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DC (LEG/SG) 118013/2© UCLES 2016 [Turn over

Cambridge International ExaminationsCambridge International General Certificate of Secondary Education

*2096705365*

MATHEMATICS 0580/42Paper 4 (Extended) October/November 2016 2 hours 30 minutesCandidates 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.

The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.

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0580/42/O/N/16© UCLES 2016

1 (a) (i) Each yearthe value of a car decreases by 15% of its value at the beginning of that year. Alberto buys a car for $18 000.

Calculate the value of Alberto’s car after 3 years.

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

(ii) Belinda bought a car one year ago. The value of this car has decreased by 15% to $14025.

Calculate how much Belinda paid for the car.

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

(b) Chris invested some money at a rate of 5% per year compound interest. After 2 years the value of this investment is $286.65 .

Calculate how much Chris invested.

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

100 15 85

18000 X G855

11054.25

100 1590 85

85 14025

140258Gt

410016500

Px f 057 286.65D 286.65

cozy260

260

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0580/42/O/N/16© UCLES 2016 [Turnover

(c) Dani invested $200 and after 2 years the value of this investment is $224.72 .

Calculate the rate of interest per year when the interest is

(i) simple,

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

(ii) compound.

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

Iooxrx 2700

24 72

A 24 72 100

200 2 G 18

200x HED 224.72

ltfoo 224TOi fT236 1 xloo 6

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0580/42/O/N/16© UCLES 2016

2 (a) Complete the table of values for y x x3 13

2= - + .

x –1.5 –1 –0.5 0 0.5 1 1.5 2 2.5 3

y –2.38 –0.33 0.71 0.79 0.33 –0.13 –0.33 –0.04 [2]

(b) Draw the graph of y x x3 13

2= - + for 1.5 3xG G- .

The first 3 points have been plotted for you.

2

1

1 2 30

–1

–2

–3

–1x

y

[4]

I I

it

5


(c) Using your graph, solve the equations.

(i) x x3 1 03

2- + =

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

(ii) x x x3 1 03

2- + + =

x = ................................................ [2]

(d) Two tangents to the graph of y x x3 13

2= - + can be drawn parallel to the x-axis.

(i) Write down the equation of each of these tangents.

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

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

(ii) For x0 3G G , write down the smallest possible value of y.

y = ................................................ [1]

yo 0.9 1.4 2.55

GI sett a Y 0.6

y l

y 0.33

0.33

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3D

C

B

A

North180 m

240 m

85°

50°

NOT TOSCALE

The diagram shows a field, ABCD. AD = 180 m and AC = 240 m. Angle ABC = 50° and angle ACB = 85°.

(a) Use the sine rule to calculate AB.

AB = ............................................ m [3]

(b) The area of triangle ACD = 12 000 m2.

Show that angle CAD = 33.75°, correct to 2 decimal places.

[3]

I

fg

shifts5 Y AB 24oxsinSinko

AB 312 1055569312

42 180 240x since 12000

Since 12000 2 QE180 240

sin Ea 33.748988633.75

7


(c) Calculate BD.

BD = ............................................ m [5]

(d) The bearing of D from A is 030°.

Find the bearing of

(i) B from A,

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

(ii) A from B.

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

BD2 312774805 21312 180

78.757

BD 2 107831 455

BD 328.3770014

328

30 33.75 45 108.75

180 108.75 71 25 288.75

360 71 25 288 75

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4 200 people run 10 km. The table shows some information about the times, t minutes, taken to run the 10 km.

Time (t�minutes) t30 401 G t0 44 51 G t 045 51 G t05 551 G t 055 61 G t0 06 81 G

Frequency 8 22 95 55 14 6

(a) Howard takes 40 minutes to run the 10 km.

Calculate his average speed in kilometres per hour.

........................................ km/h [2]

(b) Calculate an estimate of the mean time.

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

(c) Complete the histogram to show the information in the table.

20

18

16

14

12

10

8

6

4

2

030 40 50 60 70 80

t

Time (minutes)

Frequencydensity

[4]

7 443 15 15

info yzfofg55lIs7iIEo

ToIalFxx 9840µm 9284 49.2

him

mmmm

9


(d) (i) Use the frequency table opposite to complete the cumulative frequency table.

Time (t�minutes) t 40G t 45G t 05G t 55G t 06G t 08G

Cumulative frequency 8 30 194 200

[1]

(ii) Draw a cumulative frequency diagram to show the information in the table above.

200

180

160

140

120

100

80

60

40

20

030 40 50 60 70 80

t

Time (minutes)

Cumulativefrequency

[3]

(iii) Use your diagram to find

(a) the median,

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

(b) the 90th percentile,

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

(c) the number of people who took more than 58 minutes to run the 10 km.

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

125 180

It

2002

100 48

0.9 200 180 55

12

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5 The probability that a plant will produce flowers is 87 .

The flowers are either red or yellow. If the plant produces flowers, the probability that the flowers are red is 4

3 .

(a) (i) Complete the tree diagram by writing a probability beside each branch.

Flowers

No flowers

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

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

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

............Red

Yellow

[2]

(ii) Calculate the probability that a plant, chosen at random, will produce red flowers.

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

34

7 8 44

18

71g x34

132

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(iii) Two plants are chosen at random.

Calculate the probability that both will produce red flowers.

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

(b) Alphonse buys 200 of these plants.

Calculate the number of plants that are expected to produce flowers.

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

(c) Gabriel has 1575 plants with red flowers.

Estimate the total number of plants that Gabriel has.

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

78 34

2ER and ER

441

1024200

78

175

312 1575i214 s a 2400

3242331224007 32

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6 (a)

0.8 cm

1.5 cm1.1 cm

0.8 cmNOT TOSCALE

The diagram shows two sweets. The cuboid has length 1.5 cm, width 1.1 cm and height 0.8 cm. The cylinder has height 0.8 cm and the same volume as the cuboid.

(i) Calculate the volume of the cuboid.

..........................................cm3 [2]

(ii) Calculate the radius of the cylinder.

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

(iii) Calculate the difference between the surface areas of the two sweets.

..........................................cm2 [5]

1.5 1.1 081.32

MxPx0.8 132

the 1.32 HE0.81T0.725

i i2xHx 7255

7.466.946846755

difference 0.513

13


(b) A bag of sweets contains x orange sweets and y lemon sweets. Each orange sweet costs 2 cents and each lemon sweet costs 3 cents.

The cost of a bag of sweets is less than 24 cents. There are at least 9 sweets in each bag. There are at least 2 lemon sweets in each bag.

(i) One of the inequalities that shows this information is x y2 3 241+ .

Write down the other two inequalities.

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

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

(ii) On the grid, by shading the unwanted regions, show the region which satisfies the three inequalities.

12

y

1110987654321

0 1 2 3 4 5 6 7 8 9 10 11 12x

[4]

(iii) Find the lowest cost of a bag of sweets. Write down the value of x and the value of y that give this cost.

Lowest cost = .................................... cents

x = .............................................

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

Xt y39Y 72

2xt3y 424

f4r.io

Hwa

7 2 2 3 20

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7 (a) $1= 3.67 dirhams

Calculate the value, in dollars, of 200 dirhams. Give your answer correct to 2 decimal places.

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

(b) (i) Write as a single fraction, in its simplest form.

x x1000

11000-+

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

(ii) One day in 2014, 1 euro was worth x rand. One year later, 1 euro was worth (x + 1) rand.

Winston changed 1000 rand into euros in both years. In 2014 he received 4.50 euros more than in 2015.

Write an equation in terms of x and show that it simplifies to

x x9 9 2000 02 + - = .

[3]

i3.67A

20037Gt

54 50

10006cm 1000GB 1000xGCtD

occoctD1000AGED

1000 1,9007 45

1000 4.5 1000 4.500745 2

45 22000 9 2 921000 4.5614D qjr 9x 2000 0

15


(iii) Use the quadratic formula to solve the equation x x9 9 2000 02 + - = . Show all your working and give your answers correct to 2 decimal places.

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

(iv) Calculate the number of euros Winston received in 2014. Give your answer correct to 2 decimal places.

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

gce bt.TL a 9lo 9C

2ooo2a9t8 C4TEooo X

18 x 9 572081

91772081 C or18

go 9 77208118 IT

14.42 15.42

Kuro 14.42rad

I 69.35

4.4.42

1000i 14.42

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0580/42/O/N/16© UCLES 2016

8 (a)

NOT TOSCALE

B

E

A

D

O

C

u°

v°

80°

A, B, C and D lie on the circle, centre O. DAE is a straight line.

Find the value of u and the value of v.

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

v = ................................................ [2]

(b)

NOT TOSCALE

O

G

H

The diagram shows a circle, centre O, radius 8 cm.� � GH is a chord of length 10 cm.

Calculate the length of the perpendicular from O to�GH.

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

Too

80160

8 mom

87

82527

6.24

17


(c) K,�L,�M�and�N lie on the circle.� � KM and LN intersect at X.� � KL�= 9.7 cm, KX�= 4.8 cm,� � LX�= 7.8 cm and NX�= 2.5 cm.

M

L

NOT TOSCALE

N

K

X

2.5 cm

4.8 cm7.8 cm

9.7 cm

Calculate MN.

MN = .......................................... cm [2]

(d) All lengths are in centimetres.

NOT TOSCALE

SR

Q

Y

P

2x

x� � P, Q, R and S lie on the circle. � � PR and QS intersect at Y.� � PY = 2x and YS = x.

The area of triangle YRS x x125 1= -^ h.

The area of triangle YQP x x 1= +^ h.

Find the value of x.

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

Scalefactor

41 1.922.59.7 1.92

5.05

Length SF 21 2

Area SF 4232 4 Foo 8zx

4 fzoux17 04041 2 8

x2 x Etx2 4

4

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9 (a) 3 2y x= + ,x 0!

(i) Find the value of y when x 6=- .

y = ................................................ [1]

(ii) Find x in terms of y.

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

(b) g( ) 2x x= - h( ) 2x x=

(i) Find g(5).

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

(ii) Find hhh(2).

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

2 6

y362 1 5

1.5

g 3 2

g F ZouaByer

2

GET 2 53

had 22 4HDhtt 24 16

HUG 2 6553665536

19


(iii) Find x when g( ) h(3)x = .

x = ................................................ [2]

(iv) Find x when ( )g x 1–1 =- .

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

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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.

10 The perimeter of each of the three shapes is 60 cm.

Find x in each part.

(a) Rectangle

3x

x NOT TOSCALE

x = .......................................... cm [2]

(b)

Triangle 3x

4x

NOT TOSCALE

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

(c)

Sector

x

x

O

NOT TOSCALE

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

6 2 86 60 7.5

sat E

iffff