ALEVELPAPERZ2025
Mark Scheme (Results)
Summer 2025
Pearson Edexcel GCE
In Mathematics (9MA0)
Paper 01 Pure Mathematics
,ALEVELPAPERZ2025
Question Scheme Marks AOs
1 (a) (4, −4) or e.g. x = 4, y = −4 o.e. B1 1.1b
(1)
(b) −4, y =
(−4, 6) or e.g. x = 6 o.e. B1 1.1b
(1)
(c) (6, ...) or (..., 5) or x = 6 or y = 5 o.e. M1 1.1b
(6, 5) or x = 6 and y = 5 A1 1.1b
(2)
(4 marks)
Notes:
General guidelines for all parts:
Remember to check answers written against the questions.
If there is any contradiction, mark the answers given in the body of the scripts.
If there is no labelling, mark the responses in the order given.
The coordinates need to be values not just a calculation e.g. not 6 − 2 for 4
Points can be written as a coordinate pair or separately as= x ...,
= y ...
Do not allow coordinates written the wrong way round but isw if necessary
e.g. x =4, y =−4 → (−4, 4) scores B1 and isw
Condone missing brackets (one or both) e.g. x = 4, y = −4 or (4, − 4 or 4, − 4 for (4, − 4)
Condone a missing comma e.g. (4 − 4) for (4, − 4)
Condone use of a semi-colon e.g. (4 ; − 4) for (4, − 4)
4 4
Condone vector notation e.g. for (4, − 4) and condone
−4 −4
(a)
B1: (4, −4) o.e. see above
(b)
B1: (−4, 6) o.e. see above
(c)
M1: One correct coordinate. See above.
A1: Both coordinates correct. See above.
Note that M0A1 is not a possible mark profile.
Note that in part (c), some candidates show their thinking by transforming the point
piecewise e.g. (6, −4) → (6, 4) → (6,8) → (6, 5)
In such cases, mark their final pair of coordinates
,Question Scheme Marks AOs
2 (a) (i) Centre ( −3, 4 ) B1 1.1b
2
(ii) States or implies that r = 24 or r = 24 M1 1.1b
2 6 A1 1.1b
(3)
(b) Attempts a valid method
e.g. Finds distance of centre from origin, M1 3.1a
Sets y = 0 and finds values of x
Correct calculations, reason and conclusion (see notes) A1 2.4
(2)
(5 marks)
Notes:
Mark (i) and (ii) together
(a)(i)
B1: Centre ( −3, 4 ) Accept without brackets. May be written e.g. x =
−3, y =
4
(a)(ii)
2
M1: States or implies that r = 24 or r = 24 . A final answer of 24 or 2 6 implies the radius
May multiply out the brackets, collect terms ( x 2 + y 2 + 6 x − 8 y + 1 =
0 ) and states the
62 (−8) 2
radius is r 2 = + − 1 o.e. Do not condone slips for this mark.
4 4
A1: 2 6 isw if they proceed to write as a decimal
(b) Note that if their radius is incorrect in (a) then maximum score is M1A0 unless they
restart in (b)
M1: Attempts a valid method. For example
• Finds the distance (or distance 2) of the centre from the origin.
They must be attempting ( d = ) (± "3") 2 + ("± "4") 2 = ... or
( d = ) (± "3"− 0)
2 2
+ (± "4"− 0) 2 = ... and proceed to a value.
May be seen as substituting the coordinates of the origin into the equation for C
proceeding to a value for the left hand side e.g. 25 (to be able to compare with 24)
• Sets y = 0 and attempts to solve ( x + 3)2 + ( −4 )2= 24 ⇒ x= ... (at least one value)
• Sets x = 0 and attempts to solve ( 3)2 + ( y − 4 )2 = 24 ⇒ y = ... (at least one value)
In each method the starting expression or equation must be correct but do not be concerned
by slips when evaluating or processing in finding the distance, the x coordinate or y
coordinate.
, A1: Correct calculation(s), reason and conclusion examples:
Calculation examples Reason examples Conclusion examples
25 > 24 o.e.
e.g. d = 25
2
or
or
5 > 24 o.e. (allow 4.9 or
e.g. (d =) 5
better)
e.g. ( x + 3)2 + ( −4 )2 =24 e.g. origin does NOT lie within
⇒ ( x =) − 3 ± 8 roots are both negative (same circle / origin lies outside
signs) o.e. circle / not in circle o.e.
(allow decimals awrt −0.2 and
awrt −5.8 )
e.g. ( 3)2 + ( y − 4 )2 =
24
⇒ ( y =) 4 ± 15 roots are both positive (same
signs) o.e.
(allow decimals awrt 0.1 and
awrt 7.9 )
Note if their reasoning is incorrect e.g. referring to the radius as 24 instead of 24 then A0
but allow referencing to “the radius of C” provided their radius in (a) was correct.
Note if they give a reason that the origin does not lie inside the circle C because e.g. 25 ≠ 24 this
scores M1A0 (M1 for 25 but A0 incorrect reasoning)
Mark Scheme (Results)
Summer 2025
Pearson Edexcel GCE
In Mathematics (9MA0)
Paper 01 Pure Mathematics
,ALEVELPAPERZ2025
Question Scheme Marks AOs
1 (a) (4, −4) or e.g. x = 4, y = −4 o.e. B1 1.1b
(1)
(b) −4, y =
(−4, 6) or e.g. x = 6 o.e. B1 1.1b
(1)
(c) (6, ...) or (..., 5) or x = 6 or y = 5 o.e. M1 1.1b
(6, 5) or x = 6 and y = 5 A1 1.1b
(2)
(4 marks)
Notes:
General guidelines for all parts:
Remember to check answers written against the questions.
If there is any contradiction, mark the answers given in the body of the scripts.
If there is no labelling, mark the responses in the order given.
The coordinates need to be values not just a calculation e.g. not 6 − 2 for 4
Points can be written as a coordinate pair or separately as= x ...,
= y ...
Do not allow coordinates written the wrong way round but isw if necessary
e.g. x =4, y =−4 → (−4, 4) scores B1 and isw
Condone missing brackets (one or both) e.g. x = 4, y = −4 or (4, − 4 or 4, − 4 for (4, − 4)
Condone a missing comma e.g. (4 − 4) for (4, − 4)
Condone use of a semi-colon e.g. (4 ; − 4) for (4, − 4)
4 4
Condone vector notation e.g. for (4, − 4) and condone
−4 −4
(a)
B1: (4, −4) o.e. see above
(b)
B1: (−4, 6) o.e. see above
(c)
M1: One correct coordinate. See above.
A1: Both coordinates correct. See above.
Note that M0A1 is not a possible mark profile.
Note that in part (c), some candidates show their thinking by transforming the point
piecewise e.g. (6, −4) → (6, 4) → (6,8) → (6, 5)
In such cases, mark their final pair of coordinates
,Question Scheme Marks AOs
2 (a) (i) Centre ( −3, 4 ) B1 1.1b
2
(ii) States or implies that r = 24 or r = 24 M1 1.1b
2 6 A1 1.1b
(3)
(b) Attempts a valid method
e.g. Finds distance of centre from origin, M1 3.1a
Sets y = 0 and finds values of x
Correct calculations, reason and conclusion (see notes) A1 2.4
(2)
(5 marks)
Notes:
Mark (i) and (ii) together
(a)(i)
B1: Centre ( −3, 4 ) Accept without brackets. May be written e.g. x =
−3, y =
4
(a)(ii)
2
M1: States or implies that r = 24 or r = 24 . A final answer of 24 or 2 6 implies the radius
May multiply out the brackets, collect terms ( x 2 + y 2 + 6 x − 8 y + 1 =
0 ) and states the
62 (−8) 2
radius is r 2 = + − 1 o.e. Do not condone slips for this mark.
4 4
A1: 2 6 isw if they proceed to write as a decimal
(b) Note that if their radius is incorrect in (a) then maximum score is M1A0 unless they
restart in (b)
M1: Attempts a valid method. For example
• Finds the distance (or distance 2) of the centre from the origin.
They must be attempting ( d = ) (± "3") 2 + ("± "4") 2 = ... or
( d = ) (± "3"− 0)
2 2
+ (± "4"− 0) 2 = ... and proceed to a value.
May be seen as substituting the coordinates of the origin into the equation for C
proceeding to a value for the left hand side e.g. 25 (to be able to compare with 24)
• Sets y = 0 and attempts to solve ( x + 3)2 + ( −4 )2= 24 ⇒ x= ... (at least one value)
• Sets x = 0 and attempts to solve ( 3)2 + ( y − 4 )2 = 24 ⇒ y = ... (at least one value)
In each method the starting expression or equation must be correct but do not be concerned
by slips when evaluating or processing in finding the distance, the x coordinate or y
coordinate.
, A1: Correct calculation(s), reason and conclusion examples:
Calculation examples Reason examples Conclusion examples
25 > 24 o.e.
e.g. d = 25
2
or
or
5 > 24 o.e. (allow 4.9 or
e.g. (d =) 5
better)
e.g. ( x + 3)2 + ( −4 )2 =24 e.g. origin does NOT lie within
⇒ ( x =) − 3 ± 8 roots are both negative (same circle / origin lies outside
signs) o.e. circle / not in circle o.e.
(allow decimals awrt −0.2 and
awrt −5.8 )
e.g. ( 3)2 + ( y − 4 )2 =
24
⇒ ( y =) 4 ± 15 roots are both positive (same
signs) o.e.
(allow decimals awrt 0.1 and
awrt 7.9 )
Note if their reasoning is incorrect e.g. referring to the radius as 24 instead of 24 then A0
but allow referencing to “the radius of C” provided their radius in (a) was correct.
Note if they give a reason that the origin does not lie inside the circle C because e.g. 25 ≠ 24 this
scores M1A0 (M1 for 25 but A0 incorrect reasoning)
