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1 – 2016 Feb Mar 0580/980 – 42
2016
1 Math 2016 Feb Mar – V42
1 Math 2017 Feb Mar – 42 (solved Paper)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
READ
THESE
INSTRUCTIONS
FIRST
Write
your
Centre
number,
candidate
number
and
name
on
all
the
work
you
hand
in.
Write
in
dark
blue
or
black
pen.
You
may
use
an
HB
pencil
for
any
diagrams
or
graphs.
Do
not
use
staples,
paper
clips,
glue
or
correction
uid.
DO
NOT
WRITE
IN
ANY
BARCODES.
Answer
all
questions.
If
working
is
needed
for
any
question
it
must
be
shown
below
that
question.
Electronic
calculators
should
be
used.
If
the
degree
of
accuracy
is
not
speci
ed
in
the
question,
and
if
the
answer
is
not
exact,
give
the
answer
to
three
signi
cant
gures.
Give
answers
in
degrees
to
one
decimal
place.
For
π
,
use
either
your
calculator
value
or
3.142.
At
the
end
of
the
examination,
fasten
all
your
work
securely
together.
The
number
of
marks
is
given
in
brackets
[
]
at
the
end
of
each
question
or
part
question.
The
total
of
the
marks
for
this
paper
is
130.
MATHEMATICS
0580/42
Paper
4
(Extended)
February/March
2016
2
hours
30
minutes
Candidates
answer
on
the
Question
Paper.
Additional
Materials:
Electronic
calculator
Geometrical
instruments
Tracing
paper
(optional)
Cambridge
International
Examinations
Cambridge
International
General
Certi
cate
of
Secondary
Education
This
document
consists
of
16
printed
pages.
[Turn
over
DC
(ST/SW)
112494/2
©
UCLES
2016
CANDIDATE
NAME
CENTRE
NUMBER
CANDIDATE
NUMBER
The
syllabus
is
approved
for
use
in
England,
Wales
and
Northern
Ireland
as
a
Cambridge
International
Level
1/Level
2
Certi
cate.
EduTakers.com
EduTakers.com

Ink Drawings
Ink Drawings](https://lh4.googleusercontent.com/WBSnvq99Q3_doUopRPTGXfzJLJDC3pCqmSWYcZlyq6XBD5idIBVw6qCq9BDJ6unlAzlINpw5I9eSP8UDcMMdXJi34uYyxCx7BTjroeGmWcE_7DfrUWvL4xxJhYH6be_bbtsWrJDWfzs69GM2zrtsGvI)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
2
0580/42/F/M/16
©
UCLES
2016
1
Aasha,
Biren
and
Cemal
share
$640
in
the
ratio
8
:
15
:
9.
(a)
Show
that
Aasha
receives
$160.
[1]
(b)
Calculate
the
amount
that
Biren
and
Cemal
receive.
Biren
$
..................................................
Cemal
$
..................................................[2]
(c)
Aasha
uses
her
$160
to
buy
some
books.
Each
book
costs
$15.25
.
Find
the
greatest
number
of
books
that
she
can
buy.
..................................................
[2]
(d)
Biren
spends
8
3
of
his
share
on
clothes
and
3
1
of
his
share
on
a
computer.
Find
the
fraction
of
his
share
that
he
has
left.
Write
your
fraction
in
its
lowest
terms.
..................................................
[3]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
READ
THESE
INSTRUCTIONS
FIRST
Write
your
Centre
number,
candidate
number
and
name
on
all
the
work
you
hand
in.
Write
in
dark
blue
or
black
pen.
You
may
use
an
HB
pencil
for
any
diagrams
or
graphs.
Do
not
use
staples,
paper
clips,
glue
or
correction
uid.
DO
NOT
WRITE
IN
ANY
BARCODES.
Answer
all
questions.
If
working
is
needed
for
any
question
it
must
be
shown
below
that
question.
Electronic
calculators
should
be
used.
If
the
degree
of
accuracy
is
not
speci
ed
in
the
question,
and
if
the
answer
is
not
exact,
give
the
answer
to
three
signi
cant
gures.
Give
answers
in
degrees
to
one
decimal
place.
For
π
,
use
either
your
calculator
value
or
3.142.
At
the
end
of
the
examination,
fasten
all
your
work
securely
together.
The
number
of
marks
is
given
in
brackets
[
]
at
the
end
of
each
question
or
part
question.
The
total
of
the
marks
for
this
paper
is
130.
MATHEMATICS
0580/42
Paper
4
(Extended)
February/March
2016
2
hours
30
minutes
Candidates
answer
on
the
Question
Paper.
Additional
Materials:
Electronic
calculator
Geometrical
instruments
Tracing
paper
(optional)
Cambridge
International
Examinations
Cambridge
International
General
Certi
cate
of
Secondary
Education
This
document
consists
of
16
printed
pages.
[Turn
over
DC
(ST/SW)
112494/2
©
UCLES
2016
CANDIDATE
NAME
CENTRE
NUMBER
CANDIDATE
NUMBER
The
syllabus
is
approved
for
use
in
England,
Wales
and
Northern
Ireland
as
a
Cambridge
International
Level
1/Level
2
Certi
cate.
EduTakers.com
EduTakers.com


































Ink Drawings
Ink Drawings](https://lh4.googleusercontent.com/fyMFSvpzQJ5xj8Sa8JnS4j0oESlmaXHmNwu_MFYypsOSzLqGT64JfJnk4_8gje89L4XGODQkg6Mpq6I6JGijaTp1Iq5LiNxep_QBd0VFIdMik39DOlRxHRr3Vd7UkwnV0CicBdChCsJsp3VljKnPkjE)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
3
0580/42/F/M/16
©
UCLES
2016
[Turn
over
2
In
this
question
use
a
ruler
and
compasses
only.
Show
all
your
construction
arcs.
The
diagram
shows
a
triangular
field
ABC
.
The
scale
is
1
centimetre
represents
50
metres.
C
B
Scale
:
1cm
to
50m
A
(a)
Construct
the
locus
of
points
that
are
equidistant
from
A
and
B
.
[2]
(b)
Construct
the
locus
of
points
that
are
equidistant
from
the
lines
AB
and
AC
.
[2]
(c)
The
two
loci
intersect
at
the
point
E
.
Construct
the
locus
of
points
that
are
250
m
from
E
.
[2]
(d)
Shade
any
region
inside
the
eld
ABC
that
is
•
more
than
250
m
from
E
and
•
closer
to
AC
than
to
AB
.
[2]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
2
0580/42/F/M/16
©
UCLES
2016
1
Aasha,
Biren
and
Cemal
share
$640
in
the
ratio
8
:
15
:
9.
(a)
Show
that
Aasha
receives
$160.
[1]
(b)
Calculate
the
amount
that
Biren
and
Cemal
receive.
Biren
$
..................................................
Cemal
$
..................................................[2]
(c)
Aasha
uses
her
$160
to
buy
some
books.
Each
book
costs
$15.25
.
Find
the
greatest
number
of
books
that
she
can
buy.
..................................................
[2]
(d)
Biren
spends
8
3
of
his
share
on
clothes
and
3
1
of
his
share
on
a
computer.
Find
the
fraction
of
his
share
that
he
has
left.
Write
your
fraction
in
its
lowest
terms.
..................................................
[3]
EduTakers.com
EduTakers.comInk Drawings
Ink Drawings
Ink Drawings








Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings






Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings



Ink Drawings
Ink Drawings
Ink Drawings](https://lh3.googleusercontent.com/gt82t8FIigak8sPkQilvApViNQ0VrdzOg2Yi3Z3p2HpPsnj_vQgVNUCinHsFQV1xI-HA4lCF-XK9b4kbAjz95H0EwMO7WA1GkETdzIg5qWe8PWQtCtqIAdrIAke_gGzoUntTk9xpPWxxYjDSRIlMhuI)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
4
0580/42/F/M/16
©
UCLES
2016
3
(a)
Davinder
asked
some
people
if
they
ate
mangoes,
pineapples
or
bananas
last
week.
M
=
{
people
who
ate
mangoes
}
P
=
{
people
who
ate
pineapples
}
B
=
{
people
who
ate
bananas
}
The
Venn
diagram
shows
some
of
the
information.
M
P
B
12
1
4
......
......
......
7
5
19
people
said
they
ate
mangoes.
6
people
said
they
ate
only
pineapples.
18
people
said
they
ate
exactly
two
of
the
three
types
of
fruit.
(i)
Write
the
three
missing
values
in
the
Venn
diagram.
[3]
(ii)
Find
the
total
number
of
people
Davinder
asked.
..................................................
[1]
(iii)
Find
n(
M
P
).
..................................................
[1]
(iv)
One
person
is
chosen
at
random
from
the
people
who
ate
mangoes.
Write
down
the
probability
that
this
person
also
ate
bananas.
..................................................
[2]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
3
0580/42/F/M/16
©
UCLES
2016
[Turn
over
2
In
this
question
use
a
ruler
and
compasses
only.
Show
all
your
construction
arcs.
The
diagram
shows
a
triangular
field
ABC
.
The
scale
is
1
centimetre
represents
50
metres.
C
B
Scale
:
1cm
to
50m
A
(a)
Construct
the
locus
of
points
that
are
equidistant
from
A
and
B
.
[2]
(b)
Construct
the
locus
of
points
that
are
equidistant
from
the
lines
AB
and
AC
.
[2]
(c)
The
two
loci
intersect
at
the
point
E
.
Construct
the
locus
of
points
that
are
250
m
from
E
.
[2]
(d)
Shade
any
region
inside
the
eld
ABC
that
is
•
more
than
250
m
from
E
and
•
closer
to
AC
than
to
AB
.
[2]
EduTakers.com
EduTakers.com

























Ink Drawings
Ink Drawings](https://lh5.googleusercontent.com/bMKkJivcWnaLcwUUFwGzO83p8DKo-66TNcab7JgP3MFwOaqot7BCBYxJRmmlWS5QBoOU0v3jvtY1byV3yGr1WrVLEZt6DfgrlLonAJjWxR1S30RcYFuufq1uxvWdWGR1Oqcsd2dof2mUqeyMSLv73h4)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
5
0580/42/F/M/16
©
UCLES
2016
[Turn
over
(b)
Davinder
draws
a
speed-time
graph
for
his
bus
journey
to
the
market.
200
0
2
4
6
8
10
400
600
800
Time
(seconds)
Speed
(m/s)
1000
1200
1400
1600
Find
(i)
the
acceleration
of
the
bus
during
the
rst
200
seconds,
..........................................
m/s
2
[1]
(ii)
the
total
distance
travelled
by
the
bus,
..............................................
m
[3]
(iii)
the
average
speed
of
the
bus
for
the
whole
journey.
...........................................
m/s
[1]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
4
0580/42/F/M/16
©
UCLES
2016
3
(a)
Davinder
asked
some
people
if
they
ate
mangoes,
pineapples
or
bananas
last
week.
M
=
{
people
who
ate
mangoes
}
P
=
{
people
who
ate
pineapples
}
B
=
{
people
who
ate
bananas
}
The
Venn
diagram
shows
some
of
the
information.
M
P
B
12
1
4
......
......
......
7
5
19
people
said
they
ate
mangoes.
6
people
said
they
ate
only
pineapples.
18
people
said
they
ate
exactly
two
of
the
three
types
of
fruit.
(i)
Write
the
three
missing
values
in
the
Venn
diagram.
[3]
(ii)
Find
the
total
number
of
people
Davinder
asked.
..................................................
[1]
(iii)
Find
n(
M
P
).
..................................................
[1]
(iv)
One
person
is
chosen
at
random
from
the
people
who
ate
mangoes.
Write
down
the
probability
that
this
person
also
ate
bananas.
..................................................
[2]
EduTakers.com
EduTakers.comInk Drawings
Ink Drawings
















Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings





Ink Drawings
Ink Drawings](https://lh5.googleusercontent.com/7A4_pHLz-3J6J0ApFqWS9CnRY-84l6dtrx20Q9lgftfQDq8aZhGDK4i2tXJu74KVMhL0WaVhdBZEPjGSaJsaLIY991D9nQqg_eKZRPkLA5dQHTXat7gnjtdT5UEm2lPrGEBBJ5TOZQJYwvFOIj6LOhQ)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
6
0580/42/F/M/16
©
UCLES
2016
4
The
cumulative
frequency
diagram
shows
information
about
the
time
taken,
t
minutes,
by
60
students
to
complete
a
test.
0
10
20
30
40
50
60
10
20
30
40
50
60
Time
taken
(minutes)
Cumulative
frequency
70
80
90
100
t
(a)
Find
(i)
the
median,
...........................................
min
[1]
(ii)
the
inter-quartile
range,
...........................................
min
[2]
(iii)
the
40th
percentile,
...........................................
min
[2]
(iv)
the
number
of
students
who
took
more
than
80
minutes
to
complete
the
test.
..................................................
[2]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
5
0580/42/F/M/16
©
UCLES
2016
[Turn
over
(b)
Davinder
draws
a
speed-time
graph
for
his
bus
journey
to
the
market.
200
0
2
4
6
8
10
400
600
800
Time
(seconds)
Speed
(m/s)
1000
1200
1400
1600
Find
(i)
the
acceleration
of
the
bus
during
the
rst
200
seconds,
..........................................
m/s
2
[1]
(ii)
the
total
distance
travelled
by
the
bus,
..............................................
m
[3]
(iii)
the
average
speed
of
the
bus
for
the
whole
journey.
...........................................
m/s
[1]
EduTakers.com
EduTakers.comInk Drawings
Ink Drawings






















Ink Drawings
Ink Drawings](https://lh4.googleusercontent.com/rMqqjEuZwD3LXqML7SGn6dayLEt7eKDyTp8Ru5tM4GWK2_4qE4UVIN3OxfGhNM0S0uFJbDJZBIFEJCzJ9MJdQT0Y03GtZof-H9mktc1kAUNmU8GWVPfoLxGhVXuuIauHIyHyOE03T7ad5aidVLgLuBE)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
7
0580/42/F/M/16
©
UCLES
2016
[Turn
over
(b)
Use
the
cumulative
frequency
diagram
to
complete
the
frequency
table
below.
Time
taken
(
t
minutes)
0
t
4040
t
6060
t
7070
t
8080
t
9090
t
100
Frequency84
[3]
(c)
On
the
grid
below,
complete
the
histogram
to
show
the
information
in
the
table
in
part
(b)
.
0
1
2
3
10
20
30
40
50
60
Time
taken
(minutes)
t
Frequency
density
70
80
90
100
[4]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
6
0580/42/F/M/16
©
UCLES
2016
4
The
cumulative
frequency
diagram
shows
information
about
the
time
taken,
t
minutes,
by
60
students
to
complete
a
test.
0
10
20
30
40
50
60
10
20
30
40
50
60
Time
taken
(minutes)
Cumulative
frequency
70
80
90
100
t
(a)
Find
(i)
the
median,
...........................................
min
[1]
(ii)
the
inter-quartile
range,
...........................................
min
[2]
(iii)
the
40th
percentile,
...........................................
min
[2]
(iv)
the
number
of
students
who
took
more
than
80
minutes
to
complete
the
test.
..................................................
[2]
EduTakers.com
EduTakers.comInk Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings





















Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings

Ink Drawings
Ink Drawings](https://lh3.googleusercontent.com/AXcdMG1okv76mbv9ZGussQaU_dahqCKpfXltFtckbHbd_EKjs_P0qP5wUPdvB4KQcQlnceofMp2eHGn6PLBdIPXfT4PLFFbyaU6mKjbSe1TpnABc5k118TpRwplROM2LgUnvqoEileA-8eSRAqbYJOI)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
8
0580/42/F/M/16
©
UCLES
2016
5
(a)
Meena
sells
her
car
for
$6000.
This
is
a
loss
of
4%
on
the
price
she
paid.
Calculate
the
price
Meena
paid
for
the
car.
$
.................................................
[3]
(b)
Eisha
changes
some
euros
(€)
into
dollars
($)
when
the
exchange
rate
is
€1
=
$1.351
.
She
receives
$6000.
Calculate
how
many
euros
Eisha
changes.
Give
your
answer
correct
to
the
nearest
euro.
€
.................................................
[3]
(c)
Meena
and
Eisha
both
invest
their
$6000.
Meena
invests
her
$6000
at
a
rate
of
1.5%
per
year
compound
interest.
Eisha
invests
her
$6000
in
a
bank
that
pays
simple
interest.
After
8
years,
their
investments
are
worth
the
same
amount.
Calculate
the
rate
of
simple
interest
per
year
that
Eisha
received.
..............................................
%
[5]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
7
0580/42/F/M/16
©
UCLES
2016
[Turn
over
(b)
Use
the
cumulative
frequency
diagram
to
complete
the
frequency
table
below.
Time
taken
(
t
minutes)
0
t
4040
t
6060
t
7070
t
8080
t
9090
t
100
Frequency84
[3]
(c)
On
the
grid
below,
complete
the
histogram
to
show
the
information
in
the
table
in
part
(b)
.
0
1
2
3
10
20
30
40
50
60
Time
taken
(minutes)
t
Frequency
density
70
80
90
100
[4]
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Ink Drawings
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Ink Drawings
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Ink Drawings
Ink Drawings](https://lh6.googleusercontent.com/2hz2NHRNipWlgv-cPoz2WZzVb6ZlegyUsenf-wZg2iba4iQPY6InUOuag--XOF1NZ3Mr5jaLtR-Iszw8Ii9gQ59sALNXKxUOnuFvZ65D2cZHLJh7JwdWU73zyVlUtBQsiCosjuCnqqB32nEFMx6mUv4)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
9
0580/42/F/M/16
©
UCLES
2016
[Turn
over
6
–5–4–3–2–1
0
123456
7
x
Z
X
Y
y
–2
–1
1
2
3
4
5
6
7
8
(a)
Describe
fully
the
single
transformation
that
maps
(i)
triangle
X
onto
triangle
Y
,
.......................................................................................................................................................
.......................................................................................................................................................[3]
(ii)
triangle
X
onto
triangle
Z
.
.......................................................................................................................................................
.......................................................................................................................................................[3]
(b)
(i)
Draw
the
image
of
triangle
X
after
a
translation
by
the
vector
3
5
-
cm
.
Label
this
triangle
P
.
[2]
(ii)
Draw
the
re
ection
of
triangle
P
in
the
line
y
=
3.
[2]
(c)
Draw
the
image
of
triangle
X
after
the
transformation
represented
by
the
matrix
10
01–
cm
.
[3]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
8
0580/42/F/M/16
©
UCLES
2016
5
(a)
Meena
sells
her
car
for
$6000.
This
is
a
loss
of
4%
on
the
price
she
paid.
Calculate
the
price
Meena
paid
for
the
car.
$
.................................................
[3]
(b)
Eisha
changes
some
euros
(€)
into
dollars
($)
when
the
exchange
rate
is
€1
=
$1.351
.
She
receives
$6000.
Calculate
how
many
euros
Eisha
changes.
Give
your
answer
correct
to
the
nearest
euro.
€
.................................................
[3]
(c)
Meena
and
Eisha
both
invest
their
$6000.
Meena
invests
her
$6000
at
a
rate
of
1.5%
per
year
compound
interest.
Eisha
invests
her
$6000
in
a
bank
that
pays
simple
interest.
After
8
years,
their
investments
are
worth
the
same
amount.
Calculate
the
rate
of
simple
interest
per
year
that
Eisha
received.
..............................................
%
[5]
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Ink Drawings


Ink Drawings
Ink Drawings](https://lh6.googleusercontent.com/kPwBkrAU_VSMYCk2yWOWx-HjPNfKC4QXF5w6p8VQMjm0Br6LEZplyUA0A_rZHDa7Tqu3lz7THdx6D0TDI_D52kRHTjbcYtl9ME4-zjNgnAQ1igjOyGX6xvhXJ6vH4vOS-NoZ2h6kAtsJFdUD_E5mGQQ)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
9
0580/42/F/M/16
©
UCLES
2016
[Turn
over
6
–5–4–3–2–1
0
123456
7
x
Z
X
Y
y
–2
–1
1
2
3
4
5
6
7
8
(a)
Describe
fully
the
single
transformation
that
maps
(i)
triangle
X
onto
triangle
Y
,
.......................................................................................................................................................
.......................................................................................................................................................[3]
(ii)
triangle
X
onto
triangle
Z
.
.......................................................................................................................................................
.......................................................................................................................................................[3]
(b)
(i)
Draw
the
image
of
triangle
X
after
a
translation
by
the
vector
3
5
-
cm
.
Label
this
triangle
P
.
[2]
(ii)
Draw
the
re
ection
of
triangle
P
in
the
line
y
=
3.
[2]
(c)
Draw
the
image
of
triangle
X
after
the
transformation
represented
by
the
matrix
10
01–
cm
.
[3]
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Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings


































Ink Drawings
Ink Drawings](https://lh4.googleusercontent.com/3YMhpo1Iz2PO4ZOgicmMymnBlhviyQ6Ga5IK0RhvR7LF6t_3IfBGoQCwuFm8MyhugC2sYu-gx1TetXcS9lxZkOeDKniLxidNrdgObiyRoVH_4N1OrPj0lrhAqUyW9DuwmGemeTyPgGqAnidTLPM21YE)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
10
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©
UCLES
2016
7
The
table
shows
some
values
of
yx
x
1
2
=+
,
x
0
!
.
x
–2–1.5–1–0.75–0.50.50.7511.523
y
–1.75–1.0601.034.502.5322.25
(a)
Complete
the
table
of
values.
[3]
(b)
On
the
grid,
draw
the
graph
of
yx
x
1
2
=+
for
–
2
x
–
0.5
and
0.5
x
3.
y
x
–1
0
–2
2
–1
1
2
3
4
5
–2
1
3
[5]
EduTakers.com
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9
0580/42/F/M/16
©
UCLES
2016
[Turn
over
6
–5–4–3–2–1
0
123456
7
x
Z
X
Y
y
–2
–1
1
2
3
4
5
6
7
8
(a)
Describe
fully
the
single
transformation
that
maps
(i)
triangle
X
onto
triangle
Y
,
.......................................................................................................................................................
.......................................................................................................................................................[3]
(ii)
triangle
X
onto
triangle
Z
.
.......................................................................................................................................................
.......................................................................................................................................................[3]
(b)
(i)
Draw
the
image
of
triangle
X
after
a
translation
by
the
vector
3
5
-
cm
.
Label
this
triangle
P
.
[2]
(ii)
Draw
the
re
ection
of
triangle
P
in
the
line
y
=
3.
[2]
(c)
Draw
the
image
of
triangle
X
after
the
transformation
represented
by
the
matrix
10
01–
cm
.
[3]
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Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings






Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings






Ink Drawings
Ink Drawings](https://lh6.googleusercontent.com/0qJ7BFIcRr9f8-tEp5BLrlyk6BviDF8GjZMm3F-PDDWyKr5XjQZIne_DSi9gAw_CE3uvSHimHh_8lDHZBYllxSoNJqcJx8OK93LBRSSC5SL-Fxv-blPcy2YBUCSUqg7yul3UbCkCBurXdol6EICAMtA)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
11
0580/42/F/M/16
©
UCLES
2016
[Turn
over
(c)
Use
your
graph
to
solve
the
equation
.
x
x
1
15
2
+=
.
x
=
.................................................
[1]
(d)
The
line
yaxb
=+
can
be
drawn
on
the
grid
to
solve
the
equation
.
x
x
1
252
2
=-
.
(i)
Find
the
value
of
a
and
the
value
of
b
.
a
=
................................................
b
=
.................................................
[2]
(ii)
Draw
the
line
yaxb
=+
to
solve
the
equation
.
x
x
1
252
2
=-
.
x
=
.................................................
[3]
(e)
By
drawing
a
suitable
tangent,
nd
an
estimate
of
the
gradient
of
the
curve
at
the
point
where
x
=
2.
..................................................
[3]
EduTakers.com
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10
0580/42/F/M/16
©
UCLES
2016
7
The
table
shows
some
values
of
yx
x
1
2
=+
,
x
0
!
.
x
–2–1.5–1–0.75–0.50.50.7511.523
y
–1.75–1.0601.034.502.5322.25
(a)
Complete
the
table
of
values.
[3]
(b)
On
the
grid,
draw
the
graph
of
yx
x
1
2
=+
for
–
2
x
–
0.5
and
0.5
x
3.
y
x
–1
0
–2
2
–1
1
2
3
4
5
–2
1
3
[5]
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Ink Drawings
Ink Drawings](https://lh6.googleusercontent.com/FcTyf3B4NHR83hiikHB6WuLCdWsQ6InmWxLz-cgUbzbe_cpL7-t6YcA4X7XeHicKDpcxm-UEWsUkw0g0F_n4IuqkQWiT9y6P2_Yh521IxA_FoHXr4vBUWZAAC_yHbDfYiYRzHDeKMyCLE6gjGKs8l4Q)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
12
0580/42/F/M/16
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UCLES
2016
8
(a)
y
is
directly
proportional
to
the
positive
square
root
of
x
2
+
^
h
.
When
x
=
7,
y
=
9.
Find
y
when
x
=
23.
y
=
.................................................
[3]
(b)
Simplify.
xx
xx
412
1236
2
2
+-
++
..................................................
[5]
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EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
11
0580/42/F/M/16
©
UCLES
2016
[Turn
over
(c)
Use
your
graph
to
solve
the
equation
.
x
x
1
15
2
+=
.
x
=
.................................................
[1]
(d)
The
line
yaxb
=+
can
be
drawn
on
the
grid
to
solve
the
equation
.
x
x
1
252
2
=-
.
(i)
Find
the
value
of
a
and
the
value
of
b
.
a
=
................................................
b
=
.................................................
[2]
(ii)
Draw
the
line
yaxb
=+
to
solve
the
equation
.
x
x
1
252
2
=-
.
x
=
.................................................
[3]
(e)
By
drawing
a
suitable
tangent,
nd
an
estimate
of
the
gradient
of
the
curve
at
the
point
where
x
=
2.
..................................................
[3]
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Ink Drawings
Ink Drawings](https://lh3.googleusercontent.com/F7Wjlw993jyBKiTUAePjRI13PwvIQZr1iHq6xr1PRUZhN6naRq75jzW7N85Qr8yStojeFtNQTVoA0gqjZvtegFn2MzGR_2y_xuH0r3HxP7t34euSy2NNHdjevTO3yN4LkZpZosU4JwIF7ekCse5QVvo)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
13
0580/42/F/M/16
©
UCLES
2016
[Turn
over
(c)
W
a
Xa
=
-
Make
a
the
subject
of
the
formula.
a
=
..................................................
[5]
(d)
Write
as
a
single
fraction
in
its
simplest
form.
x
x
x
x
1
2
1
3
+
-
-
-
+
..................................................
[5]
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EduTakers.comEmbedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
12
0580/42/F/M/16
©
UCLES
2016
8
(a)
y
is
directly
proportional
to
the
positive
square
root
of
x
2
+
^
h
.
When
x
=
7,
y
=
9.
Find
y
when
x
=
23.
y
=
.................................................
[3]
(b)
Simplify.
xx
xx
412
1236
2
2
+-
++
..................................................
[5]
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Ink Drawings
Ink Drawings](https://lh4.googleusercontent.com/6aDSAUbjhX5mjXgBX4O7KZiMapQC-BT_8TsdXmbCkv4QDTZjvN38AQSozjKoCc0Bu6WGm33g0d1NaMT5zP1zLbYAo5dNqYk9rQ_IM8ZYtJRxPtX-VAwb4IUQUNSyGnp4zSHogi7_z_hNzdzAevk722g)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
14
0580/42/F/M/16
©
UCLES
2016
9
S
TQ
NOT
TO
SCALE
P
O
x
y
RG
O
is
the
origin
and
OPQRST
is
a
regular
hexagon.
OP
=
x
and
OT
=
y
.
(a)
Write
down,
in
terms
of
x
and/or
y
,
in
its
simplest
form,
(i)
R
Q
,
R
Q
=
.................................................
[1]
(ii)
PQ
,
PQ
=
.................................................
[1]
(iii)
the
position
vector
of
S
.
..................................................
[2]
(b)
The
line
SR
is
extended
to
G
so
that
SR
:
RG
=
2
:
1.
Find
GQ
,
in
terms
of
x
and
y
,
in
its
simplest
form.
GQ
=
.................................................
[2]
(c)
M
is
the
midpoint
of
OP
.
(i)
Find
MG
,
in
terms
of
x
and
y
,
in
its
simplest
form.
MG
=
.................................................
[2]
(ii)
H
is
a
point
on
TQ
such
that
TH
:
HQ
=
3
:
1.
Use
vectors
to
show
that
H
lies
on
MG
.
[2]
EduTakers.com
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13
0580/42/F/M/16
©
UCLES
2016
[Turn
over
(c)
W
a
Xa
=
-
Make
a
the
subject
of
the
formula.
a
=
..................................................
[5]
(d)
Write
as
a
single
fraction
in
its
simplest
form.
x
x
x
x
1
2
1
3
+
-
-
-
+
..................................................
[5]
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Ink Drawings
Ink Drawings




















Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings


Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings](https://lh3.googleusercontent.com/tSsFtfmn9JkxkV510a9_IEEpxwKo88JcO8ORbtiGiDsDjzsm1-JR8TKNcJIY71B7Sy46Al_rsCt3fOML2qhptyPAbgNrEcECLiPZ0V5royAuO4ShU2pywrL83w9csgdqRFaT4XUquWJGqK9zjwo2I5U)
![Embedded file printout 1-0580_m16_qp_42.pdf Machine generated alternative text:
15
0580/42/F/M/16
©
UCLES
2016
[Turn
over
10
(a)
The
ten
circles
in
the
diagram
each
have
radius
1
cm.
The
centre
of
each
circle
is
marked
with
a
dot.
Calculate
the
height
of
triangle
PQR
.
NOT
TO
SCALE
QR
P
8cm
.............................................cm
[3]
(b)
Mr
Patel
uses
whiteboard
pens
that
are
cylinders
of
radius
1
cm.
(i)
The
diagram
shows
10
pens
stacked
in
a
tray.
The
tray
is
8
cm
wide.
The
point
A
is
the
highest
point
in
the
stack.
Find
the
height
of
A
above
the
base,
BC
,
of
the
tray.
NOT
TO
SCALE
B
C
A
8cm
............................................cm
[1]
(ii)
The
diagram
shows
a
box
that
holds
one
pen.
The
box
is
a
prism
of
length
12
cm.
The
cross
section
of
the
prism
is
an
equilateral
triangle.
The
pen
touches
each
of
the
three
rectangular
faces
of
the
box.
NOT
TO
SCALE
12cm
Calculate
the
volume
of
this
box.
...........................................
cm
3
[5]
Question
11
is
printed
on
the
next
page.
EduTakers.com
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UCLES
2016
9
S
TQ
NOT
TO
SCALE
P
O
x
y
RG
O
is
the
origin
and
OPQRST
is
a
regular
hexagon.
OP
=
x
and
OT
=
y
.
(a)
Write
down,
in
terms
of
x
and/or
y
,
in
its
simplest
form,
(i)
R
Q
,
R
Q
=
.................................................
[1]
(ii)
PQ
,
PQ
=
.................................................
[1]
(iii)
the
position
vector
of
S
.
..................................................
[2]
(b)
The
line
SR
is
extended
to
G
so
that
SR
:
RG
=
2
:
1.
Find
GQ
,
in
terms
of
x
and
y
,
in
its
simplest
form.
GQ
=
.................................................
[2]
(c)
M
is
the
midpoint
of
OP
.
(i)
Find
MG
,
in
terms
of
x
and
y
,
in
its
simplest
form.
MG
=
.................................................
[2]
(ii)
H
is
a
point
on
TQ
such
that
TH
:
HQ
=
3
:
1.
Use
vectors
to
show
that
H
lies
on
MG
.
[2]
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Ink Drawings
Ink Drawings](https://lh6.googleusercontent.com/FVYnBonyFIFcyByUrdSw-k7ARE8KHr-KDu7NSC3Ecsnjg6--2H2zDMoID5iVglmy23Cy21eXgVoL6xuuiRbeYHZ-MSGRBpF00Kq2qzsHAsK8SPGiI4Q4kqO7uZKHXaagkMAw7M-MXGFEiyUUu0W4iEo)
1 Math 2017 Feb Mar – 42 (PDF and Mark Scheme)