Mathematics · May / June 2023 · Paper 11 · Question 2
YMA01
As printed in the paper
The question as text
2. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A rectangular sports pitch has length x metres and width y metres, where x > y Given that the perimeter of the pitch is 350 m,
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
2(a)[1]
2
2
350
x
+
y
=
2(b)[1]
E.g.
xy
=
7350,
x
×
y
=
7350
2(c)[4]
(175
)
7350
or (175
)
7350
x
−
x
=
−
y y
=
(
)(
)
175
73
50
0
7
0
105
0
..
.
E.g.
x
2
−
x
+
=
x
−
x
−
=
x
=
x = 70 or 105
(
>
)
=
105,
=
70
x
y
x
y
Notes:
Ignore labelling and mark all parts together.
Ignore any units given whether correct or incorrect.
(a)
B1: Correct equation. Accept any correct equation e.g. (
)
2
x
+
y
=
350,
x
+
y
=
175
(b)
7350
B1: Correct equation. Accept any correct equation e.g.
=
y
x
(c)
M1: Substitutes for x or y into either of their equations to produce a 2 or 3 term quadratic equation in
one variable. Note that terms do not need to be collected for this mark so e.g. (175
−
)
=
x
x
(175
−
y y
)
=
7350
oe is acceptable for this mark.
Condone slips when substituting if the intention is clear e.g. substituting for 2x rather than x:
x
(350
−
2 )
x
=
7350
7350
(Note, if substituting
=
into 2
x
+
2
y
=
350
they will need to multiply through by y to score
x
y
this mark. Condone slips but must produce a 2 or 3 term quadratic equation.)
dM1: Depends on the first method mark. Solves their 3 term quadratic equation, any suitable
means such as formula or by calculator (may be implied by correct values for their quadratic).
A1: Correct simplified roots of the quadratic. Do not be concerned about which is x and y for this
mark so just look for the values 70 and 105. It is possible that candidates may only select the larger
value for x (105) or the smaller value for y (70) but if both roots are found they must both be correct.
A1: Both x and y correct and correctly assigned and all previous marks scored.
Special Case:
Candidates who use Trial and Improvement in part (c) or guess the correct answers with no quadratic
formed allow a special case of M1M1A0A0. If the values are the wrong way round or both sets of
answers are offered then score special case of M1M0A0A0.
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