| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Find discriminant, state roots |
| Difficulty | Easy -1.2 This is a straightforward application of the discriminant formula (b² - 4ac) followed by direct interpretation of the sign. Both parts are routine recall with minimal calculation and no problem-solving required, making it easier than average for A-level. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((-2)^2 - 4 \times 3 \times 5\) soi | M1 | \(-56\) implies both marks. Condone \(-2^2 - 4 \times 3 \times 5\) for this mark, but if recovered then both marks can be scored |
| \(-56\) | A1 | Ignore comparisons e.g. \(-56 > 0\) etc |
| Total: [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0\) | B1FT | 'Zero' or 'None' or 'No real roots/solutions'. If they solve the 3TQ then state 'no real roots' etc then B1 as the discriminant embedded in the quadratic. Reason/justification not needed for this mark. If their (a) is incorrect then FT their discriminant value. |
| Total: [1] |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(-2)^2 - 4 \times 3 \times 5$ soi | M1 | $-56$ implies both marks. Condone $-2^2 - 4 \times 3 \times 5$ for this mark, but if recovered then both marks can be scored |
| $-56$ | A1 | Ignore comparisons e.g. $-56 > 0$ etc |
| **Total: [2]** | | |
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0$ | B1FT | 'Zero' or 'None' or 'No real roots/solutions'. If they solve the 3TQ then state 'no real roots' etc then B1 as the discriminant embedded in the quadratic. Reason/justification not needed for this mark. If their (a) is incorrect then FT their discriminant value. |
| **Total: [1]** | | |
---2
\begin{enumerate}[label=(\alph*)]
\item Find the discriminant of the equation $3 x ^ { 2 } - 2 x + 5 = 0$.
\item Use your answer to part (a) to find the number of real roots of the equation $3 x ^ { 2 } - 2 x + 5 = 0$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2024 Q2 [3]}}