Mathematics · Oct / Nov 2025 · Paper 11 · Question 9
YMA01
As printed in the paper
The question as text
9. y P 4 2 – 2 O x –2 –4 Figure 3 Figure 3 shows a sketch of part of the graph of the trigonometric function with equation y = f(x)
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
9(a)[2]
π
or equivalent such as (
)
(
= −
)
=
+
f( )
x
4sin
x
f( )
x
4cos
x
2
9(b)(i)[2]
5
π
, 4
3
9(b)(ii)[2]
π
3
,
−
2
2
Notes
Do not allow the use of degrees in this question.
If there is more than one answer for any part, score the final attempt.
Remember to check for answers written in the question.
(a)
M1: For any sine or cosine curve with an amplitude of 4 and a period of 2πand which passes
π
(
)
through the origin. E.g. (
)
(
)
= ±
±
f( )
x
= ±
4sin
±
x
,
f( )
x
4cos
x
2
Condone the use of θ for this mark and “f(x) =” (or “ ( )
f θ=”) is not required.
Do not allow ambiguous expressions e.g. (
)
(
)
= −
f( )
x
4f sin
x
Completely correct expression in terms of x e.g. (
)
= −
A1:
f( )
x
4sin
x
or equivalent such as
π
(
)
(
)
(
)
(
)
f( )
x
=
4cos
x
+
, f( )
x
=
4sin
x
+
π
, 4sin
−
x
2
“f(x) =” is not required.
(b)
Allow answers to be written as coordinates or as x = …, y = …
If more than one answer is given, mark their final answer.
Condone missing brackets e.g. 5
π
and condone punctuation other than a comma e.g. 5
, 4
3
The x coordinates must be written as single fractions but allow equivalents e.g. 10
π for 5
6
The y coordinate must be written as single number so do not allow 0 – 2 for −2
5
π
3
π
−
Do not allow coordinates the wrong way round e.g.
4, 3
or
2, 2
(b) (i)
π
5
B1:
One correct coordinate from
x
=
or y = 4
3
5
π
5
π
=
B1:
, 4
or
x
and y = 4
3
3
(b) (ii)
3
π
=
or y = −2
B1:
One correct coordinate from
x
2
π
3
π
3
−
=
and y = −2
B1:
,
2
or
x
2
2
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