the resulting equation, leaving your answers in the form $\frac{p \pm \sqrt{q}}{r}$. [5]
\item Draw the graph of $y = \frac{1}{x} + 2$, $x \neq 0$, on the grid used for part (i). [2]
\item Write down the values of $x$ which satisfy the equation $\frac{1}{x} + 2 = 2x + 3$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q4 [12]}}