Mathematics · May / June 2025 · Paper 41 · Question 1
YMA01
As printed in the paper
The question as text
1. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The curve C has equation 2 2 x 1 2 y 6 xy 7 e 13 The point P with x coordinate 1 2 lies on C.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[2]
2
−
=
+
2
−
−
=
=
2
y
3
y
7 13
2
y
3
y
20
0
y
...
5
y = −
and
y =
4
2
1(b)[6]
d
y
2
y
2
→
4 d
y x
d
y
−
→±
±
6
xy
...
x
...
y
d
x
d
y
d
y
4
y
−
6
x
−
6
y
=
14e
2
x
−
1
d
x
d
x
1
−
d
y
1 d
y
d
y
2
1
−
−
=
=
4(4)
6
6(4)
14e
2
...
d
x
2 d
x
d
x
38
1
−
=
−
y
"4"
"
"
x
13
2
−
+
=
38
x
13
y
33
0
(a)
M1:
Attempts all of the following
1
substitutesx =
into the equation for C (condoning slips),
2
collect terms and forms a 3TQ in y (terms do not need to be on one side of the equation and the ‘=0’ may be implied by subsequent working)
solves their 3TQ in y using usual rules (including via a calculator) to find at least one value for y.
If a calculator is used, the values must be correct for their 3TQ
5 , 4
−
A1:
Achieves both values
following the award of M1
2
(b)
d
y
d
y
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