| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Finding quadratic constants from real-world trajectory or context |
| Difficulty | Moderate -0.3 This is a straightforward quadratic modelling question requiring substitution to find coefficients (part a is immediate, part b involves solving simultaneous equations), then solving a quadratic inequality. Part (d) requires basic interpretation of parabola behaviour. All techniques are standard AS-level with no novel insight required, making it slightly easier than average. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| \(c = 1.14\) | B1 | AO 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| \(1.20 = 4a + 2b + 1.14\) oe and \(1.25 = 16a + 4b + 1.14\) oe | M1 | AO 3.3 |
| \(a = -0.00125,\ b = 0.0325\) | A1 | AO 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(1.29 = 1.14 + 0.0325t - 0.00125t^2\) | M1 | AO 3.1b |
| \(t = 6\) and \(20\) | A1 | AO 3.4 |
| \(6 \leq t \leq 20\) | A1 | AO 3.5a |
| Answer | Marks | Guidance |
|---|---|---|
| It will eventually predict a negative exchange rate oe (will fall below zero etc) | B1 | AO 3.5a |
## Question 15:
### Part (a):
$c = 1.14$ | **B1** | AO 3.3 | —
### Part (b):
$1.20 = 4a + 2b + 1.14$ oe and $1.25 = 16a + 4b + 1.14$ oe | **M1** | AO 3.3 | Both equations. FT their $c$
$a = -0.00125,\ b = 0.0325$ | **A1** | AO 1.1 | Fractional equivalents: $a = -\frac{1}{800}$ and $b = \frac{13}{400}$. Equivalents in standard form acceptable.
### Part (c):
$1.29 = 1.14 + 0.0325t - 0.00125t^2$ | **M1** | AO 3.1b | FT their $a, b, c$ (Can be $>$ etc)
$t = 6$ and $20$ | **A1** | AO 3.4 |
$6 \leq t \leq 20$ | **A1** | AO 3.5a | Set notation $t \in [6, 20]$ is fine but must not be soft brackets. $t \geq 6$ **and** $t \leq 20$ or $t \geq 6 \cap t \leq 20$ acceptable but NOT $t \geq 6,\ t \leq 20$
### Part (d):
It will eventually predict a **negative exchange rate** oe (will fall below zero etc) | **B1** | AO 3.5a | 'Exchange rate tends to zero' is B0. Must mention the variable 'exchange rate'. Underlined words needed.
The pages you've shared appear to be only the **contact/copyright information pages** from an OCR document — they contain no mark scheme content, questions, answers, or mark allocations.
These pages only include:
- OCR contact details (phone, email, social media)
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To extract mark scheme content, please share the **actual mark scheme pages** containing the questions, answers, and mark allocations. These would typically show tables or lists with entries like answer text, marks (M1, A1, B1, etc.), and guidance/examiner notes.15 A family is planning a holiday in Europe. They need to buy some euros before they go. The exchange rate, $y$, is the number of euros they can buy per pound. They believe that the exchange rate may be modelled by the formula\\
$y = a t ^ { 2 } + b t + c$,\\
where $t$ is the time in days from when they first check the exchange rate.\\
Initially, when $t = 0$, the exchange rate is 1.14 .
\begin{enumerate}[label=(\alph*)]
\item Write down the value of $c$.
When $t = 2 , y = 1.20$ and when $t = 4 , y = 1.25$.
\item Calculate the values of $a$ and $b$.
The family will only buy their euros when their model predicts an exchange rate of at least 1.29 .
\item Determine the range of values of $t$ for which, according to their model, they will buy their euros.
\item Explain why the family's model is not viable in the long run.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2023 Q15 [7]}}