Cambridge International Examinations Cambridge ......MATHEMATICS 0580/21 Paper 2 (Extended) May/June...

This document consists of 15 printed pages and 1 blank page.

DC (ST/FC) 130071/3

© UCLES 2017 [Turn over

Cambridge International Examinations

Cambridge International General Certificate of Secondary Education

*0243113261*

MATHEMATICS 0580/21

Paper 2 (Extended) May/June 2017

1 hour 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 70.

Compiled and edited by www.mathramanathan.wordpress.com

2

0580/21/M/J/17© UCLES 2017

1 Simplify.

(x2)5

.............................................. [1]

2 The thickness of one sheet of paper is 8 # 10-3 cm.

Work out the thickness of 250 sheets of paper.

........................................ cm [1]

3 Write 23.4571 correct to

(a) 4 significant figures,

.............................................. [1]

(b) the nearest 10.

.............................................. [1]

4 The table shows the temperatures in five places at 10 am one day in January.

Place Temperature (°C)

Helsinki -7

Chicago -10

London 3

Moscow -4

Bangkok 26

(a) Which place was the coldest?

.............................................. [1]

(b) At 2 pm the temperature in Helsinki had increased by 4 °C.

Write down the temperature in Helsinki at 2 pm.

.........................................°C [1]


3

0580/21/M/J/17© UCLES 2017 [Turn over

5 Factorise completely.

12n2 - 4mn

.............................................. [2]

6 (a) 2161r

=

Find the value of r.

r = ....................................... [1]

(b) 3 3t5=

Find the value of t.

t = ........................................ [1]

7 Without using a calculator, work out 132

75+ .

Write down all the steps of your working and give your answer as a mixed number in its simplest form.

.............................................. [3]


4

0580/21/M/J/17© UCLES 2017

8 Simon has two boxes of cards.

In one box, each card has one shape drawn on it that is either a triangle or a square.

In the other box, each card is coloured either red or blue.

Simon picks a card from each box at random.

The probability of picking a triangle card is t.

The probability of picking a red card is r.

Complete the table for the cards that Simon picks, writing each probability in terms of r and t.

Event Probability

Triangle and red

Square and red (1 - t) r

Triangle and blue

Square and blue

[3]

9 h is directly proportional to the square root of p.

h = 5.4 when p = 1.44 .

Find h when p = 2.89 .

h = ....................................... [3]


5


10

1

–1

0

1

2

3

4

5

y

x2 3 4 5 6

By shading the unwanted regions of the grid, find and label the region R that satisfies the following four

inequalities.

y G 2 y H 1 y G 2x - 1 y G 5 - x [3]

11 The two barrels in the diagram are mathematically similar.

h cm

90 cm

NOT TO

SCALE

The smaller barrel has a height of h cm and a capacity of 100 litres.

The larger barrel has a height of 90 cm and a capacity of 160 litres.

Work out the value of h.

h = ....................................... [3]


6

0580/21/M/J/17© UCLES 2017

12 A line has gradient 5.

M and N are two points on this line.

M is the point (x, 8) and N is the point (k, 23).

Find an expression for x in terms of k.

x = ....................................... [3]

13

A

E

H

D

B

C

G

F

13 cm

NOT TO

SCALE

5 cm

4 cm

The diagram shows a cuboid ABCDEFGH.

AE = 5 cm, EH = 4 cm and AG = 13 cm.

Calculate the angle between the line AG and the base EFGH of the cuboid.

.............................................. [3]


7


14 The diagram shows a regular octagon joined to an equilateral triangle.

NOT TO

SCALE

x°

Work out the value of x.

x = ....................................... [3]


8

0580/21/M/J/17© UCLES 2017

15 The diagram shows information about the first 100 seconds of a car journey.

100

2

0

4

6

8

10

12

14

16

Speed

(m/s)

18

20 30 40 50

Time (s)

60 70 80 90 100

(a) Calculate the acceleration during the first 20 seconds of the journey.

......................................m/s2 [1]

(b) Work out the total distance travelled by the car in the 100 seconds.

.......................................... m [3]


9


16 Six students revise for a test.

The scatter diagram shows the time, in hours, each student spent revising and their mark in the test.

025

30

35

40

Mark

45

50

1 2 3 4 5

Time (hours)

6 7 8 9 10

(a) The data for two more students is shown in the table.

Time (hours) 4.5 6.5

Mark 33 35

Plot these two points on the scatter diagram. [1]

(b) What type of correlation is shown on the scatter diagram?

.............................................. [1]

(c) Draw a line of best fit on the scatter diagram. [1]

(d) Another student spent 5.5 hours revising.

Estimate a mark for this student.

.............................................. [1]


10

0580/21/M/J/17© UCLES 2017

17 (a) In this Venn diagram, shade the region F G, l.

�

F G

[1]

(b) = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {x: x is an odd number}

B = {x: x is a square number}

C = {x: x is a multiple of 3}

(i) Write all the elements of in the Venn diagram below.

�

A B

C

[2]

(ii) Another number is included in the set .

This number is in the region A B C+ +l .

Write down a possible value for this number.

.............................................. [1]


11


18 The diagram shows a parallelogram OCEG.

B

b

a

C D E

F

NOT TO

SCALE

GA

H

O

O is the origin, OA a= and OB b= .

BHF and AHD are straight lines parallel to the sides of the parallelogram.

OG OA3= and OC OB2= .

(a) Write the vector HE in terms of a and b.

HE = .................................. [1]

(b) Complete this statement.

a + 2b is the position vector of point ......................... [1]

(c) Write down two vectors that can be written as 3a - b.

............................... and ............................... [2]


12

0580/21/M/J/17© UCLES 2017

19 ABCD is a rhombus with side length 10 cm.

D 40°

10 cm

B

NOT TO

SCALE

A

C

Angle ADC = 40°.

DAC is a sector of a circle with centre D.

BAC is a sector of a circle with centre B.

Calculate the shaded area.

...................................... cm2 [4]


13


20 The diagram shows a fair spinner.

1

3

34

6

Anna spins it twice and adds the scores.

(a) Complete the table for the total scores.

Score on first spin

1 3 3 4 6

Score on

second spin

1 2 4 4 5 7

3 4 6 6 7 9

3 4 6 6 7 9

4

6

[1]

(b) Write down the most likely total score.

.............................................. [1]

(c) Find the probability that Anna scores

(i) a total less than 6,

.............................................. [2]

(ii) a total of 3.

.............................................. [1]


14

0580/21/M/J/17© UCLES 2017

21 (a)

A

B

C

D

X35°

NOT TO

SCALE

v°

u°

A, B, C and D are points on the circle.

AD is parallel to BC.

The chords AC and BD intersect at X.

Find the value of u and the value of v.

u = .......................................

v = ....................................... [3]

(b)

F

G

H

NOT TO

SCALE

O

210°

p°

F, G and H are points on the circle, centre O.

Find the value of p.

p = ....................................... [2]


15

0580/21/M/J/17© UCLES 2017

22 Write as a single fraction in its simplest form.

(a) x

x x

9

32

2

-

-

.............................................. [3]

(b) x x4

32 5

2-+

+

.............................................. [3]


16

0580/21/M/J/17© UCLES 2017

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every

reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the

publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International

Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after

the live examination series.

Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local

Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

BLANK PAGE


This document consists of 16 printed pages.

DC (LK/SG) 130216/4


Cambridge International Examinations

Cambridge International General Certificate of Secondary Education

*6433049420*

MATHEMATICS 0580/41


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.


2

0580/41/M/J/17© UCLES 2017

1 An energy company charged these prices in 2013.

Electricity price Gas price

23.15 cents per day

plus

13.5 cents for each unit used

24.5 cents per day

plus

5.5 cents for each unit used

(a) (i) In 90 days, the Siddique family used 1885 units of electricity.

Calculate the total cost, in dollars, of the electricity they used.

$ ................................................ [2]

(ii) In 90 days, the gas used by the Khan family cost $198.16 .

Calculate the number of units of gas used.

........................................ units [3]

(b) In 2013, the price for each unit of electricity was 13.5 cents.

Over the next 3 years, this price increased exponentially at a rate of 8% per year.

Calculate the price for each unit of electricity after 3 years.

....................................... cents [2]

(c) Over these 3 years, the price for each unit of gas increased from 5.5 cents to 7.7 cents.

(i) Calculate the percentage increase from 5.5 cents to 7.7 cents.

............................................ % [3]


3


(ii) Over the 3 years, the 5.5 cents increased exponentially by the same percentage each year to

7.7 cents.

Calculate the percentage increase each year.

............................................ % [3]

(d) In 2015, the energy company divided its profits in the ratio

shareholders : bonuses : development : :5 2 6= .

In 2015, its profits were $390 million.

Calculate the amount the company gave to shareholders.

$ ................................... million [2]

(e) The share price of the company in June 2015 was $258.25 .

This was an increase of 3.3% on the share price in May 2015.

Calculate the share price in May 2015.

$ ............................................... [3]


4

0580/41/M/J/17© UCLES 2017

2 The time taken for each of 90 cars to complete one lap of a race track is shown in the table.

Time (t seconds) t70 711 G t7 721 1 G t7 72 31 G t7 73 41 G t7 74 51 G

Frequency 17 24 21 18 10

(a) Write down the modal time interval.

............... t1 G ............. [1]

(b) Calculate an estimate of the mean time.

.............................................. s [4]

(c) (i) Complete the cumulative frequency table.

Time (t seconds) t 71G t 72G t 73G t 74G t 75G

Cumulative frequency 17

[2]


5


(ii) On the grid, draw a cumulative frequency diagram to show this information.

90

80

70

60

50

40

30

20

10

070 71 72 73 74 75

t

Time (seconds)

Cumulative

frequency

[3]

(iii) Find the median time.

.............................................. s [1]

(iv) Find the inter-quartile range.

.............................................. s [2]

(d) One lap of the race track measures 3720 metres, correct to the nearest 10 metres.

A car completed the lap in 75 seconds, correct to the nearest second.

Calculate the upper bound for the average speed of this car.

Give your answer in kilometres per hour.

....................................... km/h [4]


6

0580/41/M/J/17© UCLES 2017

3

–1

–1

1

1 2 3 4 5 6 7 8

2

3

4

5

6

7

8

–2

–3

–4

–5

–6

–2–3–4–5–6

y

0x

A

B

(a) (i) Draw the image of triangle A after reflection in the line x 4= . [2]

(ii) Draw the image of triangle A after rotation of 90° anticlockwise about (0, 0). [2]

(iii) Draw the image of triangle A after translation by the vector 1

5-c m. [2]

(b) Describe fully the single transformation that maps triangle A onto triangle B.

..............................................................................................................................................................

.............................................................................................................................................................. [3]

(c) Find the matrix that represents the transformation in part (a)(ii).

f p [2]


7


(d) Point P has co-ordinates (4, 1).

F1

0

0

1=-c m and G 1

0

0

2= c m represent transformations.

(i) Find G(P), the image of P after the transformation represented by G.

(....................... , .......................) [2]

(ii) Find GF(P).

(....................... , .......................) [3]

(iii) Find the matrix Q such that ( )GQ P P= .

f p [3]


8

0580/41/M/J/17© UCLES 2017

4 The diagram shows the graph of ( )fy x= for . x2 5 2G G- .

–8

–9

–10

–7

–6

–5

–4

–3

–2

–1

0

1

2

3

4

5

6

7

8

9

10

–1 1 2–2

x

y


9


(a) Find f(1).

................................................. [1]

(b) Solve ( )f x 3= .

x = ................................................ [1]

(c) The equation ( )f x k= has only one solution for . x2 5 2G G- .

Write down the range of values of k for which this is possible.

................................................. [2]

(d) By drawing a suitable straight line, solve the equation f(x) = x – 5.

x = ..................... or x = ..................... or x = ..................... [3]

(e) Draw a tangent to the graph of ( )fy x= at the point where x = 1.

Use your tangent to estimate the gradient of ( )fy x= when x = 1.

................................................. [3]


10

0580/41/M/J/17© UCLES 2017

5 (a) The diagram shows a cylindrical container used to serve coffee in a hotel.

18 cm

50 cm

NOT TO

SCALE

The container has a height of 50 cm and a radius of 18 cm.

(i) Calculate the volume of the cylinder and show that it rounds to 50 900 cm3, correct to 3 significant

figures.

[2]

(ii) 30 litres of coffee are poured into the container.

Work out the height, h, of the empty space in the container.

h

NOT TO

SCALE

h = ......................................... cm [3]


11


(iii) Cups in the shape of a hemisphere are filled with coffee from the container.

The radius of a cup is 3.5 cm.

3.5 cm

NOT TO

SCALE

Work out the maximum number of these cups that can be completely filled from the 30 litres of

coffee in the container.

[The volume, V, of a sphere with radius r is V r34 3r= .]

................................................. [4]

(b) The hotel also uses glasses in the shape of a cone.

r

8.4 cm

NOT TO

SCALE

The capacity of each glass is 95 cm3.

(i) Calculate the radius, r, and show that it rounds to 3.3 cm, correct to 1 decimal place.

[The volume, V, of a cone with radius r and height h is V r h31 2r= .]

[3]

(ii) Calculate the curved surface area of the cone.

[The curved surface area, A, of a cone with radius r and slant height l is A rlr= .]

......................................... cm2 [4]


12

0580/41/M/J/17© UCLES 2017

6 (a) Expand the brackets and simplify.

(i) ( ) ( )x x4 2 5 5 3 7+ - -

................................................. [2]

(ii) ( )x 7 2-

................................................. [2]

(b) Solve.

(i) x

32

5 7+ =-

x = ................................................ [3]

(ii) ( )x x4 9 3 2 7+ = -

x = ................................................ [3]

(iii) x3 1 742 - =

x = ..................... or x = ..................... [3]


13


7 A line joins the points ( , )A 3 8- and ( , )B 2 2- .

(a) Find the co-ordinates of the midpoint of AB.

(....................... , .......................) [2]

(b) Find the equation of the line through A and B.

Give your answer in the form y mx c= + .

y = ....................................... [3]

(c) Another line is parallel to AB and passes through the point (0, 7).

Write down the equation of this line.

................................................. [2]

(d) Find the equation of the line perpendicular to AB which passes through the point (1, 5).

Give your answer in the form ax by c 0+ + = where a, b and c are integers.

................................................. [4]


14

0580/41/M/J/17© UCLES 2017

8 (a)

110°

280°

North

North38 km

50 km

A

BC

NOT TO

SCALE

A, B and C are three towns.

The bearing of B from A is 110°.

The bearing of C from B is 280°.

kmAC 38= and kmAB 50= .

(i) Find the bearing of A from B.

................................................. [2]

(ii) Calculate angle BAC.

Angle BAC = ................................................ [5]

(iii) A road is built from A to join the straight road BC.

Calculate the shortest possible length of this new road.

.......................................... km [3]


15


(b) Town A has a rectangular park.

The length of the park is x m.

The width of the park is 25 m shorter than the length.

The area of the park is 2200 m2.

(i) Show that x x25 2200 02 - - = .

[1]

(ii) Solve x x25 2200 02 - - = .

Show all your working and give your answers correct to 2 decimal places.

x = ..................... or x = ..................... [4]

Question 9 is printed on the next page.


16

0580/41/M/J/17© UCLES 2017

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every

reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the

publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International

Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after

the live examination series.

Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local

Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

9 (a) The nth term of a sequence is n8 3- .

(i) Write down the first two terms of this sequence.

....................... , ....................... [1]

(ii) Show that the number 203 is not in this sequence.

[2]

(b) Find the nth term of these sequences.

(i) 13, 19, 25, 31, …

................................................. [2]

(ii) 4, 8, 14, 22, …

................................................. [2]

(c) … , 20, 50, …

The second term of this sequence is 20 and the third term is 50.

The rule for finding the next term in this sequence is subtract y then multiply by 5.

Find the value of y and work out the first term of this sequence.

y = ................................................

First term = ................................................ [4]


® IGCSE is a registered trademark.



Cambridge International Examinations Cambridge International General Certificate of Secondary Education

MATHEMATICS 0580/21


MARK SCHEME

Maximum Mark: 70

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2017 series for most Cambridge IGCSE

®,

Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.


0580/21 Cambridge IGCSE – Mark Scheme PUBLISHED

May/June 2017

© UCLES 2017 Page 2 of 5

Abbreviations

cao correct answer only

dep dependent

FT follow through after error

isw ignore subsequent working

oe or equivalent

SC Special Case

nfww not from wrong working

soi seen or implied

Question Answer Mark Part marks

1 x10 1

2 2 1

3(a) 23.46 cao 1

3(b) 20 cao 1

4(a) Chicago 1

4(b) − 3 1

5 4n(3n – m) final answer 2 B1 for 4(3n2 – mn) or n(12n – 4m) or

2n(6n – 2m) or 2(6n2 – 2mn)

6(a) − 4 1

6(b) 1

5 or 0.2

1

7 ( )14 or 35

21 +

15

21

M1accept

( )14 or 35

21

k k

k +

15

21

k

k

2

8

21 cao

A2or A1 for

50

21 or 1

8

21 or

29

21 or 1

29

21

8 rt

(1 – t) r

(1 − r)t oe

(1 – r)(1 – t) oe

3

B1 for each

9 7.65 3 M1 for h = k p oe

M1 for h = their k p

or M2 for 5.4

1.44 =

2.89

h oe


0

©

Qu

1

1

1

0580/21

© UCLES 2017

estion

10 Co

11 76

12 k –

13 22

14 16

5(a) 0.8

5(b) 11

6(a) Po

(6

orrect region

6.9 or 76.94 t

– 3 or 3 k− +

2.6 or 22.61 t

65

8 or 4

5

180

oints plotted

.5, 35)

R

C

Answer

n identified

to 76.95

k

to 22.62

at (4.5, 33) a

R

Cambridge P

and

IGCSE – MPUBLISHED

Page 3 of 5

Mar

Mark SchemD

rk

3

SC1 fo

3M2 for

or M1

3

90

h

3M1 for

M1 for

e.g. [x =

3M2 for

or M1

3M2 for

or M1

[exterio

1

3 M2 for

(0.5 ×

or M1

1

e

P

or

r 90 ÷ 3160

100

for 3160

100 so

100

160= oe

r 5 = 23 8

k x

−−

o

r 5(k – x) = 2

=] k − 23 85

−

r sin [=] 5

13 o

for identifyin

r 360

8 +

360

3

for [exterior

or angle of tr

r

16 × 20) + (0

for part area

3

2

0

1

1 2

2

M

Part marks

or 90 × 310

16

oi or 3100

160

oe

23 – 8 or bett

8

oe

ng angle AG

0 oe

r angle of oct

riangle =] 36

3

0.5 × 4 × 30)

a

1

1

2

May/June 201

0

0

soi or

ter

GE

tagon =] 360

8

60

3 oe

) + (80 × 12)

17

0 or

oe



May/June 2017



16(b) Positive 1

16(c) Correct ruled line 1

16(d) 33.5 to 37.5 1FT FT from their line providing positive gradient

17(a) 1

17(b)(i)

2 B1 for four out of the eight regions correct

17(b)(ii) Any even square number that is also a

multiple of 3

1

18(a) 2a + b 1

18(b) D 1

18(c) CFuuur

and BGuuur

2 B1 for each

19 5.53 or 5.54 or 5.534 to 5.543… 4 M3 for

2 × {(40

360 × π × 102)– ( 1

2 × 102 × sin 40)}

or M2 for

1

2

×

102 × sin 40 and [240

] 360

× × π × 102

or M1 for

1

2

×

102 × sin 40 or [2 ]×

40

360 × π × 102

20(a) 5 7 7 8 10

7 9 9 10 12

1

20(b) 7 1

F G

A B

9 5 7 4

2 8

C

3

6

1



May/June 2017



20(c)(i) 7

25 or 0.28 or 28%

2FTFT

7

25

their

B1 for 25

k

If zero scored, then SC1 for 2

5 or

6

15 if no

values in the bottom two rows of the table.

20(c)(ii) 0 1FTFT

0

25

their

21(a) [u =] 35 1

[v =] 110 2 B1 for ACB or ADB = 35

21(b) 75 2 B1 for 150

or M1 for 360 210

2

−

22(a)

3

x

x + final answer

3 B1 for x(x – 3)

B1 for (x – 3)(x + 3)

22(b) 8 7

( 4)(2 5)

x

x x

+

− + final answer

3 B1 for common denominator of (x − 4)(2x + 5) oe

M1 for 3(2x + 5) + 2(x − 4) oe with an attempt to expand the brackets


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Cambridge International Examinations Cambridge International General Certificate of Secondary Education

MATHEMATICS 0580/41


MARK SCHEME

Maximum Mark: 130

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2017 series for most Cambridge IGCSE

®,

Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.



May/June 2017


Abbreviations

cao correct answer only

dep dependent

FT follow through after error

isw ignore subsequent working

oe or equivalent

SC Special Case

nfww not from wrong working

soi seen or implied

Question Answer Marks Part marks

1(a)(i) 275.31 2 M1 for 90 × 23.15 + 1885 × 13.5 oe

1(a)(ii) 3202 3M2 for

198.16 – 90 0.245

0.055

× oe

M1 for 90 × 0.245 or 90 × 24.5 oe

1(b) 17.[0] or 17.00 to 17.01 2M1 for 13.5 ×

38

1100

+

1(c)(i) 40 3M2 for

7.7 5.5

5.5

−[×100] oe or

7.7

5.5×100

or M1 for 7.7

5.5oe

1(c)(ii) 11.9 or 11.86 to 11.87 3M2 for 3

7.7

5.5oe

or M1 for 5.5 × x3 = 7.7 oe

1(d) 150 [million] oe 2 M1 for 390 [million] ÷ ( 5 + 2 + 6)

1(e) 250 nfww 3 M2 for 258.25 ÷ ((100 + 3.3) ÷ 100)

or M1 for 258.25 associated with

103.3[%]

2(a) 71 < t ⩽ 72 1 2(b) 72.3 or 72.27 to 72.28 nfww 4 M1 for midpoints soi (condone 1 error or

omission)

M1 for use of ∑fx with x in correct interval including both boundaries

M1 (dep on 2nd M1) for ∑fx ÷ 90

2(c)(i) 41, 62, 80, 90 2 B1 for 2 correct values



May/June 2017



2(c)(ii) Correct curve 3 B1FT their (c)(i) for 5 correct heights

B1 for 5 points plotted at upper ends of

intervals

B1FT (dep on at least B1) for increasing

curve or increasing polygon through 5

points

If zero scored, SC1FT for 4 correct points

plotted

2(c)(iii) 72.1 to 72.4 1

2(c)(iv) 1.9 to 2.2 2 M1 for UQ = 73.2 to 73.4

or LQ = 71.2 to 71.3

2(d) 180 cao nfww 4 B3 for 50 [m/s] nfww

OR

M3 for 3725 1000

74.5 3600

÷

÷

OR

M2 for 3725 ÷ 74.5

or M1 for 3725 or 74.5 seen or for

(3715 to 3725) ÷ (74.5 to 75.5)

M1 indep for multiply by 3.6 oe

3(a)(i) Image at (5, 1), (7, 1), (7, 4) 2 B1 reflection in y = 4 or x = k

3(a)(ii) Image at (–1, 1), (–4, 1), (–1, 3) 2 B1 correct size and correct orientation

wrong position

or for rotation 90° clockwise around (0, 0)

3(a)(iii) Image at (2, – 4), (4, – 4), (2, – 1) 2B1 for translation by

1

k

or 5

k −

3(b) Enlargement 1

[sf] – 0.5 oe 1

(5, 5) 1

3(c) 0 1

1 0

−

2 B1 for one correct column or row

3(d)(i) (4, 2) 2M1 for

1 0 4

0 2 1

oe



May/June 2017



3(d)(ii) (– 4, 2) 3M2 for

1 0

0 2

−

or 1 0 4

0 2 1

−

or M1 for 1 0 1 0 4

0 2 0 1 1

−

or 4

1

−

3(d)(iii) 2 01

0 12

oe isw 3

M2 for det = 2 soi or 2 0

0 1k

soi

or M1 for recognition that Q is inverse

matrix of G

or GQ = I or QG = I

4(a) –1.6 to 1.4− 1

4(b) –0.5 1

4(c) k > –4 2 B1 for identifying the –4

or for horizontal line drawn y = –4

4(d) y = x – 5 ruled

and

–2.3 to –2.1

–1.2 to –1.1

1.3 to 1.4

3 B2 for correct line and 2 correct values or

no line and 3 correct values

or B1 for no line and 2 correct values

or B1 for correct line

4(e) Tangent ruled at x = 1 B1 No daylight at point of contact. Consider

point of contact as midpoint between two

vertices of daylight, the midpoint must be

between x = 0.8 and 1.2

–6 to –4 2 Dep on B1 or close attempt at tangent at

x = 1

M1 for rise/run for their tangent at 1x =

5(a)(i) 50890 or 50893 to 50900.4 2 M1 for π × 182 × 50



May/June 2017



5(a)(ii) 20.5 or 20.52 to 20.534 3 B2 for answer 29.5 or 29.46 to 29.48

OR

M2 for ( ) ( )250900 30000 π 18− ÷ × oe

or M1 for

(figs 50.9 –figs 30) ÷ ( π× figs182) or M1 for ( ) ( )250900 30000 π 18− = × h oe

OR

alternative method

M2 for 2

3000050

π 18−

× oe

M1 for figs 30 ( )2π figs 18 50= × × − h oe

or for 2

figs 30

π figs18× oe

OR

alternative method

M2 for (50.9 30)

50.9

−× 50 oe

or M1 for (50.9 30)

50.9

− or

30

50.9× 50 oe

or M1 for

(figs 50.9 figs 30)

figs 50.9

−× 50 oe

5(a)(iii) 334 nfww 4M2 for figs 30 ÷

32 π 3.53

× oe

or M1 for 31 4 π 3.5

2 3× × oe

and B1 for 30 000

5(b)(i) 3.28[6..] or 3.29 3M2 for [ r2 = ]

95 3

8.4π×

oe

or M1 for 21 π 8.4 [ 95]

3× × =r

5(b)(ii) 93.1 to 93.6 4M3 for

2 2π 3.3 3.3 8.4× × +

or M2 for 2 23.3 8.4+

or M1 for 3.32 + 8.42

6(a)(i) –7x + 55 final answer 2 M1 for 8x + 20 or –15x + 35

or answer –7x + k or kx + 55

6(a)(ii) x2 – 14x + 49 final answer 2 M1 for 3 of x2 – 7x – 7x + 49



May/June 2017



6(b)(i) –18 3 M1 for a correct first step ie correctly

multiplying by 3 or correctly dividing by

2 or for correctly subtracting 5

M1 for correctly reaching ax = b from

their first step

6(b)(ii) 15 3 M2 for 6x – 4x = 21 + 9 oe

or

M1 for 6x – 21 or correct division by 3

or for correctly reaching ax = b from their

first step

6(b)(iii) 5 and –5 3 B2 for 5 or –5

or M1 for [x2 =] (74 + 1) ÷ 3 or better

7(a) (–0.5, 3) 2 B1 for one correct value

7(b) [y = ] –2x + 2 final answer 3M1 for

2 8

2 3

− −− −

or better

M1 for substitution of (–3, 8) or (2, –2)

or their midpoint into y = mx + c with

their m

7(c) y = –2x + 7 oe 2FT FT their (b)

M1 for y = (their–2)x + k ( k ≠ 2) or y = kx + 7 (k ≠ 0)

If zero scored, SC1 for ( )2 7− +their x

7(d) x – 2y + 9 = 0 or 2y – x – 9 = 0 oe 4 B3 for any correct equivalent in wrong

form

Or

M2 for y = ½ x + k oe (FT negative

reciprocal of their gradient in (b))

or M1 for grad = ½ (FT negative

reciprocal of their gradient in (b))

M1 for substitution of (1, 5) into

y = mx + c oe with their m

8(a)(i) 290 2 M1 for 180 + 110 oe

8(a)(ii) 156.8 or 156.7[9..] 5 B1FT for CBA = 10° (their (a) – 280)

and B3 for [angle ACB = ]13.2°

or M2 for [sin C] = 50sin( 10)

38

their

or M1 for 50 38

sin sin ( 10)C their= oe



May/June 2017



8(a)(iii) 8.68 or 8.677 to 8.684 3 M2 for [ ] 50sin( 10)=x their oe

or M1 for ( )sin 1050

=x

their oe

or M1 for a correct right-angled triangle

drawn with 50 as hypotenuse

8(b)(i) x (x – 25) = 2200 1 and no errors seen

8(b)(ii) 2( 25) ( 25) 4(1)( 2200)

2(1)

− − ± − − −or

better

B2 B1 for 2( 25) 4(1)( 2200)− − − or better

or for

225

2x

−

oe

or B1 for ( 25)

2(1)

q− − + or

( 25)

2(1)

q− − −

or both

or for

225 25

or 22002 2

+ − +

–36.04 and 61.04 final answer B1,B1 If B0B0, SC1 for values in ranges –36.042 to –36.041 and 61.041 to 61.042

seen

or for answers –36[.0] or –36.042 to

–36.041 and 61[.0] or 61.041 to 61.042

or –36.04 and 61.04 seen in working

or for –61.04 and 36.04 as final ans

9(a)(i) 5 and 13 1

9(a)(ii) 8n – 3 = 203 M1 Evaluation of 25th or 26th term with

supporting evidence or explanation

25.75 or 25

3

4

A1 Second evaluation of 25th or 26th terms

with supporting evidence or explanation

If zero scored, SC1 for 25.75 or 197 and

205 with partial evidence or explanation

9(b)(i) 6n + 7 oe final answer 2 B1 for 6n + c or kn + 7 0k ≠

9(b)(ii) n2 + n + 2 oe final answer 2 B1 for a quadratic expression

or second difference = 2

9(c) [y = ] 10 2 M1 for 5(20 – y) = 50

[First term = ] 14 2 M1 for 5(x – their y) = 20

or for 20 ÷ 5 + their y


Cambridge International Examinations Cambridge ......MATHEMATICS 0580/21 Paper 2 (Extended) May/June...

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