| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Line intersecting reciprocal curve |
| Difficulty | Moderate -0.8 This is a straightforward C1 question combining basic curve sketching with solving a quadratic equation from simultaneous equations. Part (a) requires sketching a simple reciprocal function and linear graph (routine recall), while part (b) involves substituting y = 2x + 5 into y = 3/x to get 2x² + 5x - 3 = 0, then solving by factorization or formula. All techniques are standard with no problem-solving insight required, making this easier than average. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02q Use intersection points: of graphs to solve equations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Graph with 2 branches in correct quadrants, roughly correct shape | B1 | Two branches, no touching/intersecting axes |
| Straight line cutting positive \(y\)-axis and negative \(x\)-axis | M1 | Ignore any values |
| \((0,5)\) and \((-2.5, 0)\) correctly marked | A1 | Condone mixing up \((x,y)\) as \((y,x)\) if one value is zero |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(2x+5=\frac{3}{x}\) | M1 | Multiply by \(x\); at least one of \(2x\) or \(+5\) multiplied |
| \(2x^2+5x-3=0\) or \(2x^2+5x=3\) | A1 | Condone missing \(=0\) |
| \((2x-1)(x+3)=0\) | M1 | Attempt to solve 3TQ leading to 2 values |
| \(x=-3\) or \(x=\frac{1}{2}\) | A1 | Both values required |
| \(y=\frac{3}{-3}\) or \(2\times(-3)+5\); or \(y=\frac{3}{\frac{1}{2}}\) or \(2\times(\frac{1}{2})+5\) | M1 | Substitute \(x\) into either \(\frac{3}{x}\) or \(2x+5\) |
| Points are \((-3,-1)\) and \((\frac{1}{2}, 6)\) | A1ft | Correct pairings required |
## Question 6:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Graph with 2 branches in correct quadrants, roughly correct shape | B1 | Two branches, no touching/intersecting axes |
| Straight line cutting positive $y$-axis and negative $x$-axis | M1 | Ignore any values |
| $(0,5)$ and $(-2.5, 0)$ correctly marked | A1 | Condone mixing up $(x,y)$ as $(y,x)$ if one value is zero |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $2x+5=\frac{3}{x}$ | M1 | Multiply by $x$; at least one of $2x$ or $+5$ multiplied |
| $2x^2+5x-3=0$ or $2x^2+5x=3$ | A1 | Condone missing $=0$ |
| $(2x-1)(x+3)=0$ | M1 | Attempt to solve 3TQ leading to 2 values |
| $x=-3$ or $x=\frac{1}{2}$ | A1 | Both values required |
| $y=\frac{3}{-3}$ or $2\times(-3)+5$; or $y=\frac{3}{\frac{1}{2}}$ or $2\times(\frac{1}{2})+5$ | M1 | Substitute $x$ into either $\frac{3}{x}$ or $2x+5$ |
| Points are $(-3,-1)$ and $(\frac{1}{2}, 6)$ | A1ft | Correct pairings required |
---6. The curve $C$ has equation $y = \frac { 3 } { x }$ and the line $l$ has equation $y = 2 x + 5$.
\begin{enumerate}[label=(\alph*)]
\item On the axes below, sketch the graphs of $C$ and $l$, indicating clearly the coordinates of any intersections with the axes.
\item Find the coordinates of the points of intersection of $C$ and $l$.\\
\includegraphics[max width=\textwidth, alt={}, center]{9451ec48-d955-44a8-9988-68f7c0fb9821-07_1137_1141_1046_397}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2008 Q6 [9]}}