Mathematics · May / June 2022 · Paper 11 · Question 4
YMA01
As printed in the paper
The question as text
4. y Q y = f(x) y = 1 O x P Figure 1 Figure 1 shows a sketch of a curve with equation y = f(x) The curve has a minimum at P(−1, 0) and a maximum at Q 3 2 2 , The line with equation y = 1 is the only asymptote to the curve. On separate diagrams sketch the curves with equation
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
4(i)[3]
Correct shape,
translated down.
Correct horizontal
asymptote labelled
x −
y=f( )
2
Correct maximum
and minimum points
labelled
4(ii)[3]
Correct shape,
reflected in y axis
Correct horizontal
asymptote labelled
Correct maximum
and minimum points
labelled.
Notes:
In both parts be tolerant with “pen slips” for the asymptotes. Judge the intent of the shape.
y
=
f(
x
−
2)
(i) There is no MR for sketching
. These marks are independent of each other
B1: Same shape as the original graph but translated vertically downwards.
Do not consider any coordinates here.
Look for a minimum to the left of the y axis and a maximum to the right
Be tolerant of the asymptote not being exactly at the same level at either end of the curve but withhold
the mark if it is intentionally different. Condone slight upturns at either end
B1: For y = −1 labelled as the horizontal asymptote. It must be below the x axis and the intention must be for
ends to be at the same height/level. The intention must be for the curve to be asymptotic here (at both ends)
B1: For the coordinates of the maximum and minimum points in the correct positions. E.g. 3 , 0
2
on the positive xaxis and (
)
−
1,
−
2
is in quadrant 3. Note that P and Q don't need to be seen, just their
coordinates. Coordinates may be given in the body of the script but must match with maximum and
minimum points marked in some way on the graph
y
= −
f( )
x
(ii) There is no MR for sketching
These marks are independent of each other
B1: For the correct shape, a reflection in the yaxis. The intention should be for the asymptotes to be at the
same level but be tolerant of slips. Look for the image Q’ a maximum being to the left of yaxis in
quadrant two and P’ a minimum on the positive x axis.
B1: For y = 1 labelled as the horizontal asymptote. It must be above the x axis and the intention must be for
ends to be at the same height/level. The curve must be asymptotic here (at both ends)
12
a x
(
2)
2
E.g.
−
+
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