| 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 | Sketch quadratic curve |
| Difficulty | Moderate -0.8 This is a standard C1 completing-the-square question with routine follow-up parts. Part (i) is a textbook exercise in completing the square, parts (ii)-(iv) directly use the result with minimal additional work. All techniques are fundamental and well-practiced at this level, making it easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown1.02m Graphs of functions: difference between plotting and sketching |
| Answer | Marks |
|---|---|
| 6 | i |
| Answer | Marks |
|---|---|
| iv | 4(x − 3)2 − 9 |
| Answer | Marks |
|---|---|
| crosses y axis at 27 | 4 |
| Answer | Marks |
|---|---|
| B1 | 1 for a = 4, 1 for b = 3, 2 for c = −9 or |
| Answer | Marks |
|---|---|
| not extending to negative x | 4 |
Question 6:
6 | i
ii
iii
iv | 4(x − 3)2 − 9
min at (3, −9) or ft from (i)
(2x − 3)(2x − 9)
x = 1.5 or 4.5 o.e.
sketch of quadratic the right way up
crosses x axis at 1.5 and 4.5 or ft
crosses y axis at 27 | 4
B2
M1
A2
M1
A1
B1 | 1 for a = 4, 1 for b = 3, 2 for c = −9 or
27 9
M1 for 27 − 4 × 32 or −32[=− ]
4 4
1 for each coord [e.g. may start again
and use calculus to obtain x = 3]
attempt at factorising or formula or use
of their (i) to sq rt stage
A1 for 1 correct; accept fractional equivs
eg 36/8 and 12/8
allow unsimplified
shown on graph or in table etc; condone
not extending to negative x | 4
2
3
3\begin{enumerate}[label=(\roman*)]
\item Write $4x^2 - 24x + 27$ in the form $a(x - b)^2 + c$. [4]
\item State the coordinates of the minimum point on the curve $y = 4x^2 - 24x + 27$. [2]
\item Solve the equation $4x^2 - 24x + 27 = 0$. [3]
\item Sketch the graph of the curve $y = 4x^2 - 24x + 27$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q6 [12]}}