| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Polynomial intersection with algebra |
| Difficulty | Moderate -0.3 This is a multi-part question covering standard C1 topics: factorising quadratics, sketching parabolas, using the discriminant, and solving simultaneous equations. While it has 12 marks total and requires multiple techniques, each part is routine and follows textbook methods with no novel problem-solving required. The final part involves completing the square or using the quadratic formula in surd form, which is slightly more demanding than parts (i)-(iii), but still a standard exercise. Overall, slightly easier than average due to the straightforward nature of each component. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks |
|---|---|
| 5 (i) | (2x − 3)(x + 1) |
| x = 3/2 and − 1 obtained | M2 |
| B1 | M1 for factors with one sign error |
| Answer | Marks |
|---|---|
| 5 (ii) | graph of quadratic the correct way |
| Answer | Marks |
|---|---|
| crossing y-axis at −3 | B1 |
| Answer | Marks |
|---|---|
| B1 | for x = 3/2 condone 1 and 2 marked |
| Answer | Marks |
|---|---|
| 5 (iii) | use of b2 − 4ac with numbers |
| Answer | Marks |
|---|---|
| 25 − 40 < 0 or −15 obtained | M1 |
| A1 | may be in formula |
| Answer | Marks |
|---|---|
| 5 (iv) | 2x2 − x − 3 = x2 − 5x + 10 o.e. |
| Answer | Marks |
|---|---|
| −2± 17 cao | M1 |
| Answer | Marks |
|---|---|
| A1 | attempt at eliminating y by subst or |
Question 5:
--- 5 (i) ---
5 (i) | (2x − 3)(x + 1)
x = 3/2 and − 1 obtained | M2
B1 | M1 for factors with one sign error
or giving two terms correct
allow M1 for 2(x − 1.5)(x + 1) with
no better factors seen
or ft their factors
--- 5 (ii) ---
5 (ii) | graph of quadratic the correct way
up and crossing both axes
crossing x-axis only at 3/2 and − 1
or ft from their roots in (i), or their
factors if roots not given
crossing y-axis at −3 | B1
B1
B1 | for x = 3/2 condone 1 and 2 marked
on axis and crossing roughly
halfway between;
intns must be shown labelled or
worked out nearby
--- 5 (iii) ---
5 (iii) | use of b2 − 4ac with numbers
subst (condone one error in
substitution) (may be in quadratic
formula)
25 − 40 < 0 or −15 obtained | M1
A1 | may be in formula
or (x – 2.5)2 =6.25 − 10 or (x – 2.5)2 +
3.75 = 0 oe (condone one error)
or −15 seen in formula
or (x – 2.5)2 = −3.75 oe
or x=2.5± −3.75 oe
--- 5 (iv) ---
5 (iv) | 2x2 − x − 3 = x2 − 5x + 10 o.e.
x2 + 4x − 13 [= 0]
use of quad. formula on resulting
eqn (do not allow for original
quadratics used)
−2± 17 cao | M1
M1
M1
A1 | attempt at eliminating y by subst or
subtraction
or (x + 2)2 = 17; for rearranging to
form ax2 +bx+c [=0] or to
completing square form
condone one error for each of 2nd
and 3rd M1s
or x+2=± 17 o.e.
2nd and 3rd M1s may be earned for
good attempt at completing square
as far as roots obtained\begin{enumerate}[label=(\roman*)]
\item Solve, by factorising, the equation $2x^2 - x - 3 = 0$. [3]
\item Sketch the graph of $y = 2x^2 - x - 3$. [3]
\item Show that the equation $x^2 - 5x + 10 = 0$ has no real roots. [2]
\item Find the $x$-coordinates of the points of intersection of the graphs of $y = 2x^2 - x - 3$ and $y = x^2 - 5x + 10$. Give your answer in the form $a \pm \sqrt{b}$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q5 [12]}}