Igcse maths paper 2

This document consists of 11 printed pages and 1 blank page.
DC (LK/SG) 118120/2
© UCLES 2016 [Turn over
Cambridge International Examinations
Cambridge International General Certificate of Secondary Education
*4623174243*
MATHEMATICS 0580/22
Paper 2 (Extended) October/November 2016
1 hour 30 minutes
Candidates answer on the Question Paper.
Additional Materials: Electronic calculator Geometrical instruments
Tracing paper (optional)
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
If working is needed for any question it must be shown below that question.
Electronic calculators should be used.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to
three significant figures. Give answers in degrees to one decimal place.
For r, use either your calculator value or 3.142.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 70.
The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.

2
0580/22/O/N/16© UCLES 2016
1 (a) Write 14835 correct to the nearest thousand.
................................................. [1]
(b) Write your answer to part (a) in standard form.
................................................. [1]
2
67°
42°a°
NOT TO
SCALE
Find the value of a.
a = ................................................ [2]
3 Solve the equation.
6(k – 8) = 78
k = ................................................ [2]
4
13cm
16cm
4cm
5cm
NOT TO
SCALE
Calculate the area of this trapezium.
........................................ cm2 [2]

3
0580/22/O/N/16© UCLES 2016 [Turn over
5 Simplify.
y y36 45 2
'
................................................. [2]
6 The sides of a square are 8cm, correct to the nearest centimetre.
Calculate the upper bound for the area of the square.
........................................ cm2 [2]
7 Find the positive integers that satisfy the inequality t t2 3 62+ - .
................................................. [3]
8 Solve the simultaneous equations.
You must show all your working.
x y 82
1
+ =
x y2 2- =
x = ...............................................
y = ................................................ [3]

4
0580/22/O/N/16© UCLES 2016
9 From the top of a building, 300 metres high, the angle of depression of a car, C, is 52°.
C
300m
NOT TO
SCALE
Calculate the horizontal distance from the car to the base of the building.
........................................... m [3]
10 The length of a backpack of capacity 30 litres is 53cm.
Calculate the length of a mathematically similar backpack of capacity 20 litres.
.......................................... cm [3]

5
11
A
B
C
(a) Using compasses and a straight edge only, construct the bisector of angle BAC. [2]
(b) Complete the statement.
The bisector of angle BAC is the locus of points that are ....................................................................
.............................................................................................................................................................. [1]
12 Ralf and Susie share $57 in the ratio 2 : 1.
(a) Calculate the amount Ralf receives.
$ ................................................ [2]
(b) Ralf gives $2 to Susie.
Calculate the new ratio Ralf’s money : Susie’s money.
Give your answer in its simplest form.
..................... : .....................[2]

6
0580/22/O/N/16© UCLES 2016
13 Factorise.
(a) m m3
+
................................................. [1]
(b) y25 2
-
................................................. [1]
(c) x x3 282
+ -
................................................. [2]
14 Without using your calculator, work out
4
3
3
2
8
1
+ - .
You must show all your working and give your answer as a mixed number in its simplest form.
................................................. [4]

7
15
F
R
M
2
Ᏹ
8 2 4
3
1 0
2
The Venn diagram shows the number of people who like films (F), music (M) and reading (R).
(a) Find
(i) ( )n M ,
................................................. [1]
(ii) ( )n R M, .
................................................. [1]
(b) A person is chosen at random from the people who like films.
Write down the probability that this person also likes music.
................................................. [1]
(c) On the Venn diagram, shade ( )M F R+ ,l . [1]
16 BC
2
3
= c m BA
5
6
=
-
c m
(a) Find CA.
CA = f p [2]
(b) Work out BA .
................................................. [2]

8
0580/22/O/N/16© UCLES 2016
17
125°
8cm
32cm
40cm
48cm
NOT TO
SCALE
The diagram shows the cross section of part of a park bench.
It is made from a rectangle of length 32cm and width 8cm and a curved section.
The curved section is made from two concentric arcs with sector angle 125°.
The inner arc has radius 40cm and the outer arc has radius 48cm.
Calculate the area of the cross section correct to the nearest square centimetre.
........................................ cm2 [5]

9
18
–1–2–3–4–5–6 10 2 3 4 5 6
–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
y
x
AB
(a) Describe fully the single transformation that maps triangle A onto triangle B.
..............................................................................................................................................................
.............................................................................................................................................................. [3]
(b) Draw the image of triangle A after the transformation represented by
1
0
0
1-
c m . [3]

10
0580/22/O/N/16© UCLES 2016
19 (a) Find the inverse of
2
5
3
4
-
-
c m .
f p [2]
(b) The matrix
w
w4
9
12
-
-
f p does not have an inverse.
Calculate the value of w.
w = ................................................ [4]

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20
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8
A
B
y
x
Point A has co-ordinates (3, 6).
(a) Write down the co-ordinates of point B.
(....................... , .......................) [1]
(b) Find the gradient of the line AB.
................................................. [2]
(c) Find the equation of the line that
• is perpendicular to the line AB
and
• passes through the point (0, 2).
................................................. [3]

12
0580/22/O/N/16© UCLES 2016
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
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To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International
Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after
the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
blank page

DC (NH/SW) 113299/1
*6212890302*
MATHEMATICS 0580/22
Paper 2 (Extended) May/June 2016
1 hour 30 minutes
For r, use either your calculator value or 3.142.

2
0580/22/M/J/16© UCLES 2016
1 Write 0.0000574 in standard form.
.................................................. [1]
2 Calculate.
5.0 1.79
3.07 2
3
4
-
+
.................................................. [1]
3 Write 3.5897 correct to 4 significant figures.
.................................................. [1]
4 A quadrilateral has rotational symmetry of order 2 and no lines of symmetry.
Write down the mathematical name of this quadrilateral.
.................................................. [1]
5 8 9 10 11 12 13 14 15 16
From the list of numbers, write down
(a) the square numbers,
.................................................. [1]
(b) a prime factor of 99.
.................................................. [1]
6 Simplify.
3
3
2
1
x
2
e o
.................................................. [2]

3
0580/22/M/J/16© UCLES 2016 [Turn over
7 A map is drawn to a scale of 1 : 1000000.
A forest on the map has an area of 4.6cm2.
Calculate the actual area of the forest in square kilometres.
........................................... km2 [2]
8 Solve the inequality
3
5 2
x
2+ .
.................................................. [2]
9 A regular polygon has an interior angle of 172°.
Find the number of sides of this polygon.
.................................................. [3]
10 Make p the subject of the formula.
rp + 5 = 3p + 8r
p = ................................................. [3]
11 Shahruk plays four games of golf.
His four scores have a mean of 75, a mode of 78 and a median of 77.
Work out his four scores.
.................... .................... .................... .................... [3]

4
0580/22/M/J/16© UCLES 2016
12 Write the recurring decimal 0.36o as a fraction.
[0.36o means 0.3666…]
.................................................. [3]
13 The base of a triangle is 9cm correct to the nearest cm.
The area of this triangle is 40cm2 correct to the nearest 5cm2.
Calculate the upper bound for the perpendicular height of this triangle.
............................................. cm [3]
14 Without using a calculator, work out 2
8
5
7
3
# .
Show all your working and give your answer as a mixed number in its lowest terms.
.................................................. [3]
15 y = x2 + 7x – 5 can be written in the form y = (x + a)2 + b.
Find the value of a and the value of b.
a = .................................................
b = ................................................. [3]

5
Show all your working.
3x + 4y = 14
5x + 2y = 21
x = .................................................
y = ................................................. [3]
17 The diagram shows triangle ABC.
B
A
C
(a) Using a straight edge and compasses only, construct the bisector of angle ABC. [2]
(b) Draw the locus of points inside the triangle that are 3cm from AC. [1]

6
0580/22/M/J/16© UCLES 2016
18 Find the nth term of each of these sequences.
(a) 16, 19, 22, 25, 28, …
.................................................. [2]
(b) 1, 3, 9, 27, 81, …
.................................................. [2]
19 It is estimated that the world’s population is growing at a rate of 1.14% per year.
On January 1st 2014 the population was 7.23 billion.
(a) Find the expected population on January 1st 2020.
........................................billion [2]
(b) Find the year when the population is expected to reach 10 billion.
.................................................. [2]

7
20 Deborah records the number of minutes late, t, for trains arriving at a station.
The histogram shows this information.
0
10
20
30
5 10 15
Number of minutes late
t
Frequency
density
20 25
(a) Find the number of trains that Deborah recorded.
.................................................. [2]
(b) Calculate the percentage of the trains recorded that arrived more than 10 minutes late.
...............................................% [2]

8
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21
A
B
28°
NOT TO
SCALE
O
C
In the diagram, A, B and C lie on the circumference of a circle, centre O.
Work out the size of angle ACB.
Give a reason for each step of your working.
Angle ACB = ................................................. [4]

9
22
5
3
1
2
M =
- -
e o
(a) Work out 4M.
f p [1]
(b) Work out M2.
f p [2]
(c) Find M–1, the inverse of M.
f p [2]

10
0580/22/M/J/16© UCLES 2016
23
0
1
2
3
4
5
6
7
y
x
1 2 3 4 5
The region R satisfies these inequalities.
y G 2x 3x + 4y H 12 x G 3
On the grid, draw and label the region R that satisfies these inequalities.
Shade the unwanted regions.
[5]

11
0580/22/M/J/16© UCLES 2016
24
A
B
b
NOT TO
SCALE
c
a
C
O
In the diagram, O is the origin, OA = a, OC = c and AB = b.
P is on the line AB so that AP : PB = 2 : 1.
Q is the midpoint of BC.
Find, in terms of a, b and c, in its simplest form
(a) CB,
CB = ................................................. [1]
(b) the position vector of Q,
.................................................. [2]
(c) PQ.
PQ = ................................................. [2]

12
0580/22/M/J/16© UCLES 2016
BLANK PAGE

This document consists of 12 printed pages.
DC (LEG/FD) 112489/3
*7585955107*
MATHEMATICS 0580/22
Paper 2 (Extended) February/March 2016
1 hour 30 minutes
For π, use either your calculator value or 3.142.

2
0580/22/F/M/16© UCLES 2016
1 Solve (x – 7)(x + 4) = 0.
x= ................................. or x= .................................[1]
2 Factorise 2x – 4xy.
................................................... [2]
3
B A
C
3.5m
NOT TO
SCALE
0.9m
Calculate angle BAC.
Angle BAC= .................................................. [2]
4 Solve the inequality.
6n + 3  8n
................................................... [2]

3
0580/22/F/M/16© UCLES 2016 [Turn over
5 Triangle ABCis similar to triangle PQR.
A 12.4cm
5.2cm
21.7cm
NOT TO
SCALE
C P R
Q
B
Find PQ.
PQ=............................................ cm [2]
6 Write the recurring decimal .0 4o as a fraction.
[ .0 4o means 0.444…]
................................................... [2]
7
22.3cm
27.6cm
25°
NOT TO
SCALE
Calculate the area of this triangle.
............................................cm2 [2]

4
0580/22/F/M/16© UCLES 2016
8 Find the inverse of the matrix
3
8
2
7-
-
c m.
f p [2]
9 Without using your calculator, work out 1 12
7
20
13
+ .
You must show all your working and give your answer as a mixed number in its simplest form.
................................................... [3]
10 The scale on a map is 1 : 20 000.
The area of a lake on the map is 1.6 square centimetres.
Calculate the actual area of the lake.
Give your answer in square metres.
..............................................m2 [3]

5
11
38°O
B
NOT TO
SCALE
A
25cm
The diagram shows a sector of a circle, centre O, radius 25cm.
The sector angle is 38°.
Calculate the length of the arc AB.
Give your answer correct to 4 significant figures.

AB= ............................................ cm [3]
12 A metal pole is 500cm long, correct to the nearest centimetre.
The pole is cut into rods each of length 5.8cm, correct to the nearest millimetre.
Calculate the largest number of rods that the pole can be cut into.
................................................... [3]

6
0580/22/F/M/16© UCLES 2016
13 (a) Write 2016 as the product of prime factors.
................................................... [3]
(b) Write 2016 in standard form.
................................................... [1]
14 Simplify.
(a) x y x y3 4 5 3
#
................................................... [2]
(b) p m3 2 5 3
^ h
................................................... [2]

7
15
2.8cm
5.3cm
3.6cm
p°
NOT TO
SCALE
Find the value of p.
p= .................................................. [4]
16 Raj measures the height, hcm, of 70 plants.
The table shows the information.
Height (hcm) 10  h 20 20  h 40 40  h 50 50  h 60 60  h 90
Frequency 7 15 27 13 8
Calculate an estimate of the mean height of the plants.
............................................................ cm [4]

8
0580/22/F/M/16© UCLES 2016
17 Solve the equation x x3 11 4 02
- + = .
Show all your working and give your answers correct to 2 decimal places.
x=............................ or x= ............................[4]

9
18 (a)
x°
47°
NOT TO
SCALE
Find the value of x.
x= .................................................. [1]
(b)
97°
115°
85°
NOT TO
SCALE
y°
Find the value of y.
y= .................................................. [2]
(c)
O
z°
58°
NOT TO
SCALE
The diagram shows a circle, centre O.
Find the value of z.
z= .................................................. [2]

10
0580/22/F/M/16© UCLES 2016
19
–3
–1
1
3
4
–2 –1 0 1 2 3 4
x
y
2
Find the four inequalities that define the region that is not shaded.
...................................................
...................................................
...................................................
................................................... [5]

11
20 The nth term of a sequence is an bn2
+ .
(a) Write down an expression, in terms of aand b, for the 3rd term.
................................................... [1]
(b) The 3rd term of this sequence is 21 and the 6th term is 96.
Find the value of aand the value of b.
a= ..................................................
b= .................................................. [4]
Question 21 is printed on the next page.

12
0580/22/F/M/16© UCLES 2016
21 Dan either walks or cycles to school.
The probability that he cycles to school is 3
1
.
(a) Write down the probability that Dan walks to school.
................................................... [1]
(b) When Dan cycles to school the probability that he is late is 8
1
.
When Dan walks to school the probability that he is late is 8
3
.
Complete the tree diagram.
1
3
1
8
3
8
..........
..........
..........
Cycles
Walks
Late
Late
Not late
Not late
[2]
(c) Calculate the probability that
(i) Dan cycles to school and is late,
................................................... [2]
(ii) Dan is not late.
................................................... [3]

DC (KN/SG) 106108/2
*1469358560*
MATHEMATICS 0580/22
1 hour 30 minutes

2
0580/22/O/N/15© UCLES 2015
1 Write down the difference in temperature between 8°C and −9°C.
Answer .............................................°C [1]
2
Parallelogram Trapezium Rhombus
Write down which one of these shapes has
• rotational symmetry of order 2
and
• no line symmetry.
Answer................................................... [1]
__________________________________________________________________________________________
3 Carlos changed $950 into euros (€) when the exchange rate was €1 = $1.368.
Calculate how many euros Carlos received.
Answer €................................................... [2]
__________________________________________________________________________________________
4
3
5
AB =
-
e o
Find AB .
Answer .................................................. [2]

3
5 Calculate the volume of a hemisphere with radius 5cm.
[The volume, V, of a sphere with radius r is V r
3
4 3
r= .]
Answer .......................................... cm3 [2]
6 The Venn diagram shows the number of students who study French (F), Spanish (S) and Arabic (A).
F S
A
Ᏹ
7 4
1
2 3
5
8
0
(a) Find n(A (F S)).
Answer(a) .................................................. [1]
(b) On the Venn diagram, shade the region Fl S. [1]

4
0580/22/O/N/15© UCLES 2015
7
M
3
2
4
4
=
-
-
e o N
5
1
0
2
= e o
Calculate MN.
Answer f p [2]
8 Robert buys a car for $8000.
At the end of each year the value of the car has decreased by 10% of its value at the beginning of that year.
Calculate the value of the car at the end of 7 years.
Answer $ ................................................. [2]
9 The scale on a map is 1 : 50000.
The area of a field on the map is 1.2 square centimetres.
Calculate the actual area of the field in square kilometres.
Answer .......................................... km2 [2]

5
10 Jason receives some money for his birthday.
He spends
15
11
of the money and has $14.40 left.
Calculate how much money he received for his birthday.
Answer $ .................................................. [3]
11
5cm
8cm
NOT TO
SCALE
xcm
Calculate the value of x.
Answer x = ................................................. [3]
12 Without using your calculator, work out 2
4
1
12
11
- .
You must show all your working and give your answer as a fraction in its lowest terms.
Answer .................................................. [3]

6
0580/22/O/N/15© UCLES 2015
13
ycm
12.4cm
74°
39°
NOT TO
SCALE
Calculate the value of y.
Answer y = .................................................. [3]
14 Jasjeet and her brother collect stamps.
When Jasjeet gives her brother 1% of her stamps, she has 2475 stamps left.
Calculate how many stamps Jasjeet had originally.
Answer ................................................. [3]
15 Factorise
(a) w9 1002
- ,
Answer(a) ................................................. [1]
(b) mp np mq nq6 6+ - - .
Answer(b) ................................................. [2]

7
16
26°
15cm
NOT TO
SCALE
The diagram shows a sector of a circle with radius 15cm.
Calculate the perimeter of this sector.
Answer ............................................ cm [3]
17 y is directly proportional to the square of (x − 1).
y = 63 when x = 4.
Find the value of y when x = 6.
Answer y = .................................................. [3]
18 A rectangle has length 5.8cm and width 2.4cm, both correct to 1 decimal place.
Calculate the lower bound and the upper bound of the perimeter of this rectangle.
Answer Lower bound ............................................ cm
Upper bound ............................................ cm [3]

8
0580/22/O/N/15© UCLES 2015
19 Solve the equation x x5 6 3 02
- - = .
Answer x = ............................. or x = ............................. [4]
20 A car passes through a checkpoint at time t = 0 seconds, travelling at 8m/s.
It travels at this speed for 10 seconds.
The car then decelerates at a constant rate until it stops when t = 55 seconds.
(a) On the grid, draw the speed-time graph.
0 10 20 30 40 50 60
2
4
6
8
10
t
Time (seconds)
Speed
(m/s)
[2]
(b) Calculate the total distance travelled by the car after passing through the checkpoint.
Answer(b) ............................................. m [3]

9
21 (a)
7.2cm xcm
15cm
25cm
NOT TO
SCALE
The diagram shows two jugs that are mathematically similar.
Answer(a) x = ................................................. [2]
(b)
16cm
NOT TO
SCALE
ycm
The diagram shows two glasses that are mathematically similar.
The height of the larger glass is 16cm and its volume is 375cm3.
The height of the smaller glass is ycm and its volume is 192cm3.

Find the value of y.
Answer(b) y = .................................................. [3]

10
0580/22/O/N/15© UCLES 2015
22 The table shows information about the numbers of pets owned by 24 students.
Number of pets 0 1 2 3 4 5 6
Frequency 1 2 3 5 7 3 3
(a) Calculate the mean number of pets.
Answer(a) .................................................. [3]
(b) Jennifer joins the group of 24 students.
When the information for Jennifer is added to the table, the new mean is 3.44 .
Calculate the number of pets that Jennifer has.
Answer(b) ................................................. [3]

11
0580/22/O/N/15© UCLES 2015
23 A box contains 6 red pencils and 8 blue pencils.
A pencil is chosen at random and not replaced.
A second pencil is then chosen at random.
(a) Complete the tree diagram.
First pencil Second pencil
Red
Red
Blue
Red
Blue
Blue
.......
.......
.......
.......
6
14 8
13
[2]
(b) Calculate the probability that
(i) both pencils are red,

Answer(b)(i) ................................................. [2]
(ii) at least one of the pencils is red.
Answer(b)(ii) ................................................. [3]

12
0580/22/O/N/15© UCLES 2015
BLANK PAGE

MATHEMATICS 0580/22
1 hour 30 minutes
[Turn over
DC (LEG/SG) 103618/3
© UCLES 2015
CANDIDATE
NAME
CENTRE
NUMBER
CANDIDATE
NUMBER
*9864075249*

2
0580/22/M/J/15© UCLES 2015
1 Write 53400000 in standard form.
Answer ................................................ [1]
__________________________________________________________________________________________
2 A doctor starts work at 2040 and finishes work at 0610 the next day.
How long is the doctor at work?
Give your answer in hours and minutes.
Answer ...................... h ...................... min [1]
__________________________________________________________________________________________
3 81
x
= 3
Answer x = ................................................ [1]
__________________________________________________________________________________________
4 7 9 20 3 9
(a) A number is removed from this list and the median and range do not change.
Write down this number.
Answer(a) ................................................ [1]
(b) An extra number is included in the original list and the mode does not change.
Write down a possible value for this number.
Answer(b) ................................................ [1]
__________________________________________________________________________________________

3
5 A biased 4-sided dice is rolled.
The possible scores are 1, 2, 3 or 4.
The probability of rolling a 1, 3 or 4 is shown in the table.
Score 1 2 3 4
Probability 0.15 0.3 0.35
Complete the table. [2]
__________________________________________________________________________________________
6 Solve.
5(w + 4 × 103
) = 6 × 104
Answer w = ................................................ [2]
__________________________________________________________________________________________
7
A
D E
B
C
NOT TO
SCALE
The diagram shows two straight lines, AE and BD, intersecting at C.
Angle ABC = angle EDC.
Triangles ABC and EDC are congruent.
Write down two properties of line segments AB and DE.
Answer AB and DE are ...............................................
and ............................................... [2]
__________________________________________________________________________________________

4
0580/22/M/J/15© UCLES 2015
8 5, 11, 21, 35, 53, ...
Find the nth term of this sequence.
Answer ................................................ [2]
__________________________________________________________________________________________
9 Write the recurring decimal 0.25o as a fraction.
[0.25o means 0.2555...]
Answer ................................................ [2]
__________________________________________________________________________________________
10 One year ago Ahmed’s height was 114cm.
Today his height is 120cm.
Both measurements are correct to the nearest centimetre.
Work out the upper bound for the increase in Ahmed’s height.
Answer .......................................... cm [2]
__________________________________________________________________________________________
11 M =
11 2
3 1
- -
e o
Find M–1
, the inverse of M.
Answer f p [2]
__________________________________________________________________________________________

5
4
÷ 2 3
2 .
Write down all the steps of your working and give your answer as a fraction in its simplest form.
Answer ................................................ [3]
__________________________________________________________________________________________
13
A B
E
D C F G
(x – 4)cm
(x – 1)cm
7cm
NOT TO
SCALE
(a) ABCD is a square.
Answer(a) x = ................................................ [1]
(b) Square ABCD and isosceles triangle EFG have the same perimeter.
Work out the length of FG.
Answer(b) FG = .......................................... cm [2]
__________________________________________________________________________________________

6
0580/22/M/J/15© UCLES 2015
14
The diagram shows a channel for water.
The channel lies on horizontal ground.
This channel has a constant rectangular cross section with area 0.95 m2
.
The channel is full and the water flows through the channel at a rate of 4 metres/minute.
Calculate the number of cubic metres of water that flow along the channel in 3 hours.
Answer ........................................... m3
[3]
__________________________________________________________________________________________
15 Write as a single fraction in its simplest form.
2
3
x +
–
2 5
4
x -
Answer ................................................ [3]
__________________________________________________________________________________________

7
16 (a) Find the value of
(i)
.0 5
4
1
c m ,
Answer(a)(i) ................................................ [1]
(ii) (–8) .
Answer(a)(ii) ................................................ [1]
(b) Use a calculator to find the decimal value of
0.4
3
29 3 32- # .
Answer(b) ................................................ [1]
__________________________________________________________________________________________
3
2

8
0580/22/M/J/15© UCLES 2015
17
11
3
0 4
x
y
NOT TO
SCALE
l
The diagram shows the straight line, l, which passes through the points (0, 3) and (4, 11).
(a) Find the equation of line l in the form y = mx + c.
Answer(a) y = ................................................ [3]
(b) Line p is perpendicular to line l.
Write down the gradient of line p.
Answer(b) ................................................ [1]
__________________________________________________________________________________________

9
18
5m 5m
8m
12m
NOT TO
SCALE
The diagram shows the front face of a barn.
The width of the barn is 12m.
The height of the barn is 8m.
The sides of the barn are both of height 5m.
(a) Work out the area of the front face of the barn.
Answer(a) ........................................... m2
[3]
(b) The length of the barn is 15m.
Work out the volume of the barn.
Answer(b) ........................................... m3
[1]
__________________________________________________________________________________________
15m
NOT TO
SCALE

10
0580/22/M/J/15© UCLES 2015
19 The diagram shows the positions of three points A, B and C.
A
B
C
(a) Draw the locus of points which are 4cm from C. [1]
(b) Using a straight edge and compasses only, construct the locus of points which are
equidistant from A and B. [2]
(c) Shade the region which is
• less than 4cm from C
and
• nearer to B than to A. [1]
__________________________________________________________________________________________

11
20 (a) You may use this Venn diagram to help you answer part (a).
 = {x:1  x  12, x is an integer}
M = {odd numbers}
N = {multiples of 3}
Ᏹ
M N
(i) Find n(N).
Answer(a)(i) ................................................ [1]
(ii) Write down the set M N.
Answer(a)(ii) M N = {............................................... } [1]
(iii) Write down a set P where P 1 M.
Answer(a)(iii) P = {............................................... } [1]
(b) Shade (A C) B' in the Venn diagram below.
Ᏹ
A B
C
[1]
__________________________________________________________________________________________

12
0580/22/M/J/15© UCLES 2015
21 f(x) = x2
+ 4x − 6
(a) f(x) can be written in the form (x + m)2
+ n.
Find the value of m and the value of n.
Answer(a) m = ................................................
n = ................................................ [2]
(b) Use your answer to part (a) to find the positive solution to x2
+ 4x – 6 = 0.
Answer(b) x = ................................................ [2]
__________________________________________________________________________________________

13
22 The cumulative frequency diagram shows information about the distances travelled, in kilometres, by
60 people.
60
50
40
30
20
10
10 20 30 40 50
Distance (kilometres)
60 70 80 90 100
0
Cumulative
frequency
Find
(a) the 80th percentile,
Answer(a) .......................................... km [2]
(b) the inter-quartile range,
Answer(b) .......................................... km [2]
(c) the number of people who travelled more than 60km.
Answer(c) ................................................ [2]
__________________________________________________________________________________________

14
0580/22/M/J/15© UCLES 2015
23
20 40 60 80
Time (s)
100 12010 30 50 70 90 110
20
18
16
14
12
10
8
6
4
2
0
Speed
(m/s)
The diagram shows the speed-time graph for 120 seconds of a car journey.
(a) Calculate the deceleration of the car during the first 20 seconds.
Answer(a) ........................................ m/s2
[1]
(b) Calculate the total distance travelled by the car during the 120 seconds.
Answer(b) ............................................ m [3]
(c) Calculate the average speed for this 120 second journey.
Answer(c) ......................................... m/s [1]
__________________________________________________________________________________________

15
0580/22/M/J/15© UCLES 2015
24 f(x) = 3x + 5 g(x) = x2
(a) Find g(3x).
Answer(a) ................................................ [1]
(b) Find f −1
(x), the inverse function.
Answer(b) f −1
(x) = ................................................ [2]
(c) Find ff(x).
Answer(c) ................................................ [2]
__________________________________________________________________________________________

MATHEMATICS 0580/22
Paper 2 (Extended) February/March 2015
1 hour 30 minutes
[Turn over
DC (LK/SW) 103471/2
© UCLES 2015
CANDIDATE
NAME
CENTRE
NUMBER
CANDIDATE
NUMBER
*5844397915*

2
0580/22/F/M/15© UCLES 2015
1 The number of hot drinks sold in a café decreases as the weather becomes warmer.
What type of correlation does this statement show?
Answer ................................................ [1]
__________________________________________________________________________________________
2 Find the lowest common multiple (LCM) of 24 and 32.
Answer ................................................ [2]
__________________________________________________________________________________________
3 The base of a rectangular tank is 1.2 metres by 0.9 metres.
The water in the tank is 53 centimetres deep.
Calculate the number of litres of water in the tank.
Answer ....................................... litres [2]
__________________________________________________________________________________________
4 Factorise 14p2
+ 21pq.
Answer ................................................ [2]
__________________________________________________________________________________________
5 These are the first five terms of a sequence.
13 8 3 –2 –7
Answer ................................................ [2]
__________________________________________________________________________________________

3
6
B C
A
N
In triangle ABC, CN is the bisector of angle ACB.
(a) Using a ruler and compasses only, construct the locus of points inside triangle ABC that
are 5.7cm from B. [1]
(b) Shade the region inside triangle ABC that is
• more than 5.7cm from B
and
• nearer to BC than to AC. [1]
__________________________________________________________________________________________
7
53°
x°
O
NOT TO
SCALE
The diagram shows a circle, centre O.
Answer x = ................................................ [2]
__________________________________________________________________________________________

4
0580/22/F/M/15© UCLES 2015
8 (a)
44°
x°
NOT TO
SCALE
The diagram shows an isosceles triangle.
Answer(a) x = ................................................ [1]
(b) The exterior angle of a regular polygon is 24°.
Find the number of sides of this regular polygon.
Answer(b) ................................................ [2]
__________________________________________________________________________________________
9 Ahmed, Batuk and Chand share $1000 in the ratio 8:7:5.
Calculate the amount each receives.
Answer Ahmed $ ................................................
Batuk $ ................................................
Chand $ ................................................ [3]
__________________________________________________________________________________________

5
10 Pavan saves $x each month.
His two brothers each save $4 more than Pavan each month.
Altogether the three boys save $26 each month.
(a) Write down an equation in x.
Answer(a) .......................................................................... [1]
(b) Solve your equation to find the amount Pavan saves each month.
Answer(b) $................................................. [2]
__________________________________________________________________________________________
x y8 12
1
- =
x y2 6 2
1
+ =
Answer x = ................................................
y = ................................................ [3]
__________________________________________________________________________________________

6
0580/22/F/M/15© UCLES 2015
12 The population of Olton is decreasing at a rate of 3% per year.
In 2013, the population was 50000.
Calculate the population after 4 years.
Give your answer correct to the nearest hundred.
Answer ................................................ [3]
__________________________________________________________________________________________
13 x varies directly as the cube root of y.
x = 6 when y = 8.
Find the value of x when y = 64.
Answer x = ................................................ [3]
__________________________________________________________________________________________
14 Find the equation of the line that
• is perpendicular to the line y = 3x – 1
and
• passes through the point (7, 4).
Answer ................................................ [3]
__________________________________________________________________________________________

7
15 A =
8
4
3
2
c m
Find
(a) A2
,
Answer(a) A2
= f p [2]
(b) A–1
.
Answer(b) A–1
= f p [2]
__________________________________________________________________________________________
16 Without using your calculator, work out 2 9
7
6
5
' .
Give your answer as a fraction in its lowest terms.
You must show each step of your working.
Answer ................................................ [4]
__________________________________________________________________________________________

8
0580/22/F/M/15© UCLES 2015
17 (a)
S R
P Q2a
b
NOT TO
SCALE
PQRS is a trapezium with PQ = 2SR.
= 2a and = b.
Find in terms of a and b in its simplest form.
Answer(a) = ................................................ [2]
(b)
X
M
O Yy
x NOT TO
SCALE
= x and = y.
M is a point on XY such that XM:MY = 3:5.
Find in terms of x and y in its simplest form.
Answer(b) = ................................................ [2]
__________________________________________________________________________________________

9
18
A
D C
F
B
15m
6m
18m
NOT TO
SCALE
The diagram shows a rectangular playground ABCD on horizontal ground.
A vertical flagpole CF, 6 metres high, stands in corner C.
AB = 18m and BC = 15m.
Calculate the angle of elevation of F from A.
Answer ................................................ [4]
__________________________________________________________________________________________
19 Fritz drives a distance of 381km in 2 hours and 18 minutes.
He then drives 75km at a constant speed of 30km/h.
Calculate his average speed for the whole journey.
Answer ....................................... km/h [4]
__________________________________________________________________________________________

10
0580/22/F/M/15© UCLES 2015
20 (a)
88°
57°
W
V
X
Y
Z
NOT TO
SCALE
Two straight lines VZ and YW intersect at X.
VW is parallel to YZ, angle XYZ = 57° and angle VXW = 88°.
Find angle WVX.
Answer(a) Angle WVX = ................................................ [2]
(b)
A
P Q
B C
8.4cm
12.6cm
7.2cm
NOT TO
SCALE
ABC is a triangle and PQ is parallel to BC.
BC = 12.6cm, PQ = 8.4cm and AQ = 7.2cm.
Find AC.
Answer(b) AC = .......................................... cm [2]
__________________________________________________________________________________________

11
21 (a) Simplify
(i) x0
,
Answer(a)(i) ................................................ [1]
(ii) m4
× m3
,
Answer(a)(ii) ................................................ [1]
(iii) )6 3
1
( p8 .
Answer(a)(iii) ................................................ [2]
(b) 243 3
x 2
=
Answer(b) x = ................................................ [2]
__________________________________________________________________________________________

12
0580/22/F/M/15© UCLES 2015
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.
22 f(x) = 5x – 3 g(x) = x2
(a) Find fg(–2).
Answer(a) ................................................ [2]
(b) Find gf(x), in terms of x, in its simplest form.
Answer(b) ................................................ [2]
(c) Find f–1
(x).
Answer(c) f–1
(x) = ................................................ [2]

MATHEMATICS 0580/02
Paper 2 (Extended) For Examination from 2015
SPECIMEN PAPER
1 hour 30 minutes

2
© UCLES 2012 0580/02/SP/15
1 Use your calculator to find
1.53.1
5.7545
+
×
.
Answer [2]
2 The mass of a carbon atom is 2 × 10–27
g.
How many carbon atoms are there in 6g of carbon?
Answer [2]
3 Write the following in order of size, largest first.
sin 158° cos 158° cos 38° sin 38°
Answer K K K [2]
4 Express 321.0 as a fraction in its simplest form.
Answer [3]

3
© UCLES 2012 0580/02/SP/15 [Turn over
5 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]
6
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]

4
© UCLES 2012 0580/02/SP/15
7
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
(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
xO
P
Q
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]

5
9
O
A
The point A lies on the circle centre O, radius 5cm.
(a) Using a straight edge and compasses only, construct the perpendicular bisector of the line OA.[2]
(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]

6
© UCLES 2012 0580/02/SP/15
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.
Sore
throat
No sore
throat
Flu
No flu
No flu
Flu
0.45
0.4
0.2
Calculate the probability that a person chosen at random has flu.
Answer [4]
11 Work out.
(a)
2
34
12






Answer(a)










[2]
(b)
1
34
12
−






Answer(b)










[2]

7
12
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]

8
© UCLES 2012 0580/02/SP/15
13
CA B D
O
a
b
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) [2]
(b) the vector .
Answer(b) [2]
14 T = 2π
g
l
(a) Find T when g = 9.8 and ℓ = 2.
Answer(a) T = [2]
(b) Make g the subject of the formula.
Answer(b) g = [3]

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.
16
14
12
10
8
6
4
2
Speed
(km/h)
0
1 2 3 4 5 6
Time (hours)
7 8 9 10 11 12 13
(a) Calculate the total distance travelled by the ship.
Answer(a) km [4]
(b) Calculate the average speed of the ship for the whole voyage.
Answer(b) km/h [1]

10
© UCLES 2012 0580/02/SP/15
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 × 0.9t
.
(a) Complete this table.
t (years) 0 1 2 3 4 5 6
M (grams) 450 328 266
[2]
(b) Draw the graph of M = 500 × 0.9t
.
500
400
300
200
100
0
1 2 3 4 5 6
t
M
[2]
(c) (i) Use your graph to estimate after how long the mass will be 350 grams.
Answer(c)(i) years [1]
(ii) When will the mass of the radioactive substance be zero grams?
Answer(c)(ii) years [1]

11
17 f(x) =
4
1
+x
(x ≠ O4)
g(x) = x2
– 3x
h(x) = x3
+ 1
(a) Work out fg(1).
Answer(a) [2]
(b) Find h
O1
(x).
Answer(b) h
O1
(x) = [2]
(c) Solve the equation g(x) = O2.
Answer(c) x = or x = [3]

12
© UCLES 2012 0580/02/SP/15
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 =
6
1
n(n + 1)(2n + 1).
Work out the value of T23.
Answer(a) T23 = [2]
(b) A new sequence is formed as follows.
U1 = T2 – T1 U2 = T3 – T2 U3 = T4 – T3 …….
(i) Find the values of U1 and U2.
Answer(b)(i) U1 = and U2 = [2]
(ii) Write down a formula for the nth term, Un .
Answer(b)(ii) Un = [1]
(c) The first four terms of another sequence are
V1 = 22
V2 = 22
+ 42
V3 = 22
+ 42
+ 62
V4 = 22
+ 42
+ 62
+ 82
.
By comparing this sequence with the one in part (a), find a formula for the nth term, Vn .
Answer(c) Vn = [2]

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.
MATHEMATICS 0580/22
1 hour 30 minutes
Cambridge International General Certificate of Secondary Education
[Turn over
IB14 11_0580_22/RP
© UCLES 2014
*3014020988*
The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.

2
0580/22/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 Shade the region required in each Venn diagram.
A B
(A ∪ B)'
A B
A' ∩ B
[2]
__________________________________________________________________________________________

3
5 Make r the subject of this formula.
v = p r+3
Answer r = ................................................ [2]
__________________________________________________________________________________________
6 The length, l metres, of a football pitch is 96m, correct to the nearest metre.
Complete the statement about the length of this football pitch.
Answer .................................... Y l .................................... [2]
__________________________________________________________________________________________
7 For her holiday, Alyssa changed 2800 Malaysian Ringgits (MYR) to US dollars ($) when the exchange rate
was 1 MYR = $0.325 .
At the end of her holiday she had $210 left.
(a) How many dollars did she spend?
Answer(a) $................................................. [2]
(b) She changed the $210 for 750 MYR.
What was the exchange rate in dollars for 1 MYR?
Answer(b) 1 MYR = $................................................. [1]
__________________________________________________________________________________________
6
1
÷
8
7 .
Show all your working and give your answer as a fraction in its lowest terms.
Answer ................................................ [3]
__________________________________________________________________________________________

4
0580/22/O/N/14© UCLES 2014
9
1 litre
12cm
440ml
d
NOT TO
SCALE
Two cylindrical cans are mathematically similar.
The larger can has a capacity of 1 litre and the smaller can has a capacity of 440ml.
Calculate the diameter, d, of the 440ml can.
Answer d = .......................................... cm [3]
__________________________________________________________________________________________
10 The cost of a circular patio, $C, varies as the square of the radius, r metres.
C = 202.80 when r = 2.6 .
Calculate the cost of a circular patio with r = 1.8 .
Answer $................................................. [3]
__________________________________________________________________________________________
11 A =
2
1
3
4
-
f p B =
5
2 0
7-
f p
(a) Calculate BA.
Answer(a) BA = [2]
(b) Find the determinant of A.
Answer(b) ..................................... [1]
__________________________________________________________________________________________

5
12
2 4 6 8 10 121 3 5 7 9 11
6
5
4
3
2
1
–1
0
y
x
By shading the unwanted regions of the grid, ﬁnd and label the region R which satisﬁes the following four
inequalities.
y [ 0 x [ 4 2y Y x 2y + x Y 12
[3]
__________________________________________________________________________________________
13
110°
NOT TO
SCALE
A
C
B
Triangle ABC is isosceles with AB = AC.
Angle BAC = 110° and the area of the triangle is 85cm2
.
Calculate AC.
Answer AC = .......................................... cm [3]
__________________________________________________________________________________________

6
0580/22/O/N/14© UCLES 2014
14
56°
2.25m
NOT TO
SCALE
The diagram shows a sand pit in a child’s play area.
The shape of the sand pit is a sector of a circle of radius 2.25m and sector angle 56°.
(a) Calculate the area of the sand pit.
Answer(a) ........................................... m2
[2]
(b) The sand pit is ﬁlled with sand to a depth of 0.3m.
Calculate the volume of sand in the sand pit.
Answer(b) ........................................... m3
[1]
__________________________________________________________________________________________
15 (a) Write 90 as a product of prime factors.
Answer(a) ................................................ [2]
(b) Find the lowest common multiple of 90 and 105.
Answer(b) ................................................ [2]
__________________________________________________________________________________________

7
16 A, B and C are points on a circle, centre O.
TCD is a tangent to the circle.
Angle BAC = 54°.
A
D
T
B
C
O 54°
NOT TO
SCALE
(a) Find angle BOC, giving a reason for your answer.
Answer(a) Angle BOC = ............... because .......................................................................................
............................................................................................................................................................. [2]
(b) When O is the origin, the position vector of point C is
4
3
-
e o.
(i) Work out the gradient of the radius OC.
Answer(b)(i) ................................................ [1]
(ii) D is the point (7, k).
Find the value of k.
Answer(b)(ii) k = ................................................ [1]
__________________________________________________________________________________________

8
0580/22/O/N/14© UCLES 2014
17 Alex invests $200 for 2 years at a rate of 2% per year simple interest.
Chris invests $200 for 2 years at a rate of 2% per year compound interest.
Calculate how much more interest Chris has than Alex.
Answer $................................................. [4]
__________________________________________________________________________________________

9
18 72 students are given homework one evening.
They are told to spend no more than 100 minutes completing their homework.
The cumulative frequency diagram shows the number of minutes they spend.
80
60
40
20
0
30 40 50 60 70
Minutes
80 90 100
Cumulative
frequency
(a) How many students spent more than 48 minutes completing their homework?
Answer(a) ................................................ [2]
(b) Find
(i) the median,
Answer(b)(i) ................................................ [1]
(ii) the inter-quartile range.
Answer(b)(ii) ................................................ [2]
__________________________________________________________________________________________

10
0580/22/O/N/14© UCLES 2014
19
C
O A
B
Xc
a
NOT TO
SCALE
The diagram shows a quadrilateral OABC.
= a, = c and = 2a.
X is a point on OB such that OX:XB = 1:2.
(a) Find, in terms of a and c, in its simplest form
(i) ,
Answer(a)(i) = ................................................ [1]
(ii) .
Answer(a)(ii) = ................................................ [3]
(b) Explain why the vectors and show that C, X and A lie on a straight line.
Answer(b) ..................................................................................................................................................
............................................................................................................................................................. [2]
__________________________________________________________________________________________

11
20 The diagram shows the plan, ABCD, of a park.
The scale is 1 centimetre represents 20 metres.
D
A
C
B
Scale: 1cm to 20m
(a) Find the actual distance BC.
Answer(a) ............................................ m [2]
(b) A fountain, F, is to be placed
● 160m from C
and
● equidistant from AB and AD.
On the diagram, using a ruler and compasses only, construct and mark the position of F.
Leave in all your construction lines. [5]
__________________________________________________________________________________________

12
0580/22/O/N/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
21 (a) Write as a single fraction in its simplest form.
2 1
3
x -
–
2x
1
+
Answer(a) ................................................ [3]
(b) Simplify.
2
2
2 6 56
4 16
x x
x x
-
-
+
Answer(b) ................................................ [4]

Do not use staples, paper clips, glue or correction fluid.
MATHEMATICS 0580/22
1 hour 30 minutes
[Turn over
IB14 06_0580_22/2RP
© UCLES 2014
*9522292004*
Cambridge International General Certificate of Secondary Education
The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.

2
0580/22/M/J/14© UCLES 2014
1 Calculate 2
16
1.3
3
.
Answer ................................................ [1]
__________________________________________________________________________________________
2 (a) Write 569000 correct to 2 signiﬁcant ﬁgures.
Answer(a) ................................................ [1]
(b) Write 569000 in standard form.
Answer(b) ................................................ [1]
__________________________________________________________________________________________
2x – y = 7
3x + y = 3
Answer x = ................................................
y = ................................................ [2]
__________________________________________________________________________________________

3
4
C
B A
8cm
28°
NOT TO
SCALE
Calculate the length of AB.
Answer AB = .......................................... cm [2]
__________________________________________________________________________________________
5
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]
__________________________________________________________________________________________

4
0580/22/M/J/14© UCLES 2014
6 The mass of 1cm3
of copper is 8.5 grams, correct to 1 decimal place.
Complete the statement about the total mass, T grams, of 12cm3
of copper.
Answer .............................. Y T .............................. [2]
__________________________________________________________________________________________
7 Write the following in order, smallest ﬁrst.
0.1 201
43
2 2
1
% 0.2
Answer .................. .................. .................. .................. [2]
__________________________________________________________________________________________
8 Without using your calculator, work out 6
5
– 2 2
1 1
1#` j.
Write down all the steps of your working.
Answer ................................................ [3]
__________________________________________________________________________________________

5
9 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]
__________________________________________________________________________________________
10 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]
__________________________________________________________________________________________

6
0580/22/M/J/14© UCLES 2014
11 Anita buys a computer for $391 in a sale.
The sale price is 15% less than the original price.
Calculate the original price of the computer.
Answer $ ................................................ [3]
__________________________________________________________________________________________
2
3
1
1
x x
+
+
= 0
Answer x = ................................................ [3]
__________________________________________________________________________________________

7
13 w varies inversely as the square root of x.
When x = 4, w = 4.
Find w when x = 25.
Answer w = ................................................ [3]
__________________________________________________________________________________________
14
R
O P
Q
M
r
p
NOT TO
SCALE
OPQR is a trapezium with RQ parallel to OP and RQ = 2OP.
O is the origin, = p and = r.
M is the midpoint of PQ.
Find, in terms of p and r, in its simplest form
(a) ,
Answer(a) = ................................................ [1]
(b) , the position vector of M.
Answer(b) = ................................................ [2]
__________________________________________________________________________________________

8
0580/22/M/J/14© UCLES 2014
15 M =
4
3
2
5
e o
Find
(a) M2
,
Answer(a) [2]
(b) the determinant of M.
Answer(b) ................................................ [1]
__________________________________________________________________________________________
16 Factorise completely.
(a) 4p2
q – 6pq2
Answer(a) ................................................ [2]
(b) u + 4t + ux + 4tx
Answer(b) ................................................ [2]
__________________________________________________________________________________________

9
17 (a) Simplify (3125t125
)
1
5
.
Answer(a) ................................................ [2]
(b) Find the value of p when 3
p
= 9
1
.
Answer(b) p = ................................................ [1]
(c) Find the value of w when x72
÷ xw
= x8
.
Answer(c) w = ................................................ [1]
__________________________________________________________________________________________
18
NOT TO
SCALE
The two containers are mathematically similar in shape.
The larger container has a volume of 3456cm3
and a surface area of 1024cm2
.
The smaller container has a volume of 1458cm3
.
Calculate the surface area of the smaller container.
Answer ......................................... cm2
[4]
__________________________________________________________________________________________

10
0580/22/M/J/14© UCLES 2014
19 Simplify.
2
3 21
6 7
x
x x
+
+ -
Answer ................................................ [4]
__________________________________________________________________________________________
20 32 25 18 11 4
These are the ﬁrst 5 terms of a sequence.
Find
(a) the 6th term,
Answer(a) ................................................ [1]
(b) the nth term,
Answer(b) ................................................ [2]
(c) which term is equal to –332.
Answer(c) ................................................ [2]
__________________________________________________________________________________________

11
21
P
D C
BA
M
6cm
4cm
4cm
NOT TO
SCALE
The diagram shows a pyramid on a square base ABCD with diagonals, AC and BD, of length 8cm.
AC and BD meet at M and the vertex, P, of the pyramid is vertically above M.
The sloping edges of the pyramid are of length 6cm.
Calculate
(a) the perpendicular height, PM, of the pyramid,
Answer(a) PM = .......................................... cm [3]
(b) the angle between a sloping edge and the base of the pyramid.
Answer(b) ................................................ [3]
__________________________________________________________________________________________

12
0580/22/M/J/14© UCLES 2014
22
P Q
k
m n
i
j
f
g
h
(a) Use the information in the Venn diagram to complete the following.
(i) P ∩ Q = {........................................................} [1]
(ii) P' ∪ Q = {........................................................} [1]
(iii) n(P ∪ Q)' = .................................................... [1]
(b) A letter is chosen at random from the set Q.
Find the probability that it is also in the set P.
Answer(b) ................................................ [1]
(c) On the Venn diagram shade the region P' ∩ Q. [1]
(d) Use a set notation symbol to complete the statement.
{f, g, h} ........ P
[1]

You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction ﬂuid.
MATHEMATICS 0580/22
1 hour 30 minutes
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certiﬁcate of Secondary Education
[Turn over
IB13 11_0580_22/2RP
© UCLES 2013
*8971791642*

2
0580/22/O/N/13© UCLES 2013
For
Examiner′s
Use
1 Write the following in order of size, smallest ﬁrst.
19%
5
1
.0 038 sin 11.4° 0.7195
Answer ......................... ......................... ......................... ......................... ......................... [2]
_____________________________________________________________________________________
2 Use a calculator to work out the following.
(a) 3 (–4 × 62
– 5)
Answer(a) ............................................... [1]
(b) 3 × tan 30° + 2 × sin 45°
Answer(b) ............................................... [1]
_____________________________________________________________________________________
3 Find the circumference of a circle of radius 2.5cm.
Answer ......................................... cm [2]
_____________________________________________________________________________________
4 Bruce plays a game of golf.
His scores for each of the 18 holes are shown below.
2 3 4 5 4 6 2 3 4
4 5 3 4 3 5 4 4 4
The information is to be shown in a pie chart.
Calculate the sector angle for the score of 4.
Answer ............................................... [2]
_____________________________________________________________________________________

3
For
Examiner′s
Use
5 (a) Add one line to the diagram so that it has two lines of symmetry.
[1]
(b) Add two lines to the diagram so that it has rotational symmetry of order 2.
[1]
_____________________________________________________________________________________
6 Rearrange the formula to make x the subject.
y = x2
+ 4
Answer x = ............................................... [2]
_____________________________________________________________________________________

4
0580/22/O/N/13© UCLES 2013
For
Examiner′s
Use
7
12cm
10cm
22cm
NOT TO
SCALE
Find the area of the trapezium.
Answer ........................................ cm2
[2]
_____________________________________________________________________________________
8 A hemisphere has a radius of 12cm.
Calculate its volume.
[The volume, V, of a sphere with radius r is V =
4
3 πr3
.]
Answer ........................................ cm3
[2]
_____________________________________________________________________________________
9 The exterior angle of a regular polygon is 36°.
What is the name of this polygon?
Answer ............................................... [3]
_____________________________________________________________________________________
12cm

5
For
Examiner′s
Use
10 The table shows how the dollar to euro conversion rate changed during one day.
Time 1000 1100 1200 1300 1400 1500 1600
$1 €1.3311 €1.3362 €1.3207 €1.3199 €1.3200 €1.3352 €1.3401
Khalil changed $500 into euros (€).
How many more euros did Khalil receive if he changed his money at the highest rate compared to the
lowest rate?
Answer € ................................................ [3]
_____________________________________________________________________________________
11 The speed, v, of a wave is inversely proportional to the square root of the depth, d, of the water.
v = 30 when d = 400.
Find v when d = 25.
Answer v = ............................................... [3]
_____________________________________________________________________________________
12 A circle has a radius of 8.5cm correct to the nearest 0.1cm.
The lower bound for the area of the circle is pπcm2
.
The upper bound for the area of the circle is qπcm2
.
Find the value of p and the value of q.
Answer p = ...............................................
q = ............................................... [3]
_____________________________________________________________________________________

6
0580/22/O/N/13© UCLES 2013
For
Examiner′s
Use
13 Pam wins the student of the year award in New Zealand.
She sends three photographs of the award ceremony by post to her relatives.
● one of size 13cm by 23cm to her uncle in Australia
● one of size 15cm by 23cm to her sister in China
● one of size 23cm by 35cm to her mother in the UK
Maximum lengths Australia Rest of the world
13cm by 23.5cm $1.90 $2.50
15.5cm by 23.5cm $2.40 $2.90
23cm by 32.5cm $2.80 $3.40
26cm by 38.5cm $3.60 $5.20
The cost of postage is shown in the table above.
Use this information to calculate the total cost.
Answer $ ................................................ [3]
_____________________________________________________________________________________
14
142°
D
A
O
C
B
NOT TO
SCALE
A, B and C are points on the circumference of a circle centre O.
OAD is a straight line and angle DAB = 142°.
Calculate the size of angle ACB.
Answer Angle ACB = ............................................... [3]
_____________________________________________________________________________________

7
For
Examiner′s
Use
15 Find the co-ordinates of the point of intersection of the two lines.
2x – 7y = 2
4x + 5y = 42
Answer (.............. , ..............) [3]
_____________________________________________________________________________________
16 Solve the inequality.
x
2
+
x
3
2-
5
Answer ............................................... [4]
_____________________________________________________________________________________

8
0580/22/O/N/13© UCLES 2013
For
Examiner′s
Use
17
M =
2
4
1
6
f p N =
5
1
0
5
f p
(a) Work out MN.
Answer(a) MN = [2]
(b) Find M–1
.
Answer(b) M–1
= [2]
_____________________________________________________________________________________

9
For
Examiner′s
Use
18 A(5, 23) and B(–2, 2) are two points.
(a) Find the co-ordinates of the midpoint of the line AB.
Answer(a) (............ , ............) [2]
(b) Find the equation of the line AB.
Answer(b) ............................................... [3]
(c) Show that the point (3, 17) lies on the line AB.
Answer(c)
[1]
_____________________________________________________________________________________

10
0580/22/O/N/13© UCLES 2013
For
Examiner′s
Use
19
O
E
C
F
A
D B
c
a
O is the origin.
ABCDEF is a regular hexagon and O is the midpoint of AD.
= a and = c.
Find, in terms of a and c, in their simplest form
(a) ,
Answer(a) = ............................................... [2]
(b) ,
Answer(b) = ............................................... [2]
(c) the position vector of E.
Answer(c) ............................................... [2]
_____________________________________________________________________________________

11
For
Examiner′s
Use
20 During one day 48 people visited a museum.
The length of time each person spent in the museum was recorded.
The results are shown on the cumulative frequency diagram.
50
40
30
20
10
0
1 2 3 4
Time (hours)
5 6
Cumulative
frequency
Work out
(a) the median,
Answer(a) ............................................ h [1]
(b) the 20th percentile,
Answer(b) ............................................ h [2]
(c) the inter-quartile range,
Answer(c) ............................................ h [2]
(d) the probability that a person chosen at random spends 2 hours or less in the museum.
Answer(d) ............................................... [2]
_____________________________________________________________________________________

12
0580/22/O/N/13
University of 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 2013
For
Examiner′s
Use
21
B
C A
NOT TO
SCALE6cm4cm
65°
In triangle ABC, AB = 6cm, BC = 4cm and angle BCA = 65°.
Calculate
(a) angle CAB,
Answer(a) Angle CAB = ............................................... [3]
(b) the area of triangle ABC.
Answer(b) ........................................ cm2
[3]

Do not use staples, paper clips, highlighters, glue or correction ﬂuid.
MATHEMATICS 0580/22
1 hour 30 minutes
International General Certiﬁcate of Secondary Education
[Turn over
IB13 06_0580_22/3RP
© UCLES 2013
*8742517468*

2
0580/22/M/J/13© UCLES 2013
For
Examiner′s
Use
1 Shade the required region on each Venn diagram.
A B
A' ∪ B
A B
A' ∩ B'
[2]
_____________________________________________________________________________________
2 Factorise completely.
kp + 3k + mp + 3m
Answer ............................................... [2]
_____________________________________________________________________________________
3 The ﬁrst ﬁve terms of a sequence are shown below.
13 9 5 1 –3
Answer ............................................... [2]
_____________________________________________________________________________________

3
For
Examiner′s
Use
4 Calculate (4.3 × 108
) + (2.5 × 107
) .
Give your answer in standard form.
Answer ............................................... [2]
_____________________________________________________________________________________
5
A
B C
8cm
NOT TO
SCALE
Triangle ABC has a height of 8cm and an area of 42cm².
Calculate the length of BC.
Answer BC = ......................................... cm [2]
_____________________________________________________________________________________

4
0580/22/M/J/13© UCLES 2013
For
Examiner′s
Use
6 George and his friend Jane buy copies of the same book on the internet.
George pays $16.95 and Jane pays £11.99 on a day when the exchange rate is $1 = £0.626.
Calculate, in dollars, how much more Jane pays.
Answer $ ............................................... [2]
_____________________________________________________________________________________
7 (a) Use your calculator to work out 65 – 1.72
.
Write down all the numbers displayed on your calculator.
Answer(a) ............................................... [1]
(b) Write your answer to part (a) correct to 2 signiﬁcant ﬁgures.
Answer(b) ............................................... [1]
_____________________________________________________________________________________
8 Joe measures the side of a square correct to 1 decimal place.
He calculates the upper bound for the area of the square as 37.8225cm2
.
Work out Joe’s measurement for the side of the square.
Answer ......................................... cm [2]
_____________________________________________________________________________________

5
For
Examiner′s
Use
9 A car, 4.4 metres long, has a fuel tank which holds 65 litres of fuel when full.
The fuel tank of a mathematically similar model of the car holds 0.05 litres of fuel when full.
Calculate the length of the model car in centimetres.
Answer ......................................... cm [3]
_____________________________________________________________________________________
10
85°
58°
19°
B
C
A
E
D
N
NOT TO
SCALE
A, B, C, D and E are points on a circle.
Angle ABD = 58°, angle BAE = 85° and angle BDC = 19°.
BD and CA intersect at N.
Calculate
(a) angle BDE,
Answer(a) Angle BDE = ............................................... [1]
(b) angle AND.
Answer(b) Angle AND = ............................................... [2]
_____________________________________________________________________________________

6
0580/22/M/J/13© UCLES 2013
For
Examiner′s
Use
11 Without using a calculator, work out
7
6
÷ 1
3
2
.
Write down all the steps in your working.
Answer ............................................... [3]
_____________________________________________________________________________________
5(2y – 17) = 60
Answer y = ............................................... [3]
_____________________________________________________________________________________
13 Carol invests $6250 at a rate of 2% per year compound interest.
Calculate the total amount Carol has after 3 years.
Answer $ ............................................... [3]
_____________________________________________________________________________________

7
For
Examiner′s
Use
14 y is inversely proportional to x3
.
y = 5 when x = 2.
Find y when x = 4.
Answer y = ............................................... [3]
_____________________________________________________________________________________
15 Use the quadratic equation formula to solve
2x2
+ 7x – 3 = 0 .
Answer x = .......................... or x = .......................... [4]
_____________________________________________________________________________________

8
0580/22/M/J/13© UCLES 2013
For
Examiner′s
Use
16
40
0
3 22
Time (minutes)
26
Speed
(km/h)
NOT TO
SCALE
The diagram shows the speed-time graph of a train journey between two stations.
The train accelerates for 3 minutes, travels at a constant maximum speed of 40km/h, then takes
4 minutes to slow to a stop.
Calculate the distance in kilometres between the two stations.
Answer ......................................... km [4]
_____________________________________________________________________________________

9
For
Examiner′s
Use
17 The owner of a small café records the average air temperature and the number of hot drinks he sells
each day for a week.
Air temperature (°C) 18 23 19 23 24 25 20
Number of hot drinks sold 12 8 13 10 9 7 12
(a) On the grid, draw a scatter diagram to show this information.
14
13
12
11
10
9
8
7
6
0
17 18 19 20 21 22 23 24 25 26
Air temperature (°C)
Number of
hot drinks sold
[2]
(b) What type of correlation does your scatter diagram show?
Answer(b) ............................................... [1]
(c) Draw a line of best ﬁt on the grid. [1]
_____________________________________________________________________________________
18 Solve 6x + 3 x 3x + 9 for integer values of x.
Answer ............................................... [4]
_____________________________________________________________________________________

10
0580/22/M/J/13© UCLES 2013
For
Examiner′s
Use
19
D
A
C
B
Scale: 1cm to 8m
The rectangle ABCD is a scale drawing of a rectangular football pitch.
The scale used is 1 centimetre to represent 8 metres.
(a) Construct the locus of points 40m from A and inside the rectangle. [2]
(b) Using a straight edge and compasses only, construct the perpendicular bisector of DB. [2]
(c) Shade the region on the football pitch which is more than 40m from A and nearer to D than to B.
[1]
_____________________________________________________________________________________

11
For
Examiner′s
Use
20 The heights, in metres, of 200 trees in a park are measured.
Height (hm) 2 h Ğ 6 6 h Ğ 10 10 h Ğ 13 13 h Ğ 17 17 h Ğ 19 19 h Ğ 20
Frequency 23 47 45 38 32 15
(a) Find the interval which contains the median height.
Answer(a) ............................................... [1]
(b) Calculate an estimate of the mean height.
Answer(b) ........................................... m [4]
(c) Complete the cumulative frequency table for the information given in the table above.
Height (hm) 2 h Ğ 6 h Ğ 10 h Ğ 13 h Ğ 17 h Ğ 19 h Ğ 20
Cumulative
frequency
23
[2]
_____________________________________________________________________________________

12
0580/22/M/J/13
© UCLES 2013
For
Examiner′s
Use
21 f(x) = 5x + 4 g(x) =
x2
1
, x ¸ 0 h(x) =
x
2
1
c m
Find
(a) fg(5) ,
Answer(a) ............................................... [2]
(b) gg(x) in its simplest form,
Answer(b) gg(x) = ............................................... [2]
(c) f –1
(x) ,
Answer(c) f –1
(x) = ............................................... [2]
(d) the value of x when h(x) = 8.
Answer(d) x = ............................................... [2]

IB12 11_0580_22/5RP
*3624869769*
International General Certificate of Secondary Education
MATHEMATICS 0580/22
1 hour 30 minutes
Mathematical tables (optional) Tracing paper (optional)
Do not use staples, paper clips, highlighters, glue or correction fluid.
For π , use either your calculator value or 3.142.

2
© UCLES 2012 0580/22/O/N/12
For
Examiner's
Use
1 Write the following numbers correct to one significant figure.
(a) 7682
Answer(a) [1]
(b) 0.07682
Answer(b) [1]
2 Work out 11.3139 – 2.28 × 3 2
9 .
Give your answer correct to one decimal place.
Answer [2]
3 m =
4
1
[3h2
+ 8ah + 3a2
]
Calculate the exact value of m when h = 20 and a = O5.
Answer m = [2]

3
© UCLES 2012 0580/22/O/N/12 [Turn over
For
Examiner's
Use
4
6°
6°
NOT TO
SCALE
The diagram shows two of the exterior angles of a regular polygon with n sides.
Calculate n.
Answer n = [2]
5 The Tiger Sky Tower in Singapore has a viewing capsule which holds 72 people.
This number is 75% of the population of Singapore when it was founded in 1819.
What was the population of Singapore in 1819?
Answer [2]
6 In a traffic survey of 125 cars the number of people in each car was recorded.
Number of people in each car 1 2 3 4 5
Frequency 50 40 10 20 5
Find
(a) the range,
Answer(a) [1]
(b) the median,
Answer(b) [1]
(c) the mode.
Answer(c) [1]

4
© UCLES 2012 0580/22/O/N/12
For
Examiner's
Use
7 The number of spectators at the 2010 World Cup match between Argentina and Mexico was
82000 correct to the nearest thousand.
If each spectator paid 2600 Rand (R) to attend the game, what is the lower bound for the total amount
paid?
Write your answer in standard form.
Answer R [3]
8
0.65m
85km
NOT TO
SCALE
A water pipeline in Australia is a cylinder with radius 0.65 metres and length 85 kilometres.
Calculate the volume of water the pipeline contains when it is full.
Give your answer in cubic metres.
Answer m3
[3]

5
For
Examiner's
Use
9 A shop is open during the following hours.
Monday to Friday Saturday Sunday
Opening time 0645 0730 0845
Closing time 1730 1730 1200
(a) Write the closing time on Saturday in the 12-hour clock time.
Answer(a) [1]
(b) Calculate the total number of hours the shop is open in one week.
Answer(b) h [2]
10 Solve the equation 4x O 12 = 2(11 – 3x).
Answer x = [3]

6
© UCLES 2012 0580/22/O/N/12
For
Examiner's
Use
11 List all the prime numbers which satisfy this inequality.
16 I 2x – 5 I 48
Answer [3]
12
A company sells cereals in boxes which measure 10cm by 25cm by 35cm.
They make a special edition box which is mathematically similar to the original box.
The volume of the special edition box is 15120cm3
.
Work out the dimensions of this box.
Answer cm by cm by cm [3]

7
For
Examiner's
Use
13 The mass, m, of an object varies directly as the cube of its length, l.
m = 250 when l = 5.
Find m when l = 7.
Answer m = [3]
14 (a) 





8
3 8
3
× 





8
3 8
1
= pq
Find the value of p and the value of q.
Answer(a) p =
q = [2]
(b) 5
O3
+ 5O4
= k × 5O4
Answer(b) k = [2]

8
© UCLES 2012 0580/22/O/N/12
For
Examiner's
Use
15
0
5 10 15 20 25 30 35
25
20
15
10
5
Speed
(metres per
second)
Time (seconds)
The diagram shows the speed-time graph for the last 35 seconds of a car journey.
(a) Find the deceleration of the car as it came to a stop.
Answer(a) m/s2
[1]
(b) Calculate the total distance travelled by the car in the 35 seconds.
Answer(b) m [3]

9
For
Examiner's
Use
16 A company sends out ten different questionnaires to its customers.
The table shows the number sent and replies received for each questionnaire.
Questionnaire A B C D E F G H I J
Number sent out 100 125 150 140 70 105 100 90 120 130
Number of replies 24 30 35 34 15 25 22 21 30 31
40
35
30
25
20
15
10
5
0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Numberofreplies
Number sent out
(a) Complete the scatter diagram for these results.
The first two points have been plotted for you. [2]
(b) Describe the correlation between the two sets of data.
Answer(b) [1]
(c) Draw the line of best fit. [1]

10
© UCLES 2012 0580/22/O/N/12
For
Examiner's
Use
17
y
x
1 2 3 4 5 6 7 8 9
3
2
1
0
–1
–2
A
D
B A' B'
A″ B″
C D' C'
D″ C″
(a) Describe the single transformation which maps ABCD onto A' B' C' D'.
Answer(a) [3]
(b) A single transformation maps A' B' C' D' onto A B C D.
Find the matrix which represents this transformation.
Answer(b)










[2]
18 A =










0
1
1
0
B =










−
−
01
10
On the grid on the next page, draw the image of PQRS after the transformation represented by BA.

11
For
Examiner's
Use
P Q
RS
y
x
10 2 3 4 5 6 7–7 –6 –5 –4 –3 –2 –1
4
3
2
1
–1
–2
–3
–4
[5]
19 f(x) = x2
+ 1 g(x) =
3
2+x
(a) Work out ff(O1).
Answer(a) [2]
(b) Find gf(3x), simplifying your answer as far as possible.
Answer(b) gf(3x) = [3]
(c) Find g
O1
(x).
Answer(c) g
O1
(x) = [2]

12
© UCLES 2012 0580/22/O/N/12
For
Examiner's
Use
20 (a) The two lines y = 2x + 8 and y = 2x – 12 intersect the x-axis at P and Q.
Work out the distance PQ.
Answer(a) PQ = [2]
(b) Write down the equation of the line with gradient O4 passing through (0, 5).
Answer(b) [2]
(c) Find the equation of the line parallel to the line in part (b) passing through (5, 4).
Answer(c) [3]

IB12 06_0580_22/3RP
*9357669131*
MATHEMATICS 0580/22
1 hour 30 minutes

2
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
1 The ferry from Helsinki to Travemunde leaves Helsinki at 1730 on a Tuesday.
The journey takes 28 hours 45 minutes.
Work out the day and time that the ferry arrives in Travemunde.
Answer Day Time [2]
2 T R I G O N O M E T R Y
From the above word, write down the letters which have
(a) exactly two lines of symmetry,
Answer(a) [1]
(b) rotational symmetry of order 2.
Answer(b) [1]
3 For this question, 1 x 2.
Write the following in order of size, smallest first.
x
5
5x
5
x
x O 5
Answer [2]
4 1
2
1
+
3
1
+
4
1
=
12
p
Work out the value of p.
Answer p = [2]

3
© UCLES 2012 0580/22/M/J/12 [Turn over
For
Examiner's
Use
5 A lake has an area of 63800000000 square metres.
Write this area in square kilometres, correct to 2 significant figures.
Answer km2
[2]
6 x is a positive integer and 15x – 43 5x + 2.
Work out the possible values of x.
Answer [3]
7
8cm
6cm
r
NOT TO
SCALE
The perimeter of the rectangle is the same length as the circumference of the circle.
Calculate the radius, r, of the circle.
Answer r = cm [3]

4
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
8 A car company sells a scale model 10
1
of the size of one of its cars.
Complete the following table.
Scale Model Real Car
Area of windscreen (cm2
) 135
Volume of storage space (cm3
) 408000
[3]
9
P
BA
170m
78.3°
58.4m
NOT TO
SCALE
The line AB represents the glass walkway between the Petronas Towers in Kuala Lumpur.
The walkway is 58.4 metres long and is 170 metres above the ground.
The angle of elevation of the point P from A is 78.3°.
Calculate the height of P above the ground.
Answer m [3]

5
For
Examiner's
Use
10
500
400
300
200
100
0
10 20 30 40 50 60
Time (min)
Speed
(m/min)
The diagram shows the speed-time graph for a boat journey.
(a) Work out the acceleration of the boat in metres/minute2
.
Answer(a) m/min2
[1]
(b) Calculate the total distance travelled by the boat.
Give your answer in kilometres.
Answer(b) km [2]

6
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
11 y varies directly as the square of (x – 3).
y = 16 when x = 1.
Find y when x = 10.
Answer y = [3]
12
North 5km
8km
150°
C
B
A
NOT TO
SCALE
A helicopter flies 8km due north from A to B. It then flies 5km from B to C and returns to A.
Angle ABC = 150°.
(a) Calculate the area of triangle ABC.
Answer(a) km2
[2]
(b) Find the bearing of B from C.
Answer(b) [2]

7
For
Examiner's
Use
13 The taxi fare in a city is $3 and then $0.40 for every kilometre travelled.
(a) A taxi fare is $9.
How far has the taxi travelled?
Answer(a) km [2]
(b) Taxi fares cost 30% more at night.
How much does a $9 daytime journey cost at night?
Answer(b) $ [2]
14
A B
3
2
1
0
1 2 3 4 5 6 7 8
x
y
(a) Describe fully the single transformation that maps triangle A onto triangle B.
Answer(a) [3]
(b) Find the 2 × 2 matrix which represents this transformation.
Answer(b)










[2]

8
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
15
60
50
40
30
20
10
0
10 20 30 40 50
Height (cm)
Cumulative
frequency
The cumulative frequency diagram shows information about the heights of 60 tomato plants.
Use the diagram to find
(a) the median,
Answer(a) cm [1]
(b) the lower quartile,
Answer(b) cm [1]
(c) the interquartile range,
Answer(c) cm [1]
(d) the probability that the height of a tomato plant, chosen at random, will be more than 15cm.
Answer(d) [2]

9
For
Examiner's
Use
16
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8
x
y
The diagram shows the graph of y =
2
x
+
x
2
, for 0 x Y 8.
(a) Use the graph to solve the equation
2
x
+
x
2
= 3.
Answer (a) x = or x = [2]
(b) By drawing a suitable tangent, work out an estimate of the gradient of the graph where x = 1.
Answer(b) [3]

10
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
17 (a) Find the co-ordinates of the midpoint of the line joining A(–8, 3) and B(–2, –3).
Answer(a) ( , ) [2]
(b) The line y = 4x + c passes through (2, 6).
Find the value of c.
Answer(b) c = [1]
(c) The lines 5x = 4y + 10 and 2y = kx – 4 are parallel.
Answer(c) k = [2]

11
For
Examiner's
Use
18 f(x) = (x + 2)3
– 5 g(x) = 2x + 10 h(x) =
x
1
, x ≠ 0
Find
(a) gf (x),
Answer(a) gf(x) = [2]
(b) f –1
(x),
Answer(b) f -1
(x) = [3]
(c) gh(–
5
1
).
Answer(c) [2]

12
© UCLES 2012 0580/22/M/J/12
For
Examiner's
Use
19 Find the values of x for which
(a)










−72
0
0
1
x
has no inverse,
Answer(a) x = [2]
(b)










− 8
0
0
1
2
x
is the identity matrix,
Answer (b) x = or x = [3]
(c)










− 2
0
0
1
x
represents a stretch with factor 3 and the x axis invariant.
Answer (c) x = [2]

IB11 11_0580_22/2RP
*5208945727*
MATHEMATICS 0580/22
1 hour 30 minutes

2
© UCLES 2011 0580/22/O/N/11
For
Examiner's
Use
1 A bus leaves a port every 15 minutes, starting at 0900.
The last bus leaves at 1730.
How many times does a bus leave the port during one day?
Answer [2]
2 Factorise completely ax + bx + ay + by.
Answer [2]
3 Use your calculator to find the value of
(a) 30
× 2.52
,
Answer(a) [1]
(b) 2.5– 2
.
Answer(b) [1]
4 The cost of making a chair is $28 correct to the nearest dollar.
Calculate the lower and upper bounds for the cost of making 450 chairs.
Answer lower bound $
upper bound $ [2]

3
For
Examiner's
Use
5 Jiwan incorrectly wrote 1 +
2
1
+
3
1
+
4
1
= 1
9
3
.
Show the correct working and write down the answer as a mixed number.
Answer [3]
6 The force, F, between two magnets varies inversely as the square of the distance, d, between them.
F = 150 when d = 2.
Calculate F when d = 4.
Answer F = [3]

4
© UCLES 2011 0580/22/O/N/11
For
Examiner's
Use
7 





43_
20






b
a
= 





25
8
Find the value of a and the value of b.
Answer a =
b = [3]
8 A cruise ship travels at 22 knots.
[1 knot is 1.852 kilometres per hour.]
Convert this speed into metres per second.
Answer m/s [3]

5
For
Examiner's
Use
9 A sequence is given by u1 = 1 , u2 = 3 , u3 = 5 , u4 = 7 , …
(a) Find a formula for un, the nth term.
Answer(a) un = [2]
(b) Find u29 .
Answer(b) u29 = [1]
10 Write as a single fraction in its simplest form.
10
3
+x
O
4
1
+x
Answer [3]

6
© UCLES 2011 0580/22/O/N/11
For
Examiner's
Use
11 Find the values of m and n.
(a) 2m
= 0.125
Answer(a) m = [2]
(b) 24n
× 22n
= 512
Answer(b) n = [2]
12
40
30
20
10
0
1 2 3 4 5
Time (seconds)
6 7 8 9 10
Speed
(m/s)
Small
car
Large
car
A small car accelerates from 0m/s to 40m/s in 6 seconds and then travels at this constant speed.
A large car accelerates from 0m/s to 40m/s in 10 seconds.
Calculate how much further the small car travels in the first 10 seconds.
Answer m [4]

7
For
Examiner's
Use
13
76°
O
A
B
T
C
P
North
NOT TO
SCALE
AOC is a diameter of the circle, centre O.
AT is a straight line that cuts the circle at B.
PT is the tangent to the circle at C.
Angle COB = 76°.
(a) Calculate angle ATC.
Answer(a) Angle ATC = [2]
(b) T is due north of C.
Calculate the bearing of B from C.
Answer(b) [2]

8
© UCLES 2011 0580/22/O/N/11
For
Examiner's
Use
14
R
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7
y
x
The region R is bounded by three lines.
Write down the three inequalities which define the region R.
Answer
[4]

9
For
Examiner's
Use
15
6
5
4
3
2
1
0
1 2 3 4 5 6
y
x
A
B
The points A(1, 2) and B(5, 5) are shown on the diagram .
(a) Work out the co-ordinates of the midpoint of AB.
Answer(a) ( , ) [1]
(b) Write down the column vector .
Answer(b) =










[1]
(c) Using a straight edge and compasses only, draw the locus of points which are equidistant
from A and from B. [2]

10
© UCLES 2011 0580/22/O/N/11
For
Examiner's
Use
16 In a survey of 60 cars, the type of fuel that they use is recorded in the table below.
Each car only uses one type of fuel.
Petrol Diesel Liquid Hydrogen Electricity
40 12 2 6
(a) Write down the mode.
Answer(a) [1]
(b) Olav drew a pie chart to illustrate these figures.
Calculate the angle of the sector for Diesel.
Answer(b) [2]
(c) Calculate the probability that a car chosen at random uses Electricity.
Write your answer as a fraction in its simplest form.
Answer(c) [2]

11
For
Examiner's
Use
17
O
C B
Aa
c M
4a
O is the origin, = a, = c and = 4a.
M is the midpoint of AB.
(a) Find, in terms of a and c, in their simplest form
(i) the vector ,
Answer(a)(i) = [2]
(ii) the position vector of M.
Answer(a)(ii) [2]
(b) Mark the point D on the diagram where = 3a + c. [2]
18 w =
LC
1
(a) Find w when L = 8 × 10
O3
and C = 2 × 10O9
.
Answer(a) w = [3]
(b) Rearrange the formula to make C the subject.
Answer(b) C = [3]

12
© UCLES 2011 0580/22/O/N/11
For
Examiner's
Use
19
6
5
4
3
2
1
1 2 3 4 5 6 7
0
A
B
C
y
x
A(1, 3), B(4, 1) and C(6, 4) are shown on the diagram.
(a) Using a straight edge and compasses only, construct the angle bisector of angle ABC. [2]
(b) Work out the equation of the line BC.
Answer(b) [3]
(c) ABC forms a right-angled isosceles triangle of area 6.5cm2
.
Calculate the length of AB.
Answer(c) AB = cm [2]

IB11 06_0580_22/8RP
*4065843724*
MATHEMATICS 0580/22
1 hour 30 minutes

2
© UCLES 2011 0580/22/M/J/11
For
Examiner's
Use
1 In the right-angled triangle ABC, cos C =
5
4
. Find angle A.
A
B C
NOT TO
SCALE
Answer Angle A = [2]
2 Which of the following numbers are irrational?
3
2
36 3 + 6 π 0.75 48% 8 3
1
Answer [2]
3 Show that 1
9
5
÷ 1
9
7
=
8
7
.
Answer
[2]

3
For
Examiner's
Use
4
5
3
p
3
2
Which of the following could be a value of p?
27
16
0.67 60% (0.8)2
9
4
Answer [2]
5 A meal on a boat costs 6 euros (€) or 11.5 Brunei dollars ($).
In which currency does the meal cost less, on a day when the exchange rate is €1 = $1.9037?
Answer [2]
6 Use your calculator to find the value of 2 3
.
Give your answer correct to 4 significant figures.
Answer [2]

4
© UCLES 2011 0580/22/M/J/11
For
Examiner's
Use
7 Solve the equation 4x + 6 × 103
= 8 × 104
.
Answer x = [3]
8 p varies directly as the square root of q.
p = 8 when q = 25.
Find p when q = 100.
Answer p = [3]
9 Ashraf takes 1500 steps to walk d metres from his home to the station.
Each step is 90 centimetres correct to the nearest 10cm.
Find the lower bound and the upper bound for d.
Answer Y d [3]

5
For
Examiner's
Use
10 The table shows the opening and closing times of a café.
Mon Tue Wed Thu Fri Sat Sun
Opening time 0600 0600 0600 0600 0600 (a) 0800
Closing time 2200 2200 2200 2200 2200 2200 1300
(a) The café is open for a total of 100 hours each week.
Work out the opening time on Saturday.
Answer(a) [2]
(b) The owner decides to close the café at a later time on Sunday. This increases the total number
of hours the café is open by 4%.
Work out the new closing time on Sunday.
Answer(b) [1]
11 Rearrange the formula c =
ba −
4
to make a the subject.
Answer a = [3]

6
© UCLES 2011 0580/22/M/J/11
For
Examiner's
Use
x – 5y = 0
15x + 10y = 17
Answer x =
y = [3]
13
O
y°
z°
x°54°
Q
R
P T
NOT TO
SCALE
The points P, Q and R lie on a circle, centre O.
TP and TQ are tangents to the circle.
Angle TPQ = 54°.
Calculate the value of
(a) x,
Answer(a) x = [1]
(b) y,
Answer(b) y = [1]
(c) z.
Answer(c) z = [2]

7
For
Examiner's
Use
14 60 students recorded their favourite drink.
The results are shown in the pie chart.
66°
120°
Banana
shake
Apple
juice
Lemonade
Cola
NOT TO
SCALE
(a) Calculate the angle for the sector labelled Lemonade.
Answer(a) [1]
(b) Calculate the number of students who chose Banana shake.
Answer(b) [1]
(c) The pie chart has a radius of 3cm.
Calculate the arc length of the sector representing Cola.
Answer(c) cm [2]

8
© UCLES 2011 0580/22/M/J/11
For
Examiner's
Use
15 Write the following as a single fraction in its simplest form.
5
1
+
+
x
x
–
1+x
x
Answer [4]
16
C
O
B
A
a
c
P
M
Q
NOT TO
SCALE
O is the origin and OABC is a parallelogram.
CP = PB and AQ = QB.
= a and = c .
Find in terms of a and c, in their simplest form,
(a) ,
Answer(a) = [2]
(b) the position vector of M, where M is the midpoint of PQ.
Answer(b) [2]

9
For
Examiner's
Use
17 Simplify
(a) 32x8
÷ 8x32
,
Answer(a) [2]
(b)
3
2
3
64 




 x
.
Answer(b) [2]
18
4
3
2
1
1 2 3 4 5 6 7
0
y
x
C
B
A
The lines AB and CB intersect at B.
(a) Find the co-ordinates of the midpoint of AB.
Answer(a) ( , ) [1]
(b) Find the equation of the line CB.
Answer(b) [3]

10
© UCLES 2011 0580/22/M/J/11
For
Examiner's
Use
19 f(x) = x2
g(x) = 2x
h(x) = 2x – 3
(a) Find g(3).
Answer(a) [1]
(b) Find hh(x) in its simplest form.
Answer(b) [2]
(c) Find fg(x + 1) in its simplest form.
Answer(c) [2]

11
For
Examiner's
Use
20
A
B
C
(a) On the diagram above, using a straight edge and compasses only, construct
(i) the bisector of angle ABC, [2]
(ii) the locus of points which are equidistant from A and from B. [2]
(b) Shade the region inside the triangle which is nearer to A than to B and nearer to AB than to BC.
[1]

12
© UCLES 2011 0580/22/M/J/11
For
Examiner's
Use
21 (a)
A = ( )32 B = 





− 4
6
(i) Work out AB.
Answer(a)(i) [2]
(ii) Work out BA.
Answer(a)(ii) [2]
(b) C = 





1
1
1
3
Find C–1
, the inverse of C.
Answer(b) [2]

IB10 11_0580_22/3RP
*8109996876*
MATHEMATICS 0580/22
1 hour 30 minutes

2
© UCLES 2010 0580/22/O/N/10
For
Examiner's
Use
1
For the diagram, write down
(a) the order of rotational symmetry,
Answer(a) [1]
(b) the number of lines of symmetry.
Answer(b) [1]
2 In a group of 30 students, 18 have visited Australia, 15 have visited Botswana and 5 have not visited
either country.
Work out the number of students who have visited Australia but not Botswana.
Answer [2]
3 Rearrange the formula J = mv – mu to make m the subject.
Answer m = [2]

3
For
Examiner's
Use
4
O is the centre of the circle.
DA is the tangent to the circle at A and DB is the tangent to the circle at C.
AOB is a straight line. Angle COB = 50°.
Calculate
(a) angle CBO,
Answer(a) Angle CBO = [1]
(b) angle DOC.
Answer(b) Angle DOC = [1]
5
JGR is a right-angled triangle. JR = 50m and JG = 20m.
Calculate angle JRG.
Answer Angle JRG = [2]
6 Write 0.00658
(a) in standard form,
Answer(a) [1]
(b) correct to 2 significant figures.
Answer(b) [1]
J
G R
50m
20m
NOT TO
SCALE
50°
O
A
D
C
B
NOT TO
SCALE

4
© UCLES 2010 0580/22/O/N/10
For
Examiner's
Use
7 = a + tb and = a + (3t – 5)b where t is a number.
Find the value of t when = .
Answer t = [2]
8 Show that
27
7
+
9
7
1 =
27
1
2 .
Answer
[2]
9 When a car wheel turns once, the car travels 120cm, correct to the nearest centimetre.
Calculate the lower and upper bounds for the distance travelled by the car when the wheel turns 20
times.
Answer lower bound cm
upper bound cm [2]

5
For
Examiner's
Use
10
140°
140° 140°
A B
C
D
E
NOT TO
SCALE
The pentagon has three angles which are each 140°.
The other two interior angles are equal.
Calculate the size of one of these angles.
Answer [3]
11 The resistance, R, of an object being towed through the water varies directly as the square of the
speed, v.
R = 50 when v = 10.
Find R when v = 16.
Answer R = [3]
12 Write as a single fraction, in its simplest form.
1
2
2
3
−
−
+ xx
Answer [3]

6
© UCLES 2010 0580/22/O/N/10
For
Examiner's
Use
13
NOT TO
SCALE
The diagram shows a circle of radius 5cm in a square of side 18cm.
Calculate the shaded area.
Answer cm2
[3]
14
Draw, accurately, the locus of all the points outside the triangle which are 3 centimetres away from
the triangle. [3]

7
For
Examiner's
Use
15 The air fare from Singapore to Stockholm can be paid for in Singapore dollars (S$) or Malaysian
Ringitts (RM).
One day the fare was S$740 or RM1900 and the exchange rate was S$1= RM2.448 .
How much less would it cost to pay in Singapore dollars?
Give your answer in Singapore dollars correct to the nearest Singapore dollar.
Answer S$ [3]
16 Simplify
(a)
2
1
16
81
16






x ,
Answer(a) [2]
(b)
10 4
7
16 4
32
y y
y
−
×
.
Answer(b) [2]
17
Boys Girls Total
Asia 62 28
Europe 35 45
Africa 17
Total 255
For a small international school, the holiday destinations of the 255 students are shown in the table.
(a) Complete the table. [3]
(b) What is the probability that a student chosen at random is a girl going on holiday to Europe?
Answer(b) [1]

8
© UCLES 2010 0580/22/O/N/10
For
Examiner's
Use
18
2 4
=
5 3
 
  
 
A
3 4
=
5 2
−
−
 
  
 
B
(a) Work out AB.
Answer(a) [2]
(b) Find | B |, the determinant of B.
Answer(b) [1]
(c) I is the (2 × 2) identity matrix.
Find the matrix C, where C = A – 7I .
Answer(c) [2]

9
For
Examiner's
Use
19
M
C B
P
D A
8cm
10cm
10cm
NOT TO
SCALE
The diagram represents a pyramid with a square base of side 10 cm.
The diagonals AC and BD meet at M. P is vertically above M and PB = 8cm.
(a) Calculate the length of BD.
Answer(a) BD = cm [2]
(b) Calculate MP, the height of the pyramid.
Answer(b) MP = cm [3]

10
© UCLES 2010 0580/22/O/N/10
For
Examiner's
Use
20
0
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8
y
x
(a) Draw the lines y = 2, x + y = 6 and y = 2x on the grid above. [4]
(b) Label the region R which satisfies the three inequalities
x + y [ 6, y [ 2 and y Y 2x. [1]

11
For
Examiner's
Use
21 An animal starts from rest and accelerates to its top speed in 7 seconds. It continues at this speed for
9 seconds and then slows to a stop in a further 4 seconds.
The graph shows this information.
14
12
10
8
6
4
2
0
2 4 6 8 10 12 14 16 18 20
Speed
(m/s)
Time (seconds)
(a) Calculate its acceleration during the first seven seconds.
Answer(a) m/s2
[1]
(b) Write down its speed 18 seconds after the start.
Answer(b) m/s [1]
(c) Calculate the total distance that the animal travelled.
Answer(c) m [3]

12
© UCLES 2010 0580/22/O/N/10
For
Examiner's
Use
22 (a) The line y = 2x + 7 meets the y-axis at A.
Write down the co-ordinates of A.
Answer(a) A = ( , ) [1]
(b) A line parallel to y = 2x + 7 passes through B(0, 3).
(i) Find the equation of this line.
Answer(b)(i) [2]
(ii) C is the point on the line y = 2x + 1 where x = 2.
Find the co-ordinates of the midpoint of BC.
Answer(b)(ii) ( , ) [3]

IB10 06_0580_22/3RP
*2073403047*
MATHEMATICS 0580/22
1 hour 30 minutes

2
© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
1
For the diagram, write down
Answer(a) [1]
Answer(b) [1]
2 Calculate 3sin120° − 4(sin120°)3
.
Answer [2]
3 Write the following in order of size, smallest first.
2
3
2 3− 3
3
2
2
−
Answer [2]

3
For
Examiner's
Use4 Write as a single fraction
8
3a
+
5
4
.
Answer [2]
5 Write 28
× 82
× 4
-2
in the form 2n
.
Answer [2]
6 Change 64 square metres into square millimetres.
Answer mm2
[2]
7
A B
C
The shaded area in the diagram shows the set (A ∩ C ) ∩ B'.
Write down the set shown by the shaded area in each diagram below.
A B
C
A B
C
[2]

4
© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
8
0.5
1
0
30° 60° 90° 120° 150° 180°
–1
–0.5
y
x
y = sinx
y = cosx
The diagram shows accurate graphs of y = sinx and y = cosx for 0° Y x Y 180°.
Use the graph to solve the equations
(a) sinx – cosx = 0,
Answer(a) x = [1]
(b) sinx – cosx = 0.5.
Answer(b) x = [2]
9 A fence is made from 32 identical pieces of wood, each of length 2 metres correct to the nearest
centimetre.
Calculate the lower bound for the total length of the wood used to make this fence.
Write down your full calculator display.
Answer m [3]

5
For
Examiner's
Use
10 Make x the subject of the formula.
3x
P
x
+
=
Answer x = [4]
11
O
Q
C
P T
6cm
4cm
NOT TO
SCALE
Two circles, centres O and C, of radius 6cm and 4cm respectively, touch at Q.
PT is a tangent to both circles.
(a) Write down the distance OC.
Answer(a) OC = cm [1]
(b) Calculate the distance PT.
Answer(b) PT = cm [3]

6
© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
12 The diagram represents the ski lift in Queenstown New Zealand.
37.1°
B
T
h
730m
NOT TO
SCALE
(a) The length of the cable from the bottom, B, to the top, T, is 730 metres.
The angle of elevation of T from B is 37.1°.
Calculate the change in altitude, h metres, from the bottom to the top.
Answer(a) m [2]
(b) The lift travels along the cable at 3.65 metres per second.
Calculate how long it takes to travel from B to T.
Give your answer in minutes and seconds.
Answer(b) min s [2]

7
For
Examiner's
Use
13
M =
6 3
4 5 1
x−  
  
  
.
(a) Find the matrix M.
Answer(a) M = [2]
(b) Simplify ( x 1 ) M.
Answer(b) [2]
14
y
x
–2–4 4 6 8 10 12 14 16 1820
10
8
6
4
2
By shading the unwanted regions of the grid above, find and label the region R which satisfies the
following four inequalities.
y [ 2 x + y [ 6 y Y x + 4 x + 2y Y 18 [4]

8
© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
15
0
y = 4
x
y
4 A
B
2x + y = 8 3x + y = 18
NOT TO
SCALE
(a) The line y = 4 meets the line 2x + y = 8 at the point A.
Find the co-ordinates of A.
Answer(a) A ( , ) [1]
(b) The line 3x + y = 18 meets the x axis at the point B.
Find the co-ordinates of B.
Answer(b) B ( , ) [1]
(c) (i) Find the co-ordinates of the mid-point M of the line joining A to B.
Answer(c)(i) M ( , ) [1]
(ii) Find the equation of the line through M parallel to 3x + y = 18.
Answer(c)(ii) [2]

9
For
Examiner's
Use
16 The graphs show the speeds of two cyclists, Alonso and Boris.
Alonso accelerated to 10 m/s, travelled at a steady speed and then slowed to a stop.
0
2 4 6 8 10 12 14 16
10
Speed
(m/s)
Time (seconds)
Alonso
Boris accelerated to his maximum speed, v m/s, and then slowed to a stop.
0 16
v
Speed
(m/s)
Time (seconds)
Boris
NOT TO
SCALE
Both cyclists travelled the same distance in the 16 seconds.
Calculate the maximum speed for Boris.
Answer m/s [5]

10
© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
17
O
Q R
S
T
UV
W
P
NOT TO
SCALE
8m
The diagram shows the junction of four paths.
In the junction there is a circular area covered in grass.
This circle has centre O and radius 8m.
(a) Calculate the area of grass.
Answer(a) m2
[2]
(b)
O
Q
P
12m
45°
NOT TO
SCALE
The arc PQ and the other three identical arcs, RS, TU and VW are each part of a circle, centre O,
radius 12m.
The angle POQ is 45°.
The arcs PQ, RS, TU, VW and the circumference of the circle in part(a) are painted white.
Calculate the total length painted white.
Answer(b) m [4]

11
For
Examiner's
Use
18 (a) f(x) = 1 – 2x.
(i) Find f(-5).
Answer(a)(i) [1]
(ii) g(x) = 3x – 2.
Find gf(x). Simplify your answer.
Answer(a)(ii) [2]
(b) h(x) = x2
– 5x – 11.
Solve h(x) = 0.
Show all your working and give your answer correct to 2 decimal places.
Answer(b) x = or x = [4]

12
© UCLES 2010 0580/22/M/J/10
For
Examiner's
Use
19 The braking distance, d metres, for Alex’s car travelling at v km/h is given by the formula
200d = v(v + 40).
(a) Calculate the missing values in the table.
v
(km/h)
0 20 40 60 80 100 120
d
(metres)
0 16 48 96
[2]
(b) On the grid below, draw the graph of 200d = v(v + 40) for 0 Y v Y 120.
120110100908070605040302010
100
90
80
70
60
50
40
30
20
10
0
Distance
(metres)
d
v
Speed (km/h)
[3]
(c) Find the braking distance when the car is travelling at 110km/h.
Answer(c) m [1]
(d) Find the speed of the car when the braking distance is 80m.
Answer(d) km/h [1]

IB09 11_0580_22/2RP
*3712448579*
MATHEMATICS 0580/22
1 hour 30 minutes

2
© UCLES 2009 0580/22/O/N/09
For
Examiner's
Use
1
For the diagram above write down
Answer(a) [1]
Answer(b) [1]
2 Write down the next two prime numbers after 31.
Answer and [2]
3 Use your calculator to find the value of
o 2 o 2
o o
_(cos30 ) (sin30 )
2(sin120 )(cos120 )
.
Answer [2]
4 Simplify
5
8
x
3
2
÷
1
2
x
5
2
_
.
Answer [2]

3
For
Examiner's
Use
5 In 1977 the population of China was 9.5 x 108
.
In 2007 the population of China was 1.322 x 109
.
Calculate the population in 2007 as a percentage of the population in 1977.
Answer %[2]
6
A = 0 1
4 12− −
B =
3 4
0 4−
Calculate the value of 5 |A| + |B|, where |A| and |B| are the determinants of A and B.
Answer [2]
7 Shade the region required in each Venn Diagram.
A
C
B
B' ∩(A ∩ C)
A
C
B
B' ∩(A ∪ C)
[2]

4
© UCLES 2009 0580/22/O/N/09
For
Examiner's
Use
8 Find the length of the line joining the points A(−2, 10) and B(−8, 2).
Answer AB = [2]
9 Solve the simultaneous equations
6x + 18y = 57,
2x – 3y = −8.
Answer x =
y = [3]
10 The braking distance, d, of a car is directly proportional to the square of its speed, v.
When d = 2, v = 5.
Find d when v = 40.
Answer d = [3]

5
For
Examiner's
Use
11
20cm
20cm
12cm 12cm
12cm 12cm
12cm
NOT TO
SCALE
12cm
20cm 20cm
20cm 20cm
Each of the lengths 20cm and 12cm is measured correct to the nearest centimetre.
Calculate the upper bound for the perimeter of the shape.
Answer cm [3]
12 Simplify 16 – 4(3x – 2)2
.
Answer [3]

6
© UCLES 2009 0580/22/O/N/09
For
Examiner's
Use
13 Solve the inequality 6(2 − 3x) − 4(1 − 2x)=Y= 0.
Answer [3]
14 Zainab borrows $249 from a bank to pay for a new bed.
The bank charges compound interest at 1.7% per month.
Calculate how much interest she owes at the end of 3 months.
Give your answer correct to 2 decimal places.
Answer $ [3]
15
M
O R
P Q
r
p
O is the origin and OPQR is a parallelogram whose diagonals intersect at M.
The vector OP is represented by p and the vector is represented by r.
(a) Write down a single vector which is represented by
(i) p + r,
Answer(a)(i) [1]
(ii)
2
1 p –
2
1 r.
Answer(a)(ii) [1]
(b) On the diagram, mark with a cross (x) and label with the letter S the point with position vector
2
1 p +
4
3 r. [2]

7
For
Examiner's
Use
16
85°
North
North
B
A
C
3km
3km
NOT TO
SCALE
A, B and C are three places in a desert. Tom leaves A at 0640 and takes 30 minutes to walk directly
to B, a distance of 3 kilometres. He then takes an hour to walk directly from B to C, also a distance of
3 kilometres.
(a) At what time did Tom arrive at C?
Answer (a) [1]
(b) Calculate his average speed for the whole journey.
Answer (b) km/h [2]
(c) The bearing of C from A is 085°.
Find the bearing of A from C.
Answer (c) [1]
17 (a) In 2007, a tourist changed 4000 Chinese Yuan into pounds (£) when the exchange rate was
£1 = 15.2978 Chinese Yuan.
Calculate the amount he received, giving your answer correct to 2 decimal places.
Answer(a) £ [2]
(b) In 2006, the exchange rate was £1 = 15.9128 Chinese Yuan.
Calculate the percentage decrease in the number of Chinese Yuan for each £1 from
2006 to 2007.
Answer(b) % [2]

8
© UCLES 2009 0580/22/O/N/09
For
Examiner's
Use
18
y = mx + c
y = 2x + 8
y
x
9 units
A B
NOT TO
SCALE
The line y = mx + c is parallel to the line y =2x + 8.
The distance AB is 9 units.
Find the value of m and the value of c.
Answer m = and c = [4]

9
For
Examiner's
Use
19
D
E
FA
O
B
C
68°
NOT TO
SCALE
Points A, B and C lie on a circle, centre O, with diameter AB.
BD, OCE and AF are parallel lines.
Angle CBD = 68°.
Calculate
(a) angle BOC,
Answer(a) Angle BOC = [2]
(b) angle ACE.
Answer(b) Angle ACE = [2]

10
© UCLES 2009 0580/22/O/N/09
For
Examiner's
Use
20 The number of hours that a group of 80 students spent using a computer in a week was recorded.
The results are shown by the cumulative frequency curve.
80
60
40
20
0
10 20 30 40 50 60 70
Cumulative
frequency
Number of hours
Use the cumulative frequency curve to find
(a) the median,
Answer(a) h [1]
(b) the upper quartile,
Answer(b) h [1]
(c) the interquartile range,
Answer(c) h [1]
(d) the number of students who spent more than 50 hours using a computer in a week.
Answer(d) [2]

11
For
Examiner's
Use
21
40
30
20
10
0
10 20 30 40 50 60
Speed
(m/s)
Time (seconds)
car
truck
The graph shows the speed of a truck and a car over 60 seconds.
(a) Calculate the acceleration of the car over the first 45 seconds.
Answer(a) m/s2
[2]
(b) Calculate the distance travelled by the car while it was travelling faster than the truck.
Answer(b) m [3]

12
© UCLES 2009 0580/22/O/N/09
For
Examiner's
Use
22 f(x) = 4x + 1 g(x) = x3
+ 1 h(x) =
3
12 +x
(a) Find the value of gf(0).
Answer(a) [2]
(b) Find fg(x). Simplify your answer.
Answer(b) [2]
(c) Find h -1
(x).
Answer(c) [2]

IB09 06_0580_22/FP
*8649386434*
MATHEMATICS 0580/22, 0581/22
1 hour 30 minutes
Second Variant Question Paper

2
© UCLES 2009 0580/22/M/J/09
For
Examiner's
Use
For
Examiner's
Use
1
(a) Write down the order of rotational symmetry of the diagram.
Answer(a) [1]
(b) Draw all the lines of symmetry on the diagram. [1]
74%
8
15
18
25
_
1
27
20
 
 
 
Answer [2]
3 At 0518 Mr Ho bought 950 fish at a fish market for $3.08 each.
85 minutes later he sold them all to a supermarket for $3.34 each.
(a) What was the time when he sold the fish?
Answer(a) [1]
(b) Calculate his total profit.
Answer(b) $ [1]

3
For
Examiner's
Use
4 Shade the region required in each Venn Diagram.
A
C
B A B
A ∩ B ∩ C A ∪ B′ [2]
5 A =
_ 6 7
3_ 4
 
 
 
Find A–1
, the inverse of the matrix A.
Answer
 
 
 
 
  [2]
6 In 2005 there were 9 million bicycles in Beijing, correct to the nearest million.
The average distance travelled by each bicycle in one day was 6.5km correct to one decimal place.
Work out the upper bound for the total distance travelled by all the bicycles in one day.
Answer km [2]
7 Find the co-ordinates of the mid-point of the line joining the points A(4, –7) and B(8, 13).
Answer ( , ) [2]

4
© UCLES 2009 0580/22/M/J/09
For
Examiner's
Use
8
O
G
A
F
B
E
C
D
a
g
The diagram is made from three identical parallelograms.
O is the origin. = a and = g.
Write down in terms of a and g
(a) ,
Answer(a) [1]
(b) the position vector of the centre of the parallelogram BCDE.
Answer(b) [1]
9 Rearrange the formula to make y the subject.
x +
8
y
= 1
Answer y = [3]
10 Write
1
c
+
1
d
–
_c d
cd
as a single fraction in its simplest form.
Answer [3]

5
For
Examiner's
Use
11 In January Sunanda changed £20000 into dollars when the exchange rate was $3.92 = £1.
In June she changed the dollars back into pounds when the exchange rate was $3.50 = £1.
Calculate the profit she made, giving your answer in pounds (£).
Answer £ [3]
12 Solve the simultaneous equations
2x + 3y = 4,
y = 2x – 12.
Answer x =
y = [3]
13 A spray can is used to paint a wall.
The thickness of the paint on the wall is t. The distance of the spray can from the wall is d.
t is inversely proportional to the square of d.
t = 0.4 when d = 5.
Find t when d = 4.
Answer t = [3]

6
© UCLES 2009 0580/22/M/J/09
For
Examiner's
Use
14 (a) There are 109
nanoseconds in 1 second.
Find the number of nanoseconds in 8 minutes, giving your answer in standard form.
Answer(a) [2]
(b) Solve the equation 5(x + 3×106
) = 4×107
.
Answer(b) x = [2]
15
18°
25°
h
T
B A
C
80m
NOT TO
SCALE
Mahmoud is working out the height, h metres, of a tower BT which stands on level ground.
He measures the angle TAB as 25°.
He cannot measure the distance AB and so he walks 80 m from A to C, where angle ACB = 18° and
angle ABC = 90°.
Calculate
(a) the distance AB,
Answer(a) m [2]
(b) the height of the tower, BT.
Answer(b) m [2]

7
For
Examiner's
Use
16 Using a straight edge and compasses only, draw the locus of all points inside the quadrilateral
ABCD which are equidistant from the lines AC and BD.
Show clearly all your construction arcs.
A
B
D
C
[4]

8
© UCLES 2009 0580/22/M/J/09
For
Examiner's
Use
17
y
x
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8
A
B
(a) Describe fully the single transformation which maps triangle A onto triangle B.
Answer(a) [2]
(b) On the grid, draw the image of triangle A after rotation by 90° clockwise about the point (4, 4).
[2]
18 Two similar vases have heights which are in the ratio 3:2.
(a) The volume of the larger vase is 1080cm3
.
Calculate the volume of the smaller vase.
Answer(a) cm3
[2]
(b) The surface area of the smaller vase is 252cm2
.
Calculate the surface area of the larger vase.
Answer(b) cm2
[2]

9
For
Examiner's
Use
19
A
D
F
G
C
B
H
E
O
40°
6cm
12cm
NOT TO
SCALE
The diagram shows part of a fan.
OFG and OAD are sectors, centre O, with radius 18 cm and sector angle 40°.
B, C, H and E lie on a circle, centre O and radius 6 cm.
Calculate the shaded area.
Answer cm2
[4]

10
© UCLES 2009 0580/22/M/J/09
For
Examiner's
Use
20
6
5
4
3
2
1
0
–1
–2
–3
–4
–5
y
x
1 2 3 4 5 6
(a) Draw the three lines y = 4, 2x – y = 4 and x + y = 6 on the grid above. [4]
(b) Write the letter R in the region defined by the three inequalities below.
y Y 4 2x – y [ 4 x + y [ 6 [1]

11
For
Examiner's
Use
21
=
6
4 3
x 
 
 
A =
2 3
2 1
 
 
 
B
(a) Find AB.
Answer(a)
 
 
 
 
  [2]
(b) When AB = BA, find the value of x.
Answer(b) x = [3]
Question 22 is on the next page

12
© UCLES 2009 0580/22/M/J/09
For
Examiner's
Use
22
AP T
B
C
D
O
34°
58°
NOT TO
SCALE
A, B, C and D lie on the circle, centre O.
BD is a diameter and PAT is the tangent at A.
Angle ABD = 58° and angle CDB = 34°.
Find
(a) angle ACD,
Answer(a) Angle ACD = [1]
(b) angle ADB,
Answer(b) Angle ADB = [1]
(c) angle DAT,
Answer(c) Angle DAT = [1]
(d) angle CAO.
Answer(d) Angle CAO = [2]

IB08 11_0580_22/3RP
*2077738702*
For Examiner's Use
MATHEMATICS 0580/22, 0581/22
1 hour 30 minutes
DO NOT WRITE IN THE BARCODE.

2
© UCLES 2008 0580/22/O/N/08
For
Examiner's
Use
1
For this diagram, write down
Answer(a) [1]
Answer(b) [1]
2
–2
1
8
3
1
0
9
4
1
3
0
4
3
2
The answer to this matrix multiplication is of order a × b.
Find the values of a and b.
Answer a = b = [2]
3 Work out the value of 1 + 2
43 +
5 + 6
.
Answer [2]

3
For
Examiner's
Use
4 A light on a computer comes on for 38500 microseconds.
One microsecond is 10-6
seconds.
Work out the length of time, in seconds, that the light is on
(a) in standard form,
Answer(a) s [1]
(b) as a decimal.
Answer(b) s [1]
5
A B
D C
ABCD is a square.
It is rotated through 90° clockwise about B.
Draw accurately the locus of the point D. [2]

4
© UCLES 2008 0580/22/O/N/08
For
Examiner's
Use
6 sin x° = 0.707107 and 0 Y x Y 180.
Find the two values of x.
Answer x = or x = [2]
7 A rectangle has sides of length 2.4cm and 6.4cm correct to 1 decimal place.
Calculate the upper bound for the area of the rectangle as accurately as possible.
Answer cm2
[2]
8 (a) Factorise ax2
+ bx2
.
Answer(a) [1]
(b) Make x the subject of the formula
ax2
+ bx2
– d2
= p2
.
Answer(b) x = [2]

5
For
Examiner's
Use
9
y
x
y =
2x +
5
A
CO
B
NOT TO
SCALE
The distance AB is 11 units.
(a) Write down the equation of the line through B which is parallel to y = 2x + 5.
Answer(a) [2]
(b) Find the co-ordinates of the point C where this line crosses the x axis.
Answer(b) ( , ) [1]
10 Solve these simultaneous equations.
x + 3y – 11 = 0
3x – 4y – 7 = 0
Answer x =
y = [3]

6
© UCLES 2008 0580/22/O/N/08
For
Examiner's
Use
11 Write as a single fraction in its simplest form
5 2_
_5 +1 2 3x x
.
Answer [3]
_2 5 2 .
7 5
x
Answer [3]
13 The quantity p varies inversely as the square of (q + 2).
p = 4 when q = 2.
Find p when q = 8.
Answer p = [3]

7
For
Examiner's
Use
14 A spacecraft made 58376 orbits of the Earth and travelled a distance of 2.656 × 109
kilometres.
(a) Calculate the distance travelled in 1 orbit correct to the nearest kilometre.
Answer(a) km [2]
(b) The orbit of the spacecraft is a circle.
Calculate the radius of the orbit.
Answer(b) km [2]
15 f(x) = tan x°, g(x) = 2x + 6.
Find
(a) f(45),
Answer(a) [1]
(b) fg(87),
Answer(b) [2]
(c) g-1
(f(x)).
Answer(c) [2]

8
© UCLES 2008 0580/22/O/N/08
For
Examiner's
Use
16 In an experiment, the number of bacteria, N, after x days, is N = 1000 × 1.4x
.
(a) Complete the table.
x 0 1 2 3 4
N
[2]
(b) Draw a graph to show this information.
5000
4000
3000
2000
1000
0
1 2 3 4
N
x
[2]
(c) How many days does it take for the number of bacteria to reach 3000?
Give your answer correct to 1 decimal place.
Answer(c) days [1]

9
For
Examiner's
Use
17
A
B
C
O
q
p
O is the origin. Vectors p and q are shown in the diagram.
(a) Write down, in terms of p and q, in their simplest form
(i) the position vector of the point A,
Answer(a)(i) [1]
(ii) BC ,
Answer(a)(ii) [1]
(iii) BC − AC.
Answer(a)(iii) [2]
(b) If | p | = 2, write down the value of | AB |.
Answer(b) [1]

10
© UCLES 2008 0580/22/O/N/08
For
Examiner's
Use
18
20
10
30
0 180160 20014012010080604020
Tanah Merah ExpoTime (s)
Speed
(m/s)
The graph shows the train journey between Tanah Merah and Expo in Singapore.
Work out
(a) the acceleration of the train when it leaves Tanah Merah,
Answer(a) m/s2
[2]
(b) the distance between Tanah Merah and Expo,
Answer(b) m [3]
(c) the average speed of the train for the journey.
Answer(c) m/s [1]

11
For
Examiner's
Use
19
P
Q
30°O
S
R
10cm
5cm
NOT TO
SCALE
OPQ is a sector of a circle, radius 10cm, centre O. Angle POQ = 50°.
ORS is a sector of a circle, radius 5cm, also centre O. Angle ROS = 30°.
(a) Calculate the shaded area.
Answer(a) cm2
[3]
(b) Calculate the perimeter of the shaded area, PORSOQP.
Answer(b) cm [3]
Question 20 is on page 12

12
© UCLES 2008 0580/22/O/N/08
For
Examiner's
Use
20 A new school has x day students and y boarding students.
The fees for a day student are $600 a term.
The fees for a boarding student are $1200 a term.
The school needs at least $720000 a term.
(a) Show that this information can be written as x + 2y [ 1200.
Answer (a)
[1]
(b) The school has a maximum of 900 students.
Write down an inequality in x and y to show this information.
Answer(b) [1]
(c) Draw two lines on the grid below and write the letter R in the region which represents these two
inequalities.
y
x
900
0
1200
Number of
boarding
students
Number of day students
[4]
(d) What is the least number of boarding students at the school?
Answer(d) [1]

IB08 06_0580_22/RP
*0499803612*
For Examiner's Use
MATHEMATICS 0580/22, 0581/22
1 hour 30 minutes
DO NOT WRITE IN ANY BARCODES

2
© UCLES 2008 0580/22/M/J/08
For
Examiner's
Use
1 Write down the next two prime numbers after 53.
Answer and [2]
2 Simplify 7 7_+
3 9 18
x x x .
Answer [2]
3 Lin scored 21 marks in a test and Jon scored 15 marks.
Calculate Lin’s mark as a percentage of Jon’s mark.
Answer % [2]
4 (a) The formula for the nth term of the sequence
1, 5, 14, 30, 55, 91, … is
6
1)1)(2( ++ nnn
.
Find the 15th term.
Answer(a) [1]
(b) The nth term of the sequence 17, 26, 37, 50, 65,... is (n + 3)2
+ 1.
Write down the formula for the nth term of the sequence 26, 37, 50, 65, 82,…
Answer(b) [1]

3
For
Examiner's
Use
5 A holiday in Europe was advertised at a cost of €330.
The exchange rate was $1 = €1.07.
Calculate the cost of the holiday in dollars, giving your answer correct to the nearest cent.
Answer $ [2]
399
401
598
601
698
701
Answer [2]
7 Write the number 2045.4893 correct to
(a) 2 decimal places,
Answer(a) [1]
(b) 2 significant figures.
Answer(b) [1]
8 Simplify (16x4
)
3
4 .
Answer [2]

4
© UCLES 2008 0580/22/M/J/08
For
Examiner's
Use
9 A straight line passes through two points with co-ordinates (6,10) and (0, 7).
Work out the equation of the line.
Answer [3]
10 A cylindrical glass has a radius of 4 centimetres and a height of 6 centimetres.
A large cylindrical jar full of water is a similar shape to the glass.
The glass can be filled with water from the jar exactly 216 times.
Work out the radius and height of the jar.
Answer radius cm
height cm [3]
11
A xcm
3xcm
26cm
B
C
NOT TO
SCALE
120°
In triangle ABC, AB = 3xcm, AC = xcm, BC = 26cm and angle BAC = 120°.
Calculate the value of x.
Answer x = [3]

5
For
Examiner's
Use
12 = {1,2,3,4,5,6,7,9,11,16} P = {2,3,5,7,11} S = {1,4,9,16} M = {3,6,9}
(a) Draw a Venn diagram to show this information.
[2]
(b) Write down the value of n(M′∩P).
Answer(b) [1]
_2 5
8
x K== + 4
3
x .
Answer [3]

6
© UCLES 2008 0580/22/M/J/08
For
Examiner's
Use
14 Sitora has two plants in her school classroom.
Plant A needs a lot of light and must not be more than 2.5metres from the window.
Plant B needs very little light and must be further from the window than from the door.
For each plant, draw accurately the boundary of the region in which it can be placed.
In the diagram, 1centimetre represents 1metre.
door window
[3]
15 Work out
2 1 2
1 5 0
_
3 2 4
4
_
3
_ 8
.
Answer [3]

7
For
Examiner's
Use
16 Find the co-ordinates of the point of intersection of the straight lines
2x + 3y = 11,
3x – 5y = −12.
Answer ( , ) [3]
17 A student played a computer game 500 times and won 370 of these games.
He then won the next x games and lost none.
He has now won 75% of the games he has played.
Answer x = [4]

8
© UCLES 2008 0580/22/M/J/08
For
Examiner's
Use
18 f(x) = x3
− 3x2
+ 6x – 7 and g(x) = 2x − 3.
Find
(a) f(−1),
Answer(a) [1]
(b) gf(x),
Answer(b) [2]
(c) g−1
(x).
Answer(c) [2]

9
For
Examiner's
Use
19
–5 –4 –3 –2 –1 1 2 3 4 50
5
4
3
2
1
–1
–2
–3
–4
–5
y
x
B
A
(a) A transformation is represented by the matrix
_10
_1 0
.
(i) On the grid above, draw the image of triangle A after this transformation.
[2]
(ii) Describe fully this transformation.
Answer(a)(ii) [2]
(b) Find the 2 by 2 matrix representing the transformation which maps triangle A onto triangle B.
Answer(b) [2]

10
© UCLES 2008 0580/22/M/J/08
For
Examiner's
Use
NOT TO
SCALE
beach sea 95°
100m
160m
O
A
B
C
D
20 The shaded area shows a beach.
AD and BC are circular arcs, centre O.
OB = 160m, OD = 100m and angle AOD = 95°.
(a) Calculate the area of the beach ABCD in square metres.
Answer(a) m2
[3]
(b) The beach area is covered in sand to a depth of 1.8m.
Calculate the volume of the sand in cubic metres.
Answer(b) m3
[1]
(c) Write both the following answers in standard form.
(i) Change your answer to part(b) into cubic millimetres.
Answer(c)(i) mm3
[1]
(ii) Each grain of sand has a volume of 2mm3
correct to the nearest mm3
.
Calculate the maximum possible number of grains of sand on the beach.
Answer(c)(ii) [2]

11
© UCLES 2008 0580/22/M/J/08
For
Examiner's
Use
21
800m
600m
200m
A D
C
FE
B
NOT TO
SCALE
N
ABCD, BEFC and AEFD are all rectangles.
ABCD is horizontal, BEFC is vertical and AEFD represents a hillside.
AF is a path on the hillside.
AD = 800m, DC = 600m and CF = 200m.
(a) Calculate the angle that the path AF makes with ABCD.
Answer(a) [5]
(b) In the diagram D is due south of C.
Jasmine walks down the path from F to A in bad weather. She cannot see the path ahead.
The compass bearing she must use is the bearing of A from C.
Calculate this bearing.
Answer(b) [3]

12
0580/22/M/J/08
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Igcse maths paper 2

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Igcse maths paper 2