| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Tangent to curve: find equation |
| Difficulty | Moderate -0.8 This is a standard C1 completing-the-square question with routine follow-up parts. Part (i) is textbook completing the square, (ii)-(iii) are direct applications, and (iv) involves solving a quadratic equation and recognizing a repeated root indicates tangency—all well-practiced techniques with no novel insight required. Easier than average A-level questions. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02e Complete the square: quadratic polynomials and turning points1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks |
|---|---|
| 3 | ii |
| Answer | Marks |
|---|---|
| iv | 3 |
| Answer | Marks |
|---|---|
| A1 | mark final answer; 1 for a = 3, |
| Answer | Marks |
|---|---|
| line and curve are same when x = 4 | 3 |
Question 3:
3 | ii
iii
iv | 3
1+1
G1
G1
M1
M1
M1
A1
A1 | mark final answer; 1 for a = 3,
2 for b = 7 or M1 for −32 + 2;
bod 3 for (x − 3) − 7
accept (0, 2) o.e. seen in this part [eg
in table] if 2 not marked as intercept
on graph
accept 3 and −7 marked on axes
level with turning pt., or better; no ft
for (0, 2) as min
or their (i) = 2x − 14
dep on first M1; condone one error
or correct use of formula, giving
equal roots; allow (x + 4)2 o.e.
ft x2 + 8x + 16
if M0M0M0, allow SC2 for showing
(4, −6) is on both graphs (need to go
on to show line is tgt to earn more)
or for use of calculus to show grad of
line and curve are same when x = 4 | 3
2
2
5
12\begin{enumerate}[label=(\roman*)]
\item Express $x^2 - 6x + 2$ in the form $(x - a)^2 - b$. [3]
\item State the coordinates of the turning point on the graph of $y = x^2 - 6x + 2$. [2]
\item Sketch the graph of $y = x^2 - 6x + 2$. You need not state the coordinates of the points where the graph intersects the $x$-axis. [2]
\item Solve the simultaneous equations $y = x^2 - 6x + 2$ and $y = 2x - 14$. Hence show that the line $y = 2x - 14$ is a tangent to the curve $y = x^2 - 6x + 2$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q3 [12]}}