| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Sketch quadratic curve |
| Difficulty | Moderate -0.8 This is a straightforward C1 completing-the-square question with standard follow-ups. Part (i) is routine algebraic manipulation, parts (ii)-(iii) are direct applications requiring axis intercepts and sketching, and part (iv) involves equating expressions and solving a linear equation. All techniques are standard textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02e 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 |
|---|---|
| 5 | ii |
| Answer | Marks |
|---|---|
| iv | (x − 3.5)2 − 6.25 |
| Answer | Marks |
|---|---|
| x = ½ or 0.5 or 2/4 cao | 33 |
| Answer | Marks |
|---|---|
| A1 | B1for a = 7/2 o.e, |
| Answer | Marks |
|---|---|
| one intn | 3 |
Question 5:
5 | ii
iii
iv | (x − 3.5)2 − 6.25
(3.5, −6.25) o.e. or ft from
their (i)
(0, 6) (1, 0) (6, 0)
curve of correct shape
fully correct intns and min in
4th quadrant
x2 − 7x + 6 = x2 − 3x + 4
2 = 4x
x = ½ or 0.5 or 2/4 cao | 33
1+1
3
G1
G1
M1
M1
A1 | B1for a = 7/2 o.e,
B2 for b = −25/4 o.e. or M1
for 6 − (7/2)2 or 6 − (their a)2
allow x = 3.5 and y = −6.25 or
ft; allow shown on graph
1 each [stated or numbers
shown on graph]
or 4x − 2 = 0 (simple linear
form; condone one error)
condone no comment re only
one intn | 3
2
5
3\begin{enumerate}[label=(\roman*)]
\item Write $x^2 - 7x + 6$ in the form $(x - a)^2 + b$. [3]
\item State the coordinates of the minimum point on the graph of $y = x^2 - 7x + 6$. [2]
\item Find the coordinates of the points where the graph of $y = x^2 - 7x + 6$ crosses the axes and sketch the graph. [5]
\item Show that the graphs of $y = x^2 - 7x + 6$ and $y = x^2 - 3x + 4$ intersect only once. Find the $x$-coordinate of the point of intersection. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q5 [13]}}