Cambridge

IGCSECambridge International ExaminationsCambridge International General Certificate of Secondary Education

CANDIDATENAME

CANDIDATENUMBER

CENTRENUMBER

MATHEMATICS

Paper 1 (Core)

SPECIMEN PAPER

Candidates answer on the Question Paper.

Additional Materials: Electronic calculatorTracing paper (optional)

0580/01For Examination from 2015

1 hour

Geometrical instruments

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.

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 n, use either your calculator value or 3.142.

At the end of the examination, fasten all your work securely together.The number o f marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 56.

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

This document consists of 11 printed pages and 1 blank page.

|S§ CAMBRIDGE© u c le s 2012 [Turn over

2

1

The diagram shows the map of part of an orienteering course. Sanji runs from the start, S, to the point A.

Write as a column vector.

Answer [1]

42 When Ali takes a penalty, the probability that he will score a goal is —

Ali takes 30 penalties.

Find how many times he is expected to score a goal.

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

3 The ratio of Anne’s height : Ben’s height is 7 : 9. Anne’s height is 1.4 m.

Find Ben’s height.

Answer .................................................. m [2]

© UCLES 2012 0580/01/SP/15

3

4 The distance between the centres of two villages is 8 km.A map on which they are shown has a scale of 1 : 50 000.

Calculate the distance between the centres of the two villages on the map. Give your answer in centimetres.

Answer ,„ cm [2]

Frequency

Favourite colour

The bar chart shows the favourite colours of students in a class.

(a) How many students are in the class?

Answer(a) [1]

(b) Write down the modal colour.

Answer(b) [1]

5

© UCLES 2012 0580/01/SP/15 [Turn over

4

6 Use your calculator to find45 x 5.75

3.1 +1.5

Answer

7 (a) Calculate 60% of 200.

[2]

Answer (a) ................................................. [1]

(b) Write 0.36 as a fraction.Give your answer in its lowest terms.

Answer(b) ................................................. [2]

8 A circle has a radius of 50 cm.

(a) Calculate the area of the circle in cm2.

Answer(a) .................................................... cm2 [2]

(b) Write your answer to p a rt (a) in m2.

Answer(b) .................................................... m2 [1]

© UCLES 2012 0580/01/SP/15

5

Temperature(°C)

Time

The graph shows the temperature in Paris from 6 am to 6 pm one day.

(a) What was the temperature at 9 am?

Answer(a) ...............................

(b) Between which two times was the temperature decreasing?

Answer(b) ..................... and

(c) Work out the difference between the maximum and minimum temperatures shown.

°C [1]

[1]

Answer(c) °C [1]

9

10 (a) Write down the mathematical name of a quadrilateral that has exactly two lines of symmetry.

Answer (a) ................................................. [1]

(b) Write down the mathematical name of a triangle with exactly one line of symmetry.

Answer(b) ................................................. [1]

(c) Write down the order of rotational symmetry of a regular pentagon.

Answer (c) ................................................. [1]

© UCLES 2012 0580/01/SP/15 [Turn over

11 Without using your calculator, work out —2

2 1

V 3 + 4 jShow all your working clearly and give your answer as a fraction.

6

Answer [3]

12y

The diagram shows the graph of y = (x + 1)2 for -4 Y x

(a) On the same grid, draw the line y = 3.

(b) Use your graph to find the solutions of (x + 1)2 = 3. Give each solution correct to 1 decimal place.

[1]

Answer(b) x = ..................... o rx = [2]

x

© UCLES 2012 0580/01/SP/15

7

13

NOT TO SCALE

The front of a house is in the shape of a hexagon with two right angles. The other four angles are all the same size.

Calculate the size of one of these angles.

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

14 (a) Expand and simplify.

2(3x - 2) + 3(x - 2)

Answer(a) ................................................. [2]

(b) Expand.x(2x2 - 3)

Answer(b) ................................................. [2]

© UCLES 2012 0580/01/SP/15 [Turn over

15

5 0 -

4 0 -

| 30

<D

^ ona 20W

10-

><

s \

A

X X- X ><

10 20 30 40 50 60 70 80

Mathematics test mark

The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an English test by 15 students.

(a) Describe the correlation.

Answer(a) [1]

(b) The mean for the Mathematics test is 47.3 .The mean for the English test is 30.3 .

Plot the mean point (47.3, 30.3) on the scatter diagram above.

(c) (i) Draw the line of best fit on the diagram above.

(ii) One student missed the English test.She received 45 marks in the Mathematics test.

Use your line to estimate the mark she might have gained in the English test.

Answer(c)(u)

[1]

[1]

[1]

8

0

© UCLES 2012 0580/01/SP/15

9

16 (a)

NOT TO SCALE

E

In the diagram, AB is parallel to DE. Angle ABC = 110°.

Find angle BDE.

(b)

Answer(a) Angle BDE = [2]

TA is a tangent at A to the circle, centre O. Angle OAB = 50°.

Find the value of

(i) y,

Answer(b)(i) y =

(ii) z,

Answer(b)(ii) z =

(iii) t.

[1]

[1]

Answer(b)(iii) t = [1]

© UCLES 2012 0580/01/SP/15 [Turn over

10

17

NOT TO SCALE

The diagram shows a ladder, of length 8 m, leaning against a vertical wall. The bottom of the ladder stands on horizontal ground, 3 m from the wall.

(a) Find the height of the top of the ladder above the ground.

Answer(a) m [3]

(b) Use trigonometry to calculate the value of y .

Answer(b) y = [2]

© UCLES 2012 0580/01/SP/15

18 (a) Lucinda invests $500 at a rate of 5% per year simple interest.

Calculate the interest Lucinda has after 3 years.

11

Answer(a) $ ................................................. [2]

(b) Andy invests $500 at a rate of 5% per year compound interest.

Calculate how much more interest Andy has than Lucinda after 3 years.

Answer(b) $ ................................................. [4]

© UCLES 2012 0580/01/SP/15

12

BLANK PAGE

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.

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.

© UCLES 2012 0580/01/SP/15

Cambridge

IGCSEC am bridge In ternational Exam inationsCambridge International General Certificate of Secondary Education

MATHEMATICS 0580/01

Paper 1 (Core) For Examination from 2015

SPECIMEN MARK SCHEME

1 hour

MAXIMUM MARK: 56

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

This document consists of 4 printed pages.

|S§ CAMBRIDGE© u c le s 2012 [Turn over

2

Types of m arkM marks are given for a correct method.A marks are given for an accurate answer following a correct method.B marks are given for a correct statement or step.D marks are given for a clear and appropriately accurate drawing.P marks are given for accurate plotting of points.E marks are given for correctly explaining or establishing a given result. SC marks are given for special cases that are worthy of some credit.

Abbreviationscao correct answer onlycso correct solution onlydep dependentft follow through after errorisw ignore subsequent workingoe or equivalentSC Special Casewww without wrong workingart anything rounding tosoi seen or implied

Qu. Answers M ark P a rt M arks

1r- 3j 14 J 1

2 24 or 24 out of 30 24

M1 for — x 305

3 1.8 2 M1 for 1.4 t 7 or SC1 for answer 180

4 16 2 B1 for 1cm to 0.5km oe or 800 000 (cm) or figs 16

5 (a) 25

(b) Green cao

1

1

6 7.5(0) cao 2. 258.75M1 for---------

4.6

7 (a) 120 1

(b) — cao25

2 f 36 18 B1 for-----or —100 50

8 (a) 7853 to 7855or 7850 or 7860 www

2 M1 for n x 502

(b) 0.7853 to 0.7855 or 0.785 or 0.786 1ft Their (a) t 10 000 evaluated

9 (a) 15

(b) 2 (pm), 6 (pm)

(c) 15

1

1

1 Allow -15

10 (a) Rectangle or rhombus

(b) Isosceles (triangle)

(c) 5 cao

1

1

1

Either one or both given

© UCLES 2012 0580/01/SM/15

3

1111k----- final answer www24k

B1

M1

A1

B1

M1

A1

Method 1 (Addition first)

8 3 8 + 3— + — or ------ oe12 12 12

1 x their 112 x their 12

Method 2 (Multiplication first)

2 1 1 1— + — or — + — oe 6 8 3 8

ad + bc „ . a c---------- for their — +—

bd b d

If M0, SC1 if 11 is only followed b y 1 1 12 24

or if zero, SC1 if work is entirely in decimals with answer of 0.458 3 to 0.45835

12 (a) Correct ruled line

(b) -2.7, 0.7

1

1, 1ft B2ft their ruled line through (0, 3) for two intersections given to 1 decimal place or B1 for -2.70 to -2.75 and 0.70 to 0.75 or B1ft their ruled line through (0, 3) for two intersections not given to 1 decimal place

13 135 cao 3 M1 for 720 or (6 - 2) x 180 oe seen in working and M1 for equation 180 + 4x = their 720 orM1 for (360 - 180) ^ 4 (= 45) oe seen in workingand M1 dep for 180 - their 45

14 (a) 9x - 10 final answer

(b) 2x3 - 3x final answer

2

2

B1 for 6x - 4 or 3x - 6or for answer of 9x + j , or kx - 10

B1 for answer in form 2x3 + m or n - 3x

15 (a) Negative

(b) Correct point

(c) (i) Accurate ruled line

(ii) English mark

1

1

1

1ft

Ignore embellishments

Follow through their (c)(i)

16 (a) 70

(b) (i) (y =) 80

(ii) (z =) 40

(iii) (t =) 10

2

1

1

1ft

B1 for angle ABD = 70° stated or seen on the diagram

Follow through 90 - their y or 50 - their z

© UCLES 2012 0580/01/SM/15 [Turn over

4

17 (a) 7.42 or 7.416... cao 3 M2 for 2 - 32) orcomplete alternate method

or M1 for x2 + 32 = 82 or better

(b) 67.97 to 68(.0) cao 23

M1 for cos (y) = — oe 8

18 (a) 75 2- 500 x 5 x 3

M1 f o r -------------- oe100

or SC1 for answer of 575

(b) 3.81(25) 4 M2 for 500 x 1.05 x 1.05 x 1.05or M1 for 500 x 1.05 x 1.05A1 for 578.81(25) or 78.81(25) seenand A1ft for value of 500(1.05)3 - 500 - their (a)

© UCLES 2012 0580/01/SM/15

Cambridge

IGCSECambridge International ExaminationsCambridge International General Certificate of Secondary Education

CANDIDATENAME

CENTRENUMBER

CANDIDATENUMBER

MATHEMATICS

Paper 2 (Extended)

SPECIMEN PAPER

Candidates answer on the Question Paper.

Additional Materials: Electronic calculatorTracing paper (optional)

0580/02For Examination from 2015

1 hour 30 minutes

Geometrical instruments

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.

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 n, use either your calculator value or 3.142.

At the end of the examination, fasten all your work securely together.The number o f 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.

This document consists of 12 printed pages.

Egg CAMBRIDGE© u c le s 2012 [Turn over

1 Use your calculator to find45 x 5.75

3.1 +1.5

2

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

2 The mass of a carbon atom is 2 x 10 27 g.

How many carbon atoms are there in 6 g of carbon?

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

3 Write the following in order of size, largest first.

sin 158° cos 158° cos 38° sin 38°

Answer .................. > .................. > .................. > __ ........... [2]

4 Express 0.123 as a fraction in its simplest form.

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

© UCLES 2012 0580/02/SP/15

3

5 A circle has a radius of 50 cm.

(a) Calculate the area of the circle in cm2.

Answer(a) cm2 [2]

(b) Write your answer to p a rt (a) in m .

Answer(b) m 2 [1]

NOT TO SCALE

6

The front of a house is in the shape of a hexagon with two right angles. The other four angles are all the same size.

Calculate the size of one of these angles.

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

© UCLES 2012 0580/02/SP/15 [Turn over

4

7

TA is a tangent at A to the circle, centre O.Angle OAB = 50°.

Find the value of

(a) y,

Answer(a)y = .................................................... [1]

(b) z,

Answer(b)z= .................................................... [1]

(c) t.

Answer ( c) t= .................................................... [1]

8 This is a sketch of two lines P and Q.

y

The two lines P and Q are perpendicular. The equation of line P is y = 2x.Line Q passes through the point (0, 10).

Work out the equation of line Q.

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

© UCLES 2012 0580/02/SP/15

5

The point A lies on the circle centre O, radius 5 cm.

(a) Using a straight edge and compasses only, construct the perpendicular bisector of the line OA.[2]

9

O

The point A lies on the circle centre O, radius 5 cm.

(b) The perpendicular bisector meets the circle at the points C and D.

Measure and write down the size of the angle AOD.

Answer(b) Angle AOD = ................................................. [1]

© u c l e s 2012 0580/02/SP/15 [Turn over

6

10 In a flu epidemic 45% of people have a sore throat.If a person has a sore throat the probability of not having flu is 0.4.If a person does not have a sore throat the probability of having flu is 0.2.

Calculate the probability that a person chosen at random has flu.

Answer [4]

11 Work out.

(a)/ \ 2

2 1 '

Answer(a) [2]

(b)V 4 3 J

Answer(b) [2]

© UCLES 2012 0580/02/SP/15

Engl

ish

test

mar

k7

12

5 0 -

4 0 -

3 0 -

2 0 -

10 -

A

10 20 30 40 50 60 70 80

Mathematics test mark

0

The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an English test by 15 students.

(a) Describe the correlation.

Answer (a) ................................................. [1]

(b) The mean for the Mathematics test is 47.3 .The mean for the English test is 30.3 .

Plot the mean point (47.3, 30.3) on the scatter diagram above. [1]

(c) (i) Draw the line of best fit on the diagram above. [1]

(ii) One student missed the English test.She received 45 marks in the Mathematics test.

Use your line to estimate the mark she might have gained in the English test.

Answer(c)(ii) ................................................. [1]

© UCLES 2012 0580/02/SP/15 [Turn over

8

D

[2]

[2]

14

(a) Find T when g = 9.8 and I = 2

Answer(a) T = ................................................. [2]

(b) Make g the subject of the formula.

Answer(b) g = ................................................. [3]

13

A and B have position vectors a and b relative to the origin O.C is the midpoint of AB and B is the midpoint of AD.

Find, in terms of a and b, in their simplest form

(a) the position vector of C,

Answer(a)

(b) the vector CD.

Answer(b)

© UCLES 2012 0580/02/SP/15

9

15 A container ship travelled at 14 km/h for 8 hours and then slowed down to 9 km/h over a period of 30 minutes.

It travelled at this speed for another 4 hours and then slowed to a stop over 30 minutes.

The speed-time graph shows this voyage.

Speed (km / h)

(a) Calculate the total distance travelled by the ship.

Answer(a)

(b) Calculate the average speed of the ship for the whole voyage.

km [4]

Answer(b) ................................................... km/h [1]

© UCLES 2012 0580/02/SP/15 [Turn over

16 The mass of a radioactive substance is decreasing by 10% a year.

The mass, M grams, after t years, is given by the formula M = 500 x 0.9f.

(a) Complete this table.

10

t (years) 0 1 2 3 4 5 6

M (grams) 450 328 266[2]

(b) Draw the graph of M = 500 x 0.9(.

M i \

5 0 0 - ....... M..........I— .....U-;..... .................... :••!....... --U........f - ..... i...........[..... ;-;-i....... ............. I

400-

300-

200-

100-

T2

T4

T6

[2]

(c) (i) Use your graph to estimate after how long the mass will be 350 grams.

Answer(c)(\) .........

(ii) When will the mass of the radioactive substance be zero grams?

years [1]

Answer(c)(ii) ............................................... years [1]

0

© UCLES 2012 0580/02/SP/15

17

(a) Work out fg(1).

11

f(x) =x + 4 (x * - 4 )

g(x) = x - 3x

h(x) = x3 + 1

1

Answer(a) ................................................. [2]

(b) Find ho1(x).

Answer(b) h '(x) = ................................................. [2]

(c) Solve the equation g(x) = - 2 .

Answer(c) x = ..................... o rx = ...................... [3]

Question 18 is prin ted on the next page.

© UCLES 2012 0580/02/SP/15 [Turn over

18 The first four terms of a sequence are

T1 = 12 T2 = 12 + 22 T3 = 12 + 22 + 32 T4 = 12 + 22 + 32 + 42 .

(a) The nth term is given by Tn = — n(n + 1)(2n + 1).

12

6

Work out the value of T23.

Answer(a) T23 = ................................................. [2]

(b) A new sequence is formed as follows.

Ui = T2 - Ti U 2 = T3 - T2 U3 = T4 - T3 .....

(i) Find the values of U 1 and U2.

Answer(b)(\) Ui = ............... and U2 = ........................... [2]

(ii) Write down a formula for the nth term, Un .

Answer (b){ii) U„ = ................................................. [1]

(c) The first four terms of another sequence are

V 1 = 22 V2 = 22 + 42 V3 = 22 + 42 + 62 V4 = 22 + 42 + 62 + 82.

By comparing this sequence with the one in p a rt (a), find a formula for the nth term, Vn .

Answer(c) V„ = ................................................. [2]

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.

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.

© UCLES 2012 0580/02/SP/15

Cambridge

IGCSEC am bridge In ternational Exam inationsCambridge International General Certificate of Secondary Education

MATHEMATICS 0580/02

Paper 2 (Extended) For Examination from 2015

SPECIMEN MARK SCHEME

1 hour 30 minutes

MAXIMUM MARK: 70

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

This document consists of 4 printed pages.

|S§ CAMBRIDGE© u c le s 2012 [Turn over

2

Types of m arkM marks are given for a correct method.A marks are given for an accurate answer following a correct method.B marks are given for a correct statement or step.D marks are given for a clear and appropriately accurate drawing.P marks are given for accurate plotting of points.E marks are given for correctly explaining or establishing a given result. SC marks are given for special cases that are worthy of some credit.

Abbreviationscao correct answer onlycso correct solution onlydep dependentft follow through after errorisw ignore subsequent workingoe or equivalentSC Special Casewww without wrong workingart anything rounding tosoi seen or implied

Qu. Answers M ark P a rt M arks

1 7.5(0) cao2

^ „ 258.75M1 for---------

4.6

2 3 x 1027 2 M1 for 6 t (2 x 10-27)

3 cos38 sin38 sin158 cos158 2 M1 correct decimals seen0.7(88..) 0.6(15..) 0.3(74..) -0.9(271..)

441

3333

123B2 f o r ----- oe fraction

999or M1 for 1000[x] = 123.123... oe

5 (a) 7853 to 7855or 7850 or 7860 www

(b) 0.7853 to 0.7855 or 0.785 or 0.786

2

1ft

M1 for n x 502

Their (a) t 10 000 evaluated

6 135 cao 3 M1 for 720 or (6 - 2) x 180 oe seen in working and M1 for equation 180 + 4x = their 720 orM1 for (360 - 180) t 4 (= 45) oe seen in workingand M1 dep for 180 - their 45

7 (a) (y =) 80

(b) (z =) 40

(c) (t =) 10

1

1

1ft Follow through 90 - their y or 50 - their z

© UCLES 2012 0580/02/SM/15

3

8y = - 1 x +10 oe

23

M2 for - 1 x +10 2

or M1 for gradient identified as - 2

or intercept as 10 (not on diagram) e.g. y = mx + 10 or

1y = ---- x + c

29 (a) Correct perpendicular bisector with

arcs

(b) 60°

2

1

B1 correct lineB1 correct construction arcs

10 190.38 or — 50

4 B1 0.8, 0.6 or 0.55 thenM1 0.45 x their 0.6 M1 0.2 x their 0.55or M2 1 - (0.45 x 0.4 + 0.55 x their 0.8)

11f 8 5 ^

(a)^ 20 13

f 11 - 1 \(b) 2 2 oe

- 2 1 V 2 1 V

2

2

B1 two or three entries correct

1 ( a c ̂ , / 3 - A B ^ B1 (k )

2 ^b d ) v \ - 4 2 )

12 (a) Negative

(b) Correct point

(c) (i) Accurate ruled line

(ii) English mark

1

1

1

1ft

Ignore embellishments

Follow through their (c)(i)

13 , x 1 1(a) —a + — b oe2 2

(b) -1 — a + 1 — b oe2 2

2

2

M1 unsimplified or any correct route

e.g a + — (b - a) or OA + AC

M1 unsimplified or any correct route

e.g. CD = 11 AB or b - a + — (b - a) 2 2

14 (a) 2.84

4 n 21(b) T 2 oe

2

3

M1 correct substitution of g and I seen

M1 each correct move but third move marked on answer line

15 (a) 156

(b) 12

4

1ft

M1 intention to find area under graph B2 completely correct area statement or B1 two areas found correctly (or one trapezium area)

Their (a)/13

© UCLES 2012 0580/02/SM/15 [Turn over

4

16 (a) 500, 405, 364-365, 295 (...) 2 B2

(b) 5 points plotted within correct square 1 P1 ft from table

correct curve drawn within 1 mm of points plotted

1 C1

(c) (i) 3.3-3.4

(ii) Never oe

1

1

B1 ft from their curve or line reading at 350 g

17 (a)12

2 B1 f(-2) seen

(b) 3V(x - 1) or 3 x -1 2 M1 x -1 = j 3 or 3V(y - 1)

(c) 1 2 3 M2 (x - 1)(x - 2) = 0or M1 (x + a)(x + b) = 0 whereab = 2 or a + b = -3If 0 scored give M1 for x2 - 3x + 2 = 0

18 (a) 4324 cao 2 M 11 x 23 x 24 x 47 or better 6

(b) (i) 4, 9

(ii) (n + 1)2 or n2 + 2n + 1

2

1

B1 either correct

(c)2— n(n+ 1)(2n + 1) oe 2 M1 recognising Vn = 4Tn

© UCLES 2012 0580/02/SM/15

Cambridge

IGCSEC am bridge In ternational Exam inationsCambridge International General Certificate of Secondary Education

CANDIDATENAME

CANDIDATENUMBER

CENTRENUMBER

MATHEMATICS

Paper 3 (Core)

SPECIMEN PAPER

Candidates answer on the Question Paper.

Additional Materials: Electronic calculatorTracing paper (optional)

0580/03

For Examination from 2015

2 hours

Geometrical instruments

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.

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 n , use either your calculator value or 3.142.

At the end of the examination, fasten all your work securely together.The number o f marks is given in brackets [ ] at the end of each question or part question.The total of the marks for this paper is 104.

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

This document consists of 16 printed pages.

|S§ CAMBRIDGE© u c le s 2012 [Turn over

2

1 (a) Write twenty five million in figures.

Answer(a) [1]

(b) Write the following in order of size, starting with the smallest.

2

365% 0.6

Answer(b) < < [1]

(c) In a sale a coat costing $250 is reduced to $200.

Find the percentage decrease in the cost.

Answer(c) % [3]

(d)

120 students are asked to choose their favourite sport. The results are shown in the pie chart.

Calculate the number of students who chose

(i) basketball,

NOT TO SCALE

Answer(d)(i)

(ii) football.

[1]

Answer(d)(ii) [2]

© UCLES 2012 0580/03/SP/15

2 The distance between Geneva and Gstaad is 150 km.

(a) Write 150 in standard form.

3

Answer (a) ................................................. [1]

(b) A car took 1 — hours to travel from Geneva to Gstaad. 2

Calculate the average speed of the car.

Answer(b) .................................................... km/h [1]

(c) A bus left Gstaad at 10 15.It arrived in Geneva at 12 30.

Calculate the time, in hours and minutes, that the bus took for the journey.

Answer(c) ................... h ................... min [1]

(d) Another bus left Geneva at 13 55.It travelled at an average speed of 60 km/h.

Find the time it arrived in Gstaad.

Answer(d) ................................................. [2]

(e) The distance of 150 km is correct to the nearest 10 km.

Complete the statement for the distance, d km, from Geneva to Gstaad.

Answer(e) ................... d < ................... [2]

© UCLES 2012 0580/03/SP/15 [Turn over

4

Use the num bers in the list above to answer all the following questions.

(a) Write down

(i) two even numbers,

Answer (a)(\) ............... , ............. [1]

(ii) two prime numbers,

Answer(a)(ii) ............... , ............. [2]

(iii) a square number,

Answer (a)( iii) ....................................... [1]

(iv) two factors of 90 .

Answer(a)( iv) ............... , ............. [2]

(b) (i) Calculate the mean of the seven numbers.

Answer(b)(i) ....................................... [2]

(ii) Find the median.

Answer (b)( ii) ....................................... [2]

(iii) Find the range.

Answer(b){ iii) ....................................... [1]

3 36 29 41 45 15 10 13

© UCLES 2012 0580/03/SP/15

5

(c) A number from the list is chosen at random.

Find the probability that the number is

(i) even,

Answer (c)(i) ....................................... [1]

(ii) a multiple of 5.

Answer(c)(n) ....................................... [1]

© UCLES 2012 0580/03/SP/15 [Turn over

6

4 (a) Using the exchange rates

$1 = 0.70 Euros and $1 = 90 Yen

change

(i) $100 to Euros,

Answer(a)(i) .............................................. Euros [1]

(ii) 100 Yen to dollars.

Answerlajiu) $ ................................................ [2]

(b) Tania went on holiday to Switzerland.The exchange rate was $1 = 1.04 Swiss francs (CHF).She changed $1500 to Swiss francs and paid 1% commission.

(i) How much commission, in dollars, did she pay?

Answer(b)(i) $ ................................................. [1]

(ii) Show that she received CHF 1544.40.

Answer (b)(ii)

[2]

(c) Tania spent CHF 950 on her holiday.She converted the remaining Swiss francs back into dollars. She paid CHF 10 to make the exchange.

Calculate the amount, in dollars, Tania received.

Answer(c) $ ..................................................... [3]

© UCLES 2012 0580/03/SP/15

7

5

(a) Find the gradient of the line l.

Answer(a) ................................................. [2]

(b) (i) Complete the table below for x + 2y = 6 .

x 0 2

y 0

[3]

(ii) On the grid, draw the line x + 2y = 6 for -4 Y x Y 6 . [2]

(c) The equation of the line I is 4x + 3y = 4.

Use your diagram to solve the simultaneous equations 4x + 3y = 4 and x + 2y = 6 .

Answer(c) x =

y = ..................................................... [2]

© u c l e s 2012 0580/03/SP/15 [Turn over

6 (a)

8

A B

The line AB is drawn above.

Parts (i), (iii), and (v) m ust be completed using a ru ler and compasses only.All construction arcs m ust be clearly shown.

(i) Construct triangle ABC with AC = 7 cm and BC = 6 cm. [2]

(ii) Measure angle BAC.

Answer(a) (ii) Angle BA C = ................................................. [1]

(iii) Construct the bisector of angle ABC. [2]

(iv) The bisector of angle ABC meets AC at T.

Measure the length of AT.

Answer(a)(iv) A T = .................................................... cm [1]

(v) Construct the perpendicular bisector of the line BC . [2]

(vi) Shade the region that is

• nearer to B than to Cand

• nearer to BC than to AB . [1]

© UCLES 2012 0580/03/SP/15

(b) A ship sails 40 km on a bearing of 040° from P to Q.

(i) Using a scale of 1 centimetre to represent 5 kilometres, make a scale drawing of the path of the ship.

Mark the point Q .

9

North

P

Scale: 1 cm = 5 km[2]

(ii) At Q the ship changes direction and sails 30 km on a bearing of 160° to the point R.

Draw the path of the ship. [2]

(iii) Find how far, in kilometres, the ship is from the starting position P .

Answer(b)(iii) . km [1]

(iv) Measure the bearing of P from R .

Answer(b)(iv) [1]

© UCLES 2012 0580/03/SP/15 [Turn over

7 (a) Solve the equation 2(x + 4) = 3(x + 2) + 8 .

10

Answer(a) x = ................................................. [3]

(b) Make z the subject of za + b = 3 .

Answer(b) z = ................................................. [2]

(c) Find x when 2x3 = 54 .

Answer(c) x = ................................................. [2]

© UCLES 2012 0580/03/SP/15

11

(d) A rectangular field has a length of x metres.The width of the field is (2x - 5) metres.

(i) Show that the perimeter of the field is (6x - 10) metres.

Answer (d)(i)

[2]

(ii) The perimeter of the field is 50 metres.

Find the length of the field.

Answer(d)(ii) length = .................................................. m [2]

© u c l e s 2012 0580/03/SP/15 [Turn over

12

y8

The diagram shows two shapes A and B.

(a) Describe fully the single transformation which maps A onto B.

Answer(a) ................................................................................................................................................. ...... [2]

(b) On the grid, draw the line x = 2. [1]

(c) On the grid, draw the image of shape A after the following transformations.

(i) Reflection in the line x = 2. Label the image C. [1]

(ii) Enlargement, scale factor 2, centre (0, 0). Label the image D. [2]

© UCLES 2012 0580/03/SP/15

13

9 (a) Factorise completely 3x2 + 12x.

Answer(a) ................................................. [2]

(b) Find the value of a3 + 3b2 when a = 2 and b = -2 .

Answer(b) ................................................. [2]

(c) Simplify 3x4 x 2x3.

Answer(c) ................................................. [2]

© UCLES 2012 0580/03/SP/15 [Turn over

10

14

The diagram shows a ramp in the form of a triangular prism.The cross-section is a right-angled triangle of length 5 m and height 2 m.

(a) Find the value of x .Give your answer correct to 1 decimal place.

Answer(a) x = ................................................. [3]

(b) Find the area of the cross-section.

Answer(b) .................................................... m2 [2]

(c) The ramp is 10 m long.

Calculate the volume of the ramp.

Answer(c) .................................................... m3 [1]

© UCLES 2012 0580/03/SP/15

15

(d) Calculate the total surface area of all five faces of the ramp.

Answer(d) .................................................... m2 [3]

(e) Each face of the ramp is painted.Paint costs $2.25 per square metre.

Calculate the total cost of the paint.

Answer(e) $ .................................................... [1]

Question 11 is prin ted on the next page.

© u c l e s 2012 0580/03/SP/15 [Turn over

16

11

Diagram 1 Diagram 2 Diagram 3

The diagrams show a sequence of shapes.

(a) On the grid, draw Diagram 4. [1]

(b) Complete the table showing the number of lines in each diagram.

Diagram (n) Number of lines

1 6

2 11

3

4

5

[3]

[1]

[2]

[1]

. [2]

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.

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.

(c) Work out the number of lines in Diagram 8.

Answer(c)

(d) Write down an expression, in terms of n, for the number of lines in Diagram n.

Answer (d)

(e) Work out the number of lines in Diagram 100.

Answer (e)

(f) The number of lines in Diagramp is 66.

Find the value of p.

Answer (f) p =

© UCLES 2012 0580/03/SP/15

Cambridge

IGCSEC am bridge In ternational Exam inationsCambridge International General Certificate of Secondary Education

MATHEMATICS 0580/03

Paper 3 (Core) For Examination from 2015

SPECIMEN MARK SCHEME

2 hours

MAXIMUM MARK: 104

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

This document consists of 5 printed pages and 1 blank page.

|S§ CAMBRIDGE© u c le s 2012 [Turn over

2

Types of markM marks are given for a correct method.A marks are given for an accurate answer following a correct method.B marks are given for a correct statement or step.D marks are given for a clear and appropriately accurate drawing.P marks are given for accurate plotting of points.E marks are given for correctly explaining or establishing a given result. SC marks are given for special cases that are worthy of some credit.

Abbreviationscao correct answer onlycso correct solution onlydep dependentft follow through after errorisw ignore subsequent workingoe or equivalentSC Special Casewww without wrong workingart anything rounding tosoi seen or implied

Qu. Answers Mark Part Marks

1 (a) 25 000 000 cao 1

(b) 0.6 < 65% < - 3

1

(c) 20% 3 B1 for 50 seen M1 for their 50 x 100250

or B1 for 0.8 or 80 seenM1 for 1 - their 0.8 or 100 - their 80

(d) (i) 30 1

(ii) 40 2 M1 for 360 - (90 + 150) implied by 120 seen

2 (a) 1.5(0) x 102 cao 1

(b) 100 cao 1

(c) 2 hours 15 minutes cao 1

(d) 16(:) 25 (pm) or (0)425 pm 2 M1 for 2.5 (oe), 2hrs 30 min

(e) 145 < d < 155 2 B1 for each value in correct place

© UCLES 2012 0580/03/SM/15

3

3 (a) (i) 36, 10 1

(ii) 29, 41, 13 any two 2 B1 for each

(iii) 36 1

(iv) 45, 15, 10 any two 2 B1 for each

(b) (i) 27 2 B1 for 36 + 29 + ... + 13 seen implied by 189

(ii) 29 2 M1 for attempting to order the numbers

(iii) 35 cao 1

(c) (i)2— oe7

1

(ii)3— oe7

1ft Their denominator from (c)(i)

4 (a) (i) 70 cao 1

(ii) 1.11(11...) 2 B1 for 100 - 90, 10 - 9, 119

(b) (i) 15 cao 1

(ii) (1500 - 15) x 1.04 2 B1 for x 1.04, 1560, 15.60

(c) 561.92 3 M1 for 1544.40 - 950 - 10 (584.40) oe M1 indep for ^ 1.04

5 (a)- 4 3

oe, -1 .2 to -1 .4 2 r. riseB1 for attempt a t -----run

(b) (i) 3, 2, 6 3 B1 for each value

(ii) Correct continuous line 2ft Minimum length (0,3) to (6,0) B1 for plotting their 3 points

(c) x = -2 , y = 4 2ft B1 for their x, B1 for their y from their intersections

© UCLES 2012 0580/03/SM/15 [Turn over

4

6 (a) (i) Correct construction 2 B1 for two lines or B1 for accurate arcs seen or B1 for one correct line with two arcs SC1 for AC = 6 and BC = 7 with arcs

(ii) 47° (45 - 49) 1ft Strict ft their (a)(i)

(iii) Correct construction 2ft Their (a)(i) B1 for accurate arcs no line or B1 for accurate line drawn no arcs or B1 for accurate line with arcs bisecting another angle

(iv) 4 (3.8 - 4.2) 1ft Strict ft their (iii) with intersection on opposite side of triangle

(v) Correct construction 2ft B1 for accurate arcs no line orB1 for accurate line drawn no arcs orB1 for accurate line with arcs, bisecting AB or AC

(vi) Correct region shaded 1ft ft is for boundaries of correct perpendicular bisector of their BC and correct angle bisector of their ABC, with or without arcs

(b) (i) Correct scale drawing of PQ 2 B1 for accurate angle 40o, B1 for PQ 8cm

(ii) Correct scale drawing of their QR 2 B1 for accurate angle 160o, B1 for QR 6cm

(iii) 35 to 37 1ft Measure x 5 ± 1km

(iv) 264 to 268 1ft

7 (a) -6 www 3 M2 for 8 = x + 6 + 8 or better or -x + 8 = 6 + 8 or better M1 for 2x + 8 or 3x + 6 or 3x + 14

(b)3 - b 3------- or —

a a

Ia

b 2 B1 for 3 - b seen or z + — = —a a

(c) 3 254

B1 for — or better 2

SC1 for embedded answerie 2 x 33 = 54 or 2 x 3 x 3 x 3 = 54

(d) (i) x + x + 2x —5 + 2x — 5 = 6x - 10 2 M1 accept 2x + 2(2x - 5) or 2(x + 2x - 5) E1 dep

(ii) 10 2 M1 for 6x - 10 = 50

8 (a) Translation' 0^

, - 6 )2 B1 for translation B1 for column vector

(b) Correct line drawn 1 Continuous full line. Accept freehand.

(c) (i) Correct reflection 1ft Their (b)

(ii) Correct enlargement 2 B1 for any other enlargement scale factor 2

9 (a) 3x(x + 4) 2 B1 for 3(x2 + 4x) or B1 for x(3x + 12) or B1 for 3x(x + 4) seen (if not final answer)

(b) 20 2 B1 for 8 or 12 seen

(c) 6x7 2 B1 for kx7 or for 6xk , k ^ 0

© UCLES 2012 0580/03/SM/15

5

10 (a) 5.4 cao 3 M1 for 22 + 52 (= x2) implied by 29A1 5.38(51..) or V29 or 5.39B1 indep for rounding their answer to 1 decimalplace

(b) 5 2 M1 for 0.5 x 5 x 2 oe

(c) 50 1ft 10 x their (b)

(d) 134 3ft M2 for 2 x their (b) + 10 x their (a) + 2 x 10 +5 x 10 or betterM1 for any 3 faces correct

(e) 301.5(0) 1ft Their (d) x 2.25

11 (a) Correct shape drawn 1

(b) 16, 21, 26 3 B1 for each SC1 “their 16” + 5 SC1 “their 21” + 5

(c) 41 1

(d) 5n + 1 2 B1 for 5n, B1 for +1

(e) 501 1ft Their (d) if linear

(f) 13 2ft Their (d) if linear B1 for their (d) = 66

© UCLES 2012 0580/03/SM/15

BLANK PAGE

6

© UCLES 2012 0580/03/SM/15

Cambridge

IGCSEC am bridge In ternational Exam inationsCambridge International General Certificate of Secondary Education

CANDIDATENAME

CENTRENUMBER

CANDIDATENUMBER

MATHEMATICS

Paper 4 (Extended)

SPECIMEN PAPER

Candidates answer on the Question Paper.

Additional Materials: Electronic calculatorTracing paper (optional)

0580/04

For Examination from 2015

2 hours 30 minutes

Geometrical instruments

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.

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 n use either your calculator value or 3.142.

At the end of the examination, fasten all your work securely together.The number o f 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.

This document consists of 16 printed pages.

|S§ CAMBRIDGE© u c le s 2012 [Turn over

2

1 (a) Abdullah and Jasmine bought a car for $9000.Abdullah paid 45% of the $9000 and Jasmine paid the rest.

(i) How much did Jasmine pay towards the cost of the car?

Answer(a){i) $ ................................................. [2]

(ii) Write down the ratio of the payments Abdullah : Jasmine in its simplest form.

Answer (a)( ii) ................... : ................. [1]

(b) Last year it cost $2256 to run the car.Abdullah, Jasmine and their son Henri share this cost in the ratio 8 : 3 : 1.Calculate the amount each paid to run the car.

Answer(b) Abdullah $ .................................................

Jasmine $ .................................................

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

(c) (i) A new truck costs $15 000 and loses 23% of its value each year.Calculate the value of the truck after three years.

Answer(c)(i) $ ................................................. [3]

(ii) Calculate the overall percentage loss of the truck’s value after three years.

Answer(c)(ii) .................................................. % [3]

© UCLES 2012 0580/04/SP/15

2 (a) Find the integer values for x which satisfy the inequality -3 < 2x -1 Y 6 .

Answer(a) ................................................. [3]

(b) Simplifyx 2 + 3x - 1 0

x 2 - 25

3

Answer(b) ................................................. [4]

5 2 2(c) (i) Show t h a t ---------1-------- = 3 can be simplified to 3x - 13x - 8 = 0.

x - 3 x +1

Answer(c)(i)

[3]

(ii) Solve the equation 3x2 - 13x - 8 = 0.

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

Answer(c)(ii) x = ................... o rx = ................... [4]

© UCLES 2012 0580/04/SP/15 [Turn over

4

3 The table shows information about the heights of 120 girls in a swimming club.

Height (h metres) Frequency

1.3 < h Y 1.4 4

1.4 < h Y 1.5 13

1.5 < h Y 1.6 33

1.6 < h Y 1.7 45

1.7 < h Y 1.8 19

1.8 < h Y 1.9 6

(a) (i) Write down the modal class.

Answer(a)(i) ................................................ m [1]

(ii) Calculate an estimate of the mean height. Show all of your working.

Answer(a)(ii) ................................................ m [4]

(b) Girls from this swimming club are chosen at random to swim in a race.Calculate the probability that

(i) the height of the first girl chosen is more than 1.8 metres,

Answer(b)(i) .................................................... [1]

(ii) the heights of both the first and second girl chosen are 1.8 metres or less.

Answer(b)(n) ................................................... [3]

© UCLES 2012 0580/04/SP/15

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

5

Height (h metres) Cumulative frequency

h Y 1.3 0

h Y 1.4 4

h Y 1.5 17

h Y 1.6 50

h Y 1.7

h Y 1.8 114

h Y 1.9[1]

(ii) Draw the cumulative frequency graph on the grid.

120 -

Cumulativefrequency

110-

100-

9 0 -

80

70

6 0 -

5 0 -

4 0 -

3 0 -

20

10

1.3 1.4

(d) Use your graph to find

(i) the median height,

(ii) the 30th percentile.

1.5 1.6

Height (m)

1.7 1.8h

1.9

[3]

Answer(d)(i) .................................................. m [1]

Answer (d){ii) ................................................. m [1]

0

© UCLES 2012 0580/04/SP/15 [Turn over

6

NOT TO SCALE

4r

The diagram shows a plastic cup in the shape of a cone with the end removed. The vertical height of the cone in the diagram is 20 cm.The height of the cup is 8 cm.The base of the cup has radius 2.7 cm.

(a) (i) Show that the radius, r, of the circular top of the cup is 4.5 cm.

Answer(a)(i)

[2]

(ii) Calculate the volume of water in the cup when it is full.1 2

[The volume, V, of a cone with radius r and height h is V = — nr h.]3

Answer(a)in) ................................................. cm3 [4]

© UCLES 2012 0580/04/SP/15

(b) (i) Show that the slant height, s, of the cup is 8.2 cm.

Answer(b)(i)

7

(ii) Calculate the curved surface area of the outside of the cup.[The curved surface area, A, of a cone with radius r and slant height l is A = nrl.]

Answer(b)(ii)

[3]

cm2 [5]

© UCLES 2012 0580/04/SP/15 [Turn over

8

5 (a) Complete the table for the function f(x) = ------ 3x - 1 .2

x -3 -2 -1.5 -1 0 1 1.5 2 3 3.5

f(x) -5.5 1.8 1.5 -3.5 -3.8 -3 9.9

(b) On the grid draw the graph of y = f(x) for —3 Y x Y 3.5 .

[3]

yA

8-

6-

4-

2-

2 3 43 -2 -1 0 1

-2 -

•_4-

► x

[4]

3

© UCLES 2012 0580/04/SP/15

9

(c) Use your graph to

(i) solve f(x) = 0.5,

Answer(c)(i) x = ............. or x =

(ii) find the inequalities for k, so that f(x) = k has only 1 answer.

or x = [3]

Answer(c)(ii) k <

k > [2]

(d) (i) On the same grid, draw the graph of y = 3x - 2 for — 1 Y x Y 3.5 . [3]

3X 3(ii) The e q u a tio n ------ 3x -1 = 3x - 2 can be written in the form x + ax + b = 0.

2Find the values of a and b.

Answer(d)(n) a= ................ and b = ................. [2]

3x(iii) Use your graph to find the positive answers t o ------ 3x - 1 = 3x - 2 for — 3 Y x Y 3.5 .

2

Answer(d)(m) x = ............... o rx = ................. [2]

© UCLES 2012 0580/04/SP/15 [Turn over

10

C

NOT TO SCALE

6

The quadrilateral ABCD represents an area of land.There is a straight road from A to C.AB = 79 m, AD = 120 m and CD = 95 m.Angle BCA = 26° and angle CDA = 77°.

(a) Show that the length of the road, AC, is 135 m correct to the nearest metre.

Answer(a)

[4]

(b) Calculate the size of the obtuse angle ABC.

© UCLES 2012

Answer(b) Angle ABC = ................................................. [4]

0580/04/SP/15

(c) A straight path is to be built from B to the nearest point on the road AC.

Calculate the length of this path.

11

Answer(c) .............................................. m [3]

(d) Houses are to be built on the land in triangle ACD.Each house needs at least 180 m2 of land.

Calculate the maximum number of houses which can be built.Show all of your working.

Answer(d) ..................................................... [4]

© UCLES 2012 0580/04/SP/15 [Turn over

12

y

(a) Describe fully the single transformation which maps

(i) triangle A onto triangle B,

Answer (a){ i) .................................................................................................................................... [2]

(ii) triangle A onto triangle C,

Answer (a)( ii) .................................................................................................................................... [3]

(iii) triangle A onto triangle D .

Answer(a)( iii) ................................................................................................................................... [3]

© UCLES 2012 0580/04/SP/15

7

13

(b) Draw the image of

(i) triangle B after a translation of <- 5 ̂V 2 ,

[2]

(ii) triangle B after a transformation by the matrix ( 2 0 N

v ° 2 y[3]

(c) Describe fully the single transformation represented by the matrix

Answer(c)

[3]

© UCLES 2012 0580/04/SP/15 [Turn over

14

8 Mr Chang hires x large coaches andy small coaches to take 300 students on a school trip.Large coaches can carry 50 students and small coaches 30 students.There is a maximum of 5 large coaches.

(a) Explain clearly how the following two inequalities satisfy these conditions.

(i) x Y 5

Answer (a)( i) ..................................................................................................................................... [1]

(ii) 5x + 3y [ 30

Answer (a)(ii) ....................................................................................................................................

Mr Chang also knows that x + y Y 10.

(b) On the grid, show the information above by drawing three straight lines and shading the unw anted regions.

yI L

10

8

4

2 -

10[5]

x0

© UCLES 2012 0580/04/SP/15

(c) A large coach costs $450 to hire and a small coach costs $350.

(i) Find the number of large coaches and the number of small coaches that would give the minimum hire cost for this school trip.

15

Answer(c)(i) Large coaches ....................................................

Small coaches .................................................... [2]

(ii) Calculate this minimum cost.

Answer(c)in) $ ............................................. [1]

9 The number, P, of penguins in a colony, t years after the year 2000, is given by

P = 2500 x 1.02'.

(a) (i) How many penguins were in the colony in the year 2000?

Answer (a){ i) ................................................. [1]

(ii) What information is given by 1.02 in the formula?

Answer (a)(ii) ....................................................................................................................................

(b) Using trial and improvement, or otherwise, find in which year the number of penguins in the colony will first be greater than 5000.

© UCLES 2012

Answer(b) ................................................. [3]

Question 10 is printed on the next page.

0580/04/SP/15 [Turn over

16

10 (a) John wants to estimate the value of n.He measures the circumference of a circular pizza as 105 cm and its diameter as 34 cm, both correct to the nearest centimetre.

Calculate the lower bound of his estimate of the value of n.Give your answer correct to 3 decimal places.

Answer (a) ................................................. [4]

(b) The volume of a cylindrical can is 550 cm3, correct to the nearest 10 cm3.The height of the can is 12 cm correct to the nearest centimetre.

Calculate the upper bound of the radius of the can.Give your answer correct to 3 decimal places.

Answer (b) .................................................... cm [5]

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.

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.

© UCLES 2012 0580/04/SP/15

Cambridge

IGCSEC am bridge In ternational Exam inationsCambridge International General Certificate of Secondary Education

MATHEMATICS 0580/04

Paper 4 (Extended) For Examination from 2015

SPECIMEN MARK SCHEME

2 hours 30 minutes

MAXIMUM MARK: 130

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

This document consists of 7 printed pages and 1 blank page.

|S§ CAMBRIDGE© u c le s 2012 [Turn over

2

Types of m arkM marks are given for a correct method.A marks are given for an accurate answer following a correct method.B marks are given for a correct statement or step.D marks are given for a clear and appropriately accurate drawing.P marks are given for accurate plotting of points.E marks are given for correctly explaining or establishing a given result. SC marks are given for special cases that are worthy of some credit.

Abbreviationscao correct answer onlycso correct solution onlydep dependentft follow through after errorisw ignore subsequent workingoe or equivalentSC Special Casewww without wrong workingart anything rounding tosoi seen or implied

Qu. Answers M ark P a rt M arks

1 (a) (i) 4950

(ii) 9 : 11

(b) 1504

564

188

(c) (i) 6847.99 or 6848 or 6850

(ii) 54.3 (54.33 to 54.35)

2

1

1

1

1

3

3ft

M1 for 9000 x 0.55 oe

Accept 1 : 1.22 or 0.818 : 1After 4050 in (a)(i) allow SC1 for 11 : 9 etc

After 0 scored M1 for 2256 + (8 + 3 + 1) soi

M2 for 15000 x 0.773 oe (6847. (..)ww imp M2) or M1 for 150 00 x 0.772 oe soi (8893.5)After 0 scored SC1 for art 27913 or 27910 or 27900

ft their (15000 - their (c)(i))/15000 x 100 to 3sf or better bu t not for negative answer or from 4650 in (c)(i) leading to 69%M2 for 1 - 0.773 (0.543..)or their (15000 - their (c)(i))/15000 (x 100)or SC2ft their (c)(i)/15000 x 100 correctlyevaluated (45.65 to 45.67 or 45.7)or M1 for 0.773 (0.45 65..)or their (c)(i)/15000

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(a) 0, 1, 2, 3

(b) — 2 www final answer x - 5

(c) (i) 5(x + 1) + 2(x - 3) = 3(x + 1)(x - 3) oe

x2 - 3x + x - 3 or better seen

3x2 - 13x - 8 = 0

— i —

(ii)(-13) ± V (-13 )2 - 4(3)(-8)

2(3)

4.88 and -0.55 cao

M l

B l

E l

B lB l

B lB l

Additional values count as errorsB2 for one error/omission or B1 for two errors/omissionsAfter B0,M2 for -1 < x < 3.5 seen, allow 7/2 for 3.5 or M1 for -1 < x or x < 3.5 or x = -1 and x = 3.5 Allow M2 for 0 < x < 4 or M1 for x > 0 or x < 4

M3 for(x + 5)(x - 2) (x + 5)(x - 5)

or M2 for (x + 5)(x - 2) seenor M1 for (x + a)(x + b) where ab = -10or a + b = 3and M1 for (x + 5)(x - 5) seen

Allow if still over common denominator

Allow x2 - 2x - 3 seen or 3x2 - ^ + 3x - 9 or better seen

With no errors seen and brackets correctly expanded on both sides

In square root B1 for (-13)2 - 4(3)(-8) or better (265)

If in form

B1 for - (-13) and 2(3) or better

SC1 for 4.88 and - 0.55 seen or - 0.5 and 4.9 or - 0.546... and 4.879 to 4.880

2 3

4

r r

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(a) (i) 1.6 < h < 1.7

(ii) {1.35 x 4 + 1.45 x13 + 1.55 x33 + 1.65 x 45 + 1.75 x 19 + 1.85 x 6}- 120

(b) (i)

(ii)

1.62 or 1.616 to 1.617

6 120

2147

oe

2380oe (0.902(1..))

(c) (i) 95, 120

(ii) Plots 7 points correctly exact or in correct square

Curve or lines through 7 points

(d) (i) 1.61 to 1.63

(ii) 1.555 to 1.57

1

M3

A1

1

P2ft

C1ft

1ft

1ft

Condone alternative notation used for class

(194/120)M1 for mid-values soi (allow one slip) and M1 for use of YJX with x in correct interval (allow one more slip)and M1 depend on 2nd M for dividing by 120

www4

Accept dec/% to 3 sf or better but not ratio isw cancelling/conversion (also for (ii))

k k - 1 kM2 f o r -----x -------w h e re ----- is 1 - their (b)(i)

120 119 120or i f k = 114or M1 for 1 - their (b)(i) or for 114/120 seen After 0 scored SC2 for ans 1/476 oe or SC1 for 6/120 x 5/119

P1ft for 5 or 6 correct plots

ft their increasing curve within 1 mm of points

ft their 60th reading on inc. curve to nearest 0.01

ft their 36th reading on inc. curve

(a) (i) 2.7 x — oe = 4.512

(ii) 1/3n x 4.52 x 20 - 1/3n x 2.72 x 12 or(1 - (3/5)3) x 1/3n x 4.52 x 20 oe

332.3 to 332.6 or 332 or 333

(b) (i) 82 + (4.5 - 2.7)2 oe

sq root

8.2

(ii) 185 or 186 or 185.5 or 185.45 to 185.51

E2

M3

A1

M1

M1

E1

M1 for (SF =) 20/12 or 12/20 (but not from 2.7/4.5 or 4.5/2.7)

M1 for 1/3n x 4.52 x 20 (424 ... or 135n) and M1 for 1/3n x 2.72 x 12 (91.6..or 29.16n)

e.g. Alt: 202 + 4.52 and 122 + 2.72

Dep on 1st M1 Alt: 20.5 - 12.3 Other complete correct methods are M2

No errors seen

M4 for n x 4.5 x 20.5 - n x 2.7 x 12.3or other complete correct methodor M3 for n x 4.5 x 20.5 or n x 2.7 x 12.3(290 or 92.25n) (104.3...or 33.21n)or B2 for (slant height of large cone =) 20.5or (slant height of removed cone =) 12.3

o r V 2 ^or M1 forV4T52 + 202 or 12/8 x 8.2 oe or 20/8 x 8.2 oe

72 + 122

3

1

3

4

5

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5 (a) 1, -1 , 3.5 1,1,1

(b) 10 correct points plotted P3ft P2ft for 8 or 9 correct P1ft for 6 or 7 correct Allow points to be implied from curve

Smooth curve through at least 8 points and correct shape

C1ft Correct cubic shape, not ruled

(c) (i) -2 .2 to -2.1

-0.65 to -0.45

1ft

1ft

Correct or ft their x values

2.5 to 2.7 1ft If ft and more than 3 solns then 2 marks maximum

(ii) (k <) -4 to -3 .7 1ft Correct or ft their graph for y values at max and min

(k >) 1.7 to 2 1ft After 0 scored SC1 for both correct but reversed

(d) (i) Ruled line gradient 3 andjy-intercept -2 over the range -1 to 3. 5

3 B2 for correct but freehand or shortor M1 for a ruled line of gradient 3 or passesthrough (0, -2 ) (but not y = -2)

(ii) (a =) -12, (b =) 2 1,1 After 0, M1 for x3- 6x- 6x-2 + 4 (=0) or better

(iii) 0.1 to 0.2 and 3.3 to 3.4 cao 1,1

6 (a) 1202 + 952 - 2 x 120 x 95 x cos77 M2 M1 for implicit version

135.26 . or 135.3 E2 A1 for 18295 to 18297

(b), . . their135 x sin26(sin#) = ----------------------

79

48.5 to 48.7 isw

M2

A1

~ sin# sin26M1 f o r ----------- = -------- oe

their135 79

131 or 131.3 to 131.5 www4 B1ft ft for 180 - their 48.5 to 48.7 dep on sine rule or sine used

(c) (Angle A =) 22.5 to 22.7 B1ft ft 154 - their (b), also accept angle B = 67.3 to 67.5 (ft their (b) - 64)

‘Path’/79 = sin (their A) oe M1 Dep on B1 and their A < 90 eg 79 cos 67.4

30.2 to 30.5 www3 A1

(d) 1 x 120 x 95 x sin 77 oe2

M1 (5554)

Their area + 180 M1 Dep on area attempt

30.8 to 30.9 A1

30 B1ft ft their 30.8 to 30.9 truncated dep on at least M1 earnedAfter M2 answer 30 www scores A1B1 Answer 30 ww scores 0

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7 (a) (a) (i) Reflection only B1 Spoilt if extras

y = -2 B1

(ii) Enlargement only B1 Spoilt if extras

12

B1

(1, 4) B1

(iii) Rotation only B1 Spoilt if extras

90° clockwise oe B1 Accept -90° or (+)270°

Around (1, -3) B1

(b) (i) Triangle at (-4, 4), (-1, 4), (-1, 5) 2( - 5 ̂ ( k ̂

B1 for translation of orV k J V2 J

After B0, SC1 for translation of 5 small squares to the left and 2 small squares up

(ii) Triangle at (2, 4), (8, 4), (8, 6) 3 B1 for each correct co-ordinate (max B2) plotted I f no/wrong plots allow SC2 for 3 correct co-ordinates shown in working or SC1 for any 2correct co-ordinates shown

or M1 for"2 0N

v0 2,

42

12

(c) Rotation or Enlargement 1

180 oe or SF -1 1

origin 1 Accept (0, 0) or O

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8 (a) (i) There are up to 5 large coaches oe

1 E.g. cannot hire more than 5 large coachesThe maximum is 5 large coachesThe large coaches are less than or equal to 5

(ii) 50x + 30y > 300 oe E2 No errorsAllow in words provided cleare.g. 50 in large coaches and 30 in small coachesmust equal 300 seats or moreM1 for associating 50 with x or large coachesand 30 with y or small coaches

(b) Freehand lines -1 penalise once.All lines must be long enough to make full boundary of their region accept dashed or solid lines

x = 5 ruled L1

x + y = 10 ruled L1

5x + 3jy = 30 ruled L2 L1 for ruled line with intercepts at (0, 10) or (6, 0) within 2mm by eye at intercepts (extend if line is short)

Correct region indicated cao R1 Allow if slight inaccuracy(s) in diagonal lines Allow any clear indication of region

5 2

(c) 11

After 5 and 2 in working ignore attempts to calculate costs

(ii) 2950 1ft ft their 5 x 450 + their 2 x 350 provided positive integers

9 (a) (i) 2500

(ii) Increase of 2% (per year)

1

1

(b) 2036 (accept 2035) 3 M2 for t = 35 to 36 (inclusive) identified e.g. 1.0235 = 1.999, 1.0236 = 2.039 or equivalent with values of POR M1 for one correct trial of P (or 1.02*) with t [ 20 (condone t not an integer)

10 (a) 3.028 or 3.029 cao 4 B3 for 3.0289(85...)or M1 for their 105/their 34(their 105 in range 104 to 106 and their 34 inrange 33 to 35)and B1 for 104.5 or 34.5 or 34.499.. selected

(b) n r2 their h = their V M1 Where V is in range 540 to 560 and h is in range 11 to 13

2 their V (r = )--------------

n x their hM1 Implies previous method (15.36 implies M2)

If using 545 and 12.5 then 13.88 (leading to 3.73) If using 550 and 12 then 14.59 (leading to 3.82)

Sq root M1 Dep on M2, can be implied from answers

Selects 555 or 554.99.. and 11.5 B1 Indep

3.919 cao A1 If trials then 5 or 0

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© UCLES 2012 0580/04/SM/15