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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
*4065843724*
0580/22
MATHEMATICS
May/June 2011
Paper 2 (Extended)
1 hour 30 minutes
Candidates answer on the Question Paper.
Additional Materials:
Electronic calculator
Mathematical tables (optional)
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 a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, 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 π , use either your calculator value or 3.142.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 70.
This document consists of 12 printed pages.
IB11 06_0580_22/8RP
© UCLES 2011
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![2
1
4
In the right-angled triangle ABC, cos C =
For
Examiner's
Use
. Find angle A.
5
A
NOT TO
SCALE
B
C
Answer Angle A =
2
Which of the following numbers are irrational?
2
3
36
3 +
6
π
0.75
Answer
3
[2]
Show that
1
5
9
÷1
7
9
=
7
8
48%
8
1
3
[2]
.
Write down all the steps in your working.
Answer
[2]
© UCLES 2011
0580/22/M/J/11](https://image.slidesharecdn.com/0580s11qp22-140108111658-phpapp02/75/0580-s11-qp_22-2-2048.jpg)
![3
3
4
5
2
< p <
For
Examiner's
Use
3
Which of the following could be a value of p?
16
27
0.67
60%
(0.8)2
4
9
Answer
5
[2]
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?
Write down all the steps in your working.
Answer
Answer
6
Use your calculator to find the value of 2
3
[2]
[2]
.
Give your answer correct to 4 significant figures.
© UCLES 2011
0580/22/M/J/11
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![4
7
Solve the equation 4x + 6 × 103 = 8 × 104.
For
Examiner's
Use
Give your answer in standard form.
Answer x =
Answer p =
8
[3]
[3]
p varies directly as the square root of q.
p = 8 when q = 25.
Find p when q = 100.
9
Ashraf takes 1500 steps to walk d metres from his home to the station.
Each step is 90 centimetres correct to the nearest 10 cm.
Find the lower bound and the upper bound for d.
Answer
© UCLES 2011
0580/22/M/J/11
Yd<
[3]](https://image.slidesharecdn.com/0580s11qp22-140108111658-phpapp02/75/0580-s11-qp_22-4-2048.jpg)
![5
10 The table shows the opening and closing times of a café.
For
Examiner's
Use
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)
Answer a =
11 Rearrange the formula c =
© UCLES 2011
4
a−b
[1]
[3]
to make a the subject.
0580/22/M/J/11
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![6
12 Solve the simultaneous equations.
For
Examiner's
Use
x – 5y = 0
15x + 10y = 17
Answer x =
y=
[3]
13
Q
R z°
NOT TO
SCALE
O
y°
54°
x°
T
P
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]
Answer(b) y =
[1]
Answer(c) z =
[2]
(b) y,
(c) z.
© UCLES 2011
0580/22/M/J/11](https://image.slidesharecdn.com/0580s11qp22-140108111658-phpapp02/75/0580-s11-qp_22-6-2048.jpg)
![7
14 60 students recorded their favourite drink.
The results are shown in the pie chart.
Apple
juice
For
Examiner's
Use
NOT TO
SCALE
Banana
shake
66°
Lemonade
120°
Cola
(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 3 cm.
Calculate the arc length of the sector representing Cola.
Answer(c)
© UCLES 2011
0580/22/M/J/11
cm [2]
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![8
15 Write the following as a single fraction in its simplest form.
x +1
x+5
–
For
Examiner's
Use
x
x +1
[4]
Answer
16
B
P
C
NOT TO
SCALE
M
Q
c
O
A
a
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)
,
=
[2]
Answer(b)
[2]
Answer(a)
(b) the position vector of M, where M is the midpoint of PQ.
© UCLES 2011
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![9
17 Simplify
For
Examiner's
Use
(a) 32x8 ÷ 8x32,
Answer(a)
[2]
Answer(b)
[2]
2
x3 3
(b) .
64
18
y
C
4
B
3
2
1
A
0
1
2
3
4
5
6
x
7
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)
© UCLES 2011
0580/22/M/J/11
[3]
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![10
19 f(x) = x2
g(x) = 2x
For
Examiner's
Use
h(x) = 2x – 3
(a) Find g(3).
Answer(a)
[1]
Answer(b)
[2]
Answer(c)
[2]
(b) Find hh(x) in its simplest form.
(c) Find fg(x + 1) in its simplest form.
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![11
20
For
Examiner's
Use
C
B
A
(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]
Question 21 is printed on the next page.
© UCLES 2011
0580/22/M/J/11
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![12
21 (a)
A= (2 3 )
For
Examiner's
Use
6
− 4
B=
(i) Work out AB.
Answer(a)(i)
[2]
Answer(a)(ii)
[2]
Answer(b)
[2]
(ii) Work out BA.
3
1
1
1
(b) C =
Find C–1, the inverse of C.
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.
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 2011
0580/22/M/J/11](https://image.slidesharecdn.com/0580s11qp22-140108111658-phpapp02/75/0580-s11-qp_22-12-2048.jpg)
Uploaded byKing Ali
0580 s11 qp_22
This document is an exam for the International General Certificate of Secondary Education in mathematics. It consists of 12 printed pages containing 21 multiple choice and constructed response questions testing a variety of math skills. Questions cover topics like trigonometry, fractions, exponents, equations, coordinate geometry, and vectors. Students are instructed to show their work, use units where appropriate, and simplify expressions.
In this document
Powered by AI
Instructions for the IGCSE Mathematics exam including allowed materials, writing guidelines, and mark distribution.
Trigonometry problems involving angles and irrational numbers identification, along with calculator usage.
Problems on standard form calculations, direct variation between variables, and units of measurement.
Analysis of café hours, calculations for total operational time, and adjustments for new closing hours.
Solving simultaneous equations and geometric properties of circles including tangent angles.
Analyzing survey results using pie charts and calculating angles and sector lengths based on student preferences.
Simplifying algebraic expressions into fractions and calculating the position vectors in a parallelogram.
Evaluating functions and composing them to find simplified forms.
Geometric constructions using compass and straightedge, along with locating regions based on distances.
Performing operations with matrices and finding the inverse of a given matrix.
More Related Content
0580 s11 qp_22
- 1. w w ap eP m e tr .X w om .c s er UNIVERSITY OF CAMBRIDGEINTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *4065843724* 0580/22 MATHEMATICS May/June 2011 Paper 2 (Extended) 1 hour 30 minutes Candidates answer on the Question Paper. Additional Materials: Electronic calculator Mathematical tables (optional) 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 a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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 π , use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70. This document consists of 12 printed pages. IB11 06_0580_22/8RP © UCLES 2011 [Turn over
- 2. 2 1 4 In the right-angledtriangle ABC, cos C = For Examiner's Use . Find angle A. 5 A NOT TO SCALE B C Answer Angle A = 2 Which of the following numbers are irrational? 2 3 36 3 + 6 π 0.75 Answer 3 [2] Show that 1 5 9 ÷1 7 9 = 7 8 48% 8 1 3 [2] . Write down all the steps in your working. Answer [2] © UCLES 2011 0580/22/M/J/11
- 3. 3 3 4 5 2 < p < For Examiner's Use 3 Whichof the following could be a value of p? 16 27 0.67 60% (0.8)2 4 9 Answer 5 [2] 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? Write down all the steps in your working. Answer Answer 6 Use your calculator to find the value of 2 3 [2] [2] . Give your answer correct to 4 significant figures. © UCLES 2011 0580/22/M/J/11 [Turn over
- 4. 4 7 Solve the equation4x + 6 × 103 = 8 × 104. For Examiner's Use Give your answer in standard form. Answer x = Answer p = 8 [3] [3] p varies directly as the square root of q. p = 8 when q = 25. Find p when q = 100. 9 Ashraf takes 1500 steps to walk d metres from his home to the station. Each step is 90 centimetres correct to the nearest 10 cm. Find the lower bound and the upper bound for d. Answer © UCLES 2011 0580/22/M/J/11 Yd< [3]
- 5. 5 10 The tableshows the opening and closing times of a café. For Examiner's Use 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) Answer a = 11 Rearrange the formula c = © UCLES 2011 4 a−b [1] [3] to make a the subject. 0580/22/M/J/11 [Turn over
- 6. 6 12 Solve thesimultaneous equations. For Examiner's Use x – 5y = 0 15x + 10y = 17 Answer x = y= [3] 13 Q R z° NOT TO SCALE O y° 54° x° T P 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] Answer(b) y = [1] Answer(c) z = [2] (b) y, (c) z. © UCLES 2011 0580/22/M/J/11
- 7. 7 14 60 studentsrecorded their favourite drink. The results are shown in the pie chart. Apple juice For Examiner's Use NOT TO SCALE Banana shake 66° Lemonade 120° Cola (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 3 cm. Calculate the arc length of the sector representing Cola. Answer(c) © UCLES 2011 0580/22/M/J/11 cm [2] [Turn over
- 8. 8 15 Write thefollowing as a single fraction in its simplest form. x +1 x+5 – For Examiner's Use x x +1 [4] Answer 16 B P C NOT TO SCALE M Q c O A a 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) , = [2] Answer(b) [2] Answer(a) (b) the position vector of M, where M is the midpoint of PQ. © UCLES 2011 0580/22/M/J/11
- 9. 9 17 Simplify For Examiner's Use (a) 32x8÷ 8x32, Answer(a) [2] Answer(b) [2] 2 x3 3 (b) . 64 18 y C 4 B 3 2 1 A 0 1 2 3 4 5 6 x 7 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) © UCLES 2011 0580/22/M/J/11 [3] [Turn over
- 10. 10 19 f(x) =x2 g(x) = 2x For Examiner's Use h(x) = 2x – 3 (a) Find g(3). Answer(a) [1] Answer(b) [2] Answer(c) [2] (b) Find hh(x) in its simplest form. (c) Find fg(x + 1) in its simplest form. © UCLES 2011 0580/22/M/J/11
- 11. 11 20 For Examiner's Use C B A (a) On thediagram 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] Question 21 is printed on the next page. © UCLES 2011 0580/22/M/J/11 [Turn over
- 12. 12 21 (a) A= (23 ) For Examiner's Use 6 − 4 B= (i) Work out AB. Answer(a)(i) [2] Answer(a)(ii) [2] Answer(b) [2] (ii) Work out BA. 3 1 1 1 (b) C = Find C–1, the inverse of C. 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. 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 2011 0580/22/M/J/11