| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Moderate -0.8 This is a straightforward application of linear modeling requiring finding gradient from two points and checking consistency with a third point. The arithmetic is simple (gradient = 450/6 = 75), and part (b) only requires substituting t=0 to verify the model gives £1900. No complex problem-solving or conceptual depth required—below average difficulty for A-level. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=0 |
| Answer | Marks | Guidance |
|---|---|---|
| \(V = at + b\); \(2375 = 6a + b\), \(2825 = 12a + b\) | M1* (AO 3.3) | Using a linear model to set up two equations with the values given; or correct attempt to find gradient |
| Solving their two equations to find a linear model, possibly BC | M1dep* (AO 3.1a) | Using *their* gradient to find a linear model |
| \(V = 75t + 1925\) | A1 (AO 1.1) | cao |
| Answer | Marks | Guidance |
|---|---|---|
| When \(t = 0\), \(V = 1925\) | B1ft (AO 3.4) | Uses model and states initial investment is their '\(b\)'; only ft a linear model from part (a) |
| Compare *their* "1925" with 1900 and make a sensible comment about whether the straight-line model in part (a) is supported or not | B1ft (AO 3.5a) |
## Question 3(a):
$V = at + b$; $2375 = 6a + b$, $2825 = 12a + b$ | M1* (AO 3.3) | Using a linear model to set up two equations with the values given; or correct attempt to find gradient
Solving their two equations to find a linear model, possibly BC | M1dep* (AO 3.1a) | Using *their* gradient to find a linear model
$V = 75t + 1925$ | A1 (AO 1.1) | cao
**Total: [3]**
## Question 3(b):
When $t = 0$, $V = 1925$ | B1ft (AO 3.4) | Uses model and states initial investment is their '$b$'; only ft a linear model from part (a)
Compare *their* "1925" with 1900 and make a sensible comment about whether the straight-line model in part (a) is supported or not | B1ft (AO 3.5a) |
**Total: [2]**
---3 Sam invested in a shares scheme. The value, $\pounds V$, of Sam's shares was reported $t$ months after investment.
\begin{itemize}
\item Exactly 6 months after investment, the value of Sam's shares was $\pounds 2375$.
\item Exactly 1 year after investment, the value of Sam's shares was $\pounds 2825$.
\begin{enumerate}[label=(\alph*)]
\item Using a straight-line model, determine an equation for $V$ in terms of $t$.
\end{itemize}
Sam's original investment in the scheme was $\pounds 1900$.
\item Explain whether or not this fact supports the use of the straight-line model in part (a).
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q3 [5]}}