IGCSE
Mathematics (Specification A)
Sample Assessment Materials (SAMs)
Edexcel IGCSE in Mathematics (Specification A)(4MA0)
First examination 2011
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Acknowledgements
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Authorised by Roger Beard Prepared by Parul Patel
All the material in this publication is copyright © Edexcel Limited 2008
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 1
Contents
Introduction 3
Sample question papers 5 Paper 1F 7
Paper 2F 27
Paper 3H 47
Paper 4H 67
Sample mark schemes 87 General marking guidance 89
Paper 1F 91
Paper 2F 103
Paper 3H 113
Paper 4H 125
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)2
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Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 3
Introduction These sample assessment materials have been prepared to support the specification.
The aim of these materials is to provide students and centres with a general impression and flavour of the actual question papers and mark schemes in advance of the first operational examinations.
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)4
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 5
Sample question papers Paper 1F 7
Paper 2F 27
Paper 3H 47
Paper 4H 67
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)6
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 7
Examiner’s use only
Team Leader’s use only
Surname Initial(s)
Signature
Centre No.
Paper Reference
Turn over
Candidate No. 4 M A 0 1 F
Paper Reference(s)
4MA0/1FEdexcel IGCSEMathematics APaper 1F
Foundation TierSample Assessment MaterialTime: 2 hours
Materials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.
Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initial(s) and signature.Check that you have the correct question paper.Answer ALL the questions in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.
Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).There are 19 questions in this question paper. The total mark for this paper is 100.There are 20 pages in this question paper. Any blank pages are indicated.You may use a calculator.
Advice to CandidatesWrite your answers neatly and in good English.
This publication may be reproduced only in accordance with Edexcel Limited copyright policy.
©2008 Edexcel Limited.
Printer’s Log. No.
N35027AW850/R4400/57570 2/2/2/
*N35027A0120*
Question Leave Number Blank
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Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)8
IGCSE MATHEMATICS 4400
FORMULA SHEET – FOUNDATION TIER
Pythagoras’Theorema2 + b2 = c2
Volume of cylinder = r2h
Curved surface area of cylinder = 2 rh
adj = hyp cosopp = hyp sinopp = adj tan
or
opptanadj
adjcoshyp
oppsinhyp
Circumference of circle = 2 r
Area of circle = r2
Volume of prism = area of cross section length
Area of a trapezium = (a + b)h12
b
a
opp
adj
hyp
b
a
h
lengthsectioncross
r
h
r
c
IGCSE MATHEMATICS
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 9
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Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
1. (a) (i) Shade 40% of this shape.
(ii) When 40% of the shape is shaded, what percentage is unshaded?
........................... %(2)
(b) Write 40% as a decimal.
...........................(1)
(c) Write 40% as a fraction. Give your fraction in its simplest form.
...........................(2) Q1
(Total 5 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)10
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2. The diagram shows a triangle ABC on a centimetre grid.
(a) Write down the coordinates of the point
(i) A, (............. , .............)
(ii) B. (............. , .............)(2)
(b) Measure the length of the line AB. Give your answer in millimetres.
........................... mm(1)
(c) Find the perimeter of triangle ABC.
........................... mm(2)
(d) Write down the special name for triangle ABC.
............................................................(1)
(e) (i) Measure the size of angle B.
...........................°
(1)
(ii) Write down the special name for this type of angle.
............................................................(1) Q2
(Total 8 marks)
O 1 2 3 4 5 6 7 8 9 10 x
y6
5
4
3
2
1
A C
B
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 11
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3. 15 21 23 24 25 27 33 35 39
(a) From the numbers in the box, write down
(i) an even number
...........................(1)
(ii) a factor of 60
...........................(1)
(iii) a multiple of 9
...........................(1)
(iv) a square number
...........................(1)
(v) a prime number.
...........................(1)
(b) Write a number from the box on the dotted line so that each calculation is correct.
(i) ................ + 87 = 111
(ii) ................ × 46 = 1794(2) Q3
(Total 7 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)12
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4. Here are the first five terms of a number sequence.
1 7 13 19 25
(a) Write down the next term in the sequence.
...........................(1)
(b) Explain how you worked out your answer.
.......................................................................................................................................(1)
(c) Find the 11th term of the sequence.
...........................(1)
(d) The 50th term of the sequence is 295 Work out the 49th term of the sequence.
...........................(1)
Tamsin says, “Any two terms of this sequence add up to an even number.”
(e) Explain why Tamsin is right.
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................(1) Q4
(Total 5 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 13
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Q5
(Total 5 marks)
5. Here are 9 flags.
(a) Write down the letter of the flag which has:
(i) exactly one line of symmetry
...........................(1)
(ii) rotational symmetry of order 4
...........................(1)
(iii) 2 lines of symmetry and rotational symmetry of order 2
...........................(1)
(iv) no lines of symmetry and rotational symmetry of order 2
...........................(1)
(b) Write down the letter of the flag which has a rhombus on it.
...........................(1)
A B C
D E F
G H I
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)14
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6. The bar chart shows information about the number of people, in millions, who speak each of 6 languages.
(a) Write down the number of people who speak Hindi.
.................... million(1)
(b) Write down the number of people who speak Mandarin Chinese.
.................... million(1)
(c) Which language is spoken by 190 million people?
.................................(1)
125 million people speak Japanese.
(d) Draw a bar on the bar chart to show this information.(1)
(e) Find the ratio of the number of people who speak Hindi to the number of people who speak Japanese.
Give your ratio in its simplest form.
.................................(2)
Bengali Japanese
900800700600500400300200100
0Mandarin Chinese
Spanish English Hindi Arabic
Language
Numberof people(million)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 15
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330 million people speak English. 70% of these people live in the USA.
(f) Work out 70% of 330 million.
.................... million(2)
332 million people speak Spanish. 143 million of these people live in South America.
(g) Work out 143 million as a percentage of 332 million. Give your answer correct to 1 decimal place.
.................... %(2)
7. (a) Solve 2x + 9 = 1
x = ....................(2)
(b) Solve 5y – 4 = 2y + 7
y = ....................(2)
Q6
(Total 10 marks)
Q7
(Total 4 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)16
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8. The table shows information about the time in each of five cities. For each city, it shows the number of hours time difference from the time in London.
+ shows that the time is ahead of the time in London. shows that the time is behind the time in London.
CityTime difference
from London (hours)
Cairo +2
Montreal 5
Bangkok +7
Rio de Janeiro 3
Los Angeles 8
Mexico City
(a) When the time in London is 6 a.m., what is the time in:
(i) Bangkok,
................................. (ii) Los Angeles.
.................................(2)
(b) The time in Mexico City is 2 hours ahead of the time in Los Angeles. Complete the table to show the time difference of Mexico City from London.
(1)
(c) Write down the name of the city in which the time is 10 hours behind Bangkok.
.................................(1)
(d) Work out the time difference between
(i) Cairo and Montreal,
...................... hours
(ii) Rio de Janeiro and Los Angeles.
...................... hours(2) Q8
(Total 6 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 17
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9. (a) Find the value of 4 (8 – 3)
.................................(1)
(b) Put brackets in the expression below so that the answer is 19
7 + 4 × 5 – 2(1)
(c) Find 3.83
.................................(1)
(d) Find 6 76.
.................................(1) Q9
(Total 4 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)18
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10.
Write down the equation of
(i) line A,
.................................(1)
(ii) line B,
.................................(1)
(iii) line C.
.................................(1)
11. (a) Use your calculator to work out the value of
( . . ). .
3 7 4 62 8 6 3
2
Write down all the figures on your calculator display.
............................................................(2)
(b) Give your answer to part (a) correct to 2 decimal places.
.................................(1)
Q10
(Total 3 marks)
Q11
(Total 3 marks)
8
6
4
2
–2
–2 2 4 6 8O x
y
BC
A
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 19
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12. Here are five shapes.
Four of the shapes are squares and one of the shapes is a circle. One square is black. Three squares are white. The circle is black.
The five shapes are put in a bag. Alec takes at random a shape from the bag.
(a) Find the probability that he will take the black square.
.................................(1)
(b) Find the probability that he will take a white square.
.................................(2)
Jasmine takes a shape at random from the bag 150 times. She replaces the shape each time.
(c) Work out an estimate for the number of times she will take a white square.
.................................(2) Q12
(Total 5 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)20
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13. A basketball court is a rectangle, 28 m long and 15 m wide.
(a) Work out the area of the rectangle.
................................. m2
(2)
(b) In the space below, make an accurate scale drawing of the rectangle. Use a scale of 1 cm to 5 m.
(2)
14. (a) Work out the value of x2 – 5x when x = –3
.................................(2)
(b) Factorise x2 – 5x
.................................(2) Q14
(Total 4 marks)
Q13
(Total 4 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 21
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15. Hajra counted the numbers of sweets in 20 packets. The table shows information about her results.
Number of sweets Frequency
46 3
47 6
48 3
49 5
50 2
51 1
(a) What is the mode number of sweets?
.................................(1)
(b) Work out the range of the number of sweets.
.................................(2)
(c) Work out the mean number of sweets in the 20 packets.
.................................(3) Q15
(Total 6 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)22
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16.
(a) Describe fully the single transformation which maps triangle P onto triangle Q.
.......................................................................................................................................
.......................................................................................................................................(2)
(b) Describe fully the single transformation which maps triangle P onto triangle R.
.......................................................................................................................................
.......................................................................................................................................(3) Q16
(Total 5 marks)
5
4
3
2
–1–2 1 2 3 4O x
y
P
R
Q1
–1 5 6 87
–2
–3
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 23
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17. (a) Simplify, leaving your answers in index form,
(i) 75
.................................(1)
(ii) 59
.................................(1)
(b) Solve 9 4
82 2 22n×
=
n = .................................(2)
18. (a) Expand and simplify 3(4x – 5) – 4(2x + 1)
.................................(2)
(b) Expand and simplify (y + 8)(y + 3)
.................................(2)
(c) Expand p(5p2 + 4)
.................................(2)
Q17
(Total 4 marks)
Q18
(Total 6 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)24
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19. A tunnel is 38.5 km long.
(a) A train travels the 38.5 km in 21 minutes.
Work out the average speed of the train. Give your answer in km/h.
................................ km/h(3)
(b) To make the tunnel, a cylindrical hole 38.5 km long was drilled. The radius of the cylindrical hole was 4.19 m.
Work out the volume of earth, in m3, which was removed to make the hole. Give your answer correct to 3 significant figures.
................................ m3
(3)
TOTAL FOR PAPER: 100 MARKS
END
Q19
(Total 6 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 25
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Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)26
BLANK PAGE
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 27
Examiner’s use only
Team Leader’s use only
Surname Initial(s)
Signature
Centre No.
Paper Reference
Turn over
Candidate No. 4 M A 0 2 F
Paper Reference(s)
4MA0/2FEdexcel IGCSEMathematics APaper 2F
Foundation TierSample Assessment MaterialTime: 2 hours
Materials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.
Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initial(s) and signature.Check that you have the correct question paper.Answer ALL the questions in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.
Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).There are 21 questions in this question paper. The total mark for this paper is 100.There are 20 pages in this question paper. Any blank pages are indicated.You may use a calculator.
Advice to CandidatesWrite your answers neatly and in good English.
*N35028A0120*This publication may be reproduced only in accordance with Edexcel Limited copyright policy.
©2008 Edexcel Limited.
Printer’s Log. No.
N35028AW850/R4400/57570 2/2/2
Question Leave Number Blank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Total
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)28
IGCSE MATHEMATICS 4400
FORMULA SHEET – FOUNDATION TIER
Pythagoras’Theorema2 + b2 = c2
Volume of cylinder = r2h
Curved surface area of cylinder = 2 rh
adj = hyp cosopp = hyp sinopp = adj tan
or
opptanadj
adjcoshyp
oppsinhyp
Circumference of circle = 2 r
Area of circle = r2
Volume of prism = area of cross section length
Area of a trapezium = (a + b)h12
b
a
opp
adj
hyp
b
a
h
lengthsectioncross
r
h
r
c
IGCSE MATHEMATICS
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 29
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Answer ALL questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1. (a) Here is a list of numbers.
999 1999 199 9000 1009
(i) Write these numbers in order of size. Start with the smallest.
................................................................................................................................(1)
(ii) From the list, write down an even number.
.......................................(1)
(iii) From the list, write down a number that is a multiple of 9
.......................................(1)
(b) Here are four cards. Each card has a number on it.
3 4 1 2
The four cards are arranged to make the number 3412 The cards can be re-arranged to make other numbers.
(i) Write down the largest number that can be made.
.......................................(1)
(ii) Write down the smallest odd number that can be made.
.......................................(2) Q1
(Total 6 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)30
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2. On the probability scale, mark the following with a cross (x).
(i) The probability that the next baby to be born will be a boy. Label this cross A.
(ii) The probability that the day after Saturday will be Sunday. Label this cross B.
(iii) The probability that a person chosen at random has a birthday in May. Label this cross C.
3. O is the centre of the circle.
The line AB touches the circle at T.
(a) Write down the mathematical name for the line
(i) OT,
.......................................(1)
(ii) CT,
.......................................(1)
(iii) AB.
.......................................(1)
(b) Write down the mathematical name for the shaded region.
.......................................(1)
Q3
(Total 4 marks)
0 0.5 1 Q2
(Total 3 marks)
C
A
O
T
B
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 31
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4. (a) Write a number in the box so that this is a correct calculation.
189 = 3969(1)
(b) Write down the value of the 3 in the number 3969
............................................................(1)
(c) Write the number 3969 correct to the nearest 10
...........................(1)
(d) Write the number 3969 correct to the nearest 100
...........................(1)
(e) Find the square root of 3969
...........................(1)
(f) Find the cube root of 3969
(i) Write down all the figures on your calculator display.
............................................................(1)
(ii) Give your answer correct to 3 significant figures.
...........................(1) Q4
(Total 7 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)32
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5. This formula gives the cost of hiring a bike for a number of days.
cost in pounds = 4 × number of days + 2
(a) Angus hired a bike for 5 days. Calculate the cost.
£ ...........................(2)
(b) Jeevan hired a bike. The cost was £30 Calculate the number of days for which Jeevan hired the bike.
...........................(2) Q5
(Total 4 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 33
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6. Here is a list of fractions.
7
20
3
10
9
25
12
36
From the list, write down the fraction which is
(a) equivalent to 3
1
...........................(1)
(b) equal to 0.3
...........................(1)
(c) the largest.
...........................(3) Q6
(Total 5 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)34
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7. Chocolate bars cost £1.10 each. Cakes cost £1.25 each. Joshi buys 2 chocolate bars and 3 cakes. He pays with a £10 note.
Work out how much change he should receive.
£ ........................... Q7
(Total 3 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 35
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8. Here are the numbers of points scored by 8 teams in a season.
5 3 14 12 4 3 6 9
(a) Find the mode.
...........................(1)
(b) Work out the mean.
...........................(3)
(c) Find the median.
...........................(2)
(d) The team that scored 4 points was The Cheetahs. Later, The Cheetahs had points taken away because of foul play.
(i) Will the median increase or decrease or stay the same?
.......................................................
(ii) Give your reason.
................................................................................................................................
................................................................................................................................
................................................................................................................................(2)
(e) A team is chosen at random from these 8 teams. Find the probability that this team scored more than 10 points.
...........................(2) Q8
(Total 10 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)36
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9. The diagram shows a triangle drawn on a 1 cm grid.
(a) Work out the area of the triangle. State the units of your answer.
....................................... ..........................(3)
(b)
On the grid, reflect the triangle in the dotted line.(2) Q9
(Total 5 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 37
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10. Here is a number machine.
Input Add 3 Multiply by 5 Output
(a) Work out the output when the input is 6
...........................(2)
(b) Work out the input when the output is 70
...........................(2)
(c) Work out the input when the output is –85
...........................(2)
(d) Find an expression, in terms of x, for the output when the input is x.
...........................(2) Q10
(Total 8 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)38
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11.
In the diagram BCD is a straight line.
(a) Work out the size of angle x.
.......................... °
(1)
(b) (i) Work out the size of angle y.
.......................... °
(1)
(ii) Give a reason for your answer to part (b)(i).
................................................................................................................................
................................................................................................................................(1) Q11
(Total 3 marks)
Diagram NOTaccurately drawn
A
B DC
y
x50°
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 39
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12. Michelle has £4800
She gives 5
2
of the £4800 to a charity.
(a) How much money does Michelle give to the charity?
£ ...........................(2)
(b) The charity spends 85% of this money on medicines. How much money does the charity spend on medicines?
£ ...........................(2)
13. The diagram shows the lengths, in cm, of the sides of a triangle.
The perimeter of the triangle is 17 cm.
(i) Use this information to write an equation in x.
.......................................................(1)
(ii) Solve your equation.
x = ...........................(2)
Q12
(Total 4 marks)
Q13
(Total 3 marks)
x (3x – 5)
(2x + 1)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)40
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14. Anji mixes sand and cement in the ratio 7 : 2 by weight. The total weight of the mixture is 27 kg.
Calculate the weight of sand in the mixture.
........................... kg
15. Solve 5(x – 4) = 35
x = ...........................
Q14
(Total 3 marks)
Q15
(Total 3 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 41
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16. Julian has to work out 6 8 47 6
2 09
. .
. without using a calculator.
(a) Round each number in Julian’s calculation to one significant figure.
........................................................(2)
(b) Use your rounded numbers to work out an estimate for 6 8 47 6
2 09
. .
. Give your answer correct to one significant figure.
...........................(2)
(c) Without using your calculator, explain why your answer to part (b) should be larger than the exact answer.
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................(2) Q16
(Total 6 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)42
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17. The diagram shows a wall.
(a) Calculate the area of the wall.
........................... m2
(2)
(b) 1 litre of paint covers an area of 20 m2. Work out the volume of paint needed to cover the wall. Give your answer in cm3.
........................... cm3
(3)
2 m3 m
6 m
Q17
(Total 5 marks)
Diagram NOTaccurately drawn
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 43
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18. Solve the simultaneous equations
y = x + 3y = 7x
x = ...........................
y = ........................... Q18
(Total 3 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)44
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19. (a)
Calculate the value of x. Give your answer correct to 3 significant figures.
x = ...........................(3)
(b)
Calculate the length of AB. Give your answer correct to 3 significant figures.
........................... cm(3) Q19
(Total 6 marks)
5 cm
29°B
A
C
x°4.2 cm
5.1 cm
Diagram NOTaccurately drawn
Diagram NOTaccurately drawn
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 45
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20. A bag contains some marbles. The colour of each marble is red or blue or green or yellow.
A marble is taken at random from the bag. The table shows the probability that the marble is red or blue or green.
Colour Probability
Red 0.1
Blue 0.2
Green 0.1
Yellow
(a) Work out the probability that the marble is yellow.
...........................(2)
(b) Work out the probability that the marble is blue or green.
...........................(2)
The probability that the marble is made of glass is 0.8
(c) Beryl says “The probability that the marble is green or made of glass is 0.1 + 0.8 = 0.9”
Is Beryl correct? ...........................
Give a reason for your answer.
.......................................................................................................................................
.......................................................................................................................................(2)
PLEASE TURN OVER FOR QUESTION 21
Q20
(Total 6 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)46
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21.
Calculate the value of h. Give your answer correct to 3 significant figures.
h = ...........................
TOTAL FOR PAPER: 100 MARKS
END
4 cm h cm
6 cm
Q21
(Total 3 marks)
Diagram NOTaccurately drawn
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 47
Examiner’s use only
Team Leader’s use only
Surname Initial(s)
Signature
Centre No.
Paper Reference
Turn over
Candidate No. 4 M A 0 3 H
Paper Reference(s)
4MA0/3HEdexcel IGCSEMathematics APaper 3H
Higher TierSample Assessment MaterialTime: 2 hours
Materials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.
Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initial(s) and signature.Check that you have the correct question paper.Answer ALL the questions in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.
Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).There are 19 questions in this question paper. The total mark for this paper is 100.There are 20 pages in this question paper. Any blank pages are indicated.You may use a calculator.
Advice to CandidatesWrite your answers neatly and in good English.
*N35029A0120*This publication may be reproduced only in accordance with Edexcel Limited copyright policy.
©2008 Edexcel Limited.
Printer’s Log. No.
N35029AW850/R4400/57570 2/2/2
Question Leave Number Blank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Total
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)48
IGCSE MATHEMATICS 4400FORMULA SHEET – HIGHER TIER
Pythagoras’Theorem
adj = hyp cosopp = hyp sinopp = adj tan
or
opptanadj
adjcoshyp
oppsinhyp
Circumference of circle = 2 r
Area of circle = r2
Area of a trapezium = (a + b)h12
b
a
opp
adj
hyp
b
a
h
lengthsectioncross
a2 + b2 = c2
Volume of prism = area of cross section length
Volume of cylinder = r2h
Curved surface area of cylinder = 2 rh
h
r
Volume of cone = r2h
Curved surface area of cone = rl
13
r
l
r
h
Volume of sphere = r3
Surface area of sphere = 4 r2
43
r
In any triangle ABC
Sine rule:
Cosine rule: a2 = b2 + c2 – 2bc cos A
Area of triangle = ab sinC12
sin sin sina b cA B C
C
ab
c BA
The Quadratic EquationThe solutions of ax2 + bx + c = 0,where a 0, are given by
2 42
b b acxa
c
IGCSE MATHEMATICS
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 49
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Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
1. (a) Use your calculator to work out the value of
( . . )
. .
3 7 4 6
2 8 6 3
2
Write down all the figures on your calculator display.
.................................................................(2)
(b) Give your answer to part (a) correct to 2 decimal places.
.................................(1)
2. (a) Work out the value of x2 – 5x when x = –3
.................................(2)
(b) Factorise x2 – 5x
.................................(2) Q2
(Total 4 marks)
Q1
(Total 3 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)50
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3. Hajra counted the numbers of sweets in 20 packets. The table shows information about her results.
Number of sweets Frequency
46 3
47 6
48 3
49 5
50 2
51 1
Work out the mean number of sweets in the 20 packets.
................................. Q3
(Total 3 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 51
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4.
(a) Describe fully the single transformation which maps triangle P onto triangle Q.
.......................................................................................................................................
.......................................................................................................................................(2)
(b) Describe fully the single transformation which maps triangle P onto triangle R.
.......................................................................................................................................
.......................................................................................................................................(3) Q4
(Total 5 marks)
5
4
3
2
–1–2 1 2 3 4O x
y
P
R
Q1
–1 5 6 87
–2
–3
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)52
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5. (a) Simplify, leaving your answers in index form,
(i) 75
.................................(1)
(ii) 59
.................................(1)
(b) Solve 9 4
82 2 22n×
=
n = .................................(2)
6. (a) Expand and simplify 3(4x – 5) – 4(2x + 1)
.................................(2)
(b) Expand and simplify (y + 8)(y + 3)
.................................(2)
(c) Expand p(5p2 + 4)
.................................(2)
Q5
(Total 4 marks)
Q6
(Total 6 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 53
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7. A tunnel is 38.5 km long.
(a) A train travels the 38.5 km in 21 minutes.
Work out the average speed of the train. Give your answer in km/h.
................................ km/h(3)
(b) To make the tunnel, a cylindrical hole 38.5 km long was drilled. The radius of the cylindrical hole was 4.19 m.
Work out the volume of earth, in m3, which was removed to make the hole. Give your answer correct to 3 significant figures.
................................ m3
(3) Q7
(Total 6 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)54
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8. (a) Shri invested 4500 dollars. After one year, he received 270 dollars interest. Work out 270 as a percentage of 4500.
................................. %(2)
(b) Kareena invested an amount of money at an interest rate of 4.5% per year. After one year, she received 117 dollars interest. Work out the amount of money Kareena invested.
................................. dollars(2)
(c) Ravi invested an amount of money at an interest rate of 4% per year. At the end of one year, interest was added to his account and the total amount in his
account was then 3328 dollars. Work out the amount of money Ravi invested.
................................. dollars(3) Q8
(Total 7 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 55
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9. (a) Solve 5x – 4 = 2x + 7
x = .........................(2)
(b) Solve 7 2
42 3
y y
y = .........................(4) Q9
(Total 6 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)56
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10. Here are five shapes.
Four of the shapes are squares and one of the shapes is a circle. One square is black. Three squares are white. The circle is black. The five shapes are put in a bag.
(a) Jasmine takes a shape at random from the bag 150 times. She replaces the shape each time.
Work out an estimate for the number of times she will take a white square.
.................................(3)
(b) Alec takes a shape at random from the bag and does not replace it. Bashir then takes a shape at random from the bag.
Work out the probability that
(i) they both take a square,
.................................(2)
(ii) they take shapes of the same colour.
.................................(3) Q10
(Total 8 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 57
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11.
A and B are points on a circle, centre O. The lines CA and CB are tangents to the circle. CA = 5.7 cm. CO = 6.9 cm.
(a) Give a reason why angle CAO = 90°.
.......................................................................................................................................
.......................................................................................................................................(1)
(b) Calculate the perimeter of the kite CAOB. Give your answer correct to 3 significant figures.
................................ cm(5) Q11
(Total 6 marks)
B
O
AC
6.9 cm
5.7 cm
Diagram NOTaccurately drawn
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)58
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12. The grouped frequency table gives information about the weights of 60 cows.
Weight (w kg) Frequency
100 < w 200 10
200 < w 300 16
300 < w 400 15
400 < w 500 9
500 < w 600 6
600 < w 700 4
(a) Complete the cumulative frequency table.
Weight (w kg) Cumulativefrequency
100 < w 200
100 < w 300
100 < w 400
100 < w 500
100 < w 600
100 < w 700
(1)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 59
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(b) On the grid, draw the cumulative frequency graph for your table.
(2)
(c) Use your graph to find an estimate for the number of cows that weighed more than 430 kg.
Show your method clearly.
.................................(2) Q12
(Total 5 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)60
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13. Show, by shading on the grid, the region which satisfies all three of these inequalities.
y 5 y 2x y x + 1
Label your region R.
y
6
4
2
O 2 4 6 x
–2
–2
Q13
(Total 4 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 61
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14. (a) Make r the subject of the formula A = r2, where r is positive.
r = .........................(2)
The area of a circle is 14 cm2, correct to 2 significant figures.
(b) (i) Work out the lower bound for the radius of the circle. Write down all the figures on your calculator display.
............................................. cm(2)
(ii) Give the radius of the circle to an appropriate degree of accuracy. You must show working to explain how you obtained your answer.
......................... cm(2) Q14
(Total 6 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)62
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15. The frequency, f kilohertz, of a radio wave is inversely proportional to its wavelength,w metres.
When w = 200, f = 1500
(a) (i) Express f in terms of w.
f = .................................(2)
(ii) On the axes, sketch the graph of f against w.
(2)
(b) The wavelength of a radio wave is 1250 m. Calculate its frequency.
................................. kilohertz(2)
f
O w
Q15
(Total 6 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 63
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16. PQR is a triangle. E is the point on PR such that PR = 3PE. F is the point on QR such that QR = 3QF.
PQ = a, PE = b.
(a) Find, in terms of a and b,
(i) PR
.................................(1)
(ii) QR
.................................(1)
(iii) PF
.................................(1)
(b) Show that EF = k PQ where k is an integer.
(2) Q16
(Total 5 marks)
R
F
QP
Eb
a
Diagram NOTaccurately drawn
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)64
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17. A curve has equation y xx
2 16
The curve has one turning point.
Find d
d
yx
and use your answer to find the coordinates of this turning point.
................................. Q17
(Total 4 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 65
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18.
A solid hemisphere A has a radius of 2.8 cm. (a) Calculate the total surface area of hemisphere A. Give your answer correct to 3 significant figures.
......................... cm2
(3)
A larger solid hemisphere B has a volume which is 125 times the volume of hemisphere A.
(b) Calculate the total surface area of hemisphere B. Give your answer correct to 3 significant figures.
......................... cm2
(3)
PLEASE TURN OVER FOR QUESTION 19
Q18
(Total 6 marks)
A
2.8 cm
Diagram NOTaccurately drawn
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)66
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19. Solve the simultaneous equations
y = 3x – 1
x2 + y2 = 5
x = ............... , y = ...............
x = ............... , y = ...............
TOTAL FOR PAPER: 100 MARKS
END
Q19
(Total 6 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 67
Examiner’s use only
Team Leader’s use only
Surname Initial(s)
Signature
Centre No.
Paper Reference (complete below)
Turn over
Candidate No.
Examiner’s use only
Team Leader’s use only
Surname Initial(s)
Signature
Centre No.
Paper Reference
Turn over
4 M A 0 4 HPaper Reference(s)
4MA0/4HEdexcel IGCSEMathematics APaper 4H
Higher TierSample Assessment MaterialTime: 2 hours
Materials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.
Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initial(s) and signature.Check that you have the correct question paper.Answer ALL the questions in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.
Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).There are 21 questions in this question paper. The total mark for this paper is 100.There are 20 pages in this question paper. Any blank pages are indicated.You may use a calculator.
Advice to CandidatesWrite your answers neatly and in good English.
*N35030A0120*This publication may be reproduced only in accordance with Edexcel Limited copyright policy.
©2008 Edexcel Limited.
Printer’s Log. No.
N35030AW850/R4400/57570 2/2/2
Question Leave Number Blank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Total
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)68
IGCSE MATHEMATICS 4400FORMULA SHEET – HIGHER TIER
Pythagoras’Theorem
adj = hyp cosopp = hyp sinopp = adj tan
or
opptanadj
adjcoshyp
oppsinhyp
Circumference of circle = 2 r
Area of circle = r2
Area of a trapezium = (a + b)h12
b
a
opp
adj
hyp
b
a
h
lengthsectioncross
a2 + b2 = c2
Volume of prism = area of cross section length
Volume of cylinder = r2h
Curved surface area of cylinder = 2 rh
h
r
Volume of cone = r2h
Curved surface area of cone = rl
13
r
l
r
h
Volume of sphere = r3
Surface area of sphere = 4 r2
43
r
In any triangle ABC
Sine rule:
Cosine rule: a2 = b2 + c2 – 2bc cos A
Area of triangle = ab sinC12
sin sin sina b cA B C
C
ab
c BA
The Quadratic EquationThe solutions of ax2 + bx + c = 0,where a 0, are given by
2 42
b b acxa
c
IGCSE MATHEMATICS
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 69
Leave blank
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1. The diagram shows the lengths, in cm, of the sides of a triangle.
The perimeter of the triangle is 17 cm.
(i) Use this information to write an equation in x.
.......................................................(1)
(ii) Solve your equation.
x = ...........................(2)
2. Anji mixes sand and cement in the ratio 7 : 2 by weight. The total weight of the mixture is 27 kg.
Calculate the weight of sand in the mixture.
........................... kg
Q1
(Total 3 marks)
x (3x – 5)
(2x + 1)
Q2
(Total 3 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)70
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3. Solve 5(x – 4) = 35
x = ...........................
4. Julian has to work out 6 8 47 6
2 09
. .
. without using a calculator.
(a) Round each number in Julian’s calculation to one significant figure.
........................................................(2)
(b) Use your rounded numbers to work out an estimate for 6 8 47 6
2 09
. .
. Give your answer correct to one significant figure.
...........................(2)
(c) Without using your calculator, explain why your answer to part (b) should be larger than the exact answer.
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................(2) Q4
(Total 6 marks)
Q3
(Total 3 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 71
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5. The diagram shows a wall.
(a) Calculate the area of the wall.
........................... m2
(2)
(b) 1 litre of paint covers an area of 20 m2. Work out the volume of paint needed to cover the wall. Give your answer in cm3.
........................... cm3
(3) Q5
(Total 5 marks)
2 m3 m
6 m
Diagram NOTaccurately drawn
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)72
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6. Solve the simultaneous equations
y = x + 3y = 7x
x = ...........................
y = ........................... Q6
(Total 3 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 73
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7. (a)
Calculate the value of x. Give your answer correct to 3 significant figures.
x = ...........................(3)
(b)
Calculate the length of AB. Give your answer correct to 3 significant figures.
........................... cm(3) Q7
(Total 6 marks)
x°4.2 cm
5.1 cm
5 cm
29°B
A
C
Diagram NOTaccurately drawn
Diagram NOTaccurately drawn
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)74
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8. A bag contains some marbles. The colour of each marble is red or blue or green or yellow.
A marble is taken at random from the bag. The table shows the probability that the marble is red or blue or green.
Colour Probability
Red 0.1
Blue 0.2
Green 0.1
Yellow
(a) Work out the probability that the marble is yellow.
...........................(2)
(b) Work out the probability that the marble is blue or green.
...........................(2)
The probability that the marble is made of glass is 0.8
(c) Beryl says “The probability that the marble is green or made of glass is 0.1 + 0.8 = 0.9”
Is Beryl correct? ...........................
Give a reason for your answer.
.......................................................................................................................................
.......................................................................................................................................(2) Q8
(Total 6 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 75
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9.
Calculate the value of h. Give your answer correct to 3 significant figures.
h = ...........................
PLEASE TURN OVER FOR QUESTION 10
Q9
(Total 3 marks)
4 cm h cm
6 cm
Diagram NOTaccurately drawn
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)76
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10. (a)
Find the equation of the straight line that passes through the points (0, 1) and (1, 3).
........................................................(4)
(b) Write down the equation of a line parallel to the line whose equation is y = –2x + 5
........................................................(1)
(c) Write down the coordinates of the point of intersection of the two lines whose equations are y = 3x – 4 and y = –2x – 4
(..............., ...............)(1)
7
6
5
4
–1–2 1 2 3 x
y
3
–1
–2
2
1
O
Q10
(Total 6 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 77
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Q11
(Total 5 marks)
11. Here are three similar triangles.
Find the value of
(a) w,
w = ...........................(1)
(b) x,
x = ...........................(2)
(c) y.
y = ...........................(2)
56°
94°12 cm
10 cm
6 cm
30°
56°
20 cm
x cm
y cm
8 cm
4 cmw°
Diagrams NOTaccurately drawn
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)78
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12. Simplify
(a) a a
a
3 4
2
...........................(2)
(b) ( )x 6
...........................(1)
(c) 3 1
6 1
2( )
( )
x
x
...........................(2) Q12
(Total 5 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 79
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13. Here are the marks scored in a maths test by the students in two classes.
Class A 2 13 15 16 4 6 19 10 11 4 5 15 4 16 6
Class B 12 11 2 5 19 14 6 6 10 14 9
(a) Work out the interquartile range of the marks for each class.
Class A ...........................
Class B ...........................(4)
(b) Use your answers to give one comparison between the marks of Class A and the marks of Class B.
.......................................................................................................................................
.......................................................................................................................................(1)
14. Solve 5 7
11
x
xx
x = ........................... Q14
(Total 4 marks)
Q13
(Total 5 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)80
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15. There are 35 students in a group. 18 students play hockey. 12 students play both hockey and tennis. 15 students play neither hockey nor tennis.
Find the number of students who play tennis.
...........................
16. A triangle has sides of length 5 cm, 6 cm and 9 cm.
Calculate the value of x. Give your answer correct to 3 significant figures.
x =...........................
Q15
(Total 4 marks)
Q16
(Total 3 marks)
6 cm5 cm
9 cm
x°Diagram NOTaccurately drawn
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 81
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17. The functions f and g are defined as follows.
f ( )xx
1
2
g( )x x 1
(a) (i) State which value of x cannot be included in the domain of f.
...........................(1)
(ii) State which values of x cannot be included in the domain of g.
...........................(2)
(b) Calculate fg(10)
...........................(3)
(c) Express the inverse function g–1 in the form g–1(x) = ......
............................................(4) Q17
(Total 10 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)82
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18. A fair, 6-sided dice has faces numbered 1, 2, 3, 4, 5 and 6 When the dice is thrown, the number facing up is the score. The dice is thrown three times.
(a) Calculate the probability that the total score is 18
...........................(2)
(b) Calculate the probability that the score on the third throw is exactly double the total of the scores on the first two throws.
...........................(4) Q18
(Total 6 marks)
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 83
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19. (a) Calculate the area of an equilateral triangle of side 5 cm. Give your answer correct to 3 significant figures.
........................... cm2
(2)
(b) The diagram shows two overlapping circles. The centre of each circle lies on the circumference of the other circle. The radius of each circle is 5 cm. The distance between the centres is 5 cm.
Calculate the area of the shaded region. Give your answer correct to 3 significant figures.
........................... cm2
(3) Q19
(Total 5 marks)
5 cm 5 cm
5 cm
5 cm 5 cm
5 cm
Diagram NOTaccurately drawn
Diagram NOTaccurately drawn
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)84
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20. The histogram shows information about the height, h metres, of some trees.
The number of trees with heights in the class 2 < h 3 is 20
Find the number of trees with heights in the class
(a) 4 < h 8
...........................(1)
(b) 3 < h 4
...........................(2) Q20
(Total 3 marks)
Frequencydensity
Height (m)
O 1 2 3 4 5 6 7 8 9
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 85
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21. (a) Factorise 16x2 – 1
...........................(1)
(b) Hence express as the product of its prime factors
(i) 1599
...........................(3)
(ii) 1.599 106
...........................(2)
TOTAL FOR PAPER: 100 MARKS
END
Q21
(Total 6 marks)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)86
BLANK PAGE
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 87
Sample mark schemes General marking guidance 89
Paper 1F 91
Paper 2F 103
Paper 3H 113
Paper 4H 125
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)88
=
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 89
General Marking Guidance
• All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last.
• Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions.
• Examiners should mark according to the mark scheme not according to their perception of where the grade boundaries may lie.
• There is no ceiling on achievement. All marks on the mark scheme should be used appropriately.
• All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme.
• Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited.
• When examiners are in doubt regarding the application of the mark scheme to a candidate’s response, the team leader must be consulted.
• Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response.
• Types of mark o M marks: method marks o A marks: accuracy marks o B marks: unconditional accuracy marks (independent of M marks)
• Abbreviations
o cao – correct answer only o ft – follow through o isw – ignore subsequent working o SC: special case o oe – or equivalent (and appropriate) o dep – dependent o indep - independent
• No working
If no working is shown then correct answers normally score full marks If no working is shown then incorrect (even though nearly correct) answers score no marks.
• With working
If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. If it is clear from the working that the “correct” answer has been obtained from incorrect working, award 0 marks.
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)90
Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work. If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used. If there is no answer on the answer line then check the working for an obvious answer.
=
• Follow through marks
Follow through marks which involve a single stage calculation can be awarded without working since you can check the answer yourself, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given.
• Ignoring subsequent work
It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: eg. incorrect cancelling of a fraction that would otherwise be correct It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect eg algebra. Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer.
• Probability
Probability answers must be given a fractions, percentages or decimals. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability answer is given on the answer line using both incorrect and correct notation, award the marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer.
• Linear equations
Full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously indicated in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded.
• Parts of questions
Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 91
=
Pape
r 1F
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k N
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1(a)
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60
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1(b)
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1(c)
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n N
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er
Mar
k N
otes
2(b)
64
1 B1
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Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)92
Que
stio
nN
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swer
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kN
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2(c)
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77
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stio
nN
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24
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kN
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3(a)
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15
1
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kN
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3(a)
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27
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kN
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swer
Mar
kN
otes
3(a)
(v)
23
1
B1 c
ao
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 93
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
3(b)
(i)
24
1
B1 c
ao
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stio
n N
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er
Mar
k N
otes
3(b)
(ii)
39
1 B1
cao
Q
uest
ion
Num
ber
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king
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swer
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ark
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es
4(a)
31
1 B1
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Num
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ark
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es
4(b)
eg ‘
Add
6’
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Q
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ion
Num
ber
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ark
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es
4(c)
61
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ark
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es
4(d)
289
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(b)
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ark
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es
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two
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Mar
k N
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5(a)
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1 B1
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= Que
stio
n N
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Mar
k N
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5(a)
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F 1
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k N
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5(a)
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I 1
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Mar
k N
otes
5(a)
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D
1 B1
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H
1 B1
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es
6(a)
300
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6(b)
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k N
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6(c)
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swer
M
ark
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es
6(d)
100
< ba
r <
150
1 B1
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 95
= Que
stio
n N
umbe
r W
orki
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Answ
er
Mar
k N
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6(e)
30
0:12
5 12
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6(f)
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231
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k N
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6(g)
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uest
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swer
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ark
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8(a)
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ept
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Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)96
= Que
stio
n N
umbe
r W
orki
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Mar
k N
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8(a)
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10 p
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1 B1
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k N
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8(b)
−6
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k N
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8(d)
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7
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k N
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8(d)
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king
An
swer
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ark
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9(c)
54.8
72
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Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 97
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
9(d)
2.6
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swer
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ark
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10(i
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k N
otes
10(i
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ark
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10(i
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k N
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11(a
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k N
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11(b
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-tri
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Mar
k N
otes
12(a
)
51=
1 B1
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20%
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)98
= Que
stio
n N
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Mar
k N
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12(b
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k N
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12(c
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0 ×
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k N
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13(a
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× 1
5 42
0 2
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k N
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13(b
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Rect
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ide
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eac
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low
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ark
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14(a
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5 se
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Mar
k N
otes
14(b
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B1 f
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rs w
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hen
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te
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rect
SC
B1 f
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(5 −
x ),
x (x
− 5
x )
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 99
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
15(a
)
47
1 B1
cao
Q
uest
ion
Num
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king
An
swer
M
ark
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es
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1 et
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Mar
k N
otes
15(c
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6 ×
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n N
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Mar
k N
otes
16(a
)
tran
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arks
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mat
ion
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)100
= Que
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n N
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orki
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Answ
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Mar
k N
otes
16(b
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rota
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arks
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n N
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Mar
k N
otes
17(a
)(i)
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k N
otes
17(a
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Mar
k N
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17(b
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ark
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18(a
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815
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Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 101
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
18(c
)
5p3 +
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for
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19(a
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35.0=
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k N
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19(b
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500
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π
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0 00
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20 0
00
(
212
3433
.419
3.
14
212
2356
.929
3.
142
212
3708
.749
)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)102
=
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 103
=
Pap
er 2
F
Que
stio
n N
umbe
r W
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Mar
k N
otes
1(a)
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19
9, 9
99,
1009
, 19
99,
9000
1
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k N
otes
1(a)
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9000
1
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er
Mar
k N
otes
1(a)
(iii)
999
or 9
000
1 B1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
1(b)
(i)
43
21
1 B1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
1(b)
(ii)
1243
2
B2
B1 f
or n
umbe
r be
ginn
ing
wit
h 1
or e
ndin
g w
ith
1 or
3
Que
stio
n N
umbe
r W
orki
ng
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er
Mar
k N
otes
2(i)
A at
0.5
± 2
mm
1
B1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
2(ii)
B at
1
1 B1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
2(iii
)
C at
2 ≤
d ≤
25m
m f
rom
0
1 B1
ie b
etw
een
0 an
d 0.
25 e
xclu
sive
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)104
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
3(a)
(i)
Ra
dius
1
B1 a
llow
mis
spel
lings
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
3(a)
(ii)
Chor
d 1
B1 a
llow
mis
spel
lings
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
3(a)
(iii)
Tang
ent
1 B1
allo
w m
issp
ellin
gs
Que
stio
n N
umbe
r W
orki
ng
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er
Mar
k N
otes
3(b)
Sect
or
1 B1
allo
w m
issp
ellin
gs
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
4(a)
21
1 B1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
4(b)
3 1
B1 o
r 30
00 o
r 3
thou
sand
or
1000
or
thou
sand
s Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
4(c)
3970
1
B1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
4(d)
4000
1
B1
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 105
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
4(e)
63
1 B1
- Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
4(f)
(i)
15
.832
89…
1
B1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
4(f)
(ii)
15.8
1
B1 f
t fr
om f
(i)
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
5(a)
4
× 5
+ 2
22
2 M
1 A1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
5(b)
428
7
2 M
1 Al
low
430
or
ans
7.25
oe
A1
Que
stio
n N
umbe
r W
orki
ng
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er
Mar
k N
otes
6(a)
3612
1 B1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
6(b)
103
1 B1
=
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)106
== Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
6(c)
259
3 M
1 At
tem
pt t
o co
nver
t al
l to
dec
or %
or
c.d.
M
1 Al
l cor
rect
ly c
onve
rted
A1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
7 2
× 1.
10 +
3 ×
1.2
5 or
5.
95
10.0
0 −
“5.9
5”
4.05
3
M1
M1
dep
A1
Que
stio
n N
umbe
r W
orki
ng
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er
Mar
k N
otes
8(a)
3 1
B1
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stio
n N
umbe
r W
orki
ng
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er
Mar
k N
otes
8(b)
xΣ
att
empt
ed o
r 856
7 3
M1
eg 4
8.12
5 M
1 de
p A1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
8(c)
Ar
rang
e in
ord
er
5.5
oe
2 M
1 or
ans
wer
5 o
r 6
A1
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stio
n N
umbe
r W
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er
Mar
k N
otes
8(d)
(i)
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me
1 B1
inde
p Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
8(d)
(ii)
Mid
dle
unch
ange
d 1
B1 o
r st
ill 5
.5
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 107
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
8(e)
82 o
e 2
B1 n
um
B1 d
enom
Ra
tio
subt
r B1
= Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
9(a)
6cm
2 3
B2
B1 f
or 5
to
7 in
cl
B1 c
m2
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
9(b)
Tria
ngle
cor
rect
± 2
mm
2
B2
B1 f
or a
ver
tex
corr
ect
±2m
m o
r co
rrec
t si
ze a
nd o
rien
tati
on
±
2 m
m
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
10(a
) (6
+ 3
) ×
5 o
e 45
2
M1
Brac
ket
esse
ntia
l unl
ess
ans
corr
ect
A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
10(b
) 570
or
14 −
3
11
2 M
1 al
low
567
or
13.2
A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
10(c
)
558−
− 3
or
−17
− 3
−20
2 M
1 A1
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)108
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
10(d
)
5(x
+ 3)
or
(x+
3) ×
5
or
x5
+ 1
5 o
e 2
B2
B1 f
or a
nsw
er x
+ 3
× 5
B0
for
ans
wer
x5
+ 3
or
x +
15
‘x=’
sub
trac
t B1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
11(a
)
130
1 B1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
11(b
)(i)
40
1 B1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
11(b
)(ii)
Angl
e su
m o
f tr
iang
le
1 B1
Not
180
− (
90 +
50)
= Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
12(a
) 52
× 4
800
1920
2
B1 s
een
A1 c
ao
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
12(b
) 0.
85 ×
“19
20”
oe
1632
2
B1 A
llow
0.8
5 x
4800
oe
A1 c
ao
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
13(i
)
x +
x2
+ 1
+
x3−
5 =
17
1 B1
oe
eg
x6−
4==
17 IS
W n
ot ‘
=p’
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 109
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
13(i
i)
x6=
21 o
r x6
− 2
1 =
0 et
c x
= 3
.5 o
e eg
621
2
M1
ft
(i)
if
x6=
c A1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
14
9 se
en
97×
27 o
r 7
× 927
oe
21
3 B1
M
1 de
p B1
A1
21
see
n an
d an
s =
3 B1
M1A
O
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
15
x5−
20 =
35
x5=
55
11
3 M
1
M1
dep
or M
2 fo
r x
− 4
= 7
A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
16(a
)
250×
7or
7,
50,
2 2
B1 f
or 7
and
2
B1 f
or 5
0
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
16(b
) 17
5 20
0 or
100
2
M1
ft f
rom
(a)
, (1
75 s
een,
usi
ng
3or
2)
50or
48()7or
6(
cor
rect
ly
eval
’d e
g 16
8 A1
f
If
no w
king
: ft
(a)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)110
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
16(c
)
Num
ber
incr
or
6.8
and
47.6
incr
de
nom
dec
r or
2.0
9 de
cr
(b)
rnde
d up
(no
t rn
d to
1
sf)
or ‘
175’
rnd
ed t
o 20
0
2 B2
any
tw
o of
the
se
B1 a
ny o
ne o
f th
ese
Ig
nore
oth
er
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
17(a
) 6
×2
)3+
2( o
r
2 ×
6 +
21 ×
6 ×
1 o
e
15
2 M
1 A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
17(b
) 2015
× 1
000
201000
× 1
5
1000
× 2015
750
3 M
1 or
0.7
5 M
1 ft
‘15
’ fo
r M
1M1
only
A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
18
x +
3 =
x7
(
x6=
3 o
e)
y7
= x7
+ 2
1
(y6
= 21
)
x =
21,
y=
213
3
M1
y=
7(
y−3
)
y=
y7−2
1
0 =
x6
−3
A1
A1
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 111
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
19(a
) ta
n us
ed
xta
n =
2.41.5
or
xta
n =
1.2
….
oe
x =
50.5
…
3
M1
(sin
or
cos)
and
(√
(4.2
2+
5.1
2)
or 6
.6)
used
M
1 x
sin
= 5
.1/(
√ (4
.22+
5.1
2)
or
xco
s =
4.2
/(√
(4.2
2+
5.1
2)
A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
19(b
) si
n29
= AB
/5 o
r
C/si
n29
= 5/
sin9
0 A
B =
5sin
29
AB
= 2.
42…
cm
3 M
1
BC =
5co
s29
M1
A
B =
√ (5
2+
(5co
s29)
2 ) or
5co
s29
× ta
n29
A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
20(a
) 1
− (0
.1 +
0.2
+ 0
.1)
or
1 −
0.4
oe
0.
6 2
M1
or 0
.6 in
tab
le
A1 a
llow
in t
able
if n
ot c
ontr
ad o
n lin
e Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
20(b
) 0.
2 +
0.1
or
1 −
(‘0.
6’ +
0.1
) 0.
3 2
M1
or 0
.3 s
een
A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
20(c
)
(Pos
s) o
verl
ap o
r m
ut e
xcl
or d
oesn
’t w
k fo
r B
or Y
{N
o or
pos
s or
pos
s ye
s}
2 B2
B1
Can’
t te
ll an
d (N
o or
pos
s)
B1 C
orre
ct r
easo
n on
ly
B0 In
corr
ect
reas
on
B0 U
nqua
lifie
d Ye
s
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)112
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
21
42 + 6
2 (=
52)
(4
2 + 6
2 )
or
“52”
or
2√13
h =
7.21
…
3 M
1 M
1 de
p A1
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 113
=
Pap
er 3
H
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
1(a)
1.989.
68
7.57
03…
2
M1
for
8.3,
68.
89,
9.1
or 3
0.90
…
A1 A
ccep
t if
fir
st 5
fig
ures
cor
rect
Also
acc
ept
910
519
7,
910
6889
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
1(b)
7.57
1
B1 f
t fr
om (
a) if
non
-tri
vial
ie (
a) m
ust
have
mor
e th
an 2
d.p
.
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
2(a)
(−
3)2 −
5 ×
−3
24
2
M1
for
subs
tn o
r 9
or 1
5 se
en
A1 c
ao
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
2(b)
)5(
−xx
2
B2
B1 f
or f
acto
rs w
hich
, w
hen
expa
nded
and
sim
plif
ied,
giv
e tw
o
ter
ms,
one
of
whi
ch is
cor
rect
SC
B1 f
or x
(5 −
x ),
x (x
− 5
x )
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
3 (4
6 ×
3) +
(47
× 6
) +
(4
8 ×
3) +
(49
× 5
) +
(5
0 ×
2) +
(51
× 1
) or
13
8 +
282
+ 14
4 +
245
+ 10
0 +
51 o
r 96
0
“VSM
Ò=÷=OM
=
48
3 M
1 f
or f
indi
ng a
t le
ast
4 pr
oduc
ts a
nd a
ddin
g M
1 (d
ep)
for
divi
sion
by
20
A1 c
ao
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)114
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
4(a)
tran
slat
ion
3 sq
uare
s to
th
e ri
ght
and
1 sq
uare
do
wn
2 B2
B1
for
tran
slat
ion.
Acc
ept
tran
slat
e,
t
rans
late
d et
c
A
ccep
t ‘a
cros
s’ i
nste
ad o
f ‘t
o th
e
rig
ht’
B1 f
or 3
rig
ht a
nd 1
dow
n or
−
13
but
not
(3,
−1)
Thes
e m
arks
are
in
depe
nden
t bu
t aw
ard
no m
arks
if
answ
er is
not
a s
ingl
e tr
ansf
orm
atio
n
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
4(b)
rota
tion
of
90°
cloc
kwis
e ab
out
(2,
−1)
3 B3
B1
for
rota
tion
Acc
ept
rota
te,
rota
ted
etc
B1 f
or 9
0° c
lock
wis
e or
−90
° or
270
° B1
for
(2,
−1)
Thes
e m
arks
are
in
depe
nden
t bu
t aw
ard
no m
arks
if a
nsw
er is
no
t a
sing
le
tran
sfor
mat
ion
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
5(a)
(i)
78
1 B1
cao
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
5(a)
(ii)
56 1
B1 c
ao
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
5(b)
9
+ 4
− n
= 8
or
13 −
n =
8
5 2
M1
Also
aw
ard
for
2n = 2
5 , 2n =
32 o
r 25 o
n an
swer
line
A1
cao
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 115
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
6(a)
4
815
12−
−−
xx
19
4−x
2
M1
for
at le
ast
3 te
rms
corr
ect
inc
sign
s A1
cao
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
6(b)
24
83
2+
++
yy
y
2411
2+
+y
y
2 M
1 fo
r 3
term
s co
rrec
t or
y
y11
2+
seen
A1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
6(c)
5p3 +
4p
2 B2
cao
B1
for
eit
her
5 p3 or
for
+ 4p
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
7(a)
60
215.
38×
or
35.0=
6021;
35.05.
38
110
3 M
1 fo
r 21
5.38
or 1
.833
3… o
r 35.05.
38 o
r 18
3.33
3…
or 6021
or
0.35
M1
for
“1.8
333…
” ×
60 o
r "
35.0"5.
38
A1 c
ao
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
7(b)
38
500
19.42
××
π
2 12
0 00
0 3
M2
M1
for
× (
no w
ith
digi
ts 4
19)2 ×
no.
wit
h di
gits
385
A1
for
2 1
20 0
00 o
r fo
r an
swer
whi
ch r
ound
s to
2 1
20 0
00
(
212
3433
.419
3.
14
212
2356
.929
3.
142
212
3708
.749
)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)116
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
8(a)
45
0027
0×
100
6 2
M1
for
4500
270
or
0.06
or
4500
4770
or
1.06
A1 c
ao
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
8(b)
11
7 ×
5.4100
26
00
2 M
1 fo
r 5.4117
or 2
6 se
en
A1 c
ao
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
8(c)
04.13328
or 3
328
× 10
410
0
3200
3
M2
for
04.13328
or
3328
× 10
410
0
M1
for
104
3328
, 10
4% =
332
8 or
32
seen
A1 c
ao
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
9 (a
) x5
−
x2 =
7 +
4
311,
323
oe
2 M
1 fo
r co
rrec
t re
arra
ngem
ent
A1 a
lso
acce
pt 2
or
mor
e d.
p. r
ound
ed o
r tr
unca
ted
eg 3
.66,
3.6
7
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 117
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
9(b)
4
× 42
7y
−or
7 −
y2
= 4(
y2+
3)
12
82
7+
=−
yy
or
sim
pler
510
−=y
21−
oe
4
M1
for
clea
r in
tent
ion
to m
ulti
ply
both
sid
es b
y 4
or a
mul
tipl
e
of 4
.
For
exam
ple,
aw
ard
for
4 ×
427
y−
or 7
−
y2
= 4
× y2
+ 3
or
y8+
3 or
y2
+ 3
× 4
or
y2+
12
M1
for
corr
ect
expa
nsio
n of
bra
cket
s (u
sual
ly
128
+y)
or f
or
corr
ect
rear
rang
emen
t of
cor
rect
ter
ms
eg
y8+
y2=
7 −
12
A1 f
or r
educ
tion
to
corr
ect
equa
tion
of
form
ay
= b
A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
10(a
) 15
0 ×
53
90
3 Ac
cept
dec
imal
s
B1 f
or 53
see
n
M1
for
150
× 53
A1 c
ao
do n
ot a
ccep
t 15
090
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
10(b
)(i)
43
×54
2012
or
53 o
e 2
Acce
pts
deci
mal
s
M1
for
43×
54 s
een
A1
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)118
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
10(b
)(ii)
42
×53
+41
×52
208
or 52
oe
3 Ac
cept
s de
cim
als
M1
for
41×
52 o
r 42
×53
M1
(dep
) fo
r ad
ding
bot
h ab
ove
prod
ucts
A1
for
208 o
r 52
oe
SC M
1 fo
r 52
×52
or
53×
53
SC M
1 (d
ep)
for
addi
ng b
oth
abov
e pr
oduc
ts
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
11(a
)
tang
ent
at a
ny p
oint
of
a ci
rcle
and
the
rad
ius
at
that
poi
nt a
re
perp
endi
cula
r
1 B1
for
men
tion
of
tang
ent
and
radi
us o
r lin
e fr
om c
entr
e
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
11(b
) 6.
92 − 5
.72 o
r
47.6
1 −
32.4
9 or
15.
12
√(6.
92 − 5
.72 )
3.
8884
4…
2 ×
5.7
+ 2
× “3
.888
44…
”
19.2
5
M1
for
squa
ring
and
sub
trac
ting
M
1 (d
ep)
for
squa
re r
oot
A1 f
or 3
.89
or b
ette
r M
1 fo
r 2
× 5.
7 +
2 ×
“3.8
88..
” on
ly
A1 f
or 1
9.2
or a
nsw
er w
hich
rou
nds
to 1
9.2
(19.
1768
88…
)
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
12(a
)
10,
26,
41,
50,
56,
60
1 B1
cao
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 119
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
12(b
) Po
ints
cor
rect
Curv
e or
line
seg
men
ts
2B1
+ ½
sq
ft f
rom
sen
sibl
e ta
ble
B1
ft
if 4
or
5 po
ints
cor
rect
or
if p
oint
s ar
e pl
otte
d co
nsis
tent
ly
wit
hin
each
inte
rval
(in
c en
d po
ints
) at
the
cor
rect
hei
ght
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
12(c
)U
se o
f w
= 4
30 o
n gr
aph
Appr
ox 1
6 2
M1
may
be
show
n on
gra
ph o
r im
plie
d by
43,
44
or 4
5 st
ated
A1
if M
1 sc
ored
, ft
fro
m c
umul
ativ
e fr
eque
ncy
grap
h
If
no m
etho
d sh
own,
ft
only
fro
m c
orre
ct c
urve
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
13
lines
regi
on
4B3
B1
for
each
cor
rect
line
(fu
ll or
bro
ken)
Ign
ore
addi
tion
al li
nes
B1 f
or c
orre
ct r
egio
n sh
aded
in o
r ou
t or
for
cor
rect
reg
ion
lab
elle
d R
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
14(a
) r2 =
A
A2
M1
for
r2 = A
orr2 =
A
A1 Ig
nore
±
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)120
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
14(b
)(i)
5.
132.
0729
6…
2M
1 fo
r 13
.5 s
een
A1 f
or a
nsw
er w
hich
rou
nds
to 2
.073
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
14(b
)(ii)
5.
14or
2.1
4836
…
2.1
2M
1 fo
r 5.
14 o
r va
lue
whi
ch r
ound
s to
2.1
48 o
r 2.
149
cao
A1 d
ep o
n pr
evio
us 3
mar
ks in
(b)
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
15(a
)(i)
wkf
wf
3000
002
M1
may
be
impl
ied
by
200
1500
k
A1 A
lso
awar
d if
ans
wer
is f
=wk
but
kis
eva
luat
ed a
s
300
000
in (
a) o
r (b
)
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
15(a
)(ii)
f
w
2B2
B1
for
grap
h w
ith
nega
tive
gra
dien
t (i
ncre
asin
g or
con
stan
t)
e
ven
if it
tou
ches
or
cros
ses
one
or b
oth
axes
eg
f
wO
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 121
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
15(b
) f =
12
5030
0000
24
0 2
M1
for
subs
titu
tion
in f
= wk
A1 f
t fr
om k
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
16(a
)(i)
3b
1 B1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
16(a
)(ii)
3 b −
a
1 B1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
16(a
)(iii
)
32a
+ b
or a
+ 31
(3b
− a)
or 3
b −
32(3
b −
a) o
e
1 B1
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)122
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
16(b
) 32
a
or 32
PQ
or k
= 32
or a
+ 31
(3b
− a)
− b
or 32
a +
b −
b
or (
a)(i
ii) −
b
or −
b +
a +
31(3
b −
a)
or −
b +
a +
31(a
)(ii)
or 2
b −
32(3
b a
)
or 2
b −
32(a
)(ii)
o
e
2
B2 f
or 32
a or
32PQ
or
k =
32un
less
cle
arly
obt
aine
d by
non
-vec
tor
met
hod
or f
or e
xpre
ssio
n in
ter
ms
of a
and
/or
b (n
eed
not
be s
impl
ifie
d)
for
EF e
ithe
r co
rrec
t or
ft
from
(a)
B1
for
cor
rect
vec
tor
stat
emen
t w
ith
at le
ast
3 te
rms
whi
ch
incl
udes
EF
(or
FE)
in t
erm
s of
cap
ital
lett
ers
and/
or a
, b
eg P
Q =
PE
+ EF
+ F
Q
PF =
PE
+ EF
a
= b
+ EF
+ F
Q
If a
n at
tem
pt is
cro
ssed
out
and
rep
lace
d, m
ark
all a
ttem
pts,
in
clud
ing
cros
sed
out
one,
and
aw
ard
best
mar
k.
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
17
=xy dd
2x
− 216 x
“2x
± 216 x
” =
0
(2,
12)
4
B1 f
or 2
x
B1 f
or ±
216 x
or
± 16
x2
M1
A1 c
ao
For
answ
er (
2, 1
2) w
ith
no p
rece
ding
mar
ks s
core
d, a
war
d B0
B0
M1
A1
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 123
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
18(a
) 2
28.2
421
8.273
.93
M2
M1
for
each
item
Al
so a
war
d fo
r va
lues
rou
ndin
g to
24.
6 an
d to
49.
2 or
49.
3 A1
for
73.
9 or
for
ans
wer
s w
hich
rou
nds
to 7
3.9
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
18(b
) 312
5 o
r 5
seen
25
73.
89…
1850
3M
1M
1 fo
r 25
(
a)
or f
or
(2.
8 ×
5)2
2 (
2.8
5)2
or f
or s
ubst
itut
ing
r= 2
.8
5 in
the
exp
ress
ion
used
in (
a)
A1 f
or 1
850
or f
or a
ny v
alue
in r
ange
184
6.3
847
.5
ft f
rom
25
(a)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)124
== Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
19
5)1
3(2
2=
−+
xx
51
33
92
2=
+−
−+
xx
xx
or
5
16
92
2=
+−
+x
xx
04
610
2=
−−
xx
()(
)0
22
25
=−
+x
x
or (
)()
01
25
=−
+x
x
or (
)()
01
410
=−
+x
x
or
2019
66
± o
r 10
493
±
or
1049103
±
52−
=x,
512
−=y
1=x,
2=y
52−
=x,
512
−=y
1=x,
2=y
6 M
1 fo
r co
rrec
t su
bsti
tuti
on
B1 (
inde
p) f
or c
orre
ct e
xpan
sion
or
(x3=−
1)2 e
ven
if u
nsim
plif
ied
B1 f
or c
orre
ct s
impl
ific
atio
n B1
for
cor
rect
fac
tori
sati
on
or f
or c
orre
ct s
ubst
itut
ion
into
the
qua
drat
ic f
orm
ula
and
corr
ect
eval
uati
on o
f ‘ b
2 − 4
ac’
or f
or u
sing
squ
are
com
plet
ion
corr
ectl
y as
far
as
is in
dica
ted
A1 f
or b
oth
valu
es o
f x
A1 f
or c
ompl
ete,
cor
rect
sol
utio
ns
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 125
Pap
er 4
H
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
1(i)
xx2
1
x3 5
1
7 1
B1 o
e eg
x6
4 1
7 IS
W n
ot ‘
p’
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
1(ii)
x6 2
1 or
x6
21
0
etc
x=
3.5
oe
eg
6212
M1
ft
(i)
if
x6c
A1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
29
seen
97 2
7 or
7
927 o
e
213
B1 M1
dep
B1
A1 2
1 se
en a
nd a
ns
3 B
1M1A
O
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
3x5
20
35
x5=
55
113
M1
M1
dep
or M
2 fo
r x
4
7
A1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
4(a)
250×
7or
7,
50,
2 2
B1 f
or 7
and
2
B1 f
or 5
0
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
4(b)
175
200
or 1
00
2M
1 ft
fro
m (
a),
(175
see
n, u
sing
3
or2
)50
or48()7
or6(
c
orre
ctly
eval
’d e
g 16
8)
A1f
I
f no
wki
ng:
ft (
a)
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)126
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
4(c)
Num
ber
incr
or
6.8
and
47.6
incr
de
nom
dec
r or
2.0
9 de
cr
(b)
rnde
d up
(no
t rn
d to
1
sf)
or ‘
175’
rnd
ed t
o 20
0
2 B2
any
tw
o of
the
se
B1 a
ny o
ne o
f th
ese
Ig
nore
oth
er
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
5(a)
6
×2
)3+
2( o
r
2 ×
6 +
21 ×
6 ×
1 o
e
15
2 M
1 A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
5(b)
2015
× 1
000
201000
× 1
5
1000
× 2015
750
3 M
1 or
0.7
5 M
1 ft
‘15
’ fo
r M
1M1
only
A1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
6 x
+ 3
= x7
(x6
= 3
oe)
y7=
x7 +
21
(
y6=
21)
x =
21,
y=
213
3
M1
y=
)3
(7−
y
y=
y7−2
1
0 =
x6
−3
A1
A1
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 127
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
7(a)
tan
used
xta
n2.41.5
or
xta
n 1
.2…
. o
e
x 5
0.5…
3
M1
(sin
or
cos)
and
( (
4.2
2+
5.1
2)
or 6
.6)
used
M
1x
sin
= 5
.1/(
(4.
22+
5.1
2)
or c
osx
= 4.
2/(
(4.
22+
5.1
2)
A1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
7(b)
sin2
9AB
/5 o
r
C/s
in29
5
/sin
90
AB
5si
n29
AB
2.42
…cm
3
M1
B
C 5
cos2
9 M
1
AB
(5
2 (
5cos
29)2 )
or 5
cos2
9 t
an29
A1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
8(a)
1 (
0.1
+ 0.
2 +
0.1)
or
1
0.4
oe
0.
62
M1
or 0
.6 in
tab
le
A1 a
llow
in t
able
if n
ot c
ontr
ad o
n lin
e
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
8(b)
0.2
+ 0.
1 or
1
(‘0
.6’
+ 0.
1)
0.3
2M
1 or
0.3
see
n A1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
8(c)
(P
oss)
ove
rlap
or
mut
exc
l or
doe
sn’t
wk
for
B or
Y
{No
or p
oss
or p
oss
yes}
2B2
B1
Can’
t te
ll an
d (N
o or
pos
s)
B1 C
orre
ct r
easo
n on
ly
B0 In
corr
ect
reas
on
B0 U
nqua
lifie
d Ye
s
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)128
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
942 +
62 (
= 52
)
(42 +
62 )
or“5
2” o
r 2
13
h =
7.21
…
3M
1M
1 de
p A1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
10(a
) V/
H in
any
cor
rect
tr
iang
le a
ttem
pted
Gra
d =
2, m
ay b
e em
bedd
ed o
r im
plie
d
y =
‘2’ x
1
4M
1 eg
01
13
not
13
A1 M1
B2f
B1f
for
grad
. B1
for
y -
int
(lin
eqn
) or
B1f
for
jus
t ‘2
’x 1
N
o w
king
, an
s x2
1:
M1A
1 B1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
10(b
) y
=2
±c
1B1
yx2
± an
y no
. (n
ot 5
) or
lett
er o
r y
x2
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
10(c
)(0
,4)
1B1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
11(a
)
56
1B1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
11(b
)
12620x
or
84 o
e 10
or
10.0
…
2M
1 or
x/s
in30
= 2
0/si
n(18
0 3
0 5
6)
A1
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 129
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
11(c
)
6410y
or128
oe
6.6
to 6
.7 in
cl o
e 2
M1
or y
=(4
2 8
2 2
4
8
c
os‘5
6’)
or y
/sin
56 =
8/s
in(1
80
30
56)
A1 (
a)(b
): f
t (a
) M
-mks
onl
y
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
12(a
) 27 aa
or4 a
a o
r
23
aa
5 a2
M1
A1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
12(b
) 3 x
1B1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
12(c
)Co
rrec
tly
canc
el
num
bers
or
( x +
1)
21(x
+ 1
) or
0.5
(x+
1)
or21
2or
21
xx
or
equi
v
2M
1 eg
21 o
r 0.
5 or
den
om =
2
or6
)1(3x
or
63
3x o
r )1
(xk
A1 N
ot IS
W
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
13(a
) At
tem
pt a
rran
ge o
ne
set
in o
rder
St
ate
or in
dica
te
corr
ect
15 a
nd 4
or
14 a
nd 6
Clas
s A:
11
Clas
s B:
8 4
M1
M1
NB:
IQR
for
B =
8, c
heck
wki
ng
A1 A1
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)130
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
13(b
)
A m
ore
spre
ad o
r gt
er
disp
ersi
on o
r le
ss c
onsi
sten
t th
an B
1B1
B1f
Con
sist
ent
wit
h (a
). Ig
nore
oth
er.
Not
: gt
er “
rang
e” o
r “d
iffe
renc
e”or
“m
ore
cons
tant
” or
“gt
er IQ
R” o
r “g
ter
vari
ance
”
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
14x5
7 =
2 x
1
orx5
7 =
(x 1
)( x
1)
2 xx5
6 =
0
(x 2
)(x
3)
(= 0
)
or2
64
)5(
52
x =
2 or
3
4M
1 c
ondo
ne
x5 7
= x
1 ×
x 1
M
1 a
llow
dif
fere
nt o
rder
wit
h =
0 M
1 (
x 2
.5)2 +
6
6.2
5 A1 T
& I
or n
o w
king
: 4
mks
or
0 m
ks
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
152
over
lapp
ing
circ
les,
12
in o
verl
ap
6 in
H o
nly
2 in
T o
nly
144
M1
M1
or 6
pla
y H
onl
y M
2 M
1 or
20
6,
6 1
2 x
20,
20
18,
35
33:
M3
A1 a
ns 2
: M
3A0
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
1692 +
52
2 ×
5 ×
9 ×
x
cos
62
90x
cos
70
or
90
xco
s70
(x
cos
9070)
x 3
8.9
or b
ette
r3
M1
or
xco
s9
52
65
92
22
M2
M1
A1
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 131
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
17(a
)(i)
2 1
B1 o
r 2
x o
r 2
x
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
17(a
)(ii)
x <
1 2
B2
B1 f
or x
< 1
or
0,
1,
2,
3…
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
17(b
) 9
or
(10
1)
291
51 o
r 0.
2
3M
1
M1
or
2)1
(1
x
A1 ig
nore
ans
=
1 Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
17(c
)
)1(x
y
2 y=
x 1
x
2 y 1
1,
Reve
rse
orde
r sq
u, +
1
1)
(2
1x
xg
oe
4M
1 M
1
1
xy
y
M1
M1d
ep
xy
x1
M
1
2 x
1y
A1
A11
2 y M
3
12 x
y M
3
12 x
x M
3
S
C x
g1
2
1x
: B1
cond
one
x-1
if
next
ste
p
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)132
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
18(a
)
6161
61 a
lone
21
61 o
r 0.
0046
…
2M
1 0.
173 o
r 0.
163 o
r be
tter
. N
ot
kA1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
18(b
) 1,
1,
4 or
1,
2, 6
or
2,
1,
6 se
en o
r im
plie
d 1,
1,
4 an
d 1,
2,
6(or
2,
1, 6
) se
en o
r im
plie
d
361
3
721 o
r 21
63 o
r 0.
014
or
bett
er
4M
1 ie
one
rou
te
M1
ie t
wo
rout
es in
cl 1
, 1,
4
M1
ie t
hree
rou
tes
and
corr
ect
exp’
n
A12
613
or
1081
, no
wki
ng:
M0A
0
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
19(a
) ×
5×
5×
21si
n60
10.8
…2
M1
21×
5 ×
(2 5
2
25)
or
21×
5 ×
4.33
A14
)325(
M1A
O
Edexcel IGCSE in Mathematics (Specifi cation A) © Edexcel Limited 2008 Sample Assessment Materials 133
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
19(b
) se
ct =
61 5
2 o
r 13
.1
“10.
8” 2
(61
52
10.
8”)
or “
10.8
” 2
2
.26
or 261
52
0.8
”
15.4
cm
23
M1
M1
+ 2
(sec
t )
or
2 ×
sect
Allo
w e
g =
21 5
5
A1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
20(a
)
20
1M
1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
20(b
)
30
2B2 B1
1sq
rep
s fr
eq o
f 5
seen
any
whe
re
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
21(a
) 1
41
4x
x1
B1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
21(b
)(i)
16
102
1 s
een
or
impl
ied
(4 1
0 1
) (4
10
1)
or 3
9 4
1
313
41
3M
1 13
or
39 o
r 41
or
123
as f
acto
r
M1
fact
ors
3, 1
3, 4
1 or
39,
41
or 1
3, 1
23
A1 Ans
3 5s
33 M
0A0
Sample Assessment Materials © Edexcel Limited 2008 Edexcel IGCSE in Mathematics (Specifi cation A)134
= Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
21(b
)(ii)
15
99 ×
103
or 1
599
× 10
00
‘3 ×
13
× 41
’ ×
23 × 5
3 oe
2
M1
or t
ree
incl
udin
g 10
00 o
r 10
and
100
A1
f ft
(i)
× 2
3 × 5
3
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