Mathematics · May / June 2023 · Paper 11 · Question 3
YMA01
As printed in the paper
Show the answer and mark scheme
3(a)[3]
a =
3
b = ±
2
(
)
2
3
x
2
+
12
x
+
13
=
3
x
+
2
+
1
or
=
3,
=
2,
=
1
a
b
c
3(b)[3]
Correct U shape with
y
minimum in second quadrant
13
Intercept 13 on yaxis.
Vertex at (
)
−
2,1
x
Notes:
(a)
B1: Correct value for a stated or shown by working.
4
12
. May be implied by e.g. (
M1: Obtains b = ± 2. Allow unsimplified e.g.
b = ±
,
±
3
x ±
2
6
A1: Fully correct expression or correct values.
2
b
b
2
Note that there are various methods e.g.
3
12
13
ax
2
+
bx
+
c
=
a x
+
+ −
c
x
2
+
x
+
2
4
a
a
or (
)
2
+
+
=
2
+
2
+
2
+
=
3, 2
=
12,
2
+
=
13
,
=
...
a x
b
c
ax
abx
ab
c
a
ab
ab
c
b c
(b)
There must be a sketch to score marks in (b)
Labelling on the sketch takes precedence
Treat part (b) as Hence, or otherwise, i.e. part (a) may be incorrect but full marks are available in
part (b) for a correct sketch of
= 3
+12 +13
y
x
2
x
B1: Correct U shape with minimum point in the second quadrant but not on the xaxis. Do not allow a
clear V shape.
B1: Correct y intercept labelled or stated. Allow as just 13 or (0, 13) or (13, 0) as long as it is in the
correct position. If stated away from the sketch it must be as (0, 13) and correspond to the sketch.
Their curve must at least touch at (0, 13). Any other intercepts can be ignored.
B1ft: Correct vertex labelled in some way, or follow through their b and c i.e. x = −b and y = c. Must be
a turning point but could be a maximum or a minimum. Allow the labelling as shown or as x =.., y = …or
as the ordinates shown on the axes. It must correspond to the sketch. If stated away from the sketch it
must be correct or correct follow through and correspond to the sketch.
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