Mathematics · Oct / Nov 2020 · Paper 11 · Question 4
YMA01
As printed in the paper
The question as text
4. Use algebra to solve the simultaneous equations y – 3x = 4 2 + y 2 + 6x – 4y = 4 x You must show all stages of your working. (7)
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
(
)
(
)
3
x
+
4
2
3
x
+
4
y
=
3
x
+
4
⇒
x
2
+
+
6
x
−
4
=
4
or
2
y
−
4
y
−
4
y
−
4
x
=
⇒
+
y
2
+
6
−
4
y
=
4
3
3
3
(
)
(
)
5
x
2
+
9
x −
2
0
or
=
5
y
2
−
13
y
−
46
=
0
(5
x
−
1)(
x
+
2)
=
0
⇒
x
=
...
or (5
y
−
23)(
y
+
2)
=
0
⇒
y
=
...
x
=
0.2,
x
= − or
2
y
=
4.6,
y
= −
2
y
−
4
Substitutes their x into their y = 3x + 4 / Substitutes their y into their
x
=
3
1
3
23
0.2 or
,
4.6 or 4
or
x
=
y
=
5
5
5
and
x
= −
2,
y
= −
2
Notes
M1 rearrange the linear equation to y =… or x =… and attempts to fully substitute into the second
equation.
M1 Collect terms together to produce a 2 or 3 term quadratic expression = 0. The ‘= 0’ may be
implied by later work. Condone slips in their rearrangement of the equation.
A1
Correct quadratic equation in x or y. Condone the absence of “
=
0
”
They may be multiples of the main scheme. Eg
10
x
2
+
18
x −
4
=
0
or
10
y
2
−
26
y
−
92
=
0
dM1 Attempt to factorise and solve or complete the square and solve or uses a correct quadratic
formula for a 3 term quadratic and obtains at least one value of x or y. (see general guidance for
solving a quadratic). If factorising then their seen factorised expression must equal their seen
3TQ quadratic expression. If they use the quadratic formula, we must see the values embedded
in a correct formula.
Dependent on both previous method marks.
They cannot just write down their calculator values for this mark
Guidance on use of calculators for factorising quadratics and how to score:
1
....
10
x
2
+
18
x
4
0
(
5
x
−
1)(
x
+
2)
=
0
⇒
x
=
, 2
−⇒
...
max score M1M1A1 dM0 B1M1 A0
⇒
−
=
⇒
5
1
....
⇒
10
x
2
+
18
x
−
4
=
0
⇒
(
x
−
1
)(
x
+
2)
=
0
⇒
x
=
, 2
−⇒
...
max score M1M1A1 dM0 B1M1 A0
5
5
1 , 2
+
x
=
−⇒
...
max score M1M1A1 dM0 B1M1 A0
...
⇒
10
x
2
18
x
−
4
=
0
⇒
5
B1
Correct answers for either both values of x or both values of y (possibly unsimplified) which can
only be scored if they have achieved a correct 3TQ.
M1 Substitute at least one value of x to find y or vice versa. This may be implied by their final
answers.
A1
Fully correct solution with all previous marks awarded such that
coordinate is clearly paired with the other y coordinate.
Condone recovery of invisible brackets.
Make a free account to save your answers and see your weak topics and ask the AI why a wrong answer is wrong.