Mathematics · May / June 2021 · Paper 11 · Question 9
YMA01
As printed in the paper
The question as text
9. y l O x Figure 4 Figure 4 shows a sketch of the curve with equation y = tan x –2π x 2π The line l, shown in Figure 4, is an asymptote to y = tan x
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
9(a)[1]
3
π
x
=
oe
2
(b)(i)
y = 1
(ii)
5 (solutions)
Number of solutions are the number of points of intersections between the
graphs
9(b)[4]
3
π
x
=
oe
2
(b)(i)
y = 1
(ii)
5 (solutions)
Number of solutions are the number of points of intersections between the
graphs
(i)
40
(Number of solutions)
=
(ii)
(Number of solutions)
=
14
(a)
3
π
B1
x
=
oe and no others. Do not accept in degrees. It may be labelled on the graph, but it
2
3
π
must be an equation. If multiple answers are given then
x
=
oe must be identified (eg
2
may be circled)
(b)(i)
acceptable curvature – do not penalise candidates unless it is clear that a minimum point was
intended.
Correct shape and position for both branches with an asymptote in the correct position and
B1
labelled as
y = or stated in their work. Again, do not penalise the sketch unless it is clear
1
that turning points are intended. The asymptote line/dashed line does not need to be drawn
on the sketch.
(ii)
B1
5 only
B1
Number of solutions are the number of points of intersections between the graphs. (Do not
allow if they mention where they cross the xaxis).
(c)
(i)
B1ft
40
Follow through from their sketch
(eg number of intersections in first quadrant 20
×
)
(ii)
B1
14
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with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
9(c)[2]
(i)
40
(Number of solutions)
=
(ii)
(Number of solutions)
=
14
(a)
3
π
B1
x
=
oe and no others. Do not accept in degrees. It may be labelled on the graph, but it
2
3
π
must be an equation. If multiple answers are given then
x
=
oe must be identified (eg
2
may be circled)
(b)(i)
acceptable curvature – do not penalise candidates unless it is clear that a minimum point was
intended.
Correct shape and position for both branches with an asymptote in the correct position and
B1
labelled as
y = or stated in their work. Again, do not penalise the sketch unless it is clear
1
that turning points are intended. The asymptote line/dashed line does not need to be drawn
on the sketch.
(ii)
B1
5 only
B1
Number of solutions are the number of points of intersections between the graphs. (Do not
allow if they mention where they cross the xaxis).
(c)
(i)
B1ft
40
Follow through from their sketch
(eg number of intersections in first quadrant 20
×
)
(ii)
B1
14
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
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