Mathematics · Oct / Nov 2025 · Paper 31 · Question 4
YMA01
As printed in the paper
The question as text
4. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
4(a)[3]
−
3
α
=
tan
1
=
...
3
π
(
)
f( )
x
=
12 sin 2
x
−
3
(b)(i)
Minimum value
(ii)
π
5
−
=
=
π
sin 6
x
1
x
3
36
(
)13
A1:
T =
(a)
B1:
12 oee
−
3
M1:
Attempts to find
α
=
±
=
or
or
tan
1
...
3
or
π
(
)
A1:
=
−
(or exact equivalent). Must give the expression but
f( )
x
12 sin 2
x
3
accept if given in (b), not just the values for R and , but full marks can be
scored in subsequent parts from the correct values if the expression is not
explicitly stated.
4(b)[3]
(i)
B1:
3 or exact equivalent. No need to simplify. If multiple answers are given
they must clearly identify this as the minimum value to score the mark.
(ii)
π
M1:
Sets their sin 6
−
=
and attempts to find a value for x. Follow through
x
1
3
on f(3x) for their f(x).
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