Mathematics · Oct / Nov 2024 · Paper 11 · Question 7
YMA01
As printed in the paper
The question as text
7. y 5 C1 O Q x P –5 Figure 3 Figure 3 shows a plot of part of the curve C1 with equation y = –4 cos x where x is measured in radians. Points P and Q lie on the curve and are shown in Figure 3.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
7(a)[3]
3
π
Q
=
,0
(ii)
2
(b) (i)
k =
7
(ii) (
)
2 , 3
π
One root as there is one point of intersection
NB: Watch for the answers being stated next to the question rather than in the answer space.
(a)(i) Allow all marks in (a) if P and Q are mislabelled but the coordinates are correct.
B1: For one of (
)
Condone/allow one of (
)
−
2 , 4
π
−
−
360 , 4
°−
Condone for this B mark if
the coordinates are reversed.
B1: For both of (
)
−
2 , 4
π
−
(in correct order).
(a)(ii)
) 3
π
B1: (
Q
=
,0
2
(b)(i)
B1: For
k =
7
(b)(ii)
M1: For one of (
)
2 ,3
π
or follow through on the negative of their x coordinate of P or
Condone/allow one of (
360 ,3
)
and condone for the M if the
their
−
4
+
thei k
r
°
coordinates are given in the wrong order.
A1: (
)
Allow (
)
2 ,3
π
360 ,3
°
if B marks in (a) were lost due solely due to working in
degrees.
(c)
M1: Draws a line with negative gradient passing through (0, 5) and cutting the graph at least
once, with a consistent number of solutions for their sketch stated.
A1: Correct line drawn (intersecting at graph on the x axis) with correct deduction (one
root) and reason (intersects only once).
Note use of degrees only will score a maximum of B1B0 B0 B1 M1A1 M1A0, though if the
10
π is converted to degrees resulting in a “correct” graph, send to review for
consideration.
States or implies that gradient of tangent is 24
7(b)[3]
3
π
Q
=
,0
(ii)
2
(b) (i)
k =
7
(ii) (
)
2 , 3
π
One root as there is one point of intersection
NB: Watch for the answers being stated next to the question rather than in the answer space.
(a)(i) Allow all marks in (a) if P and Q are mislabelled but the coordinates are correct.
B1: For one of (
)
Condone/allow one of (
)
−
2 , 4
π
−
−
360 , 4
°−
Condone for this B mark if
the coordinates are reversed.
B1: For both of (
)
−
2 , 4
π
−
(in correct order).
(a)(ii)
) 3
π
B1: (
Q
=
,0
2
(b)(i)
B1: For
k =
7
(b)(ii)
M1: For one of (
)
2 ,3
π
or follow through on the negative of their x coordinate of P or
Condone/allow one of (
360 ,3
)
and condone for the M if the
their
−
4
+
thei k
r
°
coordinates are given in the wrong order.
A1: (
)
Allow (
)
2 ,3
π
360 ,3
°
if B marks in (a) were lost due solely due to working in
degrees.
(c)
M1: Draws a line with negative gradient passing through (0, 5) and cutting the graph at least
once, with a consistent number of solutions for their sketch stated.
A1: Correct line drawn (intersecting at graph on the x axis) with correct deduction (one
root) and reason (intersects only once).
Note use of degrees only will score a maximum of B1B0 B0 B1 M1A1 M1A0, though if the
10
π is converted to degrees resulting in a “correct” graph, send to review for
consideration.
States or implies that gradient of tangent is 24
7(c)[2]
One root as there is one point of intersection
NB: Watch for the answers being stated next to the question rather than in the answer space.
(a)(i) Allow all marks in (a) if P and Q are mislabelled but the coordinates are correct.
B1: For one of (
)
Condone/allow one of (
)
−
2 , 4
π
−
−
360 , 4
°−
Condone for this B mark if
the coordinates are reversed.
B1: For both of (
)
−
2 , 4
π
−
(in correct order).
(a)(ii)
) 3
π
B1: (
Q
=
,0
2
(b)(i)
B1: For
k =
7
(b)(ii)
M1: For one of (
)
2 ,3
π
or follow through on the negative of their x coordinate of P or
Condone/allow one of (
360 ,3
)
and condone for the M if the
their
−
4
+
thei k
r
°
coordinates are given in the wrong order.
A1: (
)
Allow (
)
2 ,3
π
360 ,3
°
if B marks in (a) were lost due solely due to working in
degrees.
(c)
M1: Draws a line with negative gradient passing through (0, 5) and cutting the graph at least
once, with a consistent number of solutions for their sketch stated.
A1: Correct line drawn (intersecting at graph on the x axis) with correct deduction (one
root) and reason (intersects only once).
Note use of degrees only will score a maximum of B1B0 B0 B1 M1A1 M1A0, though if the
10
π is converted to degrees resulting in a “correct” graph, send to review for
consideration.
States or implies that gradient of tangent is 24
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