Mathematics · Oct / Nov 2023 · Paper 11 · Question 11
YMA01
As printed in the paper
The question as text
11. y (–1, 28) C l R O x P Figure 5 Figure 5 shows part of the curve C with equation y = f(x) where 2 x x x f ( ) 2 12 14
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
11(a)[3]
2(
...)
2
x±
...(
x ±
3) ...
2
2(
x −
3)
2
−
4
11(b)[1]
(3,
−
4)
11(c)[3]
28
4 (
−−
=
= −
8)
m
−−
1 3
−
28
= −
8(
+
1)
y
x
y
= −
8
x
+
20
11(d)[3]
y
2
x
2
−
12
x
+
14
y
"2(
x −
3)
2
−
4"
)
y
" 8
−
x
+
20"
and
(or
y
2
x
2
−
12
x
+
14
y
−
8
x
+
20
y
0,
x
0
Note: answers may appear next to questions or on the diagram.
If there is a contradiction between the answer by the question/on the diagram and the main
body of the work then the answer in the main body of the work takes precedence.
(a)
2
B1:
a = which may be stated or seen in the expression
2
2(
x±
...)
.
12
...(
x ±
3) ...
2
...
±
M1:
may be implied by
b = ±. Accept unsimplified versions e.g.
3
x
4
2(
x −
3)
2
−
4
A1:
isw following a correct expression (e.g. if they proceed to state incorrect
values for a, b and/or c). If they just state the values then withhold this mark. Constants must
be integers.
SC110 2(
(slip writing missing the squared on the bracket)
x −
3)
−
4
(b)
B1ft:
(3,
−
4)
or e.g.
x
=
3,
y
= −. Condone invisible brackets. Follow through from their part (a)
4
so score for (
−
, )
b c
(c)
M1:
Attempts to find the gradient between their minimum point and ( 1, 28)
−
. Score for the
expression 28
" 4"
−−
or equivalent. They must be subtracting the correct way round. Do
−−
1 "3"
not condone sign slips for this mark. If a value appears with no method (nor implied using
their minimum point and ( 1, 28)
), then this mark cannot be scored (M0dM0A0)
−
May be part of the equation for l e.g. 28
−−
" 4"
−−
1 "3"
or 28
−−
" 4"
−−
1 "3"
=
=
−
28
+
1
+
4
−
3
y
x
y
x
dM1: Attempts to find the equation using their gradient. |It is dependent on the previous method
mark. Score for
−
28
= −
" 8"(
+
1)
or
+
4
= −
" 8"(
−
3)
but condone one sign slip
y
x
y
x
substituting in the coordinates for x and y.
If they use y
=
mx
+ they must proceed as far as
c
...
.
c =
A1:
= −
8
+
20
y
x
or <> Ignore use of and/or or equivalent notation for
(d)
Allow consistent use of either
this question.
Note that
2
x
2
−
12
x
+
14
may be expressed as
2(
x −
3)
2
−
4
Allow the use of f(x) instead of y but the use of R instead of y is not acceptable.
B1ft: One of
" 8
−
+
20"
follow through on their part (c)
y
x
2
2
−
12
+
14
"2"(
x−
"3")
2
−
"4"
y
x
x
follow through on their part (b) so
2
2
−
12
+
14
<
" 8
−
+
20"
May be part of an inconsistent set of inequalities e.g.
x
x
y
x
B1ft: Both
follow through on their part (c)
y
" 8
−
x
+
20"
2
2
y
2
x
−
12
x
+
14
follow through on their part (b) so
"2"(
x−
"3")
−
"4"
2
2
12
14
" 8
20"
May also be seen as
x
−
x
+
y
−
x
+
y
2
x
2
−
12
x
+
14
B1cso:
y
−
8
x
+
20
y
0,
x
0
Do not isw for this mark.
Also accept
2
x
2
−
12
x
+
14
y
−
8
x
+
20
y
0,
x
0
5
Accept inequalities
0
provided
x
p
p
2
0
provided
20
y
q
q
Note: The equations may be written in alternative forms e.g. 8
+
20
which is also acceptable
x
y
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