| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Two circles intersection or tangency |
| Difficulty | Moderate -0.3 This question requires completing the square to find circle centres and radii, then applying the distance formula and basic geometric reasoning about maximum/minimum distances between circles. While it involves multiple steps (4+3 marks), each step uses standard techniques with no novel insight required. It's slightly easier than average because it's a straightforward application of circle geometry formulas without any problem-solving complexity or proof elements. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
| Answer | Marks |
|---|---|
| 6(a) | (−3,5) |
| Answer | Marks |
|---|---|
| 1 | B1 |
| Answer | Marks |
|---|---|
| 2 | B1 |
| Attempt correct process for finding distance between centres | M1 |
| Obtain 15 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 6(b) | R = 4 and R = 8 | B1 |
| Obtain least or greatest distance | B1 FT | ‘15’ – R – R or ‘15’ + R + R . |
| Answer | Marks | Guidance |
|---|---|---|
| Obtain 3 and 27 | B1 FT | ‘15’ – R – R and ‘15’ + R + R . |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 6:
--- 6(a) ---
6(a) | (−3,5)
State or imply centre of C is
1 | B1
(9,−4)
State or imply centre of C is
2 | B1
Attempt correct process for finding distance between centres | M1
Obtain 15 | A1
4
Question | Answer | Marks | Guidance
--- 6(b) ---
6(b) | R = 4 and R = 8 | B1
Obtain least or greatest distance | B1 FT | ‘15’ – R – R or ‘15’ + R + R .
1 2 1 2
Obtain 3 and 27 | B1 FT | ‘15’ – R – R and ‘15’ + R + R .
1 2 1 2
3
Question | Answer | Marks | GuidanceCircles $C_1$ and $C_2$ have equations
$$x^2 + y^2 + 6x - 10y + 18 = 0 \text{ and } (x-9)^2 + (y+4)^2 - 64 = 0$$
respectively.
\begin{enumerate}[label=(\alph*)]
\item Find the distance between the centres of the circles. [4]
$P$ and $Q$ are points on $C_1$ and $C_2$ respectively. The distance between $P$ and $Q$ is denoted by $d$.
\item Find the greatest and least possible values of $d$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2024 Q6 [7]}}