Mathematics · May / June 2025 · Paper 21 · Question 2
YMA01
As printed in the paper
The question as text
2. The line joining the points (–2, 5) and (4, 15) is the diameter of a circle C.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
2(a)[5]
2
2
2
Attempts radius 2 or diameter 2: e.g.
(
4
2
)
2
(
15 5
)
2
136
D =
−−
+
−
=
Radius2 = 34
(
)
(
)
−
1
2
+
−
10
2
=
34
x
y
(
)
2(b)[2]
1,10
−
34
(a)
B1: Finds the midpoint of the two given points. Must be simplified to score this mark.
Can be implied by circle formula. Allow e.g.
=
1,
=
10
or may be without brackets. May be seen
x
y
on a diagram.
M1: Attempts to find the radius2 or diameter2. Can be implied by the circle formula e.g.
(
)
2
(
)
2
x
±
...
+
y
±
...
=
34
It does not need to be correctly labelled but they must be attempting to find the difference between the x
coordinates and the difference between the y coordinates before squaring.
Condone square rooting to find the radius or diameter (which may be all that is seen)
e.g. 2 34,
136 ( 11.66..),
=
34 ( 5.83...)
=
. Allow decimals for this mark.
May be seen embedded within
2
+
2
+
2
+
2
+
=
0
x
y
fx
gy
c
A1: Calculates the radius2 = 34 o.e. (or allow to be implied by radius =
34 )
Can be implied by circle formula or a value of
c =
67
in
x
2
+
y
2
+
2
fx
+
2
gy
+
c
=
0
M1: Attempts correct form for the circle (
)
2
(
)
2
±
''1''
+
±
''10''
=
''34''
or (
)
2
(
x
y
x
±
''1''
+
y
±
Do not allow this mark if they have clearly attempted to use their radius instead of their radius2
If they have found the length of the diameter or diameter2 however they have labelled it, then they must
have attempted to divide by 4.
They may alternatively attempt
x
2
+
y
2
+
2
fx
+
2
gy
+
c
=
0
where
f = ±
" 1"
,
g = ±
" 10"
c = ±
" 67"
If a centre has not been found or attempted with just values appearing in the equation then they must be
correct.
(
)
A1: (
)
2
(
)
2
2
−
1
+
−
10
=
34
but not (
1
)
2
(
10
)
2
34
isw after a correct answer
x
y
x
−
+
y
−
=
Also allow equivalent expressions e.g.
x
2
+
y
2
−
2
x
−
20
y
+
67
=
0
(b)
Note coordinates may be seen on a diagram. Do not allow
x = if just the midpoint from (a) is
1
stated.
B1: Either
x = or
1
10
34
Condone lack of labelling for this mark.
y =
−
Isw after an exact coordinate is seen.
dB1: Both
x = and
1
y =
10
−
34
Isw after both exact coordinates are seen. Note B0B1 is not possible.
4
16
3
16
2
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