Mathematics · Oct / Nov 2020 · Paper 11 · Question 5
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5(i)[6]
B1 Horizontal translation ←
B1 Maximum at origin
(0, 0)
(−7, 0)
B1 ( 7,0)
−
(b)
B1 Reflection in yaxis
B1 Touches at ( 2,0)
−
and passes
(−2, 0)
(5, 0)
through (5,0)
−3
B1 Passes through (0, 3)
−
(ii)a
( )
x
0
y
k
cos
3
=
⇒
=
π
=
6
3
k
=
3
⇒
k
=
2
2
(b)
π
) 4
π
(
)
(
p
=
or
q
=
3
3
π
) 4
π
(
)
(
p
=
and
q
=
3
3
Notes
(i)(a)
B1
Horizontal translation ←
The negative cubic should appear in quadrants 2, 3 and 4 only and the local maximum should be
on the x axis where
x ≤
0
. The local minimum must be in the third quadrant. Condone any part
of the graph which may look linear but withhold this mark if the graph curves back on itself.
B1 Local maximum at the origin (does not need to be labelled)
B1
Passes through (−7, 0). Allow just the x value instead of both coordinates marked on the axis or
written in the text and condone a slip of x and y the wrong way round as long as the sketch
would give the correct coordinates. May be listed but cannot be awarded without a sketch.
Condone lack of brackets. Do not allow 7 instead of 7
− but condone transcription errors if the
correct coordinate is stated in the text.
(b)
B1
Reflection in the yaxis. A positive cubic should be drawn appearing in quadrants 1, 3 and 4
only. The local maximum point should be on the x axis where
x ≤
0
and the local minimum
point should be in quadrant 4. Do not accept the local minimum on the yaxis.
B1 Touches at (−2, 0) and passes through (5, 0). Allow just the x values instead of both coordinates
marked on the axis or written in the text and condone a slip of x and y the wrong way round as
long as the sketch would give the correct coordinates. May be listed but cannot be awarded
without a sketch. Condone lack of brackets. Do not allow 2 instead of 2
− or 5
− instead of 5 but
condone transcription errors if the correct coordinates are stated in the text.
B1 Passes through (0, −3). Allow just 3
− instead of both coordinates marked on the axis or written
in the text and condone a slip of x and y the wrong way round as long as the sketch would give
the correct coordinates. May be listed but cannot be awarded without a sketch. Condone lack of
brackets.
Do not allow 3 instead of 3
− but condone transcription errors if the correct coordinate is stated
in the text.
(ii)(a)
B1
k =
2
π
) 4
π
(
)
(
B1
p
=
or
q
=
Award for sight of either of these values or equivalent. Ignore
3
3
labelling.
Allow awrt 1.05 or awrt 4.19 for this mark and allow in degrees (60 or 240).
π
) 4
π
π
4
π
(
)
(
B1
p
=
and
q
=
ignore labelling and condone
0,
,
0,
. Allow exact
3
3
3
3
equivalents.
5(ii)[3]
B1 Horizontal translation ←
B1 Maximum at origin
(0, 0)
(−7, 0)
B1 ( 7,0)
−
(b)
B1 Reflection in yaxis
B1 Touches at ( 2,0)
−
and passes
(−2, 0)
(5, 0)
through (5,0)
−3
B1 Passes through (0, 3)
−
(ii)a
( )
x
0
y
k
cos
3
=
⇒
=
π
=
6
3
k
=
3
⇒
k
=
2
2
(b)
π
) 4
π
(
)
(
p
=
or
q
=
3
3
π
) 4
π
(
)
(
p
=
and
q
=
3
3
Notes
(i)(a)
B1
Horizontal translation ←
The negative cubic should appear in quadrants 2, 3 and 4 only and the local maximum should be
on the x axis where
x ≤
0
. The local minimum must be in the third quadrant. Condone any part
of the graph which may look linear but withhold this mark if the graph curves back on itself.
B1 Local maximum at the origin (does not need to be labelled)
B1
Passes through (−7, 0). Allow just the x value instead of both coordinates marked on the axis or
written in the text and condone a slip of x and y the wrong way round as long as the sketch
would give the correct coordinates. May be listed but cannot be awarded without a sketch.
Condone lack of brackets. Do not allow 7 instead of 7
− but condone transcription errors if the
correct coordinate is stated in the text.
(b)
B1
Reflection in the yaxis. A positive cubic should be drawn appearing in quadrants 1, 3 and 4
only. The local maximum point should be on the x axis where
x ≤
0
and the local minimum
point should be in quadrant 4. Do not accept the local minimum on the yaxis.
B1 Touches at (−2, 0) and passes through (5, 0). Allow just the x values instead of both coordinates
marked on the axis or written in the text and condone a slip of x and y the wrong way round as
long as the sketch would give the correct coordinates. May be listed but cannot be awarded
without a sketch. Condone lack of brackets. Do not allow 2 instead of 2
− or 5
− instead of 5 but
condone transcription errors if the correct coordinates are stated in the text.
B1 Passes through (0, −3). Allow just 3
− instead of both coordinates marked on the axis or written
in the text and condone a slip of x and y the wrong way round as long as the sketch would give
the correct coordinates. May be listed but cannot be awarded without a sketch. Condone lack of
brackets.
Do not allow 3 instead of 3
− but condone transcription errors if the correct coordinate is stated
in the text.
(ii)(a)
B1
k =
2
π
) 4
π
(
)
(
B1
p
=
or
q
=
Award for sight of either of these values or equivalent. Ignore
3
3
labelling.
Allow awrt 1.05 or awrt 4.19 for this mark and allow in degrees (60 or 240).
π
) 4
π
π
4
π
(
)
(
B1
p
=
and
q
=
ignore labelling and condone
0,
,
0,
. Allow exact
3
3
3
3
equivalents.
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