| Exam Board | Edexcel |
|---|---|
| Module | PMT Mocks (PMT Mocks) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Easy -1.2 This is a straightforward application of linear equations requiring students to find two unknowns from two given points, then sketch a line and critique a model. The algebra is basic (solving simultaneous equations with simple numbers), and the criticism requires only common-sense reasoning about population models. This is easier than average A-level content. |
| Spec | 1.02z Models in context: use functions in modelling |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | \(P = 400 + 100t\) | A1 |
| (b) | A straight line graph \(P\) against \(t\) with coordinates \((0,400)\) and \((10,1400)\) | B1 |
| (c) | Population growth is usually modelled exponentially. | B1 |
**(a)** | $P = 400 + 100t$ | A1 | M1 For translating the problem into mathematics. Attempts to use the given equation or equivalent with either or the piece of information to form one correct equation. A1 Two correct equations e.g. $a + 5b = 900$ and $a + 8b = 1200$. M1 Solves simultaneously to find values for $a$ and $b$. E.g. $a + 5b = 900$ and $-a - 8b = -1200 \Rightarrow b = 100, a = 400$. A1 Establishes the full equation of the model with values of $a$ and $b$. |
**(b)** | A straight line graph $P$ against $t$ with coordinates $(0,400)$ and $(10,1400)$ | B1 | |
**(c)** | Population growth is usually modelled exponentially. | B1 | |
---5. A scientist is studying a population of lizards on an island and uses the linear model $P = a + b t$ to predict the future population of the lizard where $P$ is the population and $t$ is the time in years after the start of the study.
Given that
\begin{itemize}
\item The number of population was 900 , exactly 5 years after the start of the study.
\item The number of population was 1200 , exactly 8 years after the start of the study.\\
a. find a complete equation for the model.\\
b. Sketch the graph of the population for the first 10 years.\\
c. Suggest one criticism of this model.
\end{itemize}
\hfill \mbox{\textit{Edexcel PMT Mocks Q5 [6]}}