Mathematics · Oct / Nov 2021 · Paper 21 · Question 6
YMA01
As printed in the paper
Show the answer and mark scheme
6(i)(a)[2]
x
±
5
+
y
±
6
.....
=
0
Centre (
5,6
)
−
(
)
(
)
k + ±
5
2
+ ±
6
2
>
0
6(i)(b)[2]
Sets
k > −
61
−+
2
8 10
+ −
( 14)
=
Centre
,
...
; radius
2
2
6(ii)[4]
1
(
)
2
(
)
2
−−
2
8
+
10
−−
( 14)
=
...
2
Centre is (
)
3, 2
−
; radius is 13
(
)
2
(
)
2
2
(
)
2
⇒
C
2 :
x
−
3
+
y
+
2
=
13
⇒
p
−
3
+
4
=
169
⇒
p
=
...
(
)
2
(
)
2
Or
P
X
=
r
⇒
p
−
3
+
0
−
(
−
2
)
=
169
⇒
p
=
.
.
.
p =
3
+
165
only
(i) (a)
M1: Attempts to complete the square on both x and y or states the centre as (
)
±
5, 6
±
For completing the square look for (
) (
2
)
2
x
±
5
,
y
±
6
.....
=
...
Centre (
)
A1:
−
5,6
This written down can score M1 A1
Allow written as separate coordinates ie.
x
= −
5,
y
=
6
(i)(b)
(
)
(
)
(
)
(
k + ±
5
2
+ ±
6
2
>
0
. Follow through on their (
5,6
)
k + ±
5
2
+ ±
M1:
−
. Allow
They must have an inequality for this mark.
A1:
k > −
61
but allow
k
…
−
61
(ii)
C using a correct method. (If only the
M1: Attempts centre and radius (or radius squared) of
2
diameter is found it is M0)
NB the attempt at the radius may arise from an attempt at QX or RX where X is the centre.
2
2
2
Alt 6 (ii) Uses either
PQ
+
PR
=
RQ
or grad PQ ∈grad PR = −1
Correct equation. E.g.
2
2
(
p
2
)
2
10
(
p
8
)
2
14
(
2
8
)
2
(
10 14
)
2
+
+
+
−
+
= −−
+
+
−
10
14
Alternatively
×
= −
1
2
8
p
+
p
−
p
2
−
6
p
−
156
=
0
Correct method to set up and solve 3TQ. FYI
p =
3
+
165
only
M1: Attempts
2
2
2
either
PQ
+
PR
=
QR
to set up an equation in p.
or grad PR ∈grad PQ = −1 to set up an equation in p
Expect to see a correct attempt at the lengths or the gradients but condone slips.
A1:
Correct equation which may be unsimplified. See scheme
dM1: Attempts to set up and solve a 3TQ resulting in a value for p.
3
+
165
A1:
ONLY
Make a free account to save your answers and see your weak topics and ask the AI why a wrong answer is wrong.