Edexcel Level 1/Level 2 Certificate Mathematics Edexcel Level 1/Level 2 Certificate in Mathematics (KMA0) First teaching from September 2011 Sample Assessment Material (SAMs)
Edexcel Level 1/Level 2 CertificateMathematics
Edexcel Level 1/Level 2 Certificate in Mathematics (KMA0)
First teaching from September 2011
Sample Assessment
Material (SAMs)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 1
Contents
General marking guidance 2
Paper 1F 3Sample Assessment Material 3
Sample Mark Scheme 21
Paper 2F 31Sample Assessment Material 31
Sample Mark Scheme 51
Paper 3H 59Sample Assessment Material 59
Sample Mark Scheme 79
Paper 4H 89Sample Assessment Material 89
Sample Mark Scheme 109
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 20112
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.
All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, ie 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.
Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response.
Guidance on the use of codes within this mark scheme M1 – method mark A1 – accuracy mark B1 – working mark oe – or equivalent cao – correct answer only ft – follow through sc - special case
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 3
Centre Number Candidate Number
Write your name hereSurname Other names
Total Marks
Paper Reference
Turn over
*S39742A0118*
MathematicsPaper 1F
Foundation Tier
Sample Assessment MaterialTime: 2 hours
You must have:
Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
KMA0/1F
Instructions
• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answer all questions.• Without sufficient working, correct answers may be awarded no marks.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators may be used.
• You must NOT write anything on the formulae page. Anything you write on the formulae page will gain NO credit.
Information
• The total mark for this paper is 100. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.
Advice
• Read each question carefully before you start to answer it.• Write your answers neatly and in good English.• Check your answers if you have time at the end.
S39742A©2010 Edexcel Limited.
Edexcel Certificate L1/L2
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 20114
IGCSE MATHEMATICS 4400
FORMULAE 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
FORMULA SHEET – FOUNDATION TIER
You must not write on the fomulae page. Anything you do write will gain no credit.
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 5
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
1 15 21 23 24 25 27 33 35 39
From the numbers in the box, write down(5)
(i) an even number
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) a factor of 60
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(iii) a multiple of 9
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(iv) a square number
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(v) a prime number.
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(Total for Question 1 = 5 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 20116
2 The diagram shows a triangle ABC on a centimetre grid.
(a) Write down the coordinates of the point(2)
(i) A, (. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . .)
(ii) B. (. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . .)
(b) Measure the length of the line AB. Give your answer in millimetres.
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mm
(c) Find the perimeter of triangle ABC.(2)
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(d) Write down the special name for triangle ABC.(1)
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(e) (i) Measure the size of angle B.(1)
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(ii) Write down the special name for this type of angle.(1)
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(Total for Question 2 = 8 marks)
O 1 2 3 4 5 6 7 8 9 10 x
y6
5
4
3
2
1
A C
B
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 7
3 (a) Write down the number which is exactly halfway between 0.3 and 0.4
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(1)
3.7 3.8
(b) What is the reading on the scale?
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(1)
(c) Write down the value of the 4 in the number 0.746
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(1)
(d) Here is a list of numbers.
0.3 0.32 0.02 0.23 0.03
Write these numbers in order of size.Start with the smallest number.
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(1)
(e) Write 34
as a decimal.
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(1)
(f) Write 0.7 as a percentage.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %(1)
(g) Round 6.84 to the nearest whole number.
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(1)
(Total for Question 3 = 7 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 20118
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)
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(b) Explain how you worked out your answer.(1)
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(c) Find the 11th term of the sequence.(1)
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(d) The 50th term of the sequence is 295 Work out the 49th term of the sequence.
(1)
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Tamsin says, “Any two terms of this sequence add up to an even number.”
(e) Explain why Tamsin is right.(1)
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(Total for Question 4 = 5 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 9
5 Here are 9 flags.
(a) Write down the letter of the flag which has:(4)
(i) exactly one line of symmetry
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) rotational symmetry of order 4
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(iii) 2 lines of symmetry and rotational symmetry of order 2
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(iv) no lines of symmetry and rotational symmetry of order 2
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(b) Write down the letter of the flag which has a rhombus on it.(1)
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(Total for Question 5 = 5 marks)
A B C
D E F
G H I
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201110
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.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . million
(b) Write down the number of people who speak Mandarin Chinese.(1)
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(c) Which language is spoken by 190 million people?(1)
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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)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 11
330 million people speak English. 70% of these people live in the USA.
(f) Work out 70% of 330 million.(2)
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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)
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(Total for Question 6 = 10 marks)
7 (a) Solve 2x + 9 = 1(2)
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Solve 5y – 4 = 2y + 7(2)
y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 7 = 4 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201112
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.
City
Time 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:(2)
(i) Bangkok,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) Los Angeles.
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(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(2)
(i) Cairo and Montreal,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hours
(ii) Rio de Janeiro and Los Angeles.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hours
(Total for Question 8 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 13
9
£1 = 72.5 Indian rupees
(a) Change £86 to Indian rupees.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indian rupees(2)
(b) Change 8700 Indian rupees to pounds (£).
£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
(Total for Question 9 = 4 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201114
10
Write down the equation of(3)
(i) line A,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) line B,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(iii) line C.
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(Total for Question 10 = 3 marks)
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)
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(Total for Question 11 = 3 marks)
8
6
4
2
–2
–2 2 4 6 8O x
y
BC
A
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 15
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)
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(b) Find the probability that he will take a white square.(2)
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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)
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(Total for Question 12 = 5 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201116
13 A basketball court is a rectangle, 28 m long and 15 m wide.
(a) Work out the area of the rectangle.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2
(b) In the space below, make an accurate scale drawing of the rectangle. Use 1 cm to represent 5 m.
(2)
(Total for Question 13 = 4 marks)
14 (a) Work out the value of x2 – 5x when x = –3(2)
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(b) Factorise x2 – 5x(2)
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(Total for Question 14 = 4 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 17
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)
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(c) Work out the mean number of sweets in the 20 packets.(3)
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(Total for Question 15 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201118
16
P
Q
R
y4
3
2
1
-1
-2
-2 -1 0 1 2 3 4 5 6 7 x
(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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 = 5 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 19
17 (a) Simplify, leaving your answers in index form,(2)
(i) 75
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) 59
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Solve 9 4
82 2 22n×
=(2)
n = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 17 = 4 marks)
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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 18 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201120
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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . km/h
(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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m3
(Total for Question 19 = 6 marks)
TOTAL FOR PAPER = 100 MARKS
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 21
Sam
ple
Mar
k Sc
hem
e Pa
per
1F
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
1 (i
) 24
1B1
cao
1
(ii)
15
1B1
cao
1
(iii)
27
1B1
cao
1
(iv)
25
1B1
cao
1
(v)
231
B1 c
ao
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
2(a)
(i)
(1,5
)1
B12(
a)(i
i)(5
,0)
1B1
2(b)
641
B1 A
llow
+2m
m
2(c)
8(0)
+ 2
x “
64”
204
– 21
2 in
c 2
M1
Also
aw
ard
for
20.4
– 2
1.2
A1 f
t fr
om “
64”
2(d)
isos
cele
s1
B12(
e)(i
) 77
1B1
allo
w +
2
2(e)
(ii)
acut
e1
B1
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201122
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
3 (a
) 0.
351
B1 c
ao
3 (b
) 3.
741
B1 c
ao
3 (c
) hu
ndre
dths
1B1
Als
o ac
cept
4 h
undr
edth
s, 10
01,
1004
, 0.
01, 0
.04
3 (d
) 0.
02 0
.03
0.2
3 0
.3 0
.32
1B1
cao
3
(e)
0.75
1B1
cao
3
(f)
701
B1 c
ao
3 (g
) 7
1B1
cao
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
4(a)
311
B1 c
ao
4(b)
eg ‘
Add
6’
1B1
4(c)
611
B1 c
ao
4(d)
289
1B1
ft
from
(b)
4(
e)eg
‘Su
m o
f tw
o od
d nu
mbe
rs is
alw
ays
even
’ 1
B1 A
ccep
t if
‘od
d’ u
sed
corr
ectl
y
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 23
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
5(a)
(i)
B1
B1 c
ao
5(a)
(ii)
F1
B1 c
ao
5(a)
(iii)
I1
B1 c
ao
5(a)
(iv)
D1
B1 c
ao
5(b)
H1
B1 c
ao
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
6(a)
300
1B1
cao
6(
b)85
5 -
875
1B1
6(c)
Beng
ali
1B1
6(d)
100
< ba
r <
150
1B1
6(e)
300:
125
12:5
2M
1 f
or 3
00:1
25,
60:2
5 al
so f
or 1
25:3
00,
25:6
0, 5
:12
A1
6(f)
100
70 3
30
231
2M
1 fo
r 10
070
330
A1 f
or 2
31
6(g)
100
332
143
43.1
2M
1 f
or 33
214
3 o
r 0.
4307
22…
A1 f
or 4
3.1
or b
ette
r
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201124
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
7(a)
x2=
1 9
4
oe
2M
1 fo
r x2
= 1
9 [
sepa
rate
evi
denc
e of
M1
is r
equi
red]
A1
for
4
oe
7(b)
y5y2
= 7
+ 4
311,
332
oe
2M
1 fo
r y5
y2=
7 +
4 [s
epar
ate
evid
ence
of
M1
is r
equi
red]
A1 f
or
311, 3
32 o
e
Also
acc
ept
2 or
mor
e d.
p. r
ound
ed o
r tr
unca
ted
e.g.
3.6
6, 3
.67
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
8(a)
(i)
1 pm
1
B1 f
or 1
pm
Acce
pt 1
300
8(a)
(ii)
10 p
m
1B1
for
10p
m
Acce
pt 2
200
8(b)
61
B1 c
ao
8(c)
Rio
de J
anei
ro
1B1
for
Rio
de
Jane
iro
Acce
pt R
io
8(d)
(i)
71
B1 f
or 7
Ac
cept
-7
8(d)
(ii)
51
B1 f
or 5
Ac
cept
-5
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 25
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
9 (a
) 86
× 7
2.5
6235
2M
1 fo
r 86
× 7
2.5
A1 c
ao
9 (b
) 87
00 ÷
72.
5 12
02
M1
for
8700
÷ 7
2.5
A1 c
ao
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
10(i
)y
= 3
1B1
cao
10
(ii)
x =
5 1
B1 c
ao
10(i
ii)x
y1
B1 c
ao
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
11(a
) 1.989.
687.
5703
…
2M
1 fo
r 8.
3, 6
8.89
, 9.
1 or
30.
90…
A1
Acc
ept
if f
irst
5 f
igur
es c
orre
ct
Also
acc
ept
791
051
9,
910
6889
11(b
) 7.
571
B1 f
t fr
om (
a) if
non
-tri
vial
ie (
a) m
ust
have
mor
e th
an 2
d.p
.
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201126
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
12(a
) 51
1B1
for
51
Acce
pt 0
.2,
20%
12
(b)
532
M1
for
frac
tion
wit
h de
nom
inat
or 5
A1 f
or 53
, Ac
cept
0.6
, 60
%
12(c
)15
0 x
“53
”90
2M
1 fo
r 15
0 x
“53
”
A1 f
t fr
om “
53”
Do
not
acce
pt 15
090
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
13(a
) 28
× 1
5 42
02
M1
for
28 ×
15
A1 c
ao
13(b
) Re
ctan
gle
5.6c
m lo
ng a
nd
3cm
wid
e 2
B2 f
or a
n ac
cura
te s
cale
dra
win
g of
the
rec
tang
le/
Allo
w +
2m
m
B1 f
or e
ithe
r le
ngth
or
wid
th.
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
14(a
) (-
3)2
5
324
2M
1 fo
r su
bstn
or
9 or
15
seen
A1
cao
14
(b)
)5(xx
2B2
for
)5
(xxB1
for
fac
tors
whi
ch,
whe
n ex
pand
ed a
nd s
impl
ifie
d, g
ive
two
t
erm
s, o
ne o
f w
hich
is c
orre
ct S
C B1
for
x (5
- x
),x
(x -
5x )
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 27
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
15(a
) 47
1B1
cao
15
(b)
51 4
65
2M
1 f
or 5
1 4
6, 4
6 5
1 et
c
A1 c
ao
15(c
)(4
63)
(47
6)
(48
3) (
49
5)(5
02)
(51
1)
or
13
8 2
82
144
2
45
100
51 o
r 96
0
“960
” 2
0
483
M1
for
fin
ding
at
leas
t 4
prod
ucts
and
add
ing
M1
(dep
on
1st
M1)
for
div
isio
n by
20
A1 c
ao
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
16(a
)
tran
slat
ion
3 sq
uare
s to
th
e ri
ght
and
1 sq
uare
do
wn
2 B2
for
cor
rect
des
crip
tion
of
the
tran
sfor
mat
ion
B1 f
or t
rans
lati
on.
Acce
pt t
rans
late
,
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
16(b
) ro
tati
on o
f 90
° cl
ockw
ise
abou
t (2
, 1)
3
B3 f
or c
orre
ct d
escr
ipti
on o
f th
e tr
ansf
orm
atio
nB1
for
rot
atio
n
A
ccep
t ro
tate
, ro
tate
d et
c B1
for
90°
clo
ckw
ise
or
90°
or 2
70°
B1 f
or (
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
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201128
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
17(a
)(i)
78
1B1
cao
17
(a)(
ii)
561
B1 c
ao
17(b
) 9
4
n =
8 or
13n
= 8
52
M1
for
9 4
n
= 8
or b
ette
r Al
so a
war
d fo
r 2n =
25 ,
2n = 32
or
25 on
answ
er li
ne
A1 c
ao
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
18(a
) 4
815
12x
x19
4x2
M1
for
at le
ast
3 te
rms
corr
ect
inc
sign
s A1
18(b
) 24
83
2y
yy
2411
2y
y2
M1
for
3 te
rms
corr
ect
or
yy
112
seen
A118
(c)
5p3+
4p2
B2 c
ao B
1 fo
r ei
ther
5p3
or f
or+
4p
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 29
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
19(a
) 60
215.
38 o
r 35.0
=6021
;
35.05.
38
110
3M
1 fo
r 21
5.38
or 1
.833
3… o
r 35.05.
38 o
r 18
3.33
3…
or6021
or
0.35
M1
for
“1.8
333…
” 6
0 or
"
35.0"5.
38
A1 c
ao
19(b
) ×
4.1
9² ×
385
00
= 21
2343
3.41
9 m
³2
120
000
3M
2×
4.19
² ×
3850
0
[M1
for
× (
no w
ith
digi
ts 4
19)2 ×
no
wit
h di
gits
385
]
A1 f
or 2
120
000
or
for
answ
er w
hich
rou
nds
to 2
120
000
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201130
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 31
Turn over
S39745A©2010 Edexcel Limited.
*S39745A0120*
Centre Number Candidate Number
Write your name hereSurname Other names
Total Marks
Paper Reference
MathematicsPaper 2F
Foundation Tier
Sample Assessment MaterialTime: 2 hours
You must have:
Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
KMA0/2F
Instructions
• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answer all questions.• Without sufficient working, correct answers may be awarded no marks.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators may be used.
• You must NOT write anything on the formulae page. Anything you write on the formulae page will gain NO credit.
Information
• The total mark for this paper is 100. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.
Advice
• Read each question carefully before you start to answer it.• Write your answers neatly and in good English.• Check your answers if you have time at the end.
Edexcel Certificate L1/L2
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201132
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
FORMULA SHEET – FOUNDATION TIER
You must not write on the fomulae page. Anything you do write will gain no credit.
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 33
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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) From the list, write down an even number.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(iii) From the list, write down a number that is a multiple of 9
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(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.
(3)
(i) Write down the largest number that can be made.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) Write down the smallest odd number that can be made.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 1 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201134
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.
(Total for Question 2 = 3 marks)
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(3)
(i) OT,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) CT,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(iii) AB.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Write down the mathematical name for the shaded region.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 3 = 4 marks)
0 0.5 1
C
A
O
T
B
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 35
4 (a) Write the number 3969 in words(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Write a number in the box so that this is a correct calculation.
(1)
189 = 3969
(c) Write down the value of the 3 in the number 3969(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(d) Write the number 3969 correct to the nearest 10(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(e) Write the number 3969 correct to the nearest 100(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(f) Find the cube root of 3969
(i) Write down all the figures on your calculator display.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 4 = 7 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201136
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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 5 = 4 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 37
6 (a) What fraction of this shape is shaded?(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Find a fraction that is equivalent to 49 (1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) Here is a list of fractions.
720
310
925
1236
Which fraction in the list is the greatest fraction?(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 = 5 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201138
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.
£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 7 = 3 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 39
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)
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(d) The team that scored 4 points was The Cheetahs. Later, The Cheetahs had points taken away because of foul play.
(2)
(i) Will the median increase or decrease or stay the same?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) Give your reason.
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(e) A team is chosen at random from these 8 teams. Find the probability that this team scored more than 10 points.
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 = 10 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201140
9 The diagram shows a triangle drawn on a centimeter squared grid.
(a) Work out the area of the triangle.State the units of your answer.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b)(2)
On the grid, reflect the triangle in the dotted line.
(Total for Question 9 = 5 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 41
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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 = 8 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201142
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.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°
(ii) Give a reason for your answer to part (b)(i).(2)
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(Total for Question 11 = 3 marks)
A
B DC
y
x50°
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 43
12 Michelle has £4800
She gives 52 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)
£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 = 4 marks)
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.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) Solve your equation.
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 13 = 3 marks)
x (3x – 5)
(2x + 1)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201144
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
(Total for Question 14 = 3 marks)
15 Solve 5(x – 4) = 35
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 15 = 3 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 45
16 Julian has to work out 6 8 47 62 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 62 09
. ..
Give your answer correct to one significant figure.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) Without using your calculator, explain why your answer to part (b) should be greater than the exact answer.
(2)
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(Total for Question 16 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201146
17 The diagram shows a wall.
(a) Calculate the area of the wall.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2
(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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm3
(Total for Question 17 = 5 marks)
2 m3 m
6 m
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 47
18 Solve the simultaneous equations
y = x + 3y = 7x
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 18 = 3 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201148
19 (a)
Calculate the value of x. Give your answer correct to 3 significant figures.
(3)
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b)
Calculate the length of AB. Give your answer correct to 3 significant figures.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm
(Total for Question 19 = 6 marks)
5 cm
29°B
A
C
x°4.2 cm
5.1 cm
Diagram NOTaccurately drawn
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 49
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”
(2)
Is Beryl correct? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Give a reason for your answer.
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(Total for Question 20 = 6 marks)
PLEASE TURN OVER FOR QUESTION 21
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201150
21
Calculate the value of h. Give your answer correct to 3 significant figures.
h = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 21 = 3 marks)
TOTAL FOR PAPER = 100 MARKS
4 cm h cm
6 cm
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 51
Sam
ple
Mar
k Sc
hem
e Pa
per
2F
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
1(a)
(i)
19
9, 9
99,
1009
, 19
99,
9000
1B1
1(a)
(ii)
9000
1B1
1(a)
(iii)
999
or 9
000
1B1
1(b)
(i)
43
21
1B1
1(b)
(ii)
1243
2B2
B1
for
beg
in w
ith
1 or
end
wit
h 1
or 3
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
2(i)
A at
0.5
± 2
mm
1
B12(
ii)B
at 1
1
B12(
iii)
C at
2
d 2
5mm
fro
m 0
1
B1 ie
bet
wee
n 0
and
0.25
exc
lusi
ve
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
3(a)
(i)
Radi
us1
B1 a
llow
mis
spel
lings
3(
a)(i
i)Ch
ord
1B1
allo
w m
issp
ellin
gs
3(a)
(iii)
Tang
ent
1B1
allo
w m
issp
ellin
gs
3(b)
Sect
or1
B1 a
llow
mis
spel
lings
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201152
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
4(a)
Thre
e th
ousa
nd,
nine
hun
dred
and
six
ty n
ine
1B1
4(b)
211
B1 c
ao
4(c)
thou
sand
s1
B1 f
or t
hous
ands
or
3000
or
3 th
ousa
nd4(
d)39
701
B1 c
ao
4(e)
4000
1B1
cao
4(
f)(i
)
15.8
3289
…
1B1
4(f)
(ii)
15.8
1B1
ft
from
(f)
(i)
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
5(a)
4 5
2
22
2M
1 fo
r 4
5
2
A1 c
ao
5(b)
4287
2M
1 Al
low
430
or
ans
7.25
oe
A1 c
ao
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
6(a)
1251
B1 c
ao
6(b)
Answ
ers
from
,...
5015 ,412 ,
2712 ,188
1B1
cao
6(c)
2593
M1
for
atte
mpt
to
conv
ert
all t
o de
c or
% o
r c.
d. E
g 0.
35,
0.3,
0.
36,
0.33
3…
M1
for
all c
orre
ctly
con
vert
ed
A1
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 53
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
72
× 1.
10 +
3 ×
1.2
5 or
5.
9510
.00
– “5
.95”
4.05
3M
1 fo
r 2
× 1.
10 +
3 ×
1.2
5 or
5.9
5M
1 de
p on
1st
M1
A1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
8(a)
31
B1 c
ao
8(b)
x at
tem
pted
or
8567
3M
1 eg
48.
125
M1
dep
A1 c
ao
8(c)
Arra
nge
in o
rder
5.
5 oe
2
M1
for
arra
ngem
ent
in o
rder
A1
for
5.5
oe
8(d)
(i)
Sam
e1
B1 in
dep
8(d)
(ii)
Mid
dle
unch
ange
d 1
B1 o
r st
ill 5
.5
8(e)
82 o
e 2
B1 f
or d
enom
inat
or o
f 8
B1 f
or n
umer
ator
of
2 (S
C B1
for
2:8
)
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
9(a)
6cm
23
B2 f
or 6
B1
(in
depe
nden
t) f
or c
m2 o
e (B
1 fo
r 5
to 7
incl
) 9(
b)Tr
iang
le c
orre
ctly
dra
wn
2
B2 f
or c
orre
ct t
rian
gle
draw
n 2
mm
or B1
for
tw
o ve
rtic
es c
orre
ct
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201154
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
10(a
) (6
3)
5
oe
452
M1
Brac
ket
esse
ntia
l unl
ess
answ
er is
cor
rect
A1
for
45
10(b
) 570
or
14
3
112
M1
allo
w
567 o
r 13
.2
A1 c
ao
10(c
)
558- 3
or
17
3
202
M1
for
558- 3
or
17
3
A1 c
ao
10(d
) 5(
x 3
) o
r (x
3)
5
or
5x
15
oe
2B2
for
5(
x 3
) o
r (x
3)
5
or
5x
15
oe
B1 f
or a
nsw
er x
3
5
B0 f
or a
nsw
er 5
x 3
or
x 1
5 ‘x
=’ s
ubtr
act
B1
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
11(a
) 13
01
B1 c
ao
11(b
)(i)
40
1B1
cao
11
(b)(
ii)
angl
e su
m o
f tr
iang
le
1B1
for
cor
rect
rea
son
Do
not
acce
pt 1
80
(90
+ 5
0)
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
12(a
) 52
x 4
800
1920
2M
1 fo
r 52
x 4
800
A1 c
ao
12(b
) 0.
85 ×
“19
20”
oe
1632
2M
1 0.
85 ×
“19
20”
oe
A1 c
ao
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 55
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
13(i
)x
2x
1
3x
5
17
1B1
oe
eg 6
x 4
1
7
13(i
i)6
x 2
1 or
6x
21
0
etc
3.5
oe
2M
1 ft
(i)
if 6
xc
A1 f
or 3
.5 o
e, e
g
621
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
149
seen
97 2
7 or
7
927 o
e
213
B1 f
or 9
see
n
M1
(dep
B1)
for
97 2
7 or
7
927 o
e
A1 c
ao
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
155
x–
20
35
5x
= 55
11
3M
1 fo
r 5
x –
20
35
M1
dep
on 1
st M
1 or
M2
for
x 4
7
A1
(de
pend
ent
on b
oth
M m
arks
)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201156
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
16(a
) 250×
7or
7,
50,
2 2
B1 f
or 7
and
2
B1 f
or 5
0
16(b
) 17
520
0 or
100
2
M1
ft f
rom
(a)
, (1
75 s
een,
usi
ng
3or
2)
50or
48()7
or6(,
corr
ectl
y
eval
uate
d)A1
for
200
or
100
(if
no w
orki
ng o
ut u
se f
t fr
om (
a))
16
(c)
Num
erat
or in
crea
sing
or
6.8
and
47.6
incr
easi
ng
deno
min
ator
dec
reas
ing
or 2
.09
decr
easi
ng
(b)
roun
ded
up (
not
roun
ded
to 1
sf)
or
‘175
’ ro
unde
d to
200
2B2
any
tw
o of
the
se
B1 a
ny o
ne o
f th
ese
Ig
nore
oth
er
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
17(a
) 6
×2
)3+
2( o
r
2 6
21
6
1 o
e
152
M1
for
6×
2)3
+2(
or
2 6
21
6
1 o
e
A1 c
ao
17(b
) 2015
100
0 oe
75
03
M1
for
‘2015
’ oe
M1
for
‘2015
’ 1
000
oe
A1 c
ao
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 57
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
18x
3 =
7x
(6
x= 3
oe)
x
= 21
,y
= 3
213
M1
for
x 3
= 7
x oe
or
7(y
– 3)
oe
or 0
= 6
x –
3 oe
6x=
3 o
e [s
epar
ate
evid
ence
for
M1
is r
equi
red]
A1
for
x =
21
A1 f
or y
= 3
21
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
19(a
) (t
an u
sed)
tan
xº2.41.5
or
tan
x º 1
.214
285…
. oe
50.5
3M
1 (s
in o
r co
s) a
nd (
(4.
22+
5.1
2)
or 6
.6 u
sed
M1
sin
x =
5.1/
( (
4.2
2+
5.1
2)
or c
osx
= 4.
2/(
(4.
22+
5.1
2)
A1 f
or a
nsw
ers
whi
ch r
ound
to
50.5
19(b
) si
n29
AB/
5 or
A
B/si
n29
5/s
in90
A
B 5
sin2
9
2.42
3M
1 si
n29
= A
B/5
or A
B/si
n29
= 5/
sin9
0 M
1A
B 5
sin2
9
OR
M2
for
AB
(5
2 (
5cos
29)2 )
or 5
cos2
9 t
an29
A1 f
or a
nsw
ers
whi
ch r
ound
to
2.42
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201158
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
20(a
) 1
(0.
1 +
0.2
+ 0.
1)
or 1
0
.4 o
e
0.6
2M
1 or
0.6
in t
able
A1
allo
w in
tab
le if
not
con
trad
on
line
20(b
) 0.
2 +
0.1
or
1 (
‘0.6
’ +
0.1)
0.
3 oe
2
M1
0.2
+ 0.
1 or
1
(‘0
.6’
+ 0.
1)
A120
(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
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
2142 +
62 (
= 52
)
(42 +
62 )
or“5
2” o
r 2
13
7.21
3M
1 fo
r 42 +
62 (
= 52
)M
1 de
p on
1st
M1
(42 +
62 ) o
r “5
2” o
r 213
A1 f
or a
nsw
ers
whi
ch r
ound
s to
7.2
1
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 59
Centre Number Candidate Number
Write your name hereSurname Other names
Total Marks
Paper Reference
Turn over
You must have:
Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Instructions
• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answer all questions.• Without sufficient working, correct answers may be awarded no marks.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators may be used.
• You must NOT write anything on the formulae page. Anything you write on the formulae page will gain NO credit.
Information
• The total mark for this paper is 100. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.
Advice
• Read each question carefully before you start to answer it.• Write your answers neatly and in good English.• Check your answers if you have time at the end.
MathematicsPaper 3H
Higher Tier
Sample Assessment MaterialTime: 2 hours KMA0/3H
*S39743A0120*S39743A©2010 Edexcel Limited.
Edexcel Certificate L1/L2
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201160
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 sin C12
sin sin sina b c
A 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
FORMULA SHEET – HIGHER TIERYou must not write on the fomulae page. Anything you do write will gain no credit.
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 61
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 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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 1 = 3 marks)
2 (a) Work out the value of x2 – 5x when x = –3(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Factorise x2 – 5x(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 2 = 4 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201162
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.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 3 = 3 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 63
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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 4 = 5 marks)
5
4
3
2
–1–2 1 2 3 4O x
y
P
R
Q1
–1 5 6 87
–2
–3
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201164
5 (a) Simplify, leaving your answers in index form,(2)
(i) 75
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) 59
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Solve 9 4
82 2 22n×
=(2)
n = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 5 = 4 marks)
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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 65
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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . km/h
(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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m3
(Total for Question 7 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201166
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.
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dollars
(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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dollars
(Total for Question 8 = 7 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 67
9 (a) Solve 5x – 4 = 2x + 7(2)
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Solve 7 24
2 3y y(4)
y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201168
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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 = 8 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 69
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.
(5)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm
(Total for Question 11 = 6 marks)
B
O
AC
6.9 cm
5.7 cm
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201170
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.
(1)
Weight (w kg) Cumulativefrequency
100 < w 200
100 < w 300
100 < w 400
100 < w 500
100 < w 600
100 < w 700
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 71
(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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 = 5 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201172
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.
(Total for Question 13 = 4 marks)
y
6
4
2
O 2 4 6 x
–2
–2
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 73
14 (a) Make r the subject of the formula A = r2, where r is positive.(2)
r = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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.
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm
(ii) Give the radius of the circle to an appropriate degree of accuracy. You must show working to explain how you obtained your answer.
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm
(Total for Question 14 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201174
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.(3)
f = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) On the axes, sketch the graph of f against w.(1)
(b) The wavelength of a radio wave is 1250 m. Calculate its frequency.
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilohertz
(Total for Question 15 = 6 marks)
f
O w
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 75
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 = kPQ where k is a number.(2)
(Total for Question 16 = 5 marks)
R
F
QP
Eb
a
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201176
17 A curve has equation y xx
2 16
The curve has one turning point.
Find ddyx
and use your answer to find the coordinates of this turning point.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 17 = 4 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 77
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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question 18 = 6 marks)
PLEASE TURN OVER FOR QUESTION 19
A
2.8 cm
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201178
19 Solve the simultaneous equations
y = 3x – 1
x2 + y2 = 5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 19 = 6 marks)
TOTAL FOR PAPER = 100 MARKS
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 79
Sam
ple
Mar
k Sc
hem
e Pa
per
3H
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
791
051
9,
910
6889
1(b)
7.
57
1B1
ft
from
(a)
if n
on-t
rivi
al ie
(a)
mus
t ha
ve m
ore
than
2 d
.p.
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
2(a)
(-3)
2 5
-
3
24
2M
1 fo
r su
bstn
or
9 or
15
seen
A1
cao
2(
b)
)5(xx
2
M1A
1 fo
r )5
(xx
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
- 5x
)
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
346
3
4
7 6
4
8 3
4
9 5
5
0 2
51
1 o
r
138
282
1
44
245
100
51
or 9
60
“960
” 2
0
48
3M
1 f
or f
indi
ng a
t le
ast
4 pr
oduc
ts a
nd a
ddin
g M
1 (d
ep o
n 1s
t M
1) f
or d
ivis
ion
by 2
0 A1
cao
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201180
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
4(a)
tr
ansl
atio
n 3
squa
res
to
the
righ
t an
d 1
squa
re
dow
n
2 B2
for
cor
rect
des
crip
tion
of
tran
sfor
mat
ion
B1 f
or t
rans
lati
on.
Acce
pt t
rans
late
,
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
4(b)
ro
tati
on o
f 90
° cl
ockw
ise
abou
t (2
, 1)
3
B3 f
or f
or c
orre
ct d
escr
ipti
on o
f tr
ansf
orm
atio
n B1
for
rot
atio
n
A
ccep
t ro
tate
, ro
tate
d et
c B1
for
90°
clo
ckw
ise
or
90°
or 2
70°
B1 f
or (
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
1B1
cao
5(
a)(i
i)
56 1
B1 c
ao
5(b)
9 4
n
= 8
or
13
n
= 8
5 2
M1
for
9 4
n
= 8
or
13
n =
8 ,
Also
aw
ard
for
2n = 2
5 , 2n =
32 o
r 25 o
n an
swer
line
A1
cao
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 81
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
6(a)
48
1512
xx
194x
2
M1
for
at le
ast
3 te
rms
corr
ect
inc
sign
s A1
cao
6(
b)24
83
2y
yy
24
112
yy
2
M1
for
3 te
rms
corr
ect
or
yy
112
seen
A1
cao
6(
c)
5p3 +
4p
2B2
cao
B1
for
eith
er 5
p3 or
for
+ 4p
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
7(a)
6021
5.38
or
35.0=
6021;
35.05.
38
110
3M
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…
” 6
0 or
"
35.0"5.
38
A1 c
ao
7(b)
3850
019.4
2
= 21
2343
3.41
9 m
³ 2
120
000
3M
2
× 4
.19²
× 3
8500
= 2
1234
33.4
19 m
³
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
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201182
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
8(a)
4500
270
100
6
2M
1 fo
r45
0027
0 o
r 0.
06 o
r 45
0047
70 o
r 1.
06
A1 c
ao
8(b)
117
5.4100
26
00
2M
1 fo
r5.4117
or 2
6 se
en
A1 c
ao
8(c)
04.13328
or 3
328
104
100
32
00
3M
2 fo
r 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
) 5
x 2
x 7
4
311
, 3
32 o
e 2
M1
for
corr
ect
rear
rang
emen
t [s
epar
ate
evid
ence
for
M1
is
requ
ired
] A1
als
o ac
cept
2 o
r m
ore
d.p.
rou
nded
or
trun
cate
d eg
3.6
6, 3
.67
9(b)
4 42
7y
or 7
2
y
= 4(
2y
3)
12
82
7y
y o
r si
mpl
er
5-
10y
- 21 o
e
4M
1 fo
r cl
ear
inte
ntio
n to
mul
tipl
y bo
th s
ides
by
4 or
a m
ulti
ple
of
4.
For
exam
ple,
aw
ard
for
4
427
yor
7
2y
4 ×
2y
3 o
r 8
y 3
or
2y
3
4 o
r 2
y 1
2 M
1 fo
r co
rrec
t ex
pans
ion
of b
rack
ets
(usu
ally
12
8y)
or f
or
corr
ect
rear
rang
emen
t of
cor
rect
ter
ms
eg 8
y 2
y 7
1
2 A1
for
red
ucti
on t
o co
rrec
t eq
uati
on o
f fo
rm a
y =
b (d
epen
dent
on
both
M m
arks
)
A1 f
or
21 o
e (d
epen
dent
on
all p
revi
ous
mar
ks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 83
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
10(a
) 15
0 x
53
90
3Ac
cept
dec
imal
s
B1 f
or 53
see
n
M1
for
150
x 53
A1 c
ao
Do
not
acce
pt 15
090
10(b
)(i)
43
×54
2012
or
53 o
e 2
Acce
pt d
ecim
als
M1
for
43×
54
A1 f
or 2012
or
53 o
e
10
(b)(
ii)
42×
53+
41×
52
208or
52 o
e 3
Acce
pt d
ecim
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
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201184
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
1B1
for
men
tion
of
tang
ent
and
radi
us o
r lin
e fr
om c
entr
e
11(b
) 6.
92 5
.72 o
r 47
.61
32
.49
or 1
5.12
(6
.92
5.7
2 )
3.88
844…
2
5.7
+ 2
“
3.88
844…
”
19.2
5
M1
for
squa
ring
and
sub
trac
ting
M
1 (d
epen
dent
on
1st
M1)
for
squ
are
root
A1
for
3.8
9 or
bet
ter
M1
for
2 5
.7 +
2
“3.
888.
.” o
nly
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
1B1
cao
12
(b)
Poin
ts c
orre
ct
Curv
e or
line
seg
men
ts
Corr
ect
grap
h dr
awn
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
w
ithi
n ea
ch in
terv
al (
inc
end
poin
ts)
at t
he c
orre
ct h
eigh
t 12
(c)
Use
of
w =
430
on
grap
h Ap
prox
16
2M
1 m
ay b
e sh
own
on g
raph
or
impl
ied
by 4
3, 4
4 or
45
stat
ed
A1 if
M1
scor
ed,
ft f
rom
cum
ulat
ive
freq
uenc
y gr
aph
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
13
Line
s dr
awn
corr
ectl
y Co
rrec
t re
gion
labe
lled
4B3
for
Lin
es d
raw
n co
rrec
tly
[B1
for
each
cor
rect
line
- ig
nore
ad
diti
onal
line
s]
B1 f
or C
orre
ct r
egio
n la
belle
d R
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 85
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
14(a
) r2 =
A
A
2
M1
for
r2 =
A
or
r2 = A
A1 Ig
nore
±
14(b
)(i)
5.
13
2.07
296…
2
M1
for
13.5
see
n A1
for
ans
wer
whi
ch r
ound
s to
2.0
73
14(b
)(ii)
5.
14 o
r 2.
1483
6…
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)
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
15(a
)(i)
f
= wk
f
= w
3000
00
3M
1 fo
r f
= wk
, (m
ay b
e im
plie
d by
150
0 =
200k
)
M1
for
1500
= 20
0k
A1 A
lso
awar
d if
ans
wer
is f
= wk
but
k is
eva
luat
ed a
s
300
000
in (
a) o
r (b
) 15
(a)(
ii)
f
w
1B1
for
cor
rect
gra
ph
15(b
) f
= 12
5030
0000
24
0 2
M1
for
subs
titu
tion
in f
= wk
A1 f
t fr
om k
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201186
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
16(a
)(i)
3 b
1B1
16
(a)(
ii)
3b
a
1
B1
16(a
)(iii
)
32a
+ b
or a
+ 31
(3b
a)
or 3
b 32
(3b
a)
oe
1B1
16(b
) 32
a
or 32
PQ
or k
32
32a
2B2
for
32a
or 32
PQ o
r k
32un
less
cle
arly
obt
aine
d by
non
-vec
tor
met
hod
B1 f
or c
orre
ct v
ecto
r st
atem
ent
wit
h at
leas
t 3
term
s w
hich
in
clud
es E
F (o
r FE
) in
ter
ms
of c
apit
al le
tter
s an
d/or
a,
b eg
PQ
P
E E
F F
Q
PF
PE
EF
a
b +
EF
FQ
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
17
xy dd2
x
216 x
“2x
± 216 x
” 0
(2,
12)
4
B1 f
or 2
x
B1 f
or ±
216 x
or
± 16
x2
M1
for
“2x
± 216 x
” 0
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
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 87
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
18(a
) 2
28.2
×4
×21
+8.2
×
73.9
3
M2
for
22
8.2×
4×
21+
8.2×
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
ans
wer
whi
ch r
ound
s to
73.
9 18
(b)
312
5 o
r 5
seen
25
7
3.89
…
1850
3
M1
for
find
ing
the
linea
r sc
ale
fact
or 3
125
or
5 M
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)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201188
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
195
)13(
22
xx
51
33
92
2x
xx
x
or
51
69
22
xx
x
0
46
102
xx
02
22
5x
x
or
01
25
xx
or
01
410
xx
or
20
196
6 o
r 10
493
or
1049103
52 -x
, 51
2-y
1x
, 2
y
52 -x
, 51
2-y
1x
, 2
y
6M
1 fo
r co
rrec
t su
bsti
tuti
on
B1 (
inde
pend
ent)
for
cor
rect
exp
ansi
on o
r (3
x 1
)2 eve
n if
un
sim
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
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 89
Centre Number Candidate Number
Write your name hereSurname Other names
Total Marks
Paper Reference
Turn over
*S39744A0120*S39744A©2010 Edexcel Limited.
MathematicsPaper 4H
Higher Tier
KMA0/4HSample Assessement MaterialTime: 2 hours
You must have:Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Instructions
• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answer all questions.• Without sufficient working, correct answers may be awarded no marks.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators may be used.
• You must NOT write anything on the formulae page. Anything you write on the formulae page will gain NO credit.
Information
• The total mark for this paper is 100. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.
Advice
• Read each question carefully before you start to answer it.• Write your answers neatly and in good English.• Check your answers if you have time at the end.
Edexcel Certificate L1/L2
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201190
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 sin C12
sin sin sina b c
A 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
FORMULA SHEET – HIGHER TIERYou must not write on the fomulae page. Anything you do write will gain no credit.
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 91
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.(2)
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 1 = 3 marks)
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
(Total for Question 2 = 3 marks)
x (3x – 5)
(2x + 1)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201192
3 Solve 5(x – 4) = 35
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 3 = 3 marks)
4 Julian has to work out 6 8 47 62 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 62 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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 4 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 93
5 The diagram shows a wall.
(a) Calculate the area of the wall.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2
(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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm3
(Total for Question 5 = 5 marks)
2 m3 m
6 m
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201194
6 Solve the simultaneous equations
y = x + 3y = 7x
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 = 3 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 95
7 (a)
Calculate the value of x. Give your answer correct to 3 significant figures.
(3)
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b)
Calculate the length of AB. Give your answer correct to 3 significant figures.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm
(Total for Question 7 = 6 marks)
x°4.2 cm
5.1 cm
5 cm
29°B
A
C
Diagram NOTaccurately drawn
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201196
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? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
Give a reason for your answer.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 97
9
Calculate the value of h. Give your answer correct to 3 significant figures.
h = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 = 3 marks)
4 cm h cm
6 cm
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 201198
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)
(. . . . . . . . . . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . . . . . . . . . .)
(Total for Question 10 = 6 marks)
7
6
5
4
–1–2 1 2 3 x
y
3
–1
–2
2
1
O
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 99
11 Here are three similar triangles.
Find the value of
(a) w, (1)
w = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) x,(2)
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) y.(2)
y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 11 = 5 marks)
56°
94°12 cm
10 cm
6 cm
30°
56°
20 cm
x cm
y cm
8 cm
4 cmw°
Diagrams NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011100
12 Simplify
(a) a aa
3 4
2
×
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) ( )x 6
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) 3 16 1
2( )( )xx++ (2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 = 5 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 101
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.(4)
Class A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Class B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Use your answers to give one comparison between the marks of Class A and the marks of Class B.
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 13 = 5 marks)
14 Solve 5 71
1xx
x
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 14 = 4 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011102
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.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 15 = 4 marks)
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 = 3 marks)
6 cm5 cm
9 cm
x°Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 103
17 The functions f and g are defined as follows.
f ( )xx
12
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)
g–1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 17 = 10 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011104
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)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 18 = 6 marks)
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 105
19 (a) Calculate the area of an equilateral triangle of side 5 cm. Give your answer correct to 3 significant figures.
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
(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.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question 19 = 5 marks)
5 cm 5 cm
5 cm
5 cm 5 cm
5 cm
Diagram NOTaccurately drawn
Diagram NOTaccurately drawn
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011106
20 The histogram shows information about the heights, 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) (i) 4 < h 8 (2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) 3 < h 4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Find an estimate for the number of trees with heights in the interval 2.5 < h 3.5(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 20 = 3 marks)
Frequencydensity
Height (m)
O 1 2 3 4 5 6 7 8 9
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 107
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 Question 21 = 6 marks)
TOTAL FOR PAPER = 100 MARKS
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011108
BLANK PAGE
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 109
Sam
ple
Mar
k Sc
hem
e Pa
per
4H
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
1(i)
x
2
x
1
3x
5
17
1B1
oe
eg 6
x 4
1
7
ISW
not
‘=p
’
1(ii)
6x
2
1 or
6x
2
1 0
et
c x
= 3
.5 o
e eg
621
2M
1 f
t (i
) if
6x
cA1
Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
29
seen
97 2
7 or
7
927
oe
21
3B1
for
9 s
een
M1
(dep
B1)
for
97 2
7 or
7
927
oe
A1 c
ao
(for
ans
wer
3
B1M
1AO
) Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
35
x–
20
35
5x
= 55
11
3
M1
for
5x
20
35
M1
dep
on 1
st M
1 or
M2
for
x 4
7
A1
cao
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011110
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
4(a)
250×
7or
7,
50,
2 2
B1 f
or 7
and
2
B1 f
or 5
0
4(b)
175
200
or 1
00
2M
1 ft
fro
m (
a),
(175
see
n, u
sing
3
or2
)50
or48(
)7or6(
c
orre
ctly
eval
uate
d A1
for
200
or
100
(if
no w
orki
ng o
ut,
use
ft f
rom
(a)
)
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
2B2
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(
or
2 6
21
6
1
oe
15
2M
1 fo
r 6
×2
)3+
2( o
r
2 6
21
6
1
oe
A1 c
ao
5(b)
2015
100
0
201000
1
5
1000
2015
750
3M
1 fo
r 2015
1
000
oe
or 0
.75
or ¾
litr
e M
1 ft
‘15
’ fo
r M
1M1
only
A1
cao
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 111
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
6x
3 =
7x
(6x=
3
oe)
OR
7y
= 7
x 2
1(6
y=
21)
x =
21,
y=
3 21
3M
1 fo
r x
3 =
7x
6
x= 3
oe
A1 f
or x
= 21
A1 f
or y
= 3
21
OR
M1
for
7y
= 7
x 2
1
6
y=
21 o
e
A1 f
or x
= 21
A1 f
or y
= 3
21
Que
stio
nN
umbe
rW
orki
ngAn
swer
Mar
kN
otes
7(a)
tan
used
tan
x2.41.5
or
tan
x 1
.214
285…
. o
e
x 5
0.5…
3
M1
(sin
or
cos)
and
( (
4.2
2+
5.1
2)
or 6
.6)
used
M
1 si
nx
= 5.
1/(
(4.
22+
5.1
2)
or c
osx
= 4.
2/(
(4.
22+
5.1
2)
A1 f
or c
orre
ct a
nsw
er t
o 3
sf
7(b)
sin2
9 A
B/5
or
C/si
n29
5/s
in90
A
B 5
sin2
9
AB
2.42
…cm
3
M1
BC
5
cos2
9 M
1
AB
(5
2 (
5cos
29)2 )
or 5
cos2
9 t
an29
A1
for
cor
rect
ans
wer
to
3 sf
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011112
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
8(a)
1 –
(0.1
+ 0
.2 +
0.1
)
or 1
0
.4 o
e
0.6
2M
1 or
0.6
in t
able
A1
allo
w in
tab
le if
not
con
trad
on
line
8(b)
0.2
+ 0.
1 or
1
(‘0
.6’
+ 0.
1)
0.3
2M
1 or
0.3
see
n A1
0.3
oe
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 Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
942 +
62 (
= 52
)
(42 +
62 )
or
“5
2” o
r 2
13
42 + 6
2 (=
52)
(42 +
62 )
or
“52”
or
213
h =
7.21
…
3M
1 fo
r 42 +
62 (
= 52
)
M1
dep
on 1
st M
1 (4
2 + 6
2 ) or
“52”
or 2
13
A1 f
or c
orre
ct a
nsw
er t
o 3
sf
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 113
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
10(a
) V/
H in
any
cor
rect
tr
iang
le a
ttem
pted
G
rad
= 2,
may
be
embe
dded
or
impl
ied
y =
2x
1
4
M1
eg
01
13
not
13
A1fo
r 2
B2 f
t fo
r y
= ‘2
’x
1
(B1f
t fo
r ju
st ‘
2’x
1 o
r y
= x
1 (
m 2
)) (N
o w
orki
ng,
answ
er o
f 2
x 1
: M
1A1
B1)
10(b
)
y =
2x
± c
1
B1
y
2x
± an
y no
. (n
ot 5
) or
lett
er o
r y
2
x
10
(c)
(0
, 4)
1
B1
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
11(a
)
56
1B1
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
11(c
)64
=10y
or
128 o
e 6.
6 to
6.7
incl
oe
2M
1 or
y=
(42
82
2
4
8
cos
‘56’
)
or
y/s
in56
= 8
/sin
(180
3
0 5
6)
A1 (
a)(b
): f
t (a
) M
-mks
onl
y
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011114
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
12(a
) 27 aa
or
4 aa
or
23
aa
5 a
2M
1 A1
12(b
)
3 x
1B1
12
(c)
Corr
ectl
y ca
ncel
nu
mbe
rs o
r (x
+ 1
)
1 / 2(x
+ 1
) or
0.5
(x+
1)
or
212
or
2
1x
x o
r eq
uiv
2M
1 eg
21 o
r 0.
5 or
den
om =
2
or
6)1
(3x
or
63
3x o
r )1
(xkk
1
A1 N
ot IS
W
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
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
and
6
Clas
s A:
11
Clas
s B:
8 4
M1
M1
NB:
IQR
for
B =
8, c
heck
wor
king
A1
A1
13(b
)
A m
ore
spre
ad o
r gr
eate
r di
sper
sion
or
less
con
sist
ent
than
B
1B1
(B1
if c
onsi
sten
t w
ith
(a).
Igno
re o
ther
.)
Not
: gr
eate
r “r
ange
” or
“di
ffer
ence
”
or “
mor
e co
nsta
nt”
or “
grea
ter
IQR”
or
“gre
ater
var
ianc
e”
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 115
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
145
x 7
= x
2 1
or 5
x 7
=
( x 1
)( x
1
) x2
5x
6 =
0
(x 2
)( x
3
) (=
0)
or
26
4)5
(5
2
x =
2 or
3
4M
1 c
ondo
ne 5
x 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
(d
epen
dent
on
all o
ther
M m
arks
)
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
152
over
lapp
ing
circ
les,
12
in o
verl
ap
6 in
H o
nly
2 in
T o
nly
14
4M
1 M
1 or
6 p
lay
H o
nly
M2
M1
or 2
0 6
, 6
12
x 2
0, 2
0 18
, 35
3
3: M
3 A1
an
s 2:
M3A
0 Q
uest
ion
Num
ber
Wor
king
An
swer
M
ark
Not
es
1692 +
52
2 ×
5 ×
9 ×
co
sx
62
90co
sx
70
or
90
cos
x
70
(cos
x 70
/ 90)
38.9
3
M1
for
92 + 5
2 2
× 5
× 9
× c
osx
62
M1
for
90co
sx
70
or
90co
sx
70
, (c
osx
70/ 9
0)
OR
M2
for
95
26
59
cos
22
2
x
A1 f
or a
nsw
ers
whi
ch r
ound
to
38.9
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011116
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
17(a
)(ii)
x <
1 2
B2 B
1 fo
r x
< 1
or 0
, 1,
2,
3…
17
(b)
9 o
r (1
0 1
) 291
)(x
fg
51 o
r 0.
2
3M
1 fo
r 9
or
(10
1)
M1
for
211
x
A1 ig
nore
ans
= -
1 17
(c)
)1(x
y 2 y=
x 1
x2 y
1
xg
1
)1(
2 xoe
4
M1
1x
y (
y=
)
M1d
ep
1y
x (
x=..
) M
1
2 x
1
y
A1
[SC
xg
1
21
x:
B1]
UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 117
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
18(a
) 1 / 6
× 1 / 6
× 1 / 6
al
one
21
61 o
r 0.
0046
…
2M
1 0.
173 o
r 0.
163 o
r be
tter
. N
ot
kA1
18
(b)
1, 1
, 4
or 1
, 2,
6 o
r
2, 1
, 6
seen
or
impl
ied
1, 1
, 4
and
1, 2
, 6(
or 2
, 1,
6)
seen
or
impl
ied
3×
) 61 (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 A1
2
×) 61 (3
or
1081
, no
wor
king
: M
0A0
Que
stio
n N
umbe
r W
orki
ng
Answ
er
Mar
k N
otes
19(a
) ×
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UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011118
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Edexcel, a Pearson company, is the UK's largest awarding body, offering academic and vocational qualifications and testing to more than 25,000 schools, colleges, employers and other places of learning in the UK and in over 100 countries worldwide. Qualifications include GCSE, AS and A Level, NVQ and our BTEC suite of vocational qualifications from entry level to BTEC Higher National Diplomas, recognised by employers and higher education institutions worldwide. We deliver 9.4 million exam scripts each year, with more than 90% of exam papers marked onscreen annually. As part of Pearson, Edexcel continues to invest in cutting-edge technology that has revolutionised the examinations and assessment system. This includes the ability to provide detailed performance data to teachers and students which help to raise attainment.
AcknowledgementsThis document has been produced by Edexcel on the basis of consultation with teachers, examiners, consultants and other interested parties. Edexcel would like to thank all those who contributed their time and expertise to its development.
References to third-party material made in this document are made in good faith. Edexcel does not endorse, approve or accept responsibility for the content of materials, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)
Publications code Authorised by Roger Beard Prepared by Sharon Wood Publications code UG025980 All the material in this publication is copyright © Edexcel Limited 2011
Edexcel, a Pearson company, is the UK's largest awarding body, offering academic and vocational qualifications and testing to more than 25,000 schools, colleges, employers and other places of learning in the UK and in over 100 countries worldwide. Qualifications include GCSE, AS and A Level, NVQ and our BTEC suite of vocational qualifications from entry level to BTEC Higher National Diplomas, recognised by employers and higher education institutions worldwide. We deliver 9.4 million exam scripts each year, with more than 90% of exam papers marked onscreen annually. As part of Pearson, Edexcel continues to invest in cutting-edge technology that has revolutionised the examinations and assessment system. This includes the ability to provide detailed performance data to teachers and students which help to raise attainment.
AcknowledgementsThis document has been produced by Edexcel on the basis of consultation with teachers, examiners, consultants and other interested parties. Edexcel would like to thank all those who contributed their time and expertise to its development.
References to third-party material made in this document are made in good faith. Edexcel does not endorse, approve or accept responsibility for the content of materials, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)
Authorised by Roger Beard Prepared by Sharon Wood Publications code UG025980 All the material in this publication is copyright © Edexcel Limited 2011