| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| 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 coordinate geometry question requiring basic gradient calculation, verification of a line equation, and solving simultaneous linear equations. All techniques are routine C1 skills with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03a Straight lines: equation forms y=mx+c, ax+by+c=0 |
1 The point $A$ has coordinates $( 11,2 )$ and the point $B$ has coordinates $( - 1 , - 1 )$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the gradient of $A B$.
\item Hence, or otherwise, show that the line $A B$ has equation
$$x - 4 y = 3$$
\end{enumerate}\item The line with equation $3 x + 5 y = 26$ intersects the line $A B$ at the point $C$. Find the coordinates of $C$.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2005 Q1 [7]}}