| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Intersection of two lines |
| Difficulty | Moderate -0.8 This is a straightforward multi-part coordinate geometry question requiring standard techniques: finding line equations from point-gradient form, solving simultaneous equations for intersection, and calculating triangle area using the formula 1/2|base×height|. All steps are routine C1 procedures with no conceptual challenges, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.05c Area of triangle: using 1/2 ab sin(C) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Use \(n^{th}\) term \(= a+(n-1)d\) with \(d=10\), \(a=150\), \(n=8\); gives \(150+7\times10 = 220\) | M1 | Attempt to use \(n^{th}\) term formula with \(d=10\) and correct combination of \(a\) and \(n\) |
| \(= 220^*\) (Year is 2007) | A1* | Shows that 220 computers are sold in 2007 with no errors; need reference to years |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Use \(S_n = \frac{n}{2}\{2a+(n-1)d\}\) with \(d=10\), \(a=150\), \(n=14\) | M1 | Correct combination of \(a\) and \(n\) |
| \(= 7(300+13\times10)\) or \(7(150+280)\) | A1 | |
| \(= 7\times430 = 3010\) | A1 | cao; correct answer with no working implies M1A1A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Cost in year \(n\): \(900+(n-1)\times(-20)\); Sales in year \(n\): \(150+(n-1)\times10\) | M1 | Allow \(900+n\times(-20)\); allow recovery from invisible brackets |
| Cost \(= 3\times\)Sales \(\Rightarrow 900+(n-1)\times(-20) = 3(150+(n-1)\times10)\) | M1 | Attempts to write equation in \(n\); accept 3 on wrong side; allow use of 20 instead of \(-20\) |
| \(900-20n+20 = 450+30n-30 \Rightarrow 500 = 50n\) | M1 | Solves correct linear equation to achieve \(n=10\) (or \(n=9\) if using \(n\) instead of \(n-1\)) |
| \(n=10\), Year is 2009 | A1 | A0 for answer "Year 10" if 2009 not given |
# Question 8:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Use $n^{th}$ term $= a+(n-1)d$ with $d=10$, $a=150$, $n=8$; gives $150+7\times10 = 220$ | M1 | Attempt to use $n^{th}$ term formula with $d=10$ and correct combination of $a$ and $n$ |
| $= 220^*$ (Year is 2007) | A1* | Shows that 220 computers are sold in 2007 with no errors; need reference to years |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Use $S_n = \frac{n}{2}\{2a+(n-1)d\}$ with $d=10$, $a=150$, $n=14$ | M1 | Correct combination of $a$ and $n$ |
| $= 7(300+13\times10)$ or $7(150+280)$ | A1 | |
| $= 7\times430 = 3010$ | A1 | cao; correct answer with no working implies M1A1A1 |
## Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Cost in year $n$: $900+(n-1)\times(-20)$; Sales in year $n$: $150+(n-1)\times10$ | M1 | Allow $900+n\times(-20)$; allow recovery from invisible brackets |
| Cost $= 3\times$Sales $\Rightarrow 900+(n-1)\times(-20) = 3(150+(n-1)\times10)$ | M1 | Attempts to write equation in $n$; accept 3 on wrong side; allow use of 20 instead of $-20$ |
| $900-20n+20 = 450+30n-30 \Rightarrow 500 = 50n$ | M1 | Solves correct linear equation to achieve $n=10$ (or $n=9$ if using $n$ instead of $n-1$) |
| $n=10$, Year is **2009** | A1 | A0 for answer "Year 10" if 2009 not given |
---8. The line $l _ { 1 }$ passes through the point $( 9 , - 4 )$ and has gradient $\frac { 1 } { 3 }$.
\begin{enumerate}[label=(\alph*)]
\item Find an equation for $l _ { 1 }$ in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.
The line $l _ { 2 }$ passes through the origin $O$ and has gradient - 2 . The lines $l _ { 1 }$ and $l _ { 2 }$ intersect at the point $P$.
\item Calculate the coordinates of $P$.
Given that $l _ { 1 }$ crosses the $y$-axis at the point $C$,
\item calculate the exact area of $\triangle O C P$.\\
\includegraphics[max width=\textwidth, alt={}, center]{307d6e38-b8ca-4473-9f1a-94c8660c0d9c-011_104_59_2568_1882}\\
\includegraphics[max width=\textwidth, alt={}, center]{307d6e38-b8ca-4473-9f1a-94c8660c0d9c-011_104_1829_2648_114}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q8}}