| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| 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 C1 coordinate geometry question requiring basic skills: rearranging to y=mx+c form, finding axis intercepts, and solving simultaneous linear equations. All techniques are routine with no problem-solving insight needed, making it easier than average but not trivial due to the multi-part nature and algebraic manipulation required. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03a Straight lines: equation forms y=mx+c, ax+by+c=0 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Graph showing two lines \(l_1\) and \(l_2\) intersecting at \((0, 2)\), with \(l_1\) passing through \((4, 0)\) and \(l_2\) passing through the origin. | B2 B1 | |
| (b) \(l_1 \Rightarrow 6x - 2y = 0\) | ||
| \(l_2: x + 2y - 4 = 0\) | ||
| adding \(7x - 4 = 0, \quad x = \frac{4}{7}\) | M1 A1 | |
| \(\therefore\) intersect at \(\left(\frac{4}{7}, \frac{12}{7}\right)\) | A1 | (6 marks) |
**(a)** Graph showing two lines $l_1$ and $l_2$ intersecting at $(0, 2)$, with $l_1$ passing through $(4, 0)$ and $l_2$ passing through the origin. | B2 B1 |
**(b)** $l_1 \Rightarrow 6x - 2y = 0$ | |
$l_2: x + 2y - 4 = 0$ | |
adding $7x - 4 = 0, \quad x = \frac{4}{7}$ | M1 A1 |
$\therefore$ intersect at $\left(\frac{4}{7}, \frac{12}{7}\right)$ | A1 | (6 marks)The straight line $l_1$ has the equation $3x - y = 0$.
The straight line $l_2$ has the equation $x + 2y - 4 = 0$.
\begin{enumerate}[label=(\alph*)]
\item Sketch $l_1$ and $l_2$ on the same diagram, showing the coordinates of any points where each line meets the coordinate axes. [3]
\item Find, as exact fractions, the coordinates of the point where $l_1$ and $l_2$ intersect. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q3 [6]}}