Higher June 2025 Paper 2 Q22
22 The equation of circle A is \(x^2 + y^2 = 25\)
Circle A is translated by the vector \(\begin{pmatrix} 0 \\ -2 \end{pmatrix}\) to give circle B.
Sketch circle B.
Show the coordinates of
the centre of circle B
and the points where circle B meets the \(y\)-axis. (3)

| Answer | Mark | Mark scheme |
|---|---|---|
| Circle radius 5 centre \((0, -2)\) and \((0, 3)\) and \((0, -7)\) labelled | B3 | for a correct sketch of a circle with centre \((0, -2)\) and intercepts \((0, 3)\) and \((0, -7)\) labelled |
| (B2 | for a sketch of a circle with two of the 3 points indicated, or for a sketch of a circle with correct centre and radius of 5 labelled or stated) | |
| (B1 | for a sketch of a circle with the correct centre or states correct centre and radius, but does not sketch) |
Additional guidance
See diagram at end of scheme
Allow freehand circles
Ignore intersections with \(x\) axis for all marks
Accepts points marked with correct \(y\)-coordinate, eg \(-2\) on \(y\)-axis for centre
