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1 – 2019 Feb Mar 0580/980 – 42
2019
1 Math 2019 Feb Mar – V42
1 Math 2019 Feb Mar – 42 (solved Paper)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
MATHEMATICS
0580/42
Paper 4 (Extended)
February/March 2019
2 hours 30 minutes
Candidates answer on the Question Paper.
Additional Materials: Electronic calculator Geometrical instruments
Tracing paper (optional)
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 fluid.
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 specified in the question, and if the answer is not exact, give the answer to
three significant figures. Give answers in degrees to one decimal place.
For
r
, 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.
This document consists of
19
printed pages and
1
blank page.
DC (ST/SW) 164545/2
© UCLES 2019
[Turn over
Cambridge Assessment International Education
Cambridge International General Certificate of Secondary Education
EduTakers.com
EduTakers.comInk Drawings
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Ink Drawings](https://lh5.googleusercontent.com/c7kLDGc_bvpUFHHmOwL4BQBJzWHpW-IwHs7j7ETpdKfVroxXHHO3rqvx3O4yw9o9XMRR4zJo_iRGTyxd9fTyTyojptzWLqFOtWbFmCM5wprm44DWtZFls8XRDi-_flHQsZvwNRP5WPykPGHw1wPsJZw)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
2
0580/42/F/M/19
© UCLES 2019
1
Amol and Priya deliver 645 parcels in the ratio Amol : Priya
=
11 : 4.
(a)
Calculate the number of parcels Amol delivers.
................................................... [2]
(b)
Amol drives his truck at an average speed of 50 km/h.
He leaves at 07 00 and arrives at 11 15.
Calculate the distance he drives.
............................................. km [2]
(c)
Priya drives her van a distance of 54 km.
She leaves at 10 55 and arrives at 12 38.
Calculate her average speed.
.......................................... km/h [3]
(d)
Priya has 50 identical parcels.
Each parcel has a mass of 17 kg, correct to the nearest kilogram.
Find the upper bound for the total mass of the 50 parcels.
.............................................. kg [1]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
MATHEMATICS
0580/42
Paper 4 (Extended)
February/March 2019
2 hours 30 minutes
Candidates answer on the Question Paper.
Additional Materials: Electronic calculator Geometrical instruments
Tracing paper (optional)
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 fluid.
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 specified in the question, and if the answer is not exact, give the answer to
three significant figures. Give answers in degrees to one decimal place.
For
r
, 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.
This document consists of
19
printed pages and
1
blank page.
DC (ST/SW) 164545/2
© UCLES 2019
[Turn over
Cambridge Assessment International Education
Cambridge International General Certificate of Secondary Education
EduTakers.com
EduTakers.comInk Drawings
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![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
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0580/42/F/M/19
© UCLES 2019
[Turn over
(e)
67 of the 645 parcels are damaged on the journey.
Calculate the percentage of parcels that are damaged.
............................................... % [1]
(f) (i)
29 parcels each have a value of $68.
By writing each of these numbers correct to 1 significant figure, find an estimate for the total
value of these 29 parcels.
$ .................................................. [1]
(ii)
Without doing any calculation, complete this statement.
The actual total value of these 29 parcels is less than the answer to
part (f)(i)
because ...................................................................................................................................... [1]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
2
0580/42/F/M/19
© UCLES 2019
1
Amol and Priya deliver 645 parcels in the ratio Amol : Priya
=
11 : 4.
(a)
Calculate the number of parcels Amol delivers.
................................................... [2]
(b)
Amol drives his truck at an average speed of 50 km/h.
He leaves at 07 00 and arrives at 11 15.
Calculate the distance he drives.
............................................. km [2]
(c)
Priya drives her van a distance of 54 km.
She leaves at 10 55 and arrives at 12 38.
Calculate her average speed.
.......................................... km/h [3]
(d)
Priya has 50 identical parcels.
Each parcel has a mass of 17 kg, correct to the nearest kilogram.
Find the upper bound for the total mass of the 50 parcels.
.............................................. kg [1]
EduTakers.com
EduTakers.comInk Drawings
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0580/42/F/M/19
© UCLES 2019
2
x
–8
–7
–6
–5
–4
–3
–2
–1
1
2
3
4
5
6
7
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
y
A
B
C
(a)
Describe fully the
single
transformation that maps
(i)
triangle
A
onto triangle
B
,
....................................................................................................................................................
.................................................................................................................................................... [2]
(ii)
triangle
A
onto triangle
C
.
....................................................................................................................................................
.................................................................................................................................................... [3]
(b)
On the grid, draw the image of
(i)
triangle
A
after an enlargement, scale factor
2
1
-
, centre (3, 0), [2]
(ii)
triangle
A
after a translation by the vector
3
1
-
eo
, [2]
(iii)
triangle
A
after the transformation that is represented by the matrix
0
1
1
0
eo
.
[3]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
3
0580/42/F/M/19
© UCLES 2019
[Turn over
(e)
67 of the 645 parcels are damaged on the journey.
Calculate the percentage of parcels that are damaged.
............................................... % [1]
(f) (i)
29 parcels each have a value of $68.
By writing each of these numbers correct to 1 significant figure, find an estimate for the total
value of these 29 parcels.
$ .................................................. [1]
(ii)
Without doing any calculation, complete this statement.
The actual total value of these 29 parcels is less than the answer to
part (f)(i)
because ...................................................................................................................................... [1]
EduTakers.com
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[Turn over
3
Sushila, Ravi and Talika each have a bag of balls.
Each of the bags contains 10 red balls and 8 blue balls.
(a)
Sushila takes one ball at random from her bag.
Find the probability that she takes a red ball.
................................................... [1]
(b)
Ravi takes two balls at random from his bag, without replacement.
Find the probability that one ball is red and one ball is blue.
................................................... [3]
(c)
Talika takes three balls at random from her bag, without replacement.
Calculate the probability that the three balls are the same colour.
................................................... [4]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
4
0580/42/F/M/19
© UCLES 2019
2
x
–8
–7
–6
–5
–4
–3
–2
–1
1
2
3
4
5
6
7
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
y
A
B
C
(a)
Describe fully the
single
transformation that maps
(i)
triangle
A
onto triangle
B
,
....................................................................................................................................................
.................................................................................................................................................... [2]
(ii)
triangle
A
onto triangle
C
.
....................................................................................................................................................
.................................................................................................................................................... [3]
(b)
On the grid, draw the image of
(i)
triangle
A
after an enlargement, scale factor
2
1
-
, centre (3, 0), [2]
(ii)
triangle
A
after a translation by the vector
3
1
-
eo
, [2]
(iii)
triangle
A
after the transformation that is represented by the matrix
0
1
1
0
eo
.
[3]
EduTakers.com
EduTakers.comInk Drawings
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![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
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0580/42/F/M/19
© UCLES 2019
4
The diagram shows an incomplete scale drawing of a market place,
ABCD
, where
D
is on
CX
.
The scale is 1 centimetre represents 5 metres.
X
C
B
Scale : 1cm to 5m
A
D
lies on
CX
such that angle
DAB
=
75°.
(a)
On the diagram, draw the line
AD
and mark the position of
D
. [2]
(b)
Find the actual length of the side
BC
of the market place.
............................................... m [2]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
5
0580/42/F/M/19
© UCLES 2019
[Turn over
3
Sushila, Ravi and Talika each have a bag of balls.
Each of the bags contains 10 red balls and 8 blue balls.
(a)
Sushila takes one ball at random from her bag.
Find the probability that she takes a red ball.
................................................... [1]
(b)
Ravi takes two balls at random from his bag, without replacement.
Find the probability that one ball is red and one ball is blue.
................................................... [3]
(c)
Talika takes three balls at random from her bag, without replacement.
Calculate the probability that the three balls are the same colour.
................................................... [4]
EduTakers.com
EduTakers.comInk Drawings
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[Turn over
(c) In this part, use a ruler and compasses only.
Street sellers are allowed in the part of the market place that is
•
more than 35 metres from
A
and
•
nearer to
C
than to
B
and
•
nearer to
CD
than to
BC
.
On the diagram, construct and shade the region where street sellers are allowed. [7]
(d)
Write the scale of the drawing in the form 1 :
n
.
1 : .................................................. [1]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
6
0580/42/F/M/19
© UCLES 2019
4
The diagram shows an incomplete scale drawing of a market place,
ABCD
, where
D
is on
CX
.
The scale is 1 centimetre represents 5 metres.
X
C
B
Scale : 1cm to 5m
A
D
lies on
CX
such that angle
DAB
=
75°.
(a)
On the diagram, draw the line
AD
and mark the position of
D
. [2]
(b)
Find the actual length of the side
BC
of the market place.
............................................... m [2]
EduTakers.com
EduTakers.comInk Drawings
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5
The table shows some values for
yxx
10
3
2
3
=-
for
x
33
GG
-
.
x
−3−2−1.5−1
011.523
y
2.01.70
−2.0−1.6
(a)
Complete the table. [3]
(b)
On the grid, draw the graph of
yxx
10
3
2
3
=-
for
x
33
GG
-
.
y
x
1
2
–1
0
–2
–3–2–1
1
2
3
[4]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
7
0580/42/F/M/19
© UCLES 2019
[Turn over
(c) In this part, use a ruler and compasses only.
Street sellers are allowed in the part of the market place that is
•
more than 35 metres from
A
and
•
nearer to
C
than to
B
and
•
nearer to
CD
than to
BC
.
On the diagram, construct and shade the region where street sellers are allowed. [7]
(d)
Write the scale of the drawing in the form 1 :
n
.
1 : .................................................. [1]
EduTakers.com
EduTakers.comInk Drawings
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![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
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[Turn over
(c)
On the grid opposite, draw a suitable straight line to solve the equation ()
xxx
10
3
2
2
1
1
3
-=-
for
x
33
GG
-
.
x
=
....................... or
x
=
....................... or
x
=
....................... [4]
(d)
For
x
33
GG
-
, the equation
xx
10
3
21
3
-=
has
n
solutions.
Write down the value of
n
.
n
=
.................................................. [1]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
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5
The table shows some values for
yxx
10
3
2
3
=-
for
x
33
GG
-
.
x
−3−2−1.5−1
011.523
y
2.01.70
−2.0−1.6
(a)
Complete the table. [3]
(b)
On the grid, draw the graph of
yxx
10
3
2
3
=-
for
x
33
GG
-
.
y
x
1
2
–1
0
–2
–3–2–1
1
2
3
[4]
EduTakers.com
EduTakers.comInk Drawings
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Ink Drawings
Ink Drawings](https://lh3.googleusercontent.com/AXIZF3rgmkvBssoz31PLgDTVo-U0yxcmVm9LoXjMNjtEpnViSFMiFOHAs754b2WkNmD0foxG_J8OVyiWIYVm3gZ1GTKOgJNeRm0bb_pMCyglS6EasyKVe9reNIeQOpKukOqhPBcoi0b8NPOcv_6gfW4)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
9
0580/42/F/M/19
© UCLES 2019
[Turn over
(c)
On the grid opposite, draw a suitable straight line to solve the equation ()
xxx
10
3
2
2
1
1
3
-=-
for
x
33
GG
-
.
x
=
....................... or
x
=
....................... or
x
=
....................... [4]
(d)
For
x
33
GG
-
, the equation
xx
10
3
21
3
-=
has
n
solutions.
Write down the value of
n
.
n
=
.................................................. [1]
EduTakers.com
EduTakers.comInk Drawings
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Ink Drawings
Ink Drawings](https://lh4.googleusercontent.com/RqDa-fuL8S6Pr8U-pQRSlnrA88AgfcD7ljbkMKfq8C9pYc6pqkyNd6r_zYqgP2AQ13HNxBwtJ2FUtB3l1t9H--GnPj_P0KtaOq-Ij7Vkpp_GMwne5qi2PnsRMvlJYv5tplYoUY0SD8oK-iz9I_kkrc0)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
10
0580/42/F/M/19
© UCLES 2019
6
O
A
B
C
E
D
0.5cm
0.25cm
1.5cm
NOT TO
SCALE
The diagram shows a company logo made from a rectangle and a major sector of a circle.
The circle has centre
O
and radius
OA
.
OA
=
OD
=
0.5 cm and
AB
=
1.5 cm.
E
is a point on
OC
such that
OE
=
0.25 cm and angle
OED
=
90°.
(a)
Calculate the perimeter of the logo.
............................................. cm [5]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
9
0580/42/F/M/19
© UCLES 2019
[Turn over
(c)
On the grid opposite, draw a suitable straight line to solve the equation ()
xxx
10
3
2
2
1
1
3
-=-
for
x
33
GG
-
.
x
=
....................... or
x
=
....................... or
x
=
....................... [4]
(d)
For
x
33
GG
-
, the equation
xx
10
3
21
3
-=
has
n
solutions.
Write down the value of
n
.
n
=
.................................................. [1]
EduTakers.com
EduTakers.comInk Drawings
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Ink Drawings
Ink Drawings](https://lh4.googleusercontent.com/nclxH0_-LPR0tPKuY3Yd1H96Z32brbsHmVWo2n51l_9F554ObROsZCQ5dhh2Xm72BuA5txMfEvCzvPfTqJjeqByTKxRK7DnI4SRIgz2kEpUesJYLNj2XbdYNnW8QwPXMfFRwY3B3b-lpUVN_2ZWWNb4)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
11
0580/42/F/M/19
© UCLES 2019
[Turn over
(b)
Calculate the area of the logo.
............................................ cm
2
[3]
(c)
A mathematically similar logo is drawn.
The area of this logo is 77.44 cm
2
.
(i)
Calculate the radius of the major sector in this logo.
............................................. cm [3]
(ii)
A gold model is made.
This model is a prism with a cross-section of area 77.44 cm
2
.
This gold model is 15 mm thick.
One cubic centimetre of gold has a mass of 19 grams.
Calculate the mass of the gold model in kilograms.
.............................................. kg [3]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
10
0580/42/F/M/19
© UCLES 2019
6
O
A
B
C
E
D
0.5cm
0.25cm
1.5cm
NOT TO
SCALE
The diagram shows a company logo made from a rectangle and a major sector of a circle.
The circle has centre
O
and radius
OA
.
OA
=
OD
=
0.5 cm and
AB
=
1.5 cm.
E
is a point on
OC
such that
OE
=
0.25 cm and angle
OED
=
90°.
(a)
Calculate the perimeter of the logo.
............................................. cm [5]
EduTakers.com
EduTakers.comInk Drawings
Ink Drawings
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Ink Drawings
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Ink Drawings
Ink Drawings
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Ink Drawings
Ink Drawings](https://lh5.googleusercontent.com/-9A1EiWw0LzHyNwRKm0phzlwo2cBomyEPqHSm46xhmord4twEUCXNgUqbpPb-L5_uC_zRF2k-SYpbh7dblSBq2xM8AfX940csmwo3aPZKj4FlB7pvjZwFHPTZgMGG8LgaRYhd87QuNHMldlZ38DwnyQ)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
12
0580/42/F/M/19
© UCLES 2019
7 (a)
20 students each record the mass,
p
grams, of their pencil case.
The table below shows the results.
Mass
(
p
grams)
0
1
p
G
5050
1
p
G
100100
1
p
G
125125
1
p
G
150150
1
p
G
200
Frequency25463
(i)
Calculate an estimate of the mean mass.
................................................ g [4]
(ii)
Use the frequency table above to complete the cumulative frequency table.
Mass
(
p
grams)
p
G
50
p
G
100
p
G
125
p
G
150
p
G
200
Cumulative
frequency
20
[2]
(iii)
A student is chosen at random.
Find the probability that this student has a pencil case with a mass greater than 150 g.
................................................... [1]
(b)
Some students each record the mass,
m
kg, of their school bag.
Adil wants to draw a histogram to show this information.
Complete the table below.
Mass (
m
kg)
0
1
m
G
44
1
m
G
66
1
m
G
77
1
m
G
10
Frequency3242
Height of bar on
histogram (cm)
1.6 21.22.8
[2]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
11
0580/42/F/M/19
© UCLES 2019
[Turn over
(b)
Calculate the area of the logo.
............................................ cm
2
[3]
(c)
A mathematically similar logo is drawn.
The area of this logo is 77.44 cm
2
.
(i)
Calculate the radius of the major sector in this logo.
............................................. cm [3]
(ii)
A gold model is made.
This model is a prism with a cross-section of area 77.44 cm
2
.
This gold model is 15 mm thick.
One cubic centimetre of gold has a mass of 19 grams.
Calculate the mass of the gold model in kilograms.
.............................................. kg [3]
EduTakers.com
EduTakers.comInk Drawings
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Ink Drawings
Ink Drawings](https://lh6.googleusercontent.com/dbAZ1P8_rEs2dfb5VBpAQ3VIMLMy9VmuAAaITPlIh-8dmOQlFoLKFjzedFhVTgKgp7cXhihQvoBIgil_PaHxBkCwegQXihsVufCdyHIo1fMWzhfstFpF89KtnqAWDf8aRw5evimw70oMGQg0Hxpzwks)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
13
0580/42/F/M/19
© UCLES 2019
[Turn over
(c)
The frequency table below shows information about the number of books read by some students in a
reading marathon.
Number of
books read
12345678
Frequency22161094
x
2
(i)
The mean number of books read is 4.28 .
Find the value of
x
.
x
=
.................................................. [3]
(ii)
Write down the mode.
................................................... [1]
(iii)
Write down the median.
................................................... [1]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
12
0580/42/F/M/19
© UCLES 2019
7 (a)
20 students each record the mass,
p
grams, of their pencil case.
The table below shows the results.
Mass
(
p
grams)
0
1
p
G
5050
1
p
G
100100
1
p
G
125125
1
p
G
150150
1
p
G
200
Frequency25463
(i)
Calculate an estimate of the mean mass.
................................................ g [4]
(ii)
Use the frequency table above to complete the cumulative frequency table.
Mass
(
p
grams)
p
G
50
p
G
100
p
G
125
p
G
150
p
G
200
Cumulative
frequency
20
[2]
(iii)
A student is chosen at random.
Find the probability that this student has a pencil case with a mass greater than 150 g.
................................................... [1]
(b)
Some students each record the mass,
m
kg, of their school bag.
Adil wants to draw a histogram to show this information.
Complete the table below.
Mass (
m
kg)
0
1
m
G
44
1
m
G
66
1
m
G
77
1
m
G
10
Frequency3242
Height of bar on
histogram (cm)
1.6 21.22.8
[2]
EduTakers.com
EduTakers.comInk Drawings
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Ink Drawings
Ink Drawings
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Ink Drawings
Ink Drawings](https://lh4.googleusercontent.com/8400TkIeNPbncuYfR-YQbQrnu-r0vwMbHUkU_3cLFB3mJcGbbbJxkWI3K4ppvVvIMQ_LyDbZ_FT3VGsKpBQQnRpgjg9JNgcKEWFHcol3yFNV0ZCyTTEnV70T1i5e1gXZEpYDZC-Q5vFAv0k9hNH1wMw)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
14
0580/42/F/M/19
© UCLES 2019
8
(),
f
x
x
x
2
3
2
!
=
+
-
()
g
xx
85
=-
()
h
xx
6
2
=+
(a)
Work out g
4
1
eo
.
................................................... [1]
(b)
Work out ff(2).
................................................... [2]
(c)
Find gg(
x
), giving your answer in its simplest form.
................................................... [2]
(d)
Find
()
g
x
1
-
.
()
g
x
1
=
-
.................................................. [2]
(e)
Write
()()
gf
xx
-
as a single fraction in its simplest form.
................................................... [3]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
13
0580/42/F/M/19
© UCLES 2019
[Turn over
(c)
The frequency table below shows information about the number of books read by some students in a
reading marathon.
Number of
books read
12345678
Frequency22161094
x
2
(i)
The mean number of books read is 4.28 .
Find the value of
x
.
x
=
.................................................. [3]
(ii)
Write down the mode.
................................................... [1]
(iii)
Write down the median.
................................................... [1]
EduTakers.com
EduTakers.comInk Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings
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Ink Drawings
Ink Drawings
Ink Drawings












Ink Drawings
Ink Drawings
Ink Drawings](https://lh5.googleusercontent.com/B-z_pB9yEP376X24QB7leuZMXecgK9wfQmv2K-Td7oGNvyiIIOQ6sVsUzkid5bZtFe_XDrrdRsQ7MQe4Ki-m1RjmrOsHuWtNr5AfRj14Vze8Z7nQqbdAldn9SzzVIQNpWyNZ6kaMXNPohefPSZFRRds)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
15
0580/42/F/M/19
© UCLES 2019
[Turn over
(f) (i)
Show that hg(
x
)
=
19 simplifies to
xx
1620
30
2
-+
=
.
[3]
(ii)
Use the quadratic formula to solve
xx
1620
30
2
-+
=
.
Show all your working and give your answers correct to 2 decimal places.
x
=
......................... or
x
=
......................... [4]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
14
0580/42/F/M/19
© UCLES 2019
8
(),
f
x
x
x
2
3
2
!
=
+
-
()
g
xx
85
=-
()
h
xx
6
2
=+
(a)
Work out g
4
1
eo
.
................................................... [1]
(b)
Work out ff(2).
................................................... [2]
(c)
Find gg(
x
), giving your answer in its simplest form.
................................................... [2]
(d)
Find
()
g
x
1
-
.
()
g
x
1
=
-
.................................................. [2]
(e)
Write
()()
gf
xx
-
as a single fraction in its simplest form.
................................................... [3]
EduTakers.com
EduTakers.comInk Drawings
Ink Drawings
Ink Drawings
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Ink Drawings
Ink Drawings
Ink Drawings
Ink Drawings](https://lh3.googleusercontent.com/_dwKY79P8pu8Dj7DSYLH6Av5zxWnCUEcg-trhhGHPMqQkXnpjzEUIIaz3kQK9yaDrEIVplA6Zpn0WEeiPwsrWnOfThJcLkt7XBeIsyPSMyUBaQLYX58GPQe8pTHRFhmxjre31gKhQ4LWbGhbuWVjHHg)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
16
0580/42/F/M/19
© UCLES 2019
9 (a)
The Venn diagram shows two sets,
A
and
B
.
A
B
q
p
g
c
d
e
j
k
m
h
f
(i)
Use set notation to complete the statements.
(a)
d
...................
A
[1]
(b)
{
f
,
g
}
=
............................... [1]
(ii)
Complete the statement.
n (.........................)
=
6 [1]
(b)
In the Venn diagram below, shade
CD
+
l
.
CD
[1]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
15
0580/42/F/M/19
© UCLES 2019
[Turn over
(f) (i)
Show that hg(
x
)
=
19 simplifies to
xx
1620
30
2
-+
=
.
[3]
(ii)
Use the quadratic formula to solve
xx
1620
30
2
-+
=
.
Show all your working and give your answers correct to 2 decimal places.
x
=
......................... or
x
=
......................... [4]
EduTakers.com
EduTakers.comInk Drawings
Ink Drawings
Ink Drawings
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Ink Drawings
Ink Drawings](https://lh6.googleusercontent.com/dGD75RcJw2KRR-9TG7M6wTp1FgHMMQJl6OPRdDSczjqow7vqvFpWfFNq-GOAw-JWhJO4JLfh70I_5tHoo7d2RSZAVoGaVytRfgklj7c5tkcBbvgxECt07TRNhsNjDHfiSw5aRcWNsEIAc2YWcOCnfOg)
![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
17
0580/42/F/M/19
© UCLES 2019
[Turn over
(c)
50 students study at least one of the subjects geography (
G
), mathematics (
M
) and history (
H
).
18 study only mathematics.
19 study two or three of these subjects.
23 study geography.
The Venn diagram below is to be used to show this information.
G
M
H
x
x
x
7
.........
.........
.........
(i)
Show that
x
=
4.
[2]
(ii)
Complete the Venn diagram. [2]
(iii)
Use set notation to complete this statement.
()
GM
H
,,
l
=
....................... [1]
(iv)
Find n
((
))
GM
H
+,
.
................................................... [1]
EduTakers.com
EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
16
0580/42/F/M/19
© UCLES 2019
9 (a)
The Venn diagram shows two sets,
A
and
B
.
A
B
q
p
g
c
d
e
j
k
m
h
f
(i)
Use set notation to complete the statements.
(a)
d
...................
A
[1]
(b)
{
f
,
g
}
=
............................... [1]
(ii)
Complete the statement.
n (.........................)
=
6 [1]
(b)
In the Venn diagram below, shade
CD
+
l
.
CD
[1]
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![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
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0580/42/F/M/19
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[Turn over
(c)
50 students study at least one of the subjects geography (
G
), mathematics (
M
) and history (
H
).
18 study only mathematics.
19 study two or three of these subjects.
23 study geography.
The Venn diagram below is to be used to show this information.
G
M
H
x
x
x
7
.........
.........
.........
(i)
Show that
x
=
4.
[2]
(ii)
Complete the Venn diagram. [2]
(iii)
Use set notation to complete this statement.
()
GM
H
,,
l
=
....................... [1]
(iv)
Find n
((
))
GM
H
+,
.
................................................... [1]
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![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
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10 (a)
Solve the simultaneous equations.
You must show all your working.
xy
65
27
+=
xy
53
44
-=
x
=
..................................................
y
=
.................................................. [4]
(b)
y
is inversely proportional to ()
x
3
2
+
.
When
x
=
2,
y
=
8.
Find
y
when
x
=
7.
y
=
.................................................. [3]
(c)
Solve the inequality.
()()
xx
3272
1
-+
................................................... [3]
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EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
17
0580/42/F/M/19
© UCLES 2019
[Turn over
(c)
50 students study at least one of the subjects geography (
G
), mathematics (
M
) and history (
H
).
18 study only mathematics.
19 study two or three of these subjects.
23 study geography.
The Venn diagram below is to be used to show this information.
G
M
H
x
x
x
7
.........
.........
.........
(i)
Show that
x
=
4.
[2]
(ii)
Complete the Venn diagram. [2]
(iii)
Use set notation to complete this statement.
()
GM
H
,,
l
=
....................... [1]
(iv)
Find n
((
))
GM
H
+,
.
................................................... [1]
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![Embedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
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© UCLES 2019
11 (a)
The table shows the first five terms of sequence
A
and sequence
B
.
Term123456
Sequence
A
713233755
Sequence
B
1392781
(i)
Complete the table for the 6th term of each sequence. [2]
(ii)
Find the
n
th term of
(a)
sequence
A
,
................................................... [2]
(b)
sequence
B
.
................................................... [2]
(b)
The
n
th term of another sequence is
nn
43
2
++
.
Find
(i)
the 2nd term,
................................................... [1]
(ii)
the value of
n
when the
n
th term is 498.
n
=
.................................................. [3]
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EduTakers.comEmbedded file printout 1-0580_m19_qp_42.pdf Machine generated alternative text:
18
0580/42/F/M/19
© UCLES 2019
10 (a)
Solve the simultaneous equations.
You must show all your working.
xy
65
27
+=
xy
53
44
-=
x
=
..................................................
y
=
.................................................. [4]
(b)
y
is inversely proportional to ()
x
3
2
+
.
When
x
=
2,
y
=
8.
Find
y
when
x
=
7.
y
=
.................................................. [3]
(c)
Solve the inequality.
()()
xx
3272
1
-+
................................................... [3]
EduTakers.com
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1 Math 2019 Feb Mar – 42 (PDF and Mark Scheme)