Mathematics · Oct / Nov 2022 · Paper 31 · Question 8
YMA01
As printed in the paper
The question as text
8. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. π
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
8(a)[3]
15
tan
α=
8
α=
1.081
15
8(b)[4]
(i) Min f(x)
=
41
+ ×
2 "17
"
1
=
5
π
(
)
(ii) Occurs when
s
in
x
−
1
.0 1
8
=
1
x
−
1
.
0
8
1
=
x
=
..
.
2
x =
awrt 2.65
23
8(c)[1]
−
(or −4.6)
5
Awrt 1.33
8(d)[1]
Notes:
(a)
B1: For 17 only.
1
5
8
M1: Attempts an equation in α. Accept
or
. If using R accept
t n
a
α= ±
t n
a
α= ±
cos
α= ±
8
1
5
"17"
15
. Implied by a correct value for α
sin
α= ±
"17"
A1: Awrt 1.081. Must be in radians.
(b)(i)
15
M1: Attempts to apply the result from (a) to find the minimum. Allow for
41
±×
2 "their
R
"
A1: cao.
(ii)
π
M1: Attempts to solve
x
±
"
α
"
=
2
A1: cao
(c)
2
1
B1ft: Correct answer or follow through
×
their
−
5
and no other solutions.
5
(d)
B1ft: For awrt 1.33 or follow through
0.5×
their 2.65
and no other solutions.
c
os
2
θ
cos
2
θ
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