Cambridge International Examinations Cambridge International...

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DC (LK/FD) 118127/3© UCLES 2016 [Turn over

Cambridge International ExaminationsCambridge International General Certificate of Secondary Education

*2402917633*

MATHEMATICS 0580/23Paper 2 (Extended) October/November 2016 1 hour 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 70.

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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1 V = 4p2

Find V when p = 3.

V = ................................................ [1]

2 Simplify. n2 × n5

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

3

A B

C

123°

80°57°

100°

97°

NOT TOSCALE

84°

83°

96°

67°

81°

99°

113°

110°98°

70°

82°

D

The diagram shows four quadrilaterals A, B, C and D.

Which one of these could be a cyclic quadrilateral?

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

4 9 36

nF

X

xx

B

3

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4 Write in standard form.

(a) 2 470 000

................................................. [1] (b) 0.0079

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

5 Withoutusingacalculator, work out5

3

6

1+ .

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

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

6 James is an animal doctor. The table shows some information about the cats he saw in one week.

Day Monday Tuesday Wednesday Thursday Friday

Number of cats seen 2 4 1 3 2

Mean mass of a cat (kg) 1.9 0.9 2.1 1.8 2

One of the cats James saw had a mass of 4 kg.

On which day did he see this cat?

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

im2.47 106

W79 10

3

6 x8

xgXT

18 5 23Jot 30 30

2330

Thursday

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7 Write these in order of size, smallest first.

0.63 0.22 .0 09 0.42

.......................... 1 ......................... 1 ......................... 1 .........................[2] smallest

8 The length of a car is 4.2 m, correct to 1 decimal place.

Write down the upper bound and the lower bound of the length of this car.

Upper bound = .......................................... m

Lower bound = .......................................... m [2]

0.216 0.22 0.3 0.16

0.42 0.63 0.22 8.09

021 0 05 4.25

043 4.2 0.054.15

LB 4.2 0.05

5


9

0

2

0

4

6

8

10

A

BB

CC

DD

12

14

16

18

20

22

24

26

28

30

10 20 30 40 50Time (minutes)

Distance(km)

60 70 80 90

The diagram shows the distance-time graph for the first 65 minutes of a bicycle journey.

(a) There are four different parts to the journey labelled A, B, C and D.

Write down the part of the journey with the fastest speed.

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

(b) After the first 65 minutes the bicycle travels at a constant speed of 20 km/h for 15 minutes.

Draw this part of the journey on the diagram. [1]

I

Aplyhour

2 51hm

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10 Calculate.

(a) 2 10 43 2- +

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

(b) °tan

3

2 3 70#

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

11 Ahmed paid $34 000 for a car. His car decreased in value by 40% at the end of the first year. The value at the end of the second year was 10% less than the value at the end of the first year.

Calculate the value of Ahmed’s car after 2 years.

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

12

5 cm

NOT TOSCALE

The diagram shows a hemisphere with diameter 5 cm.

Calculate the volume of this hemisphere.

[The volume, V, of a sphere with radius r is V r3

4 3r= .]

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

2.90

3 17

0.6 X 34000 20400 D1styear

20400 0.9 18360I 8360

r 2 S

Iz a sphere

V Ix4g x tix 5 1,25

32.7

7


13 Write the recurring decimal .0 2o as a fraction. [ .0 2o means 0.222…]

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

14 The shaded shape is made by joining a square and a rhombus.

5 cm4.5 cm

NOT TOSCALE

Work out

(a) the perimeter of the shaded shape,

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

(b) the area of the shaded shape.

........................................ cm2 [2]

X 0.22222 92 2

10x 2.22222 9C

iox xe.roEEEEE FAll sides arethe same

5 3 5 3

30

5 5 4.5 5

Area of Square AreaorRhombus

47.5

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15 (a)

C

A

B

44°

NOT TOSCALE

Triangle ABC is an isosceles triangle with AB = CB. Angle ABC = 44°.

Find angle ACB.

Angle ACB = ............................................... [1]

(b) A regular polygon has an exterior angle of 40°.

Work out the number of sides of this polygon.

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

16 d is inversely proportional to (w + 1)2. d = 3.2 when w = 4.

Find d when w = 7.

d = ................................................ [3]

sameangle

180 442

680

361 403 00 n

g

dik3.2 65 15 80

d3.2 antd w 4 d 8

3 2µ ye 1.25

9


17 A is the point (8, 3) and B is the point (12, 1).

Find the equation of the line, perpendicular to the line AB, which passes through the point (0, 0).

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

18 f(x) =x2 ( )g x x23= -

Find

(a) f(– 5),

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

(b) gf(x),

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

(c) g –1(x).

g –1(x) = ................................................ [2]

Guy Kaye

h Yi zPerpendicular

gradientm

2

y 2xtcSublao GO

y 2x

fC D C55 25 25

g x'zI offglxtxz3 yy 3 2 sc

Applyg x g Hy 2 32 3yz.sc

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19 The curve y = x3 + 2x2 – 4x is shown on the grid.

–4

–5

–3

–2

–1

1

2

3

4

5

6

7

8

9

0–3 –2 –1 1 2x

y

(a) By drawing a suitable tangent, find an estimate of the gradient of the curve when x = 1.

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

(b) A point D lies on the curve. The x co-ordinate of D is negative. The gradient of the tangent at D is 0.

Write down the co-ordinates of D.

( .................... , .................... ) [1]

gradient 0

of 1

gradient 7 32.1 gradient 539

2 8

11


20 (a) ! = , . , , ,7 9 3952 8r% /

A = {integers} B= {irrational numbers}

Write all the elements of ! in their correct place on the Venn diagram.

A B!

[2]

(b) Shade the region in each of the Venn diagrams below.

C D!

E F

G

!

C D,l E F G+ +l [2]

A

B

9.3 f7 IT258

N

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21 (a)

A

C

B6.2 cm

4.7 cm

82°

NOT TOSCALE

Calculate the area of triangle ABC.

.........................................cm2 [2]

(b)

D

F

E

107 mm

75 mm

x°

NOT TOSCALE

The area of triangle DEF is 2050 mm2.

Work out the value of x.

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

I ft 6 2 sin 827

14.4

12 FS lot s in DC 2050

son x ffg td30.7

13


22 The table shows some information about the mass, m grams, of 200 bananas.

Mass (m grams) m90 1101 G m 1 0110 21 G m0 112 251 G m125 1401 G

Frequency 40 70 60 30

Height of column in histogram (cm) 6

Complete the table.

[4]

23 Simplify. pt t mp m

np n12 2 18 3

42 7

- + --

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

Saima all.heightsAll heights divided by'tyy

1 3.5 1

t.ggyyItl6p

Dt3ml6pD7n

6p Dftp.yy

27m

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24

00

1

2

3

4

5

6

7

1 2 3 4

R

5 6 7 8 9 10 11x

y

Find the three inequalities that define the unshaded region, R.

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

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

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

y x

132lout6g568

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25 A4

2

2

1= c m B

7

4

3

5=

-c m C2

4

3

5

1

1=-

-c m D

9

0=-c m

(a) Which of these four matrix calculations is not possible?

A+B 3C CB AD

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

(b) Calculate AB.

f p [2]

(c) Work out B –1, the inverse of B.

f p [2]

(d) Explain why matrix A does not have an inverse.

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

CB

4,21 74 34 7 12 4 4 3 2 5

2 771 4 1 2 37 1 5

36 218 I

Hxs x4E FE

45437

The determinant is 0

HI 4 1 2 2

4 4 0

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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.

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