Mathematics · Oct / Nov 2021 · Paper 11 · Question 4
YMA01
As printed in the paper
The question as text
4. y x O R Q Figure 2 Figure 2 shows a sketch of the curve with equation y = f(x), where f(x) = cos 2x o 0 x k The point Q and the point R(k, 0) lie on the curve and are shown in Figure 2.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
4(a)[3]
(
)
90, 1
−
(ii)
225
One of 1
−<
p
<
0
p =
1
,
Both 1
−<
p
<
0
p =
1
,
(a) (i)
One coordinate correct in the correct position. E.g (
)
B1
180, 1
−
°and condone for 180
x =
90
y = −. Condone
1
x =
90
Award for
or
2 for 90
Fully correct (
)
90, 1
−
B1
with or without brackets.
° and condone for 180
x =
90
x =
90
Award for
and
y = −. Condone
1
2 for 90
π
Special Case: If they give (
)
rather than (
)
−
1, 90
or
−
1, 2
90, 1
−
allow B1B0
but e.g. (
)
−
1, 180
scores B0B0 (2 errors)
Special case: If the 90 and −1 are clearly indicated on the axes for Q on the sketch,
score B1B0
(a)(ii)
B1 225 Condone 225 .° Also allow (225, 0) or (225°, 0) or 225 or 225° marked at R on the
diagram but if there is any ambiguity, the body of the script takes precedence.
For candidates who use radians in part (a), penalise this once on the first occurrence so
e.g.
π
(a)(ii) 5
π scores B1B0 B1
, 1
−
(a)(i)
2
4
π
(a)(ii) 5
π scores B0B0 B1 (2 errors)
(a)(i)
−
1, 2
4
(b)
M1
One of the ''correct'' pair, but ft on “−1” from (a).
For example if they believe that (a)(i) is (
)
180, 2
−
M1 can be awarded for either
2
p
0
p =
2
−<
<
or
Condone the use of y rather than p for this method mark e.g. condone 1
−<
y
<
0
1
y =
A1
Fully correct in terms of p
A significant number of candidates are writing their answers within the question so be
sure to check answers appearing there.
4(b)[2]
One of 1
−<
p
<
0
p =
1
,
Both 1
−<
p
<
0
p =
1
,
(a) (i)
One coordinate correct in the correct position. E.g (
)
B1
180, 1
−
°and condone for 180
x =
90
y = −. Condone
1
x =
90
Award for
or
2 for 90
Fully correct (
)
90, 1
−
B1
with or without brackets.
° and condone for 180
x =
90
x =
90
Award for
and
y = −. Condone
1
2 for 90
π
Special Case: If they give (
)
rather than (
)
−
1, 90
or
−
1, 2
90, 1
−
allow B1B0
but e.g. (
)
−
1, 180
scores B0B0 (2 errors)
Special case: If the 90 and −1 are clearly indicated on the axes for Q on the sketch,
score B1B0
(a)(ii)
B1 225 Condone 225 .° Also allow (225, 0) or (225°, 0) or 225 or 225° marked at R on the
diagram but if there is any ambiguity, the body of the script takes precedence.
For candidates who use radians in part (a), penalise this once on the first occurrence so
e.g.
π
(a)(ii) 5
π scores B1B0 B1
, 1
−
(a)(i)
2
4
π
(a)(ii) 5
π scores B0B0 B1 (2 errors)
(a)(i)
−
1, 2
4
(b)
M1
One of the ''correct'' pair, but ft on “−1” from (a).
For example if they believe that (a)(i) is (
)
180, 2
−
M1 can be awarded for either
2
p
0
p =
2
−<
<
or
Condone the use of y rather than p for this method mark e.g. condone 1
−<
y
<
0
1
y =
A1
Fully correct in terms of p
A significant number of candidates are writing their answers within the question so be
sure to check answers appearing there.
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