| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Line-curve intersection points |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing standard techniques: simultaneous equations with substitution, completing the square, and reading vertex form. All parts are routine textbook exercises requiring direct application of methods with no problem-solving insight needed. The 11 marks reflect length rather than difficulty. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02e Complete the square: quadratic polynomials and turning points1.02q Use intersection points: of graphs to solve equations |
| Answer | Marks |
|---|---|
| 4 | (i) x + 4x2 + 24x + 31 = 10 oe |
| Answer | Marks |
|---|---|
| y = 11 or 61/4 oe isw | M1 |
| Answer | Marks |
|---|---|
| A1 | for subst of x or y or subtraction to |
| Answer | Marks |
|---|---|
| 61/4) oe | or 4y2 − 105y + 671 [= 0]; |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (ii) 4(x + 3)2 – 5 isw | 4 |
| Answer | Marks |
|---|---|
| soi or for −5/4 or for 31/4 − their b2 soi | eg an answer of (x + 3)2 – 5/ earns B0 B1 M1; |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (iii)(A) x = −3 or ft (−their b) from (ii) | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (iii)(B) −5 or ft their c from (ii) | 1 |
Question 4:
4 | (i) x + 4x2 + 24x + 31 = 10 oe
4x2 + 25x + 21 [= 0]
(4x + 21)(x + 1)
x = −1 or −21/4 oe isw
y = 11 or 61/4 oe isw | M1
M1
M1
A1
A1 | for subst of x or y or subtraction to
eliminate variable; condone one error;
for collection of terms and
rearrangement to zero; condone one
error;
for factors giving at least two terms of
their quadratic correct or for subst into
formula with no more than two errors
[dependent on attempt to rearrange to
zero];
or A1 for (−1, 11) and A1 for (−21/4,
61/4) oe | or 4y2 − 105y + 671 [= 0];
eg condone spurious y = 4x2 + 25x + 21 as one error
(and then count as eligible for 3rd M1);
or (y − 11)(4y − 61);
[for full use of completing square with no more than
two errors allow 2nd and 3rd M1s simultaneously];
from formula: accept x = −1 or −42/8 oe isw
4 | (ii) 4(x + 3)2 – 5 isw | 4 | B1 for a = 4,
B1 for b = 3,
B2 for c =−5 or M1 for 31 − 4 × their b2
soi or for −5/4 or for 31/4 − their b2 soi | eg an answer of (x + 3)2 – 5/ earns B0 B1 M1;
4
1(2x + 6)2 − 5 earns B0 B0 B2;
4( earns first B1;
condone omission of square symbol
4 | (iii)(A) x = −3 or ft (−their b) from (ii) | 1 | 0 for just −3 or ft;
0 for x = −3, y = −5 or ft
4 | (iii)(B) −5 or ft their c from (ii) | 1 | allow y = −5 or ft | 0 for just (−3, −5);
bod 1 for x = −3 stated then y = −5 or ft\begin{enumerate}[label=(\roman*)]
\item Find algebraically the coordinates of the points of intersection of the curve $y = 4x^2 + 24x + 31$ and the line $x + y = 10$. [5]
\item Express $4x^2 + 24x + 31$ in the form $a(x + b)^2 + c$. [4]
\item For the curve $y = 4x^2 + 24x + 31$,
\begin{enumerate}[label=(\Alph*)]
\item write down the equation of the line of symmetry, [1]
\item write down the minimum $y$-value on the curve. [1]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q4 [11]}}