| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2019 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Optimisation via quadratic model |
| Difficulty | Moderate -0.8 This is a straightforward applied quadratic question requiring only substitution and basic interpretation of a vertex form equation. Part (a) is direct substitution (n=1), part (b) reads the maximum from the vertex form, part (c) requires finding T(4) - T(3), and part (d) asks for a simple domain restriction (T≥0). All parts are routine applications with no problem-solving insight needed, making this easier than average for AS-level. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02q Use intersection points: of graphs to solve equations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| 117 tonnes | B1 | 117 tonnes or 117 t |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| 1200 tonnes | B1 | 1200 tonnes or 1200 t |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Attempts \(\left\{1200-3\times(5-20)^2\right\} - \left\{1200-3\times(4-20)^2\right\}\) | M1 | May be implied by \(525-432\); condone attempt at \(T_4 - T_3\) |
| 93 tonnes | A1 | 93 tonnes or 93 t |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| States model only valid for values of \(n\) such that \(n \leqslant 20\) | B1 | States \(n\leqslant 20\) or \(n<20\); condone \(n\leqslant 40\) or \(n<40\) with "mass cannot be negative"; condone \(n=40\) with statement mass becomes 0 |
| States that total amount mined cannot decrease | B1 | Must state limitation on \(n\) AND explain fully using total mass; states \(n\leqslant 20\) and total mass of tin cannot decrease |
## Question 9(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| 117 tonnes | B1 | 117 tonnes or 117 t |
## Question 9(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| 1200 tonnes | B1 | 1200 tonnes or 1200 t |
## Question 9(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempts $\left\{1200-3\times(5-20)^2\right\} - \left\{1200-3\times(4-20)^2\right\}$ | M1 | May be implied by $525-432$; condone attempt at $T_4 - T_3$ |
| 93 tonnes | A1 | 93 tonnes or 93 t |
## Question 9(d):
| Answer/Working | Mark | Guidance |
|---|---|---|
| States model only valid for values of $n$ such that $n \leqslant 20$ | B1 | States $n\leqslant 20$ or $n<20$; condone $n\leqslant 40$ or $n<40$ with "mass cannot be negative"; condone $n=40$ with statement mass becomes 0 |
| States that total amount mined cannot decrease | B1 | Must state limitation on $n$ AND explain fully using total mass; states $n\leqslant 20$ and total mass of tin cannot decrease |
---\begin{enumerate}
\item A company started mining tin in Riverdale on 1st January 2019.
\end{enumerate}
A model to find the total mass of tin that will be mined by the company in Riverdale is given by the equation
$$T = 1200 - 3 ( n - 20 ) ^ { 2 }$$
where $T$ tonnes is the total mass of tin mined in the $n$ years after the start of mining.\\
Using this model,\\
(a) calculate the mass of tin that will be mined up to 1st January 2020,\\
(b) deduce the maximum total mass of tin that could be mined,\\
(c) calculate the mass of tin that will be mined in 2023.\\
(d) State, giving reasons, the limitation on the values of $n$.
\hfill \mbox{\textit{Edexcel AS Paper 1 2019 Q9 [6]}}