| Exam Board | Edexcel |
|---|---|
| Module | Paper 1 (Paper 1) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Range of parameter for intersection |
| Difficulty | Moderate -0.8 This is a straightforward question on completing the square for circles. Part (a) requires simple rearrangement to find the centre, and part (b) only needs recognizing that radius squared must be positive (r² > 0), giving k > -29. Both parts are routine applications of standard circle theory with no problem-solving insight required. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Attempts \((x-2)^2 + (y+5)^2 = \ldots\) | M1 | Attempts to complete the square |
| Centre \((2, -5)\) | A1 | Also allow written separately \(x=2,\ y=-5\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Sets \(k + 2^2 + 5^2 > 0\) | M1 | Deduces RHS of \((x\pm\ldots)^2+(y\pm\ldots)^2=\ldots\) is \(>0\) or \(\geqslant 0\) |
| \(\Rightarrow k > -29\) | A1ft | Also allow \(k \geqslant -29\); follow through on their RHS |
## Question 3:
**Part (a):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempts $(x-2)^2 + (y+5)^2 = \ldots$ | M1 | Attempts to complete the square |
| Centre $(2, -5)$ | A1 | Also allow written separately $x=2,\ y=-5$ |
**Part (b):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| Sets $k + 2^2 + 5^2 > 0$ | M1 | Deduces RHS of $(x\pm\ldots)^2+(y\pm\ldots)^2=\ldots$ is $>0$ or $\geqslant 0$ |
| $\Rightarrow k > -29$ | A1ft | Also allow $k \geqslant -29$; follow through on their RHS |
---3. A circle $C$ has equation
$$x ^ { 2 } + y ^ { 2 } - 4 x + 10 y = k$$
where $k$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the centre of $C$.
\item State the range of possible values for $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel Paper 1 Q3 [4]}}