| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Linear modelling problems |
| Difficulty | Easy -1.2 This is a straightforward linear modelling question requiring students to find a linear equation from two points, then interpret the y-intercept and x-intercept. The calculations are simple (gradient = -15/120 = -1/8), and part (c) requires only basic model evaluation. This is easier than average A-level content as it involves routine GCSE-level algebra with minimal conceptual challenge. |
| Spec | 1.02z Models in context: use functions in modelling1.03a Straight lines: equation forms y=mx+c, ax+by+c=0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Uses/implies \(V = ad + b\) | B1 | Linear model \(V=ad+b\) or \(d=mV+c\) |
| Uses both \(40=80a+b\) and \(25=200a+b\) to find either \(a\) or \(b\) | M1 | Awarded for translating problem and starting to solve; may see \(\pm\frac{25-40}{200-80}\) or \(\pm\frac{200-80}{25-40}\) |
| Uses both equations to find both \(a\) and \(b\) | dM1 | |
| \(V = -\frac{1}{8}d + 50\) | A1 | Or exact equivalent e.g. \(d=400-8V\); withhold if not in terms of \(V\) and \(d\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| States either initial volume was 50 litres or distance travelled was 400 km | B1ft | Follow through on their \(a\) and \(b\); e.g. \(V=50\) or \(40+\frac{80}{8}\) or \(\frac{400}{8}\) |
| Attempts to find both by solving \(0=-\frac{1}{8}d+50\) and \(0=400-8V\) | M1 | Complete attempt from a linear model |
| States both initial volume was 50 litres and distance travelled was 400 km | A1 | Units required for both; must be clear which answer applies to each part |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| "Poor model" as 320 km is significantly less than 400 km | B1ft | Only available if answer to (b)(ii) is \(<290\) or \(>350\); must state 320 is significantly less than "400"; not sufficient to say \(320\neq400\) or \(320<400\); condone "400 is too far from 320". Alternative: poor model because after 320 km model predicts 10 litres remaining, which is significantly more than empty tank |
## Question 7:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Uses/implies $V = ad + b$ | B1 | Linear model $V=ad+b$ or $d=mV+c$ |
| Uses both $40=80a+b$ and $25=200a+b$ to find either $a$ or $b$ | M1 | Awarded for translating problem and starting to solve; may see $\pm\frac{25-40}{200-80}$ or $\pm\frac{200-80}{25-40}$ |
| Uses both equations to find both $a$ and $b$ | dM1 | |
| $V = -\frac{1}{8}d + 50$ | A1 | Or exact equivalent e.g. $d=400-8V$; withhold if not in terms of $V$ and $d$ |
### Part (b)(i)(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| States **either** initial volume was 50 litres **or** distance travelled was 400 km | B1ft | Follow through on their $a$ and $b$; e.g. $V=50$ or $40+\frac{80}{8}$ or $\frac{400}{8}$ |
| Attempts to find **both** by solving $0=-\frac{1}{8}d+50$ **and** $0=400-8V$ | M1 | Complete attempt from a **linear** model |
| States **both** initial volume was 50 litres **and** distance travelled was 400 km | A1 | Units required for both; must be clear which answer applies to each part |
### Part (c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| "Poor model" as 320 km is significantly less than 400 km | B1ft | Only available if answer to (b)(ii) is $<290$ **or** $>350$; must state 320 is **significantly** less than "400"; not sufficient to say $320\neq400$ or $320<400$; condone "400 is too far from 320". **Alternative:** poor model because after 320 km model predicts 10 litres remaining, which is significantly more than empty tank |\begin{enumerate}
\item The distance a particular car can travel in a journey starting with a full tank of fuel was investigated.
\end{enumerate}
\begin{itemize}
\item From a full tank of fuel, 40 litres remained in the car's fuel tank after the car had travelled 80 km
\item From a full tank of fuel, 25 litres remained in the car's fuel tank after the car had travelled 200 km
\end{itemize}
Using a linear model, with $V$ litres being the volume of fuel remaining in the car's fuel tank and $d \mathrm {~km}$ being the distance the car had travelled,\\
(a) find an equation linking $V$ with $d$.
Given that, on a particular journey
\begin{itemize}
\item the fuel tank of the car was initially full
\item the car continued until it ran out of fuel\\
find, according to the model,\\
(b) (i) the initial volume of fuel that was in the fuel tank of the car,\\
(ii) the distance that the car travelled on this journey.
\end{itemize}
In fact the car travelled 320 km on this journey.\\
(c) Evaluate the model in light of this information.
\hfill \mbox{\textit{Edexcel AS Paper 1 2023 Q7 [8]}}