Mathematics · Oct / Nov 2021 · Paper 11 · Question 3
YMA01
As printed in the paper
Show the answer and mark scheme
3(i)[3]
3
3
(
)
x >
4
⇒
3
x
>
4
x
2
⇒
x
4
x
−
3
<
0
⇒
0, 4
3
0
<
x
<
4
3(ii)[3]
y
−
0
=
3(
x
+
5)
E.g.
y
<
2
x
2
−
50,
y
>
3
x
+
''15''
y
<
2
x
2
−
50,
y
>
3
x
+
15,
x
< −
5
E.g.
(i)
For the two critical values 0 and 3
B1
4
M1
Chooses the inside region for their critical values
3
3
0
<
x
<
x >
0
x <
A1
Award for exact equivalents such as
and
or
4
4
3
x x
:
>
0
∩
x
<
4
as 3
3
x >
0
x >
4
x <
(Note they may deduce that
then solve to find
which combined
4
3
gives
0
<
x
<
)
4
..........................................................................................................................................................
B1: Sketches BOTH graphs. May only see right had
branch of
hyperbola.
y =
4
M1: Chooses the inside region between 0 and
their solution to 3
4
x =
O
3
A1:
0
<
x
<
4
..........................................................................................................................................................
Special Case which is very common:
3
B1: States
x <
only
4
..........................................................................................................................................................
(ii)
B1
Correct equation for l E.g.
y
−
0
=
3(
x
+
5)
. This may be implied by e.g. sight of y >
3x + 15 or e.g. y = 3x + k and k = 15
2
M1
Two of
y
<
2
x
−
50,
y
>
3
x
+
"15",
x
<
a
where
−„
5
a
„
6.5
Follow through their straight line provided it has a gradient of 3 with a numerical “15”.
Also allow two of
y
„
2
x
2
−
50,
y
…
3
x
+
15,
x
„
a
where
−
5
„
a
„
6.5
3
x
+
15
<
y
<
2
x
2
−
50 or 3
x
+
15
„
y
„
2
x
2
−
50
Also allow
as 2 inequalities.
2
Do not allow inequalities in terms of R e.g.
R
<
2
x
−
50,
R
>
3
x
+
15.
This scores
M0.
A1
Fully defines region. E.g.
y
<
2
x
2
−
50,
y
>
3
x
+
15,
x
<
a
where 5
−„
a
„
6.5
y
„
2
x
2
−
50,
y
…
3
x
+
15,
x
„
a
where 5
−„
a
„
6.5
Also allow
If set notation is used, then they must use “∩” between any of their inequalities rather
than “∪”.
Condone attempts as long as the intention is clear.
E.g.
{
} {
x y
,
∈
:
y
<
2
x
−
50
∩
y
>
3
x
+
15
∩
x
<
a
,
x y
,
∈
:
y
<
2
x
−
50,
y
>
3
x
2
2
are acceptable.
Note regarding consistency for the A1 if −5 is used:
y
<
2
x
2
−
50,
y
>
3
x
+
15
must go with x < −5
2
y
„
2
x
−
50,
y
…
3
x
+
15
must go with x „ −5
If
−
5
<
a
„
6.5
is used then x
<
a
or x
„
a
is acceptable.
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