Mathematics · May / June 2022 · Paper 31 · Question 1
YMA01
As printed in the paper
The question as text
1. The curve C has equation 6 y = (3x – 2)
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[2]
d
y
6 3(3
2)
5
( 18(3
2) )
5
=
×
x
−
=
x
−
d
x
1(b)[4]
"18"(3
×−
1
2)
"5"
= −
18
3
1
−
18
→
18
1
1
1
"
"
y
−=
x
−
18
3
3
x
54
y
53
0
−
+
=
(a)
M1
Applies the chain rule to achieve a form of
A
(3
x −
2)
5
which may be unsimplified.
The index does not need to be processed for this mark.
Alternatively, multiplies out the brackets to achieve an expression of the form
Ax
6
+
Bx
5
+
Cx
4
+
Dx
3
+
Ex
2
+
Fx
+
G
(where all coefficients do not need to be simplified)
reduces the power by 1 on at least one of the terms. You will need to check this carefully to make sure it is
the relevant term where the power has decreased
eg
Bx
5
→
...
×
Bx
4
Condone slips in their expansion.
(The actual expansion is
64
−
576
x
+
2160
x
2
−
4320
x
3
+
4860
x
4
−
2916
x
5
+
729
x
6
)
d
y
=
18(3
x
−
2)
5
6 3(3
2)
5
A1
or unsimplified equivalent eg
×
x
−
but the index must be processed. If
d
x
they have multiplied out then accept
−
576
+
4320
x
−
12960
x
2
+
19440
x
3
−
14580
x
4
+
4374
Accept
1x for x
(b)
1
into their d
y
M1
Substitutes
x =
which must be of the form
A
(3
x −
2)
5
(or accept a
polynomial
3
d
x
of degree 5) and finds a value for d
y
d
x
M1
Finds the negative reciprocal of their gradient. May be implied by the equation of their line.
cannot be scored for setting d
y
x =
0
, solving to find x and then taking the negative
reciprocal of this.
d
1
1
dM1
Attempts to find the equation of the normal. Look for
y
−=
1
"
"
x
−
(must be a changed
18
3
gradient from their tangent gradient). It is dependent on the first method mark. If they use
53
y
=
mx
+
c
they must proceed as far as
c
=
...
=
"
"
54
A1
3
x
−
54
y
+
53
=
0
or any integer multiple of this with all terms on one side of the equation eg
−
6
x
+
108
y
−
106
=
0
You must see the = 0
isw after a correct answer is seen. Eg if they proceed to state values for a, b and c which contradict
their equation then take their equation as their final answer.
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