Igcse core papers 2002 2014

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.
© UCLES 2012 [Turn over
Cambridge International Examinations
Cambridge International General Certificate of Secondary Education
MATHEMATICS 0580/01
Paper 1 (Core) For Examination from 2015
SPECIMEN PAPER
1 hour
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.
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 π, 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 56.

2
© UCLES 2012 0580/01/SP/15
1
A
S
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]
2 When Ali takes a penalty, the probability that he will score a goal is
5
4
.
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 1.4m.
Find Ben’s height.
Answer m [2]

3
© UCLES 2012 0580/01/SP/15 [Turn over
4 The distance between the centres of two villages is 8km.
A map on which they are shown has a scale of 1:50000.
Calculate the distance between the centres of the two villages on the map.
Give your answer in centimetres.
Answer cm [2]
5
10
8
6
4
2
0
Black Silver Red
Favourite colour
Green Blue
Frequency
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]

4
© UCLES 2012 0580/01/SP/15
6 Use your calculator to find
1.53.1
5.7545
+
×
.
Answer [2]
7 (a) Calculate 60% of 200.
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 50cm.
(a) Calculate the area of the circle in cm2
.
Answer(a) cm2
[2]
(b) Write your answer to part (a) in m2
.
Answer(b) m2
[1]

5
9
30
25
20
15
10
5
0
6am 9am Midday
Time
3pm 6pm
Temperature
(°C)
The graph shows the temperature in Paris from 6am to 6pm one day.
(a) What was the temperature at 9am?
Answer(a) °C [1]
(b) Between which two times was the temperature decreasing?
Answer(b) and [1]
(c) Work out the difference between the maximum and minimum temperatures shown.
Answer(c) °C [1]
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]

6
© UCLES 2012 0580/01/SP/15
11 Without using your calculator, work out 





+
4
1
3
2
2
1
.
Show all your working clearly and give your answer as a fraction.
Answer [3]
12
y
x
10–1–2–3–4 2
9
8
7
6
5
4
3
2
1
The diagram shows the graph of y = (x + 1)2
for −4 Y x Y 2.
(a) On the same grid, draw the line y = 3. [1]
(b) Use your graph to find the solutions of (x + 1)2
= 3.
Give each solution correct to 1 decimal place.
Answer(b) x = or x = [2]

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]

8
© UCLES 2012 0580/01/SP/15
15
50
40
30
20
10
0
10 20 30 40
Mathematics test mark
Englishtestmark
50 60 70 80
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]

9
16 (a)
A B
C
D E
110°
NOT TO
SCALE
In the diagram, AB is parallel to DE.
Angle ABC = 110°.
Find angle BDE.
Answer(a) Angle BDE = [2]
(b)
t°
y°
z°
50°
O
B
A T
NOT TO
SCALE
TA is a tangent at A to the circle, centre O.
Angle OAB = 50°.
Find the value of
(i) y,
Answer(b)(i) y = [1]
(ii) z,
Answer(b)(ii) z = [1]
(iii) t.
Answer(b)(iii) t = [1]

10
© UCLES 2012 0580/01/SP/15
17
y°
8m
3m
NOT TO
SCALE
The diagram shows a ladder, of length 8m, leaning against a vertical wall.
The bottom of the ladder stands on horizontal ground, 3m 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]

11
© 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.
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]

12
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
BLANK PAGE

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.
© UCLES 2012 [Turn over
Cambridge International General Certificate of Secondary Education
MATHEMATICS 0580/03
Paper 3 (Core) For Examination from 2015
SPECIMEN PAPER
2 hours
Do not use staples, paper clips, glue or correction fluid.
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 π , use either your calculator value or 3.142.

2
© UCLES 2012 0580/03/SP/15
1 (a) Write twenty five million in figures.
Answer(a) [1]
(b) Write the following in order of size, starting with the smallest.
3
2
65% 0.6
Answer(b) I I [1]
(c) In a sale a coat costing $250 is reduced to $200.
Find the percentage decrease in the cost.
Answer(c) % [3]
(d)
Basketball
Tennis
90°
150°Football
NOT TO
SCALE
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,
Answer(d)(i) [1]
(ii) football.
Answer(d)(ii) [2]

3
2 The distance between Geneva and Gstaad is 150km.
(a) Write 150 in standard form.
Answer(a) [1]
(b) A car took 1
2
1
hours to travel from Geneva to Gstaad.
Calculate the average speed of the car.
Answer(b) km/h [1]
(c) A bus left Gstaad at 1015.
It arrived in Geneva at 1230.
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 1355.
It travelled at an average speed of 60km/h.
Find the time it arrived in Gstaad.
Answer(d) [2]
(e) The distance of 150km is correct to the nearest 10km.
Complete the statement for the distance, d km, from Geneva to Gstaad.
Answer(e) Y d I [2]

4
© UCLES 2012 0580/03/SP/15
3 36 29 41 45 15 10 13
Use the numbers in the list above to answer all the following questions.
(a) Write down
(i) two even numbers,
Answer(a)(i) , [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]

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)(ii) [1]

6
© UCLES 2012 0580/03/SP/15
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.
Answer(a)(ii) $ [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]

7
5
y
x
6
5
4
3
2
1
–1
–2
–3
0 1 2 3 4 5 6–1–2–3–4
l
(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 l is 4x + 3y = 4.
Use your diagram to solve the simultaneous equations 4x + 3y = 4 and x + 2y = 6.
Answer(c) x =
y = [2]

8
© UCLES 2012 0580/03/SP/15
6 (a)
A B
The line AB is drawn above.
Parts (i), (iii), and (v) must be completed using a ruler and compasses only.
All construction arcs must be clearly shown.
(i) Construct triangle ABC with AC = 7cm and BC = 6cm. [2]
(ii) Measure angle BAC.
Answer(a)(ii) Angle BAC = [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) AT = cm [1]
(v) Construct the perpendicular bisector of the line BC. [2]
(vi) Shade the region that is
• nearer to B than to C
and
• nearer to BC than to AB. [1]

9
(b) A ship sails 40km 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.
North
P
Scale: 1cm = 5km
[2]
(ii) At Q the ship changes direction and sails 30km 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]

10
© UCLES 2012 0580/03/SP/15
7 (a) Solve the equation 2(x + 4) = 3(x + 2) + 8.
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]

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]

12
© UCLES 2012 0580/03/SP/15
8
A
B
y
x
6
5
4
3
2
1
–1
–2
–3
–4
–5
–6
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
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]

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
× 2x3
.
Answer(c) [2]

14
© UCLES 2012 0580/03/SP/15
10
2m
5m
10m
xm
NOT TO
SCALE
The diagram shows a ramp in the form of a triangular prism.
The cross-section is a right-angled triangle of length 5m and height 2m.
(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 10m long.
Calculate the volume of the ramp.
Answer(c) m3
[1]

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 printed on the next page.

16
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
© UCLES 2012 0580/03/SP/15
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]
(c) Work out the number of lines in Diagram 8.
Answer(c) [1]
(d) Write down an expression, in terms of n, for the number of lines in Diagram n.
Answer(d) [2]
(e) Work out the number of lines in Diagram 100.
Answer(e) [1]
(f) The number of lines in Diagram p is 66.
Find the value of p.
Answer(f) p = [2]

Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
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.
MATHEMATICS 0580/11
Paper 1 (Core) May/June 2014
1 hour
Cambridge International General Certificate of Secondary Education
[Turn over
IB14 06_0580_11/2RP
© UCLES 2014
*1477753275*
The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.

2
0580/11/M/J/14© UCLES 2014
1 Work out.
10 – 3 × 2
Answer ................................................ [1]
__________________________________________________________________________________________
2 Write down the prime numbers between 20 and 30.
Answer ................................................ [1]
__________________________________________________________________________________________
3
NOT TO
SCALE
163°
59° x°
(a) Find the value of x.
Answer(a) x = ................................................ [1]
(b) One of the angles is 163°.
What type of angle is this?
Answer(b) ................................................ [1]
__________________________________________________________________________________________
4 A city has a population of ﬁve hundred and six thousand.
Write the size of the population
(a) in ﬁgures,
Answer(a) ................................................ [1]
(b) in standard form.
Answer(b) ................................................ [1]
__________________________________________________________________________________________

3
0580/11/M/J/14© UCLES 2014 [Turn over
5 p =
16.83
4.8 1.98276#
(a) In the spaces provided, write each number in this calculation correct to 1 signiﬁcant ﬁgure.
Answer(a)
............ × ............
............
[1]
(b) Use your answer to part (a) to estimate the value of p.
Answer(b) ................................................ [1]
__________________________________________________________________________________________
6 Solve the equation.
8n
2
-
= 11
Answer n = ................................................ [2]
__________________________________________________________________________________________
7 a =
3-
4
e o b =
1
5
-
e o
Work out a – 2b.
Answer f p [2]
__________________________________________________________________________________________
8 The width, wcm, of a carpet is 455cm, correct to the nearest centimetre.
Complete the statement about the value of w.
Answer ............................ Ğ w < ............................ [2]
__________________________________________________________________________________________

4
0580/11/M/J/14© UCLES 2014
9 y =
2
x
x
2
+2
2
Find the value of y when x = 6.
Give your answer as a mixed number in its simplest form.
Answer y = ................................................ [2]
__________________________________________________________________________________________
10 Use your calculator to work out 4
3
+ 2–1
.
Give your answer correct to 2 decimal places.
Answer ................................................ [2]
__________________________________________________________________________________________
11 The diagram shows a cuboid.
8cm
15cm
h
NOT TO
SCALE
The volume of this cuboid is 720cm3
.
The width is 8cm and the length is 15cm.
Calculate h, the height of the cuboid.
Answer h = .......................................... cm [2]
__________________________________________________________________________________________

5
12 The scatter diagram shows the rainfall and the average temperature in a city for the month of June,
over a period of 10 years.
30
25
20
15
10
5
0
5 10 15
Rainfall (cm)
Temperature (°C)
20 25 30
(a) What type of correlation does this scatter diagram show?
Answer(a) ................................................ [1]
(b) Describe the relationship between the rainfall and the average temperature.
Answer(b) ...........................................................................................................................................
............................................................................................................................................................. [1]
__________________________________________________________________________________________

6
0580/11/M/J/14© UCLES 2014
13 The graph can be used to convert between miles and kilometres.
80
70
60
50
40
30
20
10
0
10 20 30
Miles
Kilometres
40 50
A train travels 24 miles in 20 minutes.
Find its average speed in kilometres per hour.
Answer ....................................... km/h [2]
__________________________________________________________________________________________

7
14
127°
a°
b°
A
D
E
BC
NOT TO
SCALE
The diagram shows an isosceles triangle ABC.
DCB is a straight line and is parallel to AE.
Angle DCA = 127°.
Find the value of
(a) a,
Answer(a) a = ................................................ [2]
(b) b.
Answer(b) b = ................................................ [1]
__________________________________________________________________________________________
15 Carlo changed 800 euros (€) into dollars for his holiday when the exchange rate was €1 = $1.50 .
His holiday was then cancelled.
He changed all his dollars back into euros and he received €750.
Find the new exchange rate.
Answer €1 = $................................................. [3]
__________________________________________________________________________________________

8
0580/11/M/J/14© UCLES 2014
16 (a) Simplify the expressions.
(i) p3
× p7
Answer(a)(i) ................................................ [1]
(ii) t5
÷ t8
Answer(a)(ii) ................................................ [1]
(b) (h3
)
k
= h12
Find the value of k.
Answer(b) k = ................................................ [1]
__________________________________________________________________________________________
17
O
P R
Q
17cm
9cm
NOT TO
SCALE
The diagram shows a circle, centre O.
P, Q and R are points on the circumference.
PQ = 17cm and QR = 9cm.
(a) Explain why angle PQR is 90°.
Answer(a) ...........................................................................................................................................
............................................................................................................................................................. [1]
(b) Calculate the length PR.
Answer(b) PR = .......................................... cm [2]
__________________________________________________________________________________________

9
18 In this question, do not use your calculator and show all the steps in your working.
(a) Show that 3 5
1
– 2 8
5
= 40
23
.
Answer(a)
[2]
(b) Work out 8
7
÷ 40
23
.
Give your answer as a mixed number in its simplest form.
Answer(b) ................................................ [2]
__________________________________________________________________________________________
19 The table shows the average monthly temperature (°C) for Fairbanks, Alaska.
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Temperature (°C) –23.4 –19.8 –11.7 –0.8 9.2 15.4 16.9 13.8 7.5 –5.8 –21.4 –21.8
(a) Find
(i) the difference between the highest and the lowest temperatures,
Answer(a)(i) ........................................... °C [1]
(ii) the median.
Answer(a)(ii) ........................................... °C [2]
(b) A month is chosen at random from the table.
Find the probability that its average temperature is below zero.
Answer(b) ................................................ [1]
__________________________________________________________________________________________

10
0580/11/M/J/14© UCLES 2014
20 A bus company in Dubai has the following operating times.
Day
Starting
time
Finishing
time
Saturday 0600 2400
Sunday 0600 2400
Monday 0600 2400
Tuesday 0600 2400
Wednesday 0600 2400
Thursday 0600 2400
Friday 1300 2400
(a) Calculate the total number of hours that the bus company operates in one week.
Answer(a) ............................................. h [3]
(b) Write the starting time on Friday in the 12-hour clock.
Answer(b) ................................................ [1]
__________________________________________________________________________________________

11
21
The diagram shows a circle inside a square.
The circumference of the circle touches all four sides of the square.
(a) Calculate the area of the circle when the side of the square is 15cm.
Answer(a) ......................................... cm2
[2]
(b) Draw all the lines of symmetry on the diagram. [2]
__________________________________________________________________________________________

12
0580/11/M/J/14© UCLES 2014
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included the
22
B
C
A
27m
34m
North
NOT TO
SCALE
In the diagram, B is 27 metres due east of A.
C is 34 metres from A and due south of B.
(a) Using trigonometry, calculate angle ACB.
Answer(a) Angle ACB = ................................................ [2]
(b) Find the bearing of C from A.
Answer(b) ................................................ [2]

MATHEMATICS 0580/12
1 hour
[Turn over
IB14 06_0580_12/2RP
© UCLES 2014
*5359060919*

2
0580/12/M/J/14© UCLES 2014
1 Simplify the expression.
p + p + p + p
Answer ................................................ [1]
__________________________________________________________________________________________
2 Calculate 2
16
1.3
3
.
Answer ................................................ [1]
__________________________________________________________________________________________
3 Write down in ﬁgures
(a) three hundred and forty thousand,
Answer(a) ................................................ [1]
(b) the number that is one less than one million.
Answer(b) ................................................ [1]
__________________________________________________________________________________________
4 Write the following numbers in order, starting with the smallest.
11
5
0.2 45.4% 20
9
Answer ...................... < ...................... < ...................... < ...................... [2]
__________________________________________________________________________________________

3
5 (a) The temperature on Monday was –6°C.
On Tuesday the temperature was 3 degrees lower.
Write down the temperature on Tuesday.
Answer(a) ........................................... °C [1]
(b) The temperature on Saturday was –2°C.
The temperature on Sunday was 8°C.
Write down the difference in these two temperatures.
Answer(b) ........................................... °C [1]
__________________________________________________________________________________________
6 (a) Write 569000 correct to 2 signiﬁcant ﬁgures.
Answer(a) ................................................ [1]
(b) Write 569000 in standard form.
Answer(b) ................................................ [1]
__________________________________________________________________________________________
7 Find three numbers which have a mode of 4 and a mean of 6.
Answer ...................... , ...................... , ...................... [2]
__________________________________________________________________________________________

4
0580/12/M/J/14© UCLES 2014
8
l
P
NOT TO
SCALE
y
x
0
The equation of the line l in the diagram is y = 5 – x .
(a) The line cuts the y-axis at P.
Write down the co-ordinates of P.
Answer(a) (...................... , ......................) [1]
(b) Write down the gradient of the line l.
Answer(b) ................................................ [1]
__________________________________________________________________________________________
9 Solve the simultaneous equations.
2x – y = 7
3x + y = 3
Answer x = ................................................
y = ................................................ [2]
__________________________________________________________________________________________

5
10
C
B A
8cm
28°
NOT TO
SCALE
Calculate the length of AB.
Answer AB = .......................................... cm [2]
__________________________________________________________________________________________
11 The height of Mount Everest is 8800m, correct to the nearest hundred metres.
Complete the statement about the height, h metres, of Mount Everest.
Answer ......................... Ğ h < ......................... [2]
__________________________________________________________________________________________
12 Colin is travelling from Sydney, Australia, to Auckland, New Zealand.
(a) Colin’s bus leaves for Sydney airport at 1238.
The bus arrives at the airport at 1324.
How many minutes does the bus journey take?
Answer(a) ......................................... min [1]
(b) Colin’s ﬂight from Sydney to Auckland leaves at 1445 local time and takes 3 hours 20 minutes.
The time in Auckland is 2 hours ahead of the time in Sydney.
What is the local time in Auckland when his ﬂight arrives?
Answer(b) ................................................ [2]
__________________________________________________________________________________________

6
0580/12/M/J/14© UCLES 2014
13 (a) The scale drawing shows the positions of two villages, A and B.
The scale is 1 centimetre represents 200 metres.
North
North
B
A Scale: 1cm to 200m
(i) Measure the bearing of B from A.
Answer(a)(i) ................................................ [1]
(ii) Work out the actual distance from A to B.
Answer(a)(ii) ............................................ m [1]
(b) The post box in Village A has a volume of 84000cm3
.
The post box in Village B has a volume of 0.1m3
.
Which post box has the greater volume?
Show how you decide.
Answer(b) Post box in Village ............... [1]
__________________________________________________________________________________________

7
14 V = 3
1
Ah
(a) Find V when A = 15 and h = 7 .
Answer(a) V = ................................................ [1]
(b) Make h the subject of the formula.
Answer(b) h = ................................................ [2]
__________________________________________________________________________________________
15 At the beginning of July, Kim had a mass of 63kg.
At the end of July, his mass was 61kg.
Calculate the percentage loss in Kim’s mass.
Answer ............................................ % [3]
__________________________________________________________________________________________
16 Without using your calculator, work out 6
5
– 2 2
1 1
1#` j.
Write down all the steps of your working.
Answer ................................................ [3]
__________________________________________________________________________________________

8
0580/12/M/J/14© UCLES 2014
17 A plane is travelling at 180 metres per second.
How many minutes will it take the plane to travel 800km?
Give your answer correct to the nearest minute.
Answer ......................................... min [4]
__________________________________________________________________________________________
18 (a) The probability that FC Victoria wins the cup is 0.18 .
Work out the probability that they do not win the cup.
Answer(a) ................................................ [1]
(b) After training, the shirts are washed.
There are 5 red, 3 blue and 6 green shirts.
One shirt is taken from the washing machine at random.
Find the probability that it is
(i) red,
Answer(b)(i) ................................................ [1]
(ii) blue or green,
Answer(b)(ii) ................................................ [1]
(iii) white.
Answer(b)(iii) ................................................ [1]
__________________________________________________________________________________________

9
19
similar acute line perpendicular radius
reﬂex obtuse parallel congruent isosceles
Choose the correct word from this box to complete each of these statements.
(a)
Angle A is ..................................... [1]
(b)
Angle B is ..................................... [1]
(c)
These lines are ..................................... [1]
(d)
These lines are ..................................... [1]
__________________________________________________________________________________________
A
B

10
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20
6.7cm
NOT TO
SCALE
Each edge of this cube is 6.7cm long.
Work out
(a) the volume,
Answer(a) ......................................... cm3
[2]
(b) the surface area.
Answer(b) ......................................... cm2
[2]
__________________________________________________________________________________________

11
21
O
63°
A
B
C
NOT TO
SCALE
The diagram shows a circle, centre O with diameter AB = 15cm.
AC is a tangent to the circle at A and angle AOC = 63°.
(a) Calculate the area of the circle.
Answer(a) ......................................... cm2
[2]
(b) (i) Work out the size of angle ACO.
Answer(b)(i) Angle ACO = ................................................ [2]
(ii) Give one geometrical reason for your answer to part (b)(i).
Answer(b)(ii) ...............................................................................................................................
..................................................................................................................................................... [1]
__________________________________________________________________________________________

12
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MATHEMATICS 0580/13
1 hour
[Turn over
IB14 06_0580_13/RP
© UCLES 2014
*7662998175*

2
0580/13/M/J/14© UCLES 2014
1
–3°C 8°C –19°C 42°C –7°C
Write down the lowest temperature from this list.
Answer ........................................... °C [1]
__________________________________________________________________________________________
2 Change 6450cm into metres.
Answer ............................................ m [1]
__________________________________________________________________________________________
3
52°
x°
NOT TO
SCALE
In the diagram, a straight line intersects two parallel lines.
Find the value of x.
Answer x = ................................................ [1]
__________________________________________________________________________________________
4 Calculate.
0.2
56.2 34.8
-
-
Answer ................................................ [1]
__________________________________________________________________________________________
5 Write down the value of 70
.
Answer ................................................ [1]
__________________________________________________________________________________________

3
6 Write 45000 in standard form.
Answer ................................................ [1]
__________________________________________________________________________________________
7 Four faces of a cube are drawn on the grid.
Complete the net of this cube.
[1]
__________________________________________________________________________________________
8 Write down all the prime numbers that are greater than 30 and less than 40.
Answer ................................................ [1]
__________________________________________________________________________________________
9
a =
4
3-
e o b =
2
6
e o
Write each of the following as a single vector.
(a) 2a
Answer(a) f p [1]
(b) a – b
Answer(b) f p [1]
__________________________________________________________________________________________

4
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10 (a)
1 4 8 12 27 40
Write down the number from this list which is both a cube number and has a factor of 4.
Answer(a) ................................................ [1]
(b) 1258 is a multiple of 34.
Write down a different multiple of 34 between 1200 and 1300.
Answer(b) ................................................ [1]
__________________________________________________________________________________________
11
–3 –5 1 0 3
Three different numbers from the list are added together to give the smallest possible total.
Complete the sum below.
................. + ................. + ................. = .................
[2]
__________________________________________________________________________________________
12 The area of a square is 36cm2
.
Calculate the perimeter of this square.
Answer .......................................... cm [2]
__________________________________________________________________________________________
13 The mean of ﬁve numbers is 6.
Four of the numbers are 3, 4, 5, and 10.
Work out the number that is missing from the list.
Answer ................................................ [2]
__________________________________________________________________________________________

5
14 Find the value of 3a – 5b when a = –4 and b = 2 .
Answer ................................................ [2]
__________________________________________________________________________________________
15 Celine buys a bag of 24 tulip bulbs.
There are 8 red bulbs and 5 white bulbs.
All of the other bulbs are yellow.
Celine chooses a bulb at random from the bag.
(a) Write down the probability that the bulb is red or white.
Answer(a) ................................................ [1]
(b) Write down the probability that the bulb is yellow.
Answer(b) ................................................ [1]
__________________________________________________________________________________________
16 Find the fraction that is half-way between 2
1
and 3
2
.
Answer ................................................ [2]
__________________________________________________________________________________________

6
0580/13/M/J/14© UCLES 2014
17 Using a straight edge and compasses only, construct the perpendicular bisector of AB.
All construction arcs must be clearly shown.
A
B
[2]
__________________________________________________________________________________________
18 Michelle sells ice cream.
The table shows how many of the different ﬂavours she sells in one hour.
Flavour Vanilla Strawberry Chocolate Mango
Number sold 6 8 9 7
Michelle wants to show this information in a pie chart.
Calculate the sector angle for mango.
Answer ................................................ [2]
__________________________________________________________________________________________

7
19 Chris changes $1350 into euros (€) when €1 = $1.313 .
Calculate how much he receives.
Answer €................................................. [2]
__________________________________________________________________________________________
20
A
y
x
7
6
5
4
3
2
1
–1
–2
–3
0–1 1 2 3 4 5–2–3–4–5–6–7
Draw the image of triangle A after a translation by the vector
4
3
-
e o. [2]
__________________________________________________________________________________________

8
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21 Each exterior angle of a regular polygon is 30°.
Work out the number of sides the polygon has.
Answer ................................................ [2]
__________________________________________________________________________________________
22
46°
74° 60°
46°
x°
9.65cm
9.65cm
8.69cm
7.22cm
ycm
NOT TO
SCALE
These two triangles are congruent.
Write down the value of
(a) x,
Answer(a) x = ................................................ [1]
(b) y.
Answer(b) y = ................................................ [1]
__________________________________________________________________________________________

9
23 Without using a calculator, work out 1
4
1
–
9
7
.
Write down all the steps in your working.
Answer ............................................... [3]
__________________________________________________________________________________________
2x + 3y = 29
5x + y = 27
Answer x = ................................................
y = ................................................ [3]
__________________________________________________________________________________________

10
0580/13/M/J/14© UCLES 2014
25
1000 1004 1008 1012 1016
Time
Distance
(km)
1020 1024 1028 1032
4
3
2
1
0
Town
Home
William Toby
Toby and William cycled into town.
Their journeys are shown on the travel graph.
(a) For how many minutes did Toby stop on his journey into town?
Answer(a) ......................................... min [1]
(b) Explain what happened at 1020.
Answer(b) ........................................................................................................................................... [1]
(c) Work out how long William took to cycle into town.
Answer(c) ......................................... min [1]
(d) Calculate William’s speed in km/h.
Answer(d) ....................................... km/h [2]
__________________________________________________________________________________________

11
26 (a) Factorise completely.
15a3
– 5ab
Answer(a) ................................................ [2]
(b) Simplify.
3x2
y3
× x4
y
Answer(b) ................................................ [2]
(c) Multiply out the brackets and simplify.
3(x – 2) – 4(2x – 3)
Answer(c) ................................................ [2]
(d) Solve the equation.
8x + 9 = 3(x + 8)
Answer(d) x = ................................................ [3]
__________________________________________________________________________________________

12
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MATHEMATICS 0580/31
2 hours
[Turn over
IB14 06_0580_31/3RP
© UCLES 2014
*0224327052*

2
0580/31/M/J/14© UCLES 2014
1 (a) The angles in a triangle are in the ratio 3:4:8 .
(i) Show that the smallest angle of the triangle is 36°.
Answer(a)(i)
[2]
(ii) Work out the other two angles of the triangle.
Answer(a)(ii) ............................. and ............................. [2]
(b) Another triangle ABC has angle BAC = 35° and angle ABC = 65°.
(i) Using a protractor and straight edge complete an accurate drawing of the triangle ABC.
The side AB has been drawn for you.
A B
[2]
(ii) Measure the length, in centimetres, of the shortest side of your triangle.
Answer(b)(ii) .......................................... cm [1]
(c) A different triangle has base 7.0cm and height 5.6cm.
Calculate the area of this triangle, giving the units of your answer.
Answer(c) ....................... ..................... [3]
__________________________________________________________________________________________

3
2 (a) From the integers 50 to 100, ﬁnd
(i) a multiple of 43,
Answer(a)(i) ................................................ [1]
(ii) a factor of 165,
Answer(a)(ii) ................................................ [1]
(iii) an odd number that is also a square number,
Answer(a)(iii) ................................................ [1]
(iv) a number which is a square number and also a cube number.
Answer(a)(iv)................................................. [1]
(b) (i) Find the square root of 5929.
Answer(b)(i) ................................................ [1]
(ii) Find the lowest common multiple of 24 and 30.
Answer(b)(ii) ................................................ [2]
(c) Elena goes on a journey to the North Pole.
She leaves home at 7am on 15 July and arrives at the North Pole at 10pm on 27 July.
How long, in days and hours, did her journey take?
Answer(c) ....................... days ....................... hours [2]
__________________________________________________________________________________________

4
0580/31/M/J/14© UCLES 2014
3
S
P
T
y
x
–2 20 4 6 81 3 5 7–4–6–8 –1–3–5–7
10
9
8
7
6
5
4
3
2
1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
The diagram shows two shapes, S and T, on a 1cm2
grid.
P is the point (–2, 0).

5
(a) (i) Write down the mathematical name of shape S.
Answer(a)(i) ................................................ [1]
(ii) How many lines of symmetry does shape S have?
Answer(a)(ii) ................................................ [1]
(b) Describe the single transformation that maps shape S onto shape T.
Answer(b) ...........................................................................................................................................
............................................................................................................................................................. [2]
(c) On the grid,
(i) draw the reﬂection of shape S in the y-axis, [2]
(ii) draw the rotation of shape S about (0, 0) through 90° anti-clockwise. [2]
(d) On the grid, draw the enlargement of shape S with scale factor 2 and centre P (–2, 0).
Label the image E. [2]
(e) (i) Work out the area of shape S.
Answer(e)(i) ......................................... cm2
[2]
(ii) How many shapes, identical to shape S, will ﬁll shape E completely?
Answer(e)(ii) ................................................ [1]
(iii) Work out the area of shape E.
Answer(e)(iii) ......................................... cm2
[1]
__________________________________________________________________________________________

6
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4 Denzil grows tomatoes. He selects a random sample of 25 tomatoes.
The mass of each tomato, to the nearest 5 grams, is shown below.
55 65 50 75 65
80 70 70 55 60
70 60 65 50 75
65 70 75 80 70
55 65 70 80 55
(a) (i) Complete the frequency table.
You may use the tally column to help you.
Mass
(grams)
Tally Frequency
50
55
60
65
70
75
80
[2]
(ii) Write down the mode.
Answer(a)(ii) ............................................. g [1]
Answer(a)(iii) ............................................. g [1]
(iv) Show that the mean mass is 66g.
Answer(a)(iv)
[2]

7
(b) Denzil picks 800 tomatoes.
4% of the 800 tomatoes are damaged.
How many of these tomatoes are not damaged?
Answer(b) ................................................ [2]
(c) Denzil sells 750 of his tomatoes.
(i) The mean mass of a tomato is 66g.
Calculate the mass of the 750 tomatoes in kilograms.
Answer(c)(i) ........................................... kg [3]
(ii) Denzil sells his tomatoes at $1.40 per kilogram.
Calculate the total amount he receives from selling all the 750 tomatoes.
Answer(c)(ii) $ ................................................ [1]
(iii) The cost of growing these tomatoes was $33.
Calculate his percentage proﬁt.
Answer(c)(iii) ............................................ % [3]
__________________________________________________________________________________________

8
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5 Use a ruler and compasses only in parts (a), (c) and (d) of this question.
Show all your construction arcs.
A
B
C
D
E
P
100m
100m
120m
150m
Scale: 1cm to 20m
Maria owns a farm.
The scale drawing shows part of the boundary of the farm.

9
(a) The point F is such that AF = 140m and EF = 160m.
Angle BAF and angle DEF are both obtuse angles.
Complete the scale drawing of the farm boundary ABCDEF. [2]
(b) Write down the name of the polygon ABCDEF.
Answer(b) ................................................ [1]
(c) (i) Construct the perpendicular bisector of the side CD. [2]
(ii) Construct the bisector of angle ABC. [2]
(iii) All the farm buildings are within a region that is
● nearer to C than to D
and
● nearer to BC than to BA.
Shade the region containing the farm buildings. [1]
(d) A fence post, P, is shown on the boundary DE.
(i) Construct the locus of points that are 50m from P and also inside the farm boundary. [2]
(ii) A region for keeping pigs is within 50m of P and inside the farm boundary.
Calculate the actual area for keeping pigs.
Answer(d)(ii) ........................................... m2
[2]
__________________________________________________________________________________________

10
0580/31/M/J/14© UCLES 2014
6 (a) (i) Complete the table of values for y = x
8
, x ≠ 0 .
x –8 –4 –2 –1 1 2 4 8
y –2 2
[3]
(ii) On the grid, draw the graph of y = x
8
for –8 Ğ x Ğ –1 and 1 Ğ x Ğ 8 .
y
x
8
6
4
2
–2
–4
–6
–8
0–2–4–6–8 6 842
[4]

11
(iii) Write down the order of rotational symmetry of your graph.
Answer(a)(iii) ................................................ [1]
(b) (i) Complete this table of values for y = 1.5x + 3 .
x –6 –4 –2 0 2
y –6 3
[2]
(ii) On the grid, draw the graph of y = 1.5x + 3 . [1]
(c) Use your graphs to solve the equation x
8
= 1.5x + 3 .
Answer(c) x = .......................... or x = .......................... [2]
(d) Write down the gradient of the graph of y = 1.5x + 3 .
Answer(d) ................................................ [1]
__________________________________________________________________________________________

12
0580/31/M/J/14© UCLES 2014
7 120 people are asked how they travel to work.
The pie chart shows the results.
Bus
Car
Cycle
Walk
(a) (i) Show that 45 people travel by car.
Answer(a)(i)
[2]
(ii) A person is chosen at random from the 120 people.
Find the probability that this person travels to work by bus or by car.
Answer(a)(ii) ................................................ [2]

13
(b) One year later, the same 120 people were again asked how they travel to work.
Here is the information.
Number of people
Walk x
Cycle 31
Bus 17 more than the number of people who walk
Car 2 times the number of people who walk
(i) Use this information to complete the following equation, in terms of x.
............................................................................................. = 120 [3]
(ii) Solve the equation to ﬁnd the number of people who walk to work.
Answer(b)(ii) ................................................ [3]
__________________________________________________________________________________________

14
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8 (a) Write down an expression for the total mass of c cricket balls, each weighing 160grams, and f footballs,
each weighing 400 grams.
Answer(a) ...................................... grams [2]
(b) Expand and simplify.
3(2x – 5y) – 4(x – 2y)
Answer(b) ................................................ [2]
(c) Factorise completely.
5x2
y – 20x
Answer(c) ................................................ [2]
(d) Solve the simultaneous equations.
3x + 4y = 7
4x – 3y = 26
Answer(d) x = ................................................
y = ................................................ [4]
__________________________________________________________________________________________

15
9 (a) For these sequences, write down the next two terms and the rule for ﬁnding the next term.
(i) 84, 75, 66, 57, . . .
Answer(a)(i) ................. , ................. rule .................................................................................. [3]
(ii) 2, 6, 18, 54, . . .
Answer(a)(ii) ................. , ................. rule ................................................................................. [3]
(b) For the sequence in part (a)(i),
(i) write down an expression, in terms of n, for the nth term,
Answer(b)(i) ................................................ [2]
(ii) ﬁnd the 21st term.
Answer(b)(ii) ................................................ [2]
__________________________________________________________________________________________

16
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MATHEMATICS 0580/32
2 hours
[Turn over
IB14 06_0580_32/RP
© UCLES 2014
*4942783219*

2
0580/32/M/J/14© UCLES 2014
1 (a) Here is a list of numbers.
2 4 5 8 9 12
Write down all the numbers from this list which are
(i) odd,
Answer(a)(i) ................................................ [1]
(ii) square,
Answer(a)(ii) ................................................ [1]
(iii) cube,
Answer(a)(iii) ................................................ [1]
(iv) prime.
Answer(a)(iv) ................................................ [1]
(b) Write one of these symbols >, < or = to make each statement true.
π .................... 7
22
2^ h2
.................... 2
1 1
1
+
.................... 2
(–1)2
.................... –1
[2]
(c) Put one pair of brackets in each statement to make it true.
(i) 16 + 8 ÷ 4 – 2 = 4 [1]
(ii) 16 + 8 ÷ 4 – 2 = 20 [1]

3
(d) (i) Write 84 as a product of its prime factors.
Answer(d)(i) ................................................ [2]
(ii) Find the highest common factor of 84 and 24.
Answer(d)(ii) ................................................ [2]
(iii) Find the lowest common multiple of 84 and 24.
Answer(d)(iii) ................................................ [2]
(e) Here are the ﬁrst four terms of a sequence.
3 7 11 15
(i) Write down the next term in this sequence.
Answer(e)(i) ................................................ [1]
(ii) Explain how you found your answer.
Answer(e)(ii) ............................................................................................................................... [1]
(iii) Write down an expression for the nth term of this sequence.
Answer(e)(iii) ................................................ [2]
(iv) Explain why 125 is not in this sequence.
Answer(e)(iv) ..............................................................................................................................
..................................................................................................................................................... [1]
__________________________________________________________________________________________

4
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2
A
D C
B
180cm
120cm
240cm
NOT TO
SCALE
The diagram shows the cross section ABCD of a shed.
AD = 180cm, DC = 120cm and BC = 240cm.
(a) (i) Write down the mathematical name of the cross section ABCD.
Answer(a)(i) ................................................ [1]
(ii) Calculate the area of the cross section ABCD.
Give the units of your answer.
Answer(a)(ii) ........................... .............. [3]
(iii) The shed is a prism of length 2.5 metres.
Calculate the volume of the shed.
Give your answer in cubic metres.
Answer(a)(iii) ........................................... m3
[2]

5
(iv) Calculate the length AB.
Answer(a)(iv) AB = .......................................... cm [3]
(b) Here is a scale drawing of a garden, GHIJ.
I
H
G J
Scale: 1cm to 5m
The shed is placed in the garden so that it is
● nearer to GJ than to IJ
and
● within 20m of H.
Using a ruler and compasses only, construct and shade the region where the shed can be placed.
Show all your construction arcs. [5]
__________________________________________________________________________________________

6
0580/32/M/J/14© UCLES 2014
3 (a) Draw the line of symmetry on the shape below.
[1]
(b) Write down the order of rotational symmetry of the shape below.
Answer(b) ................................................ [1]
(c) (i)
x°
157°
72°
NOT TO
SCALE
Work out the value of x.
Answer(c)(i) x = ................................................ [1]
(ii)
y°
49°
54°
NOT TO
SCALE
Work out the value of y.
Answer(c)(ii) y = ................................................ [2]

7
(d)
A
B C
O
34°
NOT TO
SCALE
AC is a diameter of the circle, centre O.
Calculate angle ACB.
Answer(d) Angle ACB = ................................................ [2]
(e) The diagram below shows parts of shape P and shape Q.
Shape P is a regular hexagon and shape Q is another regular polygon.
The two shapes have one side in common.
100°
100°
QP
NOT TO
SCALE
Find the number of sides in shape Q.
Show each step of your working.
Answer(e) ................................................ [5]
__________________________________________________________________________________________

8
0580/32/M/J/14© UCLES 2014
4 Paolo’s football team played 46 games.
The pictogram shows some information about the number of goals scored by Paolo’s football team.
They did not score any goals in ﬁve games.
Number
of goals
Number of games
0
1
2
3
4
5
6
Key: = .................. games
(a) (i) Complete the key. [1]
(ii) Paolo’s team scored 2 goals in each of nine games.
Complete the pictogram. [1]
(b) (i) Write down the modal number of goals.
Answer(b)(i) ................................................ [1]
(ii) Find the median number of goals.
Answer(b)(ii) ................................................ [1]
Answer(b)(iii) ................................................ [1]
(iv) One of the 46 games is chosen at random.
Work out the probability that Paolo’s team scored at least 4 goals.
Answer(b)(iv) ................................................ [2]

9
(c) The table shows the total goals scored and the total points gained by 10 teams.
Team A B C D E F G H I J
Goals 31 40 46 50 43 92 60 84 68 87
Points 36 35 52 56 72 78 59 70 61 75
(i) Complete the scatter diagram.
The first six points have been plotted for you. [2]
80
70
60
50
40
30
30 40 50 60 70
Goals
80 90 100
Points
(ii) Draw the line of best fit. [1]
(iii) What type of correlation is shown?
Answer(c)(iii) ................................................ [1]
(iv) Use your line of best fit to estimate the total points gained by a team scoring 75 goals.
Answer(c)(iv) ................................................ [1]
(v) Which team only scores a few goals but gains a lot of points?
Answer(c)(v) ................................................ [1]
__________________________________________________________________________________________

10
0580/32/M/J/14© UCLES 2014
5 (a) Jasmine works for 38 hours each week and she earns $12.15 each hour.
(i) Calculate her earnings in one week.
Answer(a)(i) $ ................................................ [1]
(ii) Jasmine pays 14% of her earnings in tax.
Calculate how much money she has left after tax is paid.
Answer(a)(ii) $ ................................................ [2]
(iii) She pays 3
1
of the money she has left after tax in rent.
Calculate how much rent she pays in one year (52 weeks).
Answer(a)(iii) $ ................................................ [2]
(iv) In one week she spends $140 on food and electricity in the ratio
food:electricity = 3:2 .
Calculate how much she spends on food.
Answer(a)(iv) $ ................................................ [2]
(b) Jasmine buys a watch for 10000 Japanese Yen (¥).
The exchange rate is $1 = ¥ 80.4 .
Calculate the cost of this watch in dollars, giving your answer correct to the nearest dollar.
Answer(b) $ ................................................ [3]
__________________________________________________________________________________________

11
6 (a) Complete the table of values for y = x2
+ 2x – 3 .
x –4 –3 –2 –1 0 1 2 3 4
y 0 –3 –4 –3 0 5 21
[2]
(b) On the grid, draw the graph of y = x2
+ 2x – 3 for –4 Ğ x Ğ 4 .
y
x
25
20
15
10
5
–5
0 1 2 3 4–1–2–3–4
[4]
(c) On the grid, draw the line y = 10 . [1]
(d) Use your graphs to solve the equation x2
+ 2x – 3 = 10 for –4 Y x Y 4 .
Answer(d) x = ................................................ [1]
__________________________________________________________________________________________

12
0580/32/M/J/14© UCLES 2014
7 (a)
5p + 3r
7p – 6r
p + 2r
NOT TO
SCALE
Write an expression for the perimeter of this triangle.
Give your answer in its simplest form.
Answer(a) ................................................ [2]
(b) Another triangle has a perimeter 12w – 2z .
Calculate this perimeter when w = 16 and z = –3.
Answer(b) ................................................ [2]
(c) Solve.
(i) 5a = 32
Answer(c)(i) a = ................................................ [1]
(ii) 5b + 23 = 8
Answer(c)(ii) b = ................................................ [2]
(iii) 5c + 7 = 2(c – 10)
Answer(c)(iii) c = ................................................ [3]

13
(d) (i) Multiply out the brackets.
8(2x + 3)
Answer(d)(i) ................................................ [1]
(ii) Factorise completely.
6x2
– 12x
Answer(d)(ii) ................................................ [2]
(e) Write each expression in its simplest form.
(i) 3q4
× 5q2
Answer(e)(i) ................................................ [2]
(ii) t8
÷ t2
Answer(e)(ii) ................................................ [1]
__________________________________________________________________________________________

14
0580/32/M/J/14© UCLES 2014
8 (a) Work out.
(i) 5
3-
2
e o
Answer(a)(i) f p [1]
(ii)
5
4
-
e o +
1
3
-
e o
Answer(a)(ii) f p [1]
(b) A translation moves the point (6, 3) to the point (2, 8).
Work out the vector which represents this translation.
Answer(b) f p [1]

15
(c) A point P is translated by the vector
3
4
-
e o to the point (7, –2).
Find the co-ordinates of P.
You may use the grid below to help you.
Answer(c) (.................... , ....................) [1]
__________________________________________________________________________________________

16
0580/32/M/J/14© UCLES 2014
9
A
10
9
8
7
6
5
4
3
2
1
–1
–2
–3
–4
–5
–6–7 –5 –4 –3 –2 –1 10 2 3 4 5 6 7
x
y
B
(a) On the grid, draw the image of triangle A after the following transformations.
(i) Reﬂection in the x-axis. [1]
(ii) Rotation about (0, 0) through 180°. [2]
(iii) Translation by the vector
5-
3
e o. [2]
(b) Describe fully the single transformation that maps triangle A onto triangle B.
Answer(b) ...........................................................................................................................................
............................................................................................................................................................. [3]

2
0580/33/M/J/14© UCLES 2014
1 (a)
D
A
B
C
y
x
7
6
5
4
3
2
1
–1
–2
–3
–4
0–1 1 2 3 4 5 6–2–3–4
Four shapes, A, B, C and D, are shown on the grid.
Describe fully the single transformation that maps shape A onto
(i) shape B,
Answer(a)(i) ................................................................................................................................
..................................................................................................................................................... [2]
(ii) shape C,
Answer(a)(ii) ...............................................................................................................................
..................................................................................................................................................... [3]
(iii) shape D.
Answer(a)(iii) ..............................................................................................................................
..................................................................................................................................................... [3]

3
(b) (i)
Shade in one more square so that this shape has rotational symmetry of order 2. [1]
(ii)
Reﬂect this shape in the line of symmetry shown. [2]
__________________________________________________________________________________________

4
0580/33/M/J/14© UCLES 2014
2 A group of students take part in their school’s sports day.
(a) (i) The length, l m, that Anna throws the javelin is 23.6 metres correct to the nearest 10 centimetres.
Complete the statement about l.
Answer(a)(i) .......................... Y l < .......................... [2]
(ii) Billy throws the hammer a distance of 8 metres on his ﬁrst throw.
His second throw is 15% further.
Calculate the distance of his second throw.
Answer(a)(ii) ............................................ m [2]
(iii) Carl runs 100 metres at a speed of 8m/s.
Calculate the time it takes him to run 100m.
Answer(a)(iii) .............................................. s [1]
(iv) Change Carl’s speed of 8m/s into km/h.
Answer(a)(iv) ....................................... km/h [2]
(b) Ten students take part in both the long jump and 100m hurdles competitions.
The results are shown in the table below.
Student A B C D E F G H I J
Distance in long jump (metres) 3.25 3.60 3.75 3.90 4.10 4.20 4.30 4.40 4.65 4.70
Time for 100m hurdles (seconds) 17.3 17.4 16.7 16.1 16.5 15.8 15.3 14.8 15.5 15.0

5
(i) Complete the scatter diagram.
The first six points have been plotted for you.
18.0
17.0
16.0
15.0
14.0
3.5 4.0 4.5 5.0 5.53.0
Distance in long jump (metres)
Time for
100m hurdles
(seconds)
[2]
(ii) What type of correlation does this scatter diagram show?
Answer(b)(ii) ................................................ [1]
(iii) Describe the relationship between the distance in the long jump and the time for the 100m hurdles.
Answer(b)(iii) .............................................................................................................................. [1]
(iv) On the grid, draw the line of best fit. [1]
(v) Another student jumps 3.50m in the long jump.
Use your line of best fit to estimate the time for this student in the 100m hurdles.
Answer(b)(v) .............................................. s [1]
(vi) A different student jumps 5.20m in the long jump.
Explain why you should not use your scatter diagram to estimate their time in the 100m hurdles.
Answer(b)(vi) .............................................................................................................................. [1]
__________________________________________________________________________________________

6
0580/33/M/J/14© UCLES 2014
3 The Wong family spend the day at the zoo.
(a) The Wong family has 2 adults and 3 children aged 2, 5 and 11 years old.
Admission
Adults $8.50
Children 11-16 years $6.00
Children 3-10 years $4.50
Children under 3 years FREE
Mr Wong pays for his family to go into the zoo using a $50 note.
Work out the change he receives.
Answer(a) $ ................................................ [3]
(b) The dolphin show ﬁnishes at 1105.
It lasts for 1 hour and 20 minutes.
Write down the time the dolphin show starts.
Answer(b) ................................................ [1]
(c) Torty the tortoise was born on 27 December 1898.
Work out how many years old she was on 3 January 2003.
Answer(c) ....................................... years [1]
(d) Last year, the ratio snakes:lizards = 3:5 .
There were 45 lizards.
(i) Work out how many snakes there were last year.
Answer(d)(i) ................................................ [2]
(ii) This year, there are 3 more snakes and the same number of lizards.
Write down the new ratio snakes:lizards.
Give your answer in its simplest form.
Answer(d)(ii) ....................... : ....................... [2]
(e) Mr Wong hires a vehicle to drive around the zoo.
The cost is $25 for the ﬁrst hour and $7.50 for every extra half hour.
He pays $85 altogether.
For how long does he hire the vehicle?
Answer(e) ...................................... hours [3]

7
(f) Mrs Wong wants to buy some food for the giraffes.
Small Bag
225g
60 cents
Medium Bag
250g
70 cents
Large Bag
325g
90 cents
Work out which bag is the best value for money.
Show how you decide.
Answer(f) ................................................ [3]
(g) The diagram shows a map of the zoo.
North
Entrance
Flamingos
North
Exit
Scale: 1cm to 50m
(i) Measure the bearing of the ﬂamingos from the entrance.
Answer(g)(i) ................................................ [1]
(ii) Xanthe looks after all the animals within 200m of the exit.
Draw accurately the locus of points inside the zoo which are 200m from the exit. [2]
(iii) A shop, S, is on a bearing of 212° from the entrance and a bearing of 293° from the exit.
Mark the point S on the map. [3]
__________________________________________________________________________________________

8
0580/33/M/J/14© UCLES 2014
4 The ages of 15 children who go to a swimming club are shown below.
10 11 10 12 12
13 11 12 12 12
12 10 11 11 11
(a) Complete the frequency table.
You may use the tally column to help you.
Age Tally Frequency
10
11
12
13
[2]
(b) For the ages of the 15 children, ﬁnd
(i) the range,
Answer(b)(i) ................................................ [1]
(ii) the mode,
Answer(b)(ii) ................................................ [1]
(iii) the median,
Answer(b)(iii) ................................................ [1]
(iv) the mean.
Answer(b)(iv) ................................................ [2]
(c) One child is chosen at random from the group.
Write down the probability that the child’s age is
(i) 10,
Answer(c)(i) ................................................ [1]
(ii) more than 13.
Answer(c)(ii) ................................................ [1]
__________________________________________________________________________________________

9
5 (a) (i) Write down the name of a solid which is not a prism.
Answer(a)(i) ................................................ [1]
(ii) A prism has a cross-sectional area, A, and height, h.
Write down an expression, in terms of A and h, for the volume of the prism.
Answer(a)(ii) ................................................ [1]
(b) The volume, V, of a cylinder with radius r and height h is V = πr2
h .
(i) Calculate the volume of a cylinder with radius 3cm and height 12cm.
Answer(b)(i) ......................................... cm3
[2]
(ii) Ravi puts 150 identical marbles in the cylinder.
He fills the cylinder to the top with 160cm3
of water.
Find the volume of one marble.
Give your answer correct to 2 significant figures.
Answer(b)(ii) ......................................... cm3
[4]
(iii) Make r the subject of the formula V = πr2
h .
Answer(b)(iii) r = ................................................ [2]
__________________________________________________________________________________________

10
0580/33/M/J/14© UCLES 2014
6
y
x
6
5
4
3
2
1
–1
–2
–3
–4
–5
–6
0–1 1 2 3 4 5 6–2–3–4–5–6
(a) On the grid, draw the graphs of
(i) y = 5, [1]
(ii) x = –3. [1]
(b) (i) Write down the co-ordinates of the point of intersection of y = 5 and x = –3.
Answer(b)(i) (...................... , ......................) [1]
(ii) Write down the equation of a line parallel to y = 5.
Answer(b)(ii) ................................................ [1]

11
(c) (i) Complete the table of values for the function y = x2
– 3x .
x –2 –1 0 1 2 3 4 5
y 4 0 0 4
[2]
(ii) On the grid, draw the graph of y = x2
– 3x for –2 Y x Y 5 .
y
x
11
10
9
8
7
6
5
4
3
2
1
–1
–2
–3
–4
0–1 1 2 3 4 5 6–2–3
[4]
(iii) Write down the co-ordinates of the lowest point of the graph.
Answer(c)(iii) (...................... , ......................) [1]
__________________________________________________________________________________________

12
0580/33/M/J/14© UCLES 2014
7 Today it is Simon’s birthday.
(a) Simon is x years old.
Katy is twice as old as Simon.
Bob is 8 years younger than Simon.
(i) Write expressions, in terms of x, for the ages of Katy and Bob.
Answer(a)(i) Katy ................................................
Bob ................................................ [2]
(ii) The sum of their three ages is 40 years.
Write an equation in terms of x.
Answer(a)(ii) ................................................ [1]
(iii) Solve your equation for x.
Answer(a)(iii) x = ................................................ [2]
(b) Simon’s birthday cake weighs 600 grams.
He eats 8
1
of the cake.
Katy eats 25% of the cake.
Bob eats 0.3 of the cake.
Find the weight of the cake that is left.
Answer(b) ............................................. g [4]

13
(c) Aunty Millie gives Simon $150 for his birthday.
He invests the money in a bank at a rate of 6% per year compound interest.
Calculate the total amount Simon will have after 3 years.
Answer(c) $................................................. [3]
(d) One of Simon’s presents is a bag of sweets.
He decides to eat the sweets in a sequence.
On day 1 he eats 1 sweet, on day 2 he eats 5 sweets, on day 3 he eats 9 sweets and so on.
(i) Describe in words the rule for continuing the sequence 1, 5, 9, 13, 17 ..... .
Answer(d)(i) ................................................................................................................................ [1]
(ii) Write down an expression for the number of sweets he eats on day n.
Answer(d)(ii) ................................................ [2]
__________________________________________________________________________________________

14
0580/33/M/J/14© UCLES 2014
8 (a)
h
10cm
NOT TO
SCALE
The triangle has an area of 30cm2
and a base of 10cm.
Calculate the perpendicular height h of the triangle.
Answer(a) h = ......................................... cm [2]
(b)
NOT TO
SCALE
D C
A B
8cm
14cm
7cm
AB is parallel to CD.
AB is 14cm and CD is 8cm.
The perpendicular distance between AB and CD is 7cm.
(i) Write down the mathematical name for the quadrilateral ABCD.
Answer(b)(i) ................................................ [1]
(ii) Calculate the area of ABCD.
Answer(b)(ii) ......................................... cm2
[2]

15
(c) An isosceles triangle has an angle of 40°.
Tikka draws the triangle with angles 40°, 70° and 70°.
Kanwarpreet draws a different correct triangle.
What angles did Kanwarpreet use?
Answer(c) 40°, .............. , .............. [2]
__________________________________________________________________________________________

16
0580/33/M/J/14© UCLES 2014
9
A
C
B
O
NOT TO
SCALE
The diagram shows a circle with diameter AB and centre O.
C is a point on the circumference of the circle.
(a) Explain how you know that angle ACB is 90° without having to measure it.
Answer(a) ........................................................................................................................................... [1]
(b) AB = 13cm and AC = 5cm.
Calculate the length BC.
Answer(b) BC = .......................................... cm [3]
(c) Calculate angle ABC.
Answer(c) Angle ABC = ................................................ [2]

2
0580/11/O/N/14© UCLES 2014
1
y
x
5
4
3
2
1
–1
–2
–3
–4
–5
0–1 1 2 3 4–2–3–4–5–6
A
B
Points A and B are shown on the grid.
Write as a column vector.
Answer f p [1]
__________________________________________________________________________________________
2 Write 15.0782 correct to
(a) one decimal place,
Answer(a) ................................................ [1]
(b) the nearest 10.
Answer(b) ................................................ [1]
__________________________________________________________________________________________

3
0580/11/O/N/14© UCLES 2014 [Turn over
3
Write down the letters in the word above that have
(a) exactly one line of symmetry,
Answer(a) ................................................ [1]
(b) rotational symmetry of order 2.
Answer(b) ................................................ [1]
__________________________________________________________________________________________
4
A
B
C
105°
k°
98°
NOT TO
SCALE
In the diagram, all four lines are straight.
Angle A = 105°, angle B = 90° and angle C = 98°.
Find the value of k.
Answer k = ................................................ [2]
__________________________________________________________________________________________

4
0580/11/O/N/14© UCLES 2014
5 These are the heights, correct to the nearest centimetre, of 12 children.
132 114 151 130 132 145 163 142 153 170 132 125
Find the median height.
Answer .......................................... cm [2]
__________________________________________________________________________________________
6 Write the following in order of size, smallest ﬁrst.
π 3.14 7
22
3.142 3
Answer ..................... < ..................... < ..................... < ..................... < ..................... [2]
smallest
__________________________________________________________________________________________
7 Without using a calculator, work out
4
1
+
6
1 .
Write down all the steps in your working and give your answer as a fraction in its simplest form.
Answer ................................................ [2]
__________________________________________________________________________________________

5
8 Factorise completely.
8w2
x – 12wy
Answer ................................................ [2]
__________________________________________________________________________________________
9 A cylinder has radius 3.6cm and height 16cm.
Calculate the volume of the cylinder.
Answer ......................................... cm3
[2]
__________________________________________________________________________________________
10 Cheryl recorded the midday temperatures in Seoul for one week in January.
Day Mon Tue Wed Thu Fri Sat Sun
Temperature (°C) –4 –5 –3 –11 –8 –3 –1
(a) Write down the mode.
Answer(a) ........................................... °C [1]
(b) On how many days was the temperature lower than the mode?
Answer(b) ................................................ [1]
__________________________________________________________________________________________

6
0580/11/O/N/14© UCLES 2014
11 Simplify.
10x – 15 – 6x + 8
Answer ................................................ [2]
__________________________________________________________________________________________
12 (a) Write down a 2-digit odd number that is a factor of 182.
Answer(a) ................................................ [1]
(b) Find all the prime factors of 182.
Answer(b) ................................................ [2]
__________________________________________________________________________________________
13 (a) Write 2.8 × 102
as an ordinary number.
Answer(a) ................................................ [1]
(b) Work out 2.5 × 108
× 2 × 10–2
.
Give your answer in standard form.
Answer(b) ................................................ [2]
__________________________________________________________________________________________

7
14 To hire a bicycle it costs $6 for each day, plus a ﬁxed charge of $15.
(a) Maria pays $39 to hire a bicycle.
How many days does she hire it for?
Answer(a) ........................................ days [2]
(b) Write down a formula for the cost, C dollars, to hire a bicycle for d days.
Answer(b) C = ................................................ [1]
__________________________________________________________________________________________
15
140°
NOT TO
SCALE
A B
C
The diagram shows two sides, AB and BC, of a regular polygon.
Angle ABC = 140°.
Find the number of sides of this regular polygon.
Answer ................................................ [3]
__________________________________________________________________________________________

8
0580/11/O/N/14© UCLES 2014
16
O
A
B
E
C
D
x°
y°
24°
NOT TO
SCALE
The diagram shows a circle with centre O.
ED is a tangent to the circle at C.
AB is parallel to ED and angle ACO = 24°.
Find the value of
(a) x,
Answer(a) x = ................................................ [1]
(b) y.
Answer(b) y = ................................................ [2]
__________________________________________________________________________________________

9
17 Dominic invests $850 at a rate of 3.5% per year compound interest.
Calculate the total amount he has after 3 years.
Answer $................................................. [3]
__________________________________________________________________________________________
18 On a ship, the price of a gift is 24 euros (€) or $30.
What is the difference in the price on a day when the exchange rate is €1 = $1.2378?
Give your answer in dollars, correct to the nearest cent.
Answer $................................................. [3]
__________________________________________________________________________________________

10
0580/11/O/N/14© UCLES 2014
19
4cm
7cm
NOT TO
SCALE
The diagram shows a prism.
The cross section is an equilateral triangle.
On the grid, draw an accurate net of the prism.
The base is drawn for you.
[3]
__________________________________________________________________________________________

11
5x + 2y = 16
3x – 4y = 7
Answer x = ................................................
y = ................................................ [3]
__________________________________________________________________________________________
21 (a) Find the value of 5x2
when x = –4.
Answer(a) ................................................ [2]
(b) Make x the subject of the formula y = 5x2
.
Answer(b) x = ................................................ [2]
__________________________________________________________________________________________

12
0580/11/O/N/14© UCLES 2014
22
Q
P16km
9km
North
NOT TO
SCALE
The diagram shows the route of a ship that leaves a port, P.
It travels due west for 16km and then changes course to due south for 9km.
(a) Calculate the straight line distance PQ.
Answer(a) PQ = .......................................... km [2]
(b) Use trigonometry to calculate the bearing of P from Q.
Answer(b) ................................................ [2]

MATHEMATICS 0580/12
Paper 1 (Core) October/November 2014
1 hour
This document consists of 10 printed pages and 2 blank pages.
[Turn over
IB14 11_0580_12/RP
© UCLES 2014
*5594379073*

2
0580/12/O/N/14© UCLES 2014
1 Insert one pair of brackets only to make the following statement correct.
6 + 5 × 10 – 8 = 16
[1]
__________________________________________________________________________________________
2 Calculate
1.26 0.72
8.24 2.56
-
+ .
Answer ................................................ [1]
__________________________________________________________________________________________
3
Write down the order of rotational symmetry of this shape.
Answer ................................................ [1]
__________________________________________________________________________________________
4 (a) Write down two whole numbers that have a product of –15.
Answer(a) ..................... and .................... [1]
(b) During one year, the temperature in Ulaanbaatar varied from –33°C to 27°C.
Find the range of the temperatures during that year.
Answer(b) ........................................... °C [1]
__________________________________________________________________________________________

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