Mathematics · Oct / Nov 2022 · Paper 11 · Question 6

k

, 0

( 4,0)

−

2

(

0,

−

16k

)

(a)(ii)

One root because the two graphs intersect each other once

(a)(i) If multiple attempts are made then mark the last attempt. Condone if (i) and (ii) are

drawn on the same set of axes

B1

A positive cubic shape with a local maximum and a local minimum drawn anywhere on a

set of axes. Do not be concerned regarding the location of the minimum. Mark of the

intention to draw a cubic so condone aspects which may appear linear or slips of the pen.

k

B1

Intersects (not just meet) the xaxis at

x =

to the right of the yaxis and has a local

2

maximum (or minimum) on

x = − which must be to the left of the yaxis. If there is a

4

contradiction between the labelling on the graph and values stated separately then the graph

labels take precedence. Condone for example ( 4, 0)

−

labelled as (0,

−

4)

as long as it is in

the correct position on the axis

B1

yintercept is 16k

−

(which must be below the xaxis) If there is a contradiction between the

labelling on the graph and the yintercept stated separately then the graph label takes

precedence. Condone for example (0,

−

16 )

k

labelled as ( 16 , 0)

−

k

as long as it is in the

correct position on the axis

(a)(ii)

B1

Correct shaped curve in the first or second quadrant. It must not cross either axis. Do not be

concerned by any labelled asymptotes or extra “branches” appearing in these quadrants.

Mark the intention to draw a graph which does not have a clear turning point.

B1

Correct curves in the first and second quadrants and no other curves appearing in quadrants

3 and 4 (unless the cubic from (i) has been drawn on the same axes). Mark the intention to

draw a graph tending towards the axes and does not have a clear turning point. If any

asymptotes are labelled or indicated with dashed lines which are not the coordinate axes

then withhold this mark.

(b)

This mark can only be awarded provided both graphs are the correct shape and

position in part (a) (the intercepts with the axes are not needed for this mark)

B1

One root because the two graphs intersect each other once (only). Condone alternative

wording which implies they “meet” once. Do not allow references to intersecting the axes.

Examples for (a)(i)

B1B1B1

B1B1B1

Examples for (a)(ii)

B1B1

B1B1

B1B1

B1B0

B1B0

B1B0

One root because the two graphs intersect each other once

(a)(i) If multiple attempts are made then mark the last attempt. Condone if (i) and (ii) are

drawn on the same set of axes

B1

A positive cubic shape with a local maximum and a local minimum drawn anywhere on a

set of axes. Do not be concerned regarding the location of the minimum. Mark of the

intention to draw a cubic so condone aspects which may appear linear or slips of the pen.

k

B1

Intersects (not just meet) the xaxis at

x =

to the right of the yaxis and has a local

2

maximum (or minimum) on

x = − which must be to the left of the yaxis. If there is a

4

contradiction between the labelling on the graph and values stated separately then the graph

labels take precedence. Condone for example ( 4, 0)

−

labelled as (0,

−

4)

as long as it is in

the correct position on the axis

B1

yintercept is 16k

−

(which must be below the xaxis) If there is a contradiction between the

labelling on the graph and the yintercept stated separately then the graph label takes

precedence. Condone for example (0,

−

16 )

k

labelled as ( 16 , 0)

−

k

as long as it is in the

correct position on the axis

(a)(ii)

B1

Correct shaped curve in the first or second quadrant. It must not cross either axis. Do not be

concerned by any labelled asymptotes or extra “branches” appearing in these quadrants.

Mark the intention to draw a graph which does not have a clear turning point.

B1

Correct curves in the first and second quadrants and no other curves appearing in quadrants

3 and 4 (unless the cubic from (i) has been drawn on the same axes). Mark the intention to

draw a graph tending towards the axes and does not have a clear turning point. If any

asymptotes are labelled or indicated with dashed lines which are not the coordinate axes

then withhold this mark.

(b)

This mark can only be awarded provided both graphs are the correct shape and

position in part (a) (the intercepts with the axes are not needed for this mark)

B1

One root because the two graphs intersect each other once (only). Condone alternative

wording which implies they “meet” once. Do not allow references to intersecting the axes.

Examples for (a)(i)

B1B1B1

B1B1B1

Examples for (a)(ii)

B1B1

B1B1

B1B1

B1B0

B1B0

B1B0