Mathematics · May / June 2021 · Paper 11 · Question 6
YMA01
As printed in the paper
The question as text
6. The curve C has equation y = f(x), x > 0 Given that ● C passes through the point P (8, 2) −( ) fʹ(x) = 32 ● + x 3 2 3 3 x 2
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
6(a)[3]
32
5
′
f (8)
=
+ −
3
2 8
3
= −
3 8
×
2
6
5
y
−
2
= −
"
"(
x
−
8)
6
5
26
y
x
= −
+
6
3
6(b)[5]
32
1
f ( )
′
x
=
+ −
3
2
3
x
=
...
x
−
2
+ +
3 ...
x
3
3
x
2
1
4
x
−
2
→
x
−
1
, 3
x
→
x
→
3x
,
3
3
32
1
32
3
4
f( )x =
∫
x
−
2
+ −
3
2
x
3
d
x
= −
x
−
1
+
3
x
−
x
3
+
c
3
3
2
4
32
3
2
= −
×
8
−
1
+ × −
3 8
×
8
+
c
⇒
c
=
...
3
3
2
32
3
4
10
(
)
f( )x =
1
3
−
x
−
+
x
−
x
3
+
3
2
3
Ignore labelling of parts (a) and (b)
(a)
5
M1
Substitutes
to find a value for f (8)
′
. Condone slips in their substitution and
x =
8
−
6
will imply this mark.
It is for the method of finding a line passing though (8,2) using their value for f (8)
′
dM1
. Score
5
for (
)
y
−
2
= −
"
"(
x
−
8)
with both brackets correct. If they use y
=
mx
+ they must
c
6
proceed as far as c = … It is dependent on the previous method mark.
5
26
A1
y
= −
x
+
6
3
(b)
32
3
4
A1
Two terms correct of
−
x
−
1
,
+
3
x
or
−
x
3
seen (or unsimplified equivalents). The
3
2
indices must be processed.
4
32
3
(
)
A1
−
x
−
1
+
3
x
−
x
+
c
seen or unsimplified equivalent. Condone the lack of +c for this
3
3
2
mark.
10.7x−
1
is not a correct term but allow
10.6x−
&
1
.
−
−
x
8,
y
2
dM1
Substitutes
=
=
into their f(x) and proceeds to find c. It is dependent on the previous
method mark and condone slips in their rearrangement to find c.
32
3
4
10
(
)
A1
f ( )x =
1
3
or simplified equivalent. isw after a correct answer
−
x
−
+
x
−
x
3
+
3
2
3
&
32
3
4
10
10.6
4
Eg
3
3
1.5
3.3
& but do not accept rounded decimals for
−
+
x
−
x
3
+
or
−
+
x
−
x
3
+
3
x
2
3
x
the coefficients.
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