Leave blank
2. (a) Expand 3(2t + 1) (b) Expand and simplify (x + 5)(x – 3)
Q1 .................. million
(Total 3 marks)
............................... (1)
6
Ruler graduated in centimetres and
Nil
millimetres, protractor, compasses,
7
pen, HB pencil, eraser, calculator.
Tracing paper may be used.
8
9
Instructions to Candidates
The total mark for this paper is 100. The marks for parts of questions are shown in round brackets:
14
e.g. (2).
You may use a calculator.
15
Advice to Candidates
............................... (2)
............................... (2) Q5
(Total 4 marks)
6. Two points, A and B, are plotted on a centimetre grid. A has coordinates (2, 1) and B has coordinates (8, 5). (a) Work out the coordinates of the midpoint of the line joining A and B.
............................... (2)
............................................................................................................................................ (1) Q7
tanθ = opp adj
A
c
B
Sine rule a = b = c sin A sin B sin C
Cosine rule a2 = b2 + c2 – 2bc cos A
cross section
Area of triangle =
1 2
ab sin C
length
Volume of prism = area of cross section × length
h b
The Quadratic Equation The solutions of ax2 + bx + c = 0 where a ≠ 0, are given by
x = −b ± b2 − 4ac 2a
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Answer ALL TWENTY questions. Write your answers in the spaces provided. You must write down all stages in your working. 1. In July 2002, the population of Egypt was 69 million. By July 2003, the population of Egypt had increased by 2%. Work out the population of Egypt in July 2003.
Number
1
2
3
4
Probability
0.35
0.16
0.27
Magda is going to spin the pointer once. (a) Work out the probability that the pointer will stop on 4.
(b) Work out the probability that the pointer will stop on 1 or 3.
(c) Factorise 10p – 15q (d) Factorise n2 + 4n
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............................... (2)
............................... (1)
............................... (1) Q2
Mathematics
Paper 3H
Higher Tier
Monday 10 May 2004 – Morning Time: 2 hours
Page Leave Numbers Blank
3
4
5
Materials required for examination Items included with question papers
Q8
(Total 4 marks)
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Turn over
9. The grouped frequency table gives information about the distance each of 150 people travel to work.
(Total 5 marks) Turn over
3.
Leave
4.7 cm
Diagram NOT accurately drawn
blank
A circle has a radius of 4.7 cm. (a) Work out the area of the circle.
Give your answer correct to 3 significant figures.
............................... (2)
............................... (2)
Omar is going to spin the pointer 75 times.
(c) Work out an estimate for the number of times the pointer will stop on 2.
Total
Turn over
Pythagoras’ Theorem
c b
a a2 + b2 = c2
IGCSE MATHEMATICS 4400 FORMULA SHEET – HIGHER TIER
Volume
of
cone
=
1 3
πr2h
Volume of sphere =
4rea of cone = πrl
....................... cm2 (4) Q3
(Total 6 marks)
4
4. The diagram shows a pointer which spins about the centre of a fixed disc.
Leave blank
When the pointer is spun, it stops on one of the numbers 1, 2, 3 or 4. The probability that it will stop on one of the numbers 1 to 3 is given in the table.
(b) Use Pythagoras’ Theorem to work out the length of AB. Give your answer correct to 3 significant figures.
(............ , ............) (2)
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......................... cm (4) Q6
Surface area of sphere = 4πr2
r
l
h
r
hyp
θ adj
adj = hyp × cos θ opp = hyp × sin θ opp opp = adj × tan θ
or sinθ = opp hyp
In any triangle ABC C
b
a
cosθ = adj hyp
(Total 6 marks)
6
7. A = {1, 2, 3, 4} B = {1, 3, 5}
Leave blank
(a) List the members of the set
(i) A ∩ B,
(ii) A ∪ B.
...............................
(b) Explain clearly the meaning of 3 ∈ A.
Write your answers neatly and in good English.
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Printer’s Log. No.
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