Mathematics · May / June 2024 · Paper 11 · Question 10
YMA01
As printed in the paper
The question as text
10. The curve C has equation y = f(x) where x > 0 Given that x x f′(x) = 6x – 2 1 3 2 • 2 x • the point P(4, 12) lies on C
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
10(a)[4]
7 14
×
1
( )
( )
f
′
4
=
6 4
−
= −
4
2
1
−
1
m
= −
m
=
T
2
N
1
−
2
y
12
2
(
x
4
)
or
y
mx
c
y
2
x
c
12
2 4
( )
c
c
...
−
=
−
=
+
=
+
=
+
=
y
=
2
x
+
4
10(b)[6]
(
)(
)
2
x
−
1 3
x
+
2
6
x
2
+
x
−
2
3
1
1
1
−
...
=
...
=
...3
x
2
+
x
2
−
x
2
2
x
2
x
2
6
x
2
6
5
1
3
1
f
( )
x
=
−
x
−
x
+
2
x
(
+
c
)
2
2
2
2
5
3
or e.g.
1
1
6
x
2
3
5
3
x
2
2
f
( )
x
x
x
(
c
)
=
−
2
−
2
+
+
5
3
1
2
2
2
2
or e.g.
1
1
6
x
2
3
5
3
x
2
2
( )
(
)
f
x
=
−
x
2
+
x
2
−
+
c
5
3
1
2
2
2
2
( )
2
6 4
6
1
5
3
1
( )
( )
( )
12
=
−
4
−
4
+
2 4
+
c
c
=
...
2
2
2
2
5
3
5
3
1
6
1
16
(
( )
)
f
x
=
3
x
2
−
x
−
x
+
2
x
+
2
2
2
5
3
15
Notes:
(a)
B1: Correct gradient at P (may be implied)
M1: Attempts to use the perpendicular gradient rule to find the normal gradient.
−
1
1
Look for e.g.
m
=
or e.g.
m
×
m
= −−
1
m
= −
1
m
=
...
N
m
T
N
2
N
N
T
May be implied by their normal gradient.
M1(A1 on Epen): Attempts the equation of the normal using a “changed” gradient with x = 4 and y = 12
correctly placed.
Alternatively uses y = mx + c with a “changed” gradient with x = 4 and y = 12 to find a value for c.
A1: Correct equation in the required form
M1: Expands the numerator of the fraction and attempts to split.
..
x
2
3
...
x
1
...
Score for one correct index achieved from correct work e.g.
→
...
x
2
or
→
...
x
2
or
x
x
x
3
5
1
3
1
1
−
M1: Attempts to integrate a fractional power. E.g.
...
x
→
...
x
or
x
→
...
x
or
x
→
...
x
etc.
2
2
2
2
2
2
Do not allow this mark for an attempt to integrate the
x in the denominator.
A1: Any 2 correct terms simplified or unsimplified.
A1: All correct simplified or unsimplified. The “+ c” is not required here.
M1: Uses x = 4 and y = 12 following an attempt to increase at least one power x by 1 to find a value for their c.
Their c may not be fully evaluated but must be a numerical expression.
( )
A1: Correct simplified form. The
"f
x = is not required just look for the correct expression.
"
6
5
1
3
1
16
(
)
Accept equivalent simplified forms and allow
f
( )
3
2
2
x
=
x
−
x
2
+
x
2
−
x
2
+
5
3
15
Apply isw if applicable unless they multiply all terms by e.g. 15
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