2024年4月9日发(作者：鲜绣梓)
畅享冠军纯正特产？快来绵羊国正品代购！
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certifi cate of Secondary Education
*9687546924*
MATHEMATICS
0580/43
May/June 2013
2 hours 30 minutes
Paper 4 (Extended)
Candidates answer on the Question Paper.
Additional Materials:
Electronic calculator
Tracing paper (optional)
Geometrical instruments
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fl uid.
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 specifi ed in the question, and if the answer is not exact, give the answer to
three signifi cant fi gures. 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 130.
This document consists of 19 printed pages and 1 blank page.
IB13 06_0580_43/5RP
© UCLES 2013
[Turn over
畅享冠军纯正特产？快来绵羊国正品代购！
2
1 (a) A li and Ben receive a sum of money.
T hey share it in the ratio 5
:
1.
A li receives $2345.
C alculate the total amount.
Answer(a) $ ............................................... [2]
(b) Ali uses 11% of his $2345 to buy a television.
C alculate the cost of the television.
Answer(b) $ ............................................... [2]
(c) A different television costs $330.
(i) Ben buys one in a sale when this cost is reduced by 15%.
H ow much does Ben pay?
Answer(c)(i) $ ............................................... [2]
(ii) $330 is 12% less than the cost last year.
C alculate the cost last year.
Answer(c)(ii) $ ............................................... [3]
© UCLES 20130580/43/M/J/13
For
Examiner′s
Use
畅享冠军纯正特产？快来绵羊国正品代购！
3
(d) Ali invests $1500 of his share in a bank account.
The account pays compound interest at a rate of 2.3% per year.
Calculate the total amount in the account at the end of 3 years.
For
Examiner′s
Use
(e) Ali also buys a computer for $325.
He later sells this computer for $250.
Calculate Ali’s percentage loss.
Answer(d) $ ............................................... [3]
Answer(e) ........................................... % [3]
_____________________________________________________________________________________
© UCLES 20130580/43/M/J/13
[Turn over
畅享冠军纯正特产？快来绵羊国正品代购！
4
2 (a) I n this question show all your construction arcs and use only a ruler and compasses to draw
the boundaries of your region.
This scale drawing shows the positions of four towns, P, Q, R and S, on a map where 1
cm represents
For
Examiner′s
Use
10
km.
North
P
Q
Scale: 1
cm to 10 km
S
R
A nature reserve lies in the quadrilateral PQRS.
The boundaries of the nature reserve are:
● equidistant from Q and from R
● equidistant from PS and from PQ
● 60
km from R
● along QR.
(i) Shade the region which represents the nature reserve. [7]
(ii) Measure the bearing of S from P.
Answer(a)(ii) ............................................... [1]
© UCLES 20130580/43/M/J/13
畅享冠军纯正特产？快来绵羊国正品代购！
5
(b) A circular lake in the nature reserve has a radius of 45
m.
(i) Calculate the area of the lake.
For
Examiner′s
Use
(ii)
Answer(b)(i) .......................................... m
2
[2]
NOT TO
SCALE
A fence is placed along part of the circumference of the lake.
This arc subtends an angle of 210° at the centre of the circle.
Calculate the length of the fence.
Answer(b)(ii) ........................................... m [2]
_____________________________________________________________________________________
© UCLES 20130580/43/M/J/13
[Turn over
畅享冠军纯正特产？快来绵羊国正品代购！
6
3 (a) Luk wants to buy x goats and y sheep.
(i) He wants to buy at least 5 goats.
Write down an inequality in x to represent this condition.
Answer(a)(i) ............................................... [1]
For
Examiner′s
Use
(ii) He wants to buy at least 11 sheep.
Write down an inequality in y to represent this condition.
Answer(a)(ii) ............................................... [1]
(iii) He wants to buy at least 20 animals.
W rite down an inequality in x and y to represent this condition.
Answer(a)(iii) ............................................... [1]
(b) G oats cost $4 and sheep cost $8.
The maximum Luk can spend is $160.
Write down an inequality in x and y and show that it simplifi es to x + 2y Y 40 .
Answer(b)
[1]
© UCLES 20130580/43/M/J/13
畅享冠军纯正特产？快来绵羊国正品代购！
7
y
40
(c) (i) O n the grid below, draw four lines to show the four inequalities and shade the unwanted
regions.
For
Examiner′s
Use
35
30
25
20
15
10
5
0
x
510
[7]
(ii) Work out the maximum number of animals that Luk can buy.
Answer(c)(ii) ............................................... [2]
_____________________________________________________________________________________
[Turn over
© UCLES 20130580/43/M/J/13
畅享冠军纯正特产？快来绵羊国正品代购！
8
4
I
NOT TO
SCALE
H
J
F
7
cm
40
cm
E
22
cm
G
EFGHIJ is a solid metal prism of length 40
cm.
The cross section EFG is a right-angled triangle.
EF = 7
cm and EG = 22
cm.
(a) Calculate the volume of the prism.
Answer(a) ........................................ cm
3
[2]
(b) Calculate the length FJ.
Answer(b) FJ = ......................................... cm [4]
© UCLES 20130580/43/M/J/13
For
Examiner′s
Use
畅享冠军纯正特产？快来绵羊国正品代购！
9
(c) Calculate the angle between FJ and the base EGJH of the prism.
For
Examiner′s
Use
(d) The prism is melted and made into spheres.
Each sphere has a radius 1.5
cm.
Answer(c) ............................................... [3]
Work out the greatest number of spheres that can be made.
4
[The volume, V, of a sphere with radius r is V =
πr
3
.]
3
Answer(d) ............................................... [3]
(e) (i) A right-angled triangle is the cross section of another prism.
This triangle has height 4.5
cm and base 11.0
cm.
Both measurements are correct to 1 decimal place.
Calculate the upper bound for the area of this triangle.
Answer(e)(i) ........................................ cm
2
[2]
(ii) Write your answer to part (e)(i) correct to 4 signifi cant fi gures.
Answer(e)(ii) ........................................ cm
2
[1]
_____________________________________________________________________________________
© UCLES 20130580/43/M/J/13
[Turn over
畅享冠军纯正特产？快来绵羊国正品代购！
10
5 (a) Complete this table of values for the function f(x) =
1
x
– x
2
, x ¸ 0.
x
–3–2–1–0.5–0.20.20.5123
f(x)
–9.33–4.5–2–2.254.96–3.5–8.67
(b) Draw the graph of f(x) =
1
x
– x
2
for –3 Y x Y –0.2 and 0.2 Y x Y 3.
y
5
4
3
2
1
–3
–2–1
0
1
23
x
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
© UCLES 20130580/43/M/J/13
For
Examiner′s
Use
[3]
[5]
2024年4月9日发(作者：鲜绣梓)
畅享冠军纯正特产？快来绵羊国正品代购！
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certifi cate of Secondary Education
*9687546924*
MATHEMATICS
0580/43
May/June 2013
2 hours 30 minutes
Paper 4 (Extended)
Candidates answer on the Question Paper.
Additional Materials:
Electronic calculator
Tracing paper (optional)
Geometrical instruments
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fl uid.
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 specifi ed in the question, and if the answer is not exact, give the answer to
three signifi cant fi gures. 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 130.
This document consists of 19 printed pages and 1 blank page.
IB13 06_0580_43/5RP
© UCLES 2013
[Turn over
畅享冠军纯正特产？快来绵羊国正品代购！
2
1 (a) A li and Ben receive a sum of money.
T hey share it in the ratio 5
:
1.
A li receives $2345.
C alculate the total amount.
Answer(a) $ ............................................... [2]
(b) Ali uses 11% of his $2345 to buy a television.
C alculate the cost of the television.
Answer(b) $ ............................................... [2]
(c) A different television costs $330.
(i) Ben buys one in a sale when this cost is reduced by 15%.
H ow much does Ben pay?
Answer(c)(i) $ ............................................... [2]
(ii) $330 is 12% less than the cost last year.
C alculate the cost last year.
Answer(c)(ii) $ ............................................... [3]
© UCLES 20130580/43/M/J/13
For
Examiner′s
Use
畅享冠军纯正特产？快来绵羊国正品代购！
3
(d) Ali invests $1500 of his share in a bank account.
The account pays compound interest at a rate of 2.3% per year.
Calculate the total amount in the account at the end of 3 years.
For
Examiner′s
Use
(e) Ali also buys a computer for $325.
He later sells this computer for $250.
Calculate Ali’s percentage loss.
Answer(d) $ ............................................... [3]
Answer(e) ........................................... % [3]
_____________________________________________________________________________________
© UCLES 20130580/43/M/J/13
[Turn over
畅享冠军纯正特产？快来绵羊国正品代购！
4
2 (a) I n this question show all your construction arcs and use only a ruler and compasses to draw
the boundaries of your region.
This scale drawing shows the positions of four towns, P, Q, R and S, on a map where 1
cm represents
For
Examiner′s
Use
10
km.
North
P
Q
Scale: 1
cm to 10 km
S
R
A nature reserve lies in the quadrilateral PQRS.
The boundaries of the nature reserve are:
● equidistant from Q and from R
● equidistant from PS and from PQ
● 60
km from R
● along QR.
(i) Shade the region which represents the nature reserve. [7]
(ii) Measure the bearing of S from P.
Answer(a)(ii) ............................................... [1]
© UCLES 20130580/43/M/J/13
畅享冠军纯正特产？快来绵羊国正品代购！
5
(b) A circular lake in the nature reserve has a radius of 45
m.
(i) Calculate the area of the lake.
For
Examiner′s
Use
(ii)
Answer(b)(i) .......................................... m
2
[2]
NOT TO
SCALE
A fence is placed along part of the circumference of the lake.
This arc subtends an angle of 210° at the centre of the circle.
Calculate the length of the fence.
Answer(b)(ii) ........................................... m [2]
_____________________________________________________________________________________
© UCLES 20130580/43/M/J/13
[Turn over
畅享冠军纯正特产？快来绵羊国正品代购！
6
3 (a) Luk wants to buy x goats and y sheep.
(i) He wants to buy at least 5 goats.
Write down an inequality in x to represent this condition.
Answer(a)(i) ............................................... [1]
For
Examiner′s
Use
(ii) He wants to buy at least 11 sheep.
Write down an inequality in y to represent this condition.
Answer(a)(ii) ............................................... [1]
(iii) He wants to buy at least 20 animals.
W rite down an inequality in x and y to represent this condition.
Answer(a)(iii) ............................................... [1]
(b) G oats cost $4 and sheep cost $8.
The maximum Luk can spend is $160.
Write down an inequality in x and y and show that it simplifi es to x + 2y Y 40 .
Answer(b)
[1]
© UCLES 20130580/43/M/J/13
畅享冠军纯正特产？快来绵羊国正品代购！
7
y
40
(c) (i) O n the grid below, draw four lines to show the four inequalities and shade the unwanted
regions.
For
Examiner′s
Use
35
30
25
20
15
10
5
0
x
510
[7]
(ii) Work out the maximum number of animals that Luk can buy.
Answer(c)(ii) ............................................... [2]
_____________________________________________________________________________________
[Turn over
© UCLES 20130580/43/M/J/13
畅享冠军纯正特产？快来绵羊国正品代购！
8
4
I
NOT TO
SCALE
H
J
F
7
cm
40
cm
E
22
cm
G
EFGHIJ is a solid metal prism of length 40
cm.
The cross section EFG is a right-angled triangle.
EF = 7
cm and EG = 22
cm.
(a) Calculate the volume of the prism.
Answer(a) ........................................ cm
3
[2]
(b) Calculate the length FJ.
Answer(b) FJ = ......................................... cm [4]
© UCLES 20130580/43/M/J/13
For
Examiner′s
Use
畅享冠军纯正特产？快来绵羊国正品代购！
9
(c) Calculate the angle between FJ and the base EGJH of the prism.
For
Examiner′s
Use
(d) The prism is melted and made into spheres.
Each sphere has a radius 1.5
cm.
Answer(c) ............................................... [3]
Work out the greatest number of spheres that can be made.
4
[The volume, V, of a sphere with radius r is V =
πr
3
.]
3
Answer(d) ............................................... [3]
(e) (i) A right-angled triangle is the cross section of another prism.
This triangle has height 4.5
cm and base 11.0
cm.
Both measurements are correct to 1 decimal place.
Calculate the upper bound for the area of this triangle.
Answer(e)(i) ........................................ cm
2
[2]
(ii) Write your answer to part (e)(i) correct to 4 signifi cant fi gures.
Answer(e)(ii) ........................................ cm
2
[1]
_____________________________________________________________________________________
© UCLES 20130580/43/M/J/13
[Turn over
畅享冠军纯正特产？快来绵羊国正品代购！
10
5 (a) Complete this table of values for the function f(x) =
1
x
– x
2
, x ¸ 0.
x
–3–2–1–0.5–0.20.20.5123
f(x)
–9.33–4.5–2–2.254.96–3.5–8.67
(b) Draw the graph of f(x) =
1
x
– x
2
for –3 Y x Y –0.2 and 0.2 Y x Y 3.
y
5
4
3
2
1
–3
–2–1
0
1
23
x
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
© UCLES 20130580/43/M/J/13
For
Examiner′s
Use
[3]
[5]