Mathematics · Oct / Nov 2022 · Paper 11 · Question 7
YMA01
As printed in the paper
The question as text
7. y (2, 6) (–4, 6) (–1, 6) (3, 6) O x y = f(x) Figure 1 Figure 1 shows the curve with equation y = f(x). The points P(–4, 6), Q(–1, 6), R(2, 6) and S(3, 6) lie on the curve.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
7(a)[3]
−<
1
x
<
2
x
<−
4,
x
>
3
7(b)[1]
(
x =
) 1.5
(c)(i)
( 3, 6)
−
( 2, 6)
−
(4, 6)
(1, 6)
O
−
3
„
x
„
−
2
(ii)
(a)
Ignore any references to OR or AND (or equivalent use of set notation) between
−<
1
<
2
,
x >
3
,
x <−
4
x
M1
Requires one end of the inside region between 1
− and 2. Score for
x >− or
1
x <
2
,
condoning use of „
… Must be in terms of x
A1
−<
1
<
2
or any equivalent notation such as 1
−<
∩
<
2
, ( 1, 2)
and also score for
x
x
x
−
2
>
x
>−. Do not allow just two separate inequalities for this mark without AND or
1
equivalent.
B1
x >
3
,
x <−
4
(b)
1.5 or 3
B1
2 Condone (1.5, 6) or
x
=
1.5,
y
=
6
only (the ycoordinate must be correct if
stated)
(c)(i) Check the figure at the start of the question. If there is a contradiction, then the sketch
with labelled coordinates in the main body of working takes precedence. There must
be a sketch to score any marks.
B1
Sketch reflected in the yaxis with the intention to have the higher maximum turning point in
quadrant 1 and the lower maximum turning point in quadrant 2. Do not be concerned which
side of the yaxis the minimum turning point is located.
B1
Either two correct pairs of coordinates or all x coordinates correct or all y coordinates
correct. Do not be concerned with the relative locations of the coordinates in relation to each
other. The points must be in the correct quadrants, but may be stated separately. Do not be
concerned with the labelling of P, Q, R and S and the associated coordinates if they are
stated separately.
B1
All four correct coordinates (Do not penalise poor notation and may be listed as
x
=
...,
y
=
...
) Do not be concerned with the relative locations of the coordinates in relation
to each other. The points must be in the correct quadrants, but may be stated separately. Do
not be concerned with the labelling of P, Q, R and S and the associated coordinates if they
are stated separately.
(ii)
B1
−
3
„
x
„
−
2
only or any equivalent notation such as 3
−
„
x
∩
x
„
−
2
,
−
3
„
AND
„
−
2
. [ 3, 2]
−
but do not accept use of OR or ∪ if set notation is used.
x
x
Do not accept ( 3,
−
−
2)
or 3
−<<−
<
x
2
Must be in terms of x
There may be several inequalities. Mark what appears to be their final answer.
7(c)[4]
−<
1
x
<
2
x
<−
4,
x
>
3
(
x =
) 1.5
(c)(i)
( 3, 6)
−
( 2, 6)
−
(4, 6)
(1, 6)
O
−
3
„
x
„
−
2
(ii)
(a)
Ignore any references to OR or AND (or equivalent use of set notation) between
−<
1
<
2
,
x >
3
,
x <−
4
x
M1
Requires one end of the inside region between 1
− and 2. Score for
x >− or
1
x <
2
,
condoning use of „
… Must be in terms of x
A1
−<
1
<
2
or any equivalent notation such as 1
−<
∩
<
2
, ( 1, 2)
and also score for
x
x
x
−
2
>
x
>−. Do not allow just two separate inequalities for this mark without AND or
1
equivalent.
B1
x >
3
,
x <−
4
(b)
1.5 or 3
B1
2 Condone (1.5, 6) or
x
=
1.5,
y
=
6
only (the ycoordinate must be correct if
stated)
(c)(i) Check the figure at the start of the question. If there is a contradiction, then the sketch
with labelled coordinates in the main body of working takes precedence. There must
be a sketch to score any marks.
B1
Sketch reflected in the yaxis with the intention to have the higher maximum turning point in
quadrant 1 and the lower maximum turning point in quadrant 2. Do not be concerned which
side of the yaxis the minimum turning point is located.
B1
Either two correct pairs of coordinates or all x coordinates correct or all y coordinates
correct. Do not be concerned with the relative locations of the coordinates in relation to each
other. The points must be in the correct quadrants, but may be stated separately. Do not be
concerned with the labelling of P, Q, R and S and the associated coordinates if they are
stated separately.
B1
All four correct coordinates (Do not penalise poor notation and may be listed as
x
=
...,
y
=
...
) Do not be concerned with the relative locations of the coordinates in relation
to each other. The points must be in the correct quadrants, but may be stated separately. Do
not be concerned with the labelling of P, Q, R and S and the associated coordinates if they
are stated separately.
(ii)
B1
−
3
„
x
„
−
2
only or any equivalent notation such as 3
−
„
x
∩
x
„
−
2
,
−
3
„
AND
„
−
2
. [ 3, 2]
−
but do not accept use of OR or ∪ if set notation is used.
x
x
Do not accept ( 3,
−
−
2)
or 3
−<<−
<
x
2
Must be in terms of x
There may be several inequalities. Mark what appears to be their final answer.
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