Higher June 2025 Paper 4 Q17
17 The diagram shows a circle, centre (0, 0).
(a) Write down the equation of the circle. [2]
(b) Point A has coordinates (2.3, 3.3).
Show that point A does not lie on the circle and state, with a reason, whether it lies inside the circle or outside the circle. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(x^2 + y^2 = 4^2\) oe final answer | 2 | B1 for \(x^2 + y^2 = k\) (\(k \ne 0\) or 16) or answer \(a^2 + b^2 = 4^2\) oe | \(k\) could be \(r^2\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(2.3^2 + 3.3^2\) 16.18 or 16.2 or 4.02[…] | M1 B1 | If they have the correct working, produce an incorrect figure they can earn M1 B0 A1FT providing their decision is correct for their figure allow the reasoning to be in the working and condone ‘above’ for ‘outside’ see appendix for some comments | |
| a correct decision e.g. outside and (16.18 or 16.2) and 16 or 4.02[…] and 4 | A1FT | A1 is dependent on awarding M1 and is a correct decision based on their figure | |
Appendix: exemplar responses for Q17(b)
Allow the reason to be in the working.
Decision must be outside and
| Response | Mark |
|---|---|
| 16.18 is greater than 16 | 1 |
| \(16.18 \gt 16\) | 1 |
| 16.18 and 16 | 1(BOD) |
| \(16.18 \ne 16\) and is bigger | 1 |
| \(\sqrt{16.18} = 4.02[\ldots]\) which is bigger than 4 | 1 |
| Radius is \(4.02 \gt 4\) | 1 |
| above and 16.18 and 16 | 1 |
| \(4 \lt 4.02[\ldots]\) | 1 |
| \(2.3^2 \gt 4^2 - 3.3^2\) | 1 |
| \(3.3 \gt \sqrt{4^2 - 2.3^2}\) | 1 |
| Exception : \(2.3^2 + 3.3^2 = 15.73\) and inside because \(15.73 \lt 16\) | M1 B0 A1FT |
Note :
To be outside the circle \(2.3^2 + 3.3^2 \gt 4^2\) which can be rearranged to \(2.3^2 \gt 4^2 - 3.3^2\) or \(3.3^2 \gt 4^2 - 2.3^2\) all these are valid methods.