Sample Assessment Material Methods of Mathematics Unit 1 ...
Transcript of Sample Assessment Material Methods of Mathematics Unit 1 ...
Sample assessment materials
GCSE
Edexcel GCSE in Methods in Mathematics
Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 1
Contents
General Marking Guidance 2
Unit 1: Methods 1 3
Unit 1: Methods 1 Foundation Paper 5
Unit 1: Methods 1 Foundation Mark scheme 29
Unit 1: Methods 1 Higher Paper 39
Unit 1: Methods 1 Higher Mark scheme 60
Unit 2: Methods 2 69
Unit 2: Methods 2 Foundation Paper 71
Unit 2: Methods 2 Foundation Mark scheme 93
Unit 2: Methods 2 Higher Paper 101
Unit 2: Methods 2 Higher Mark scheme 123
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 20102
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.
• Mark schemes will indicate within the table where, and which strands of, QWC is being assessed. The strands are as follows:
i) ensure that text is legible and that spelling, punctuation and grammar are accurate so that meaning is clear. Comprehension and meaning is clear by using correct notation and labelling conventions.
ii) select and use a form and style of writing appropriate to purpose and to complex subject matter. Reasoning, explanation or argument is correct and appropriately structured to convey mathematical reasoning.
iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used.
Guidance on the use of codes within this mark scheme M1 – method mark A1 – accuracy mark B1 – working mark C1 – communication mark QWC – quality of written communication oe – or equivalent cao – correct answer only ft – follow through
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 3
Unit 1: Methods 1
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 20104
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 5
Centre Number Candidate Number
Write your name hereSurname Other names
Total Marks
Paper Reference
Turn over
*S38369A0126*
Edexcel GCSE
Methods in MathematicsUnit 1: Methods 1For Approved Pilot Centres ONLY
Foundation Tier
Sample Assessment MaterialTime: 1 hour 45 minutes
You must have:
Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.
5MM1F/01
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.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators must not be used.
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.• Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed – you should take particular care on these questions with your spelling, punctuation
and grammar, as well as the clarity of expression.
Advice• Read each question carefully before you start to answer it.• Keep an eye on the time.• Try to answer every question.• Check your answers if you have time at the end.
S38369A©2010 Edexcel Limited.
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 20106
GCSE Mathematics 2544
Formulae: Foundation Tier
You must not write on this formulae page.Anything you write on this formulae page will gain NO credit.
Area of trapezium = (a + b)h
Volume of prism = area of cross section × length
b
a
h
length
crosssection
12
GCSE Mathematics 2MM01
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 7
Answer ALL questions.
Write all your answers in the spaces provided.
You must write down all stages in your working.
You must NOT use a calculator.
1 The shape is made from a right-angled triangle, a parallelogram and a quadrilateral.
(a) Mark with arrows (>>) a pair of parallel lines.(1)
(b) Mark with the letter A an acute angle.(1)
(c) Mark with the letter R a reflex angle.(1)
(Total for Question 1 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 20108
2
The diagram shows a spinner as an 8 sided shape. Part of the spinner is coloured red, part is coloured green, part is coloured blue and the
rest is coloured yellow.
The spinner is spun once and lands on one colour.
(a) Which colour is the most likely? You must explain your answer.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Write down the probability of getting a red or a yellow.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jas spins the spinner once. He gets a yellow.
Yusuf then spins the spinner once.
(c) Has Yusuf got a greater chance, the same chance or a smaller chance of getting yellow than Jas had? You must explain your answer.
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 2 = 3 marks)
R
G
B
Y
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 9
3 Here is a grid of centimetre squares.
(a) Write down the coordinates of the point
(i) B,(1)
( . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . )
(ii) C.(1)
( . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . )ABCD is a quadrilateral.
The area of ABCD is 24 cm2.
(b) Write down the coordinates of D.(2)
( . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . ) E is another point on the grid.
The coordinates of the midpoint of AE are (–1, 2).
(c) Find the coordinates of E.(2)
( . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . )
(Total for Question 3 = 6 marks)
1
2
3
4
–1
–2
–3
–4
–3 –2 –1 1 2 3 4 5 6–5 –4–6 O x
y
C
A B
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201010
4 Here is a list of eight numbers.
(a) Write down two numbers from the list with a sum of 87(1)
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(b) Write down a number from the list which is
(i) a multiple of 9(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) a square number.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) Use a word from the above box to complete this sentence correctly.(1)
11 is a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . of 88
Here are the same 8 numbers drawn larger.
l l l 6 l 8 3 66 8 6 9 8 2 8 8
(d) From these numbers, write down a number which has
(i) exactly one line of symmetry,(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) two lines of symmetry and rotational symmetry of order 2,(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(iii) rotational symmetry of order 2 but no lines of symmetry.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 4 = 7 marks)
cube multiple factor product
11 16 18 36 68 69 82 88
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 11
5 Here are four shapes. The shapes have been drawn accurately.
(a) Write down the mathematical name of shape C.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neel makes the shapes accurately out of card.
Two of the shapes can be fitted together without overlapping to make a trapezium.
(b) Show how this can be done.(1)
Two of the shapes can be fitted together without overlapping to make a hexagon.
(c) Show how this can be done.(1)
(Total for Question 5 = 3 marks)
A B C D
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201012
*6
AB is a straight line.
Pinkal is trying to find the value of the angle marked x
This is what she does.
y = 38° because the angles next to each other on a straight line add up to 160°z = 52° because y + z comes to 90°
x = 318 because angles around a point add up to 360°
Pinkal has made some mistakes.
Find the mistakes and work out the correct value of x.
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°
(Total for Question 6 = 3 marks)
Diagram NOTaccurately drawn
x
z
B122°
Ay
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 13
7 Dwayne has a bag of counters. The counters are either blue or green. There are 10 blue counters and 2 green counters.
Dwayne takes a counter at random from his bag.
(a) Write down the probability it is green.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mario has a bag of counters. The counters are either blue or green. There are twice as many blue counters as green counters.
Mario takes a counter at random from his bag.
(b) Write down the probability it is blue.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Both boys put back the counter they took out.
They empty the counters from both bags into a vase.
Dwayne says that the probability of taking a blue counter from the vase is 1318
(c) What is the probability of taking a green counter from the vase?(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dwayne knows that there are between 20 and 50 counters in the bag.
(d) Work out the number of counters there are in the bag.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 7 = 4 marks)
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8
(a) Triangle ABC is equilateral.
Explain why.(2)
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PQR is a straight line.SQ = SR.
(b) (i) Work out the size of the angle marked x°.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) Give reasons for your answer.(2)
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(Total for Question 8 = 5 marks)
Diagram NOTaccurately drawn
A
B60°
60°
C
S
x° 50°P Q R
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 15
9 Here are some patterns made from squares.
(a) The diagram below shows part of Pattern number 4 Complete the diagram for Pattern number 4
(1)
(b) Find the number of squares used for Pattern number 10
You must explain your answer.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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One pattern has 31 black squares.
(c) Work out the total number of squares that this pattern has. You must show clearly how you obtained your answer.
(2)
(d) Find a rule to find the number of squares, s, in terms of the Pattern number, n.(2)
s = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 = 7 marks)
Pattern number 4
Pattern number 2 Pattern number 3 Pattern number 1
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201016
10 (a) On the grid, plot the graph of y + 2x = 10 for values of x from –1 to 5(3)
(b) Use your graph to find
(i) the value of y when x = – 0.7(1)
y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) the value of x when y = 5.4(1)
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 = 5 marks)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
–1
–2
1 2 3 4 5 6–1–2 O x
y
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 17
11 Simplify
(a) c + c + c(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) 2a + 3a – a(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) 2xy + 3xy – 6xy(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(d) 3a + 5b – a + 2b + 8 (2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 11 = 5 marks)
12 Beth says 20 – 5 × 3 is 45
Pat says 20 – 5 × 3 is 5
(a) Who is right? Give a reason for your answer.
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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(b) Work out (12 + 9) ÷ 3(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) Put in brackets to make the following calculation correct.(3)
5 + 8 × 3 − 4 + 2 = 13
(Total for Question 12 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201018
13 Here are two fractions, 34
and 45
Which is the larger fraction?
You must show clearly how you obtained your answer.
(Total for Question 13 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 19
14 There are some beads in a bag. The beads are either green, blue or yellow.
A bead is selected at random from the bag.
The probability that the bead is blue is twice the probability that the bead is green. The probability that the bead is yellow is 0.1 more than the probability that the bead
is green.
Work out the smallest number of beads there could be in the bag.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 14 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201020
15
(a) Enlarge shape S, scale factor 2, centre (0, 2).(2)
(b) Describe fully the single transformation that maps shape S onto shape T.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shape S can be transformed to shape U by a rotation followed by a translation.
(c) Describe the rotation and the translation fully.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 15 = 6 marks)
2
4
6
8
10
–2
–4
–6
–8
–6 –4 –2 2 4 6 8 10–10 –8 O x
y
T
U
S
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 21
16 Greg thinks that he has a biased dice. He throws the dice 200 times and records the score on the dice each time.
Information about the scores on the dice is shown in the table.
Score on the dice 1 2 3 4 5 6
Frequency 23 37 33 35 20 52
(a) Is the dice biased? You must show clearly how you obtained your answer.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tess has a different dice which is known to be biased. The probability that Tess throws the biased dice once and gets a 6 is 0.7
Tess throws the biased dice 250 times.
(b) Work out an estimate for the number of times she should get a 6.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201022
17
ABCDEF is a hexagon with one line of symmetry. CD is parallel to AF. The distance between CD and AF is 12 cm. The interior angles at A and F are right angles. EF = 5 cm AF = 12 cm Calculate the area of the hexagon.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question 17 = 4 marks)
A
B
C D
E
5 cm
6 cm
12 cm
12 cm
F
Diagram NOTaccurately drawn
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 23
18 (a) Solve 4t + 1 = 19(2)
t = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Solve 4w + 8 = 2w + 7(2)
w = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matt has £x Sunil has twice as much as Matt. Catrin has £5 more than Sunil.
The total amount of money they have altogether is 7 times what Matt has.
(c) Work out how much Catrin has.(2)
£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 18 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201024
19 Given that 15.8 × 6.8 = 107.44
work out the values of
(a) 0.158 × 6.8
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) 1074.4 ÷ 0.158
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 19 = 2 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 25
20 Jim has two ordinary dice. On both dice the even numbers are coloured blue and the odd numbers are coloured red.
Each dice is thrown once.
(a) Work out the probability that the numbers on the two dice are the same.(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Work out the probability of getting a blue number or the number 1(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 20 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201026
21 What is the largest value of x for which 23 + x is less than or equal to
34
?
Give your answer in its simplest form.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 21 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 27
22 The nth term of a sequence is n2 + 4
(a) Show that when n is odd, not all the terms of the sequence are prime numbers.(2)
(b) Show that when n is even, then those terms of the sequence are multiples of 4(2)
(Total for Question 22 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201028
23 This is some information about a class.
There are 35 students in a class. 17 of the students study History. 20 of the students study Geography. 8 of the students study both History and Geography.
* (a) Draw a suitable diagram that shows all this information.(4)
A student is chosen at random from the class.
(b) Find the probability that this student studies neither History nor Geography.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 23 = 5 marks)
TOTAL FOR PAPER = 100 MARKS
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 29
Uni
t 1
Foun
dati
on:
Met
hods
1
5MM
1FQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 1.
(a
)
para
llel
lines
mar
ked
1 B1
cao
(b
)
acut
e an
gle
A1
B1 c
ao a
cute
ang
le m
arke
d w
ith
A
(c
)
refl
ex a
ngle
R
1 B1
cao
ref
lex
angl
e m
arke
d w
ith
R
Tota
l for
Que
stio
n: 3
mar
ks
2.
(a)
Ye
llow
, bi
gges
t re
gion
1 B1
cao
yel
low
bec
ause
it is
the
big
gest
reg
ion
(b
)
0.5
1 B1
cao
(c
)
sam
e 1
B1 c
ao s
ame
beca
use
the
situ
atio
n is
exa
ctly
the
sam
e To
tal f
or Q
uest
ion:
3 m
arks
3.
(a
)(i)
(a
)(ii)
(2
,3)
(2, –
1)2
B1 c
ao
B1 c
ao
(b
)
D m
arke
d (–
4, –
1)2
M1
CD =
24
÷ 4
or D
plac
ed c
orre
ctly
A1
cao
(c)
(2
, 1)
2
M1
for
any
clea
r pr
oces
s to
fin
d E
, eg
cle
arly
sta
tes
or s
how
s 3
alon
g
and
1 do
wn
from
the
mid
poin
t or
2
3 ,2
4y
x+
− u
sed
A1 c
ao
Tota
l for
Que
stio
n: 6
mar
ks
4.
(a)
18
& 6
9 1
B1 f
or b
oth
(b
)(i)
(b
)(ii)
18
or
36
16 o
r 36
2
B1 f
or e
ithe
r or
bot
h B1
for
eit
her
or b
oth
(c
)
fact
or
1 B1
cao
(d)(
i)
(d)(
ii)(d
)(iii
)
18
88
or
11
69
3 B1
cao
B1
for
eit
her
or b
oth
B1 c
ao
Tota
l for
Que
stio
n: 7
mar
ks
5.
(a)
Rh
ombu
s 1
B1 c
ao
(b
)
See
diag
ram
1 B1
cao
(c
)
See
diag
ram
1 B1
cao
Tota
l for
Que
stio
n: 3
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201030
5MM
1FQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 6.
QW
C(i
i)
angl
es o
n a
line
sum
to
180°
36
0 –
52 is
no
t 31
8
3 C1
for
ang
les
on a
line
sum
to
180°
QW
C st
atem
ent
is s
uppo
rted
by
reas
onC1
for
360
– 5
2 is
not
318
QW
C: s
tate
men
t is
sup
port
ed b
y re
ason
B1 f
or t
he c
orre
ct a
nsw
er f
ollo
win
g co
rrec
t w
orki
ng
Tota
l for
Que
stio
n: 3
mar
ks
7.
(a)
12101
B1 c
ao
(b
)
321
B1 c
ao
(c
)
1851
B1 c
ao
(d
)
36
1 B1
cao
Tota
l for
Que
stio
n: 4
mar
ks
8.
(a)
Al
l ang
les
are
the
sam
e
2 B1
cao
sho
win
g th
at a
ll in
teri
or a
ngle
s ar
e 60
o
C1 f
or c
oncl
usio
n fo
llow
ing
corr
ect
reas
onin
g.
(b)(
i)(b
)(ii)
SQR
= 50
, 18
0 –
50 =
130
13
0°
Isos
cele
s tr
iang
lean
d an
gles
on
a
stra
ight
lin
e
3 M
1 fo
r id
enti
fica
tion
of
angl
e SQ
R as
50°
A1
cao
C1
rea
sons
Tota
l for
Que
stio
n: 5
mar
ks
9.
(a)
D
iagr
am
1 B1
dia
gram
(b)
41
2
B1 c
ao
C1 a
dd o
n 4
mor
e sq
uare
s un
til y
ou g
et t
o pa
tter
n nu
mbe
r 10
, or
sta
rt
wit
h pa
tter
n nu
mbe
r 4
and
add
on 2
4, o
r a
com
plet
e se
t of
the
num
ber
of s
quar
es f
rom
at
leas
t 17
to
41 o
r co
rrec
t us
e of
an
alge
brai
c fo
rmul
a
(c)
Ther
e is
alw
ays
1 le
ss w
hite
sq
uare
tha
n bl
ack
so
31 +
30
= –6
1
61Re
ason
2 B1
cao
C1
the
re is
alw
ays
1 le
ss w
hite
squ
are
than
bla
ck o
r 31
+ 3
0 =6
1
(d
)
4n+1
2
B2 f
or 4
n+
1(B
1 fo
r 4n
+ k
whe
rek
is a
con
stan
t 1
)
Tota
l for
Que
stio
n: 7
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 31
=5M
M1F
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
10.
(a)
Co
rrec
t gr
aph
3 B3
for
a f
ully
cor
rect
gra
ph
M1
for
an a
ttem
pt t
o re
arra
nge
the
equa
tion
to
y =
or t
o su
bsti
tute
a
valu
e of
x (
in t
he r
ange
–1
to 5
) in
to t
he e
quat
ion
M1
for
then
sub
stit
utin
g x
in t
he r
ange
–1
to 5
into
the
equ
atio
n
y =
10 –
2x
or in
to t
he o
rigi
nal e
quat
ion
and
atte
mpt
ing
to f
ind
yA1
cor
rect
line
dra
wn
from
–1
to 5
(b
)
x =
0.7
y =
5.4
2 B1
x =
0.7
(al
low
in t
he r
ange
± 0
.05)
B1
x=
5.4
(allo
w in
the
ran
ge ±
0.0
5)
Tota
l for
Que
stio
n: 5
mar
ks
11.
(a)
3c
1 B1
cao
(b)
4a
1 B2
cao
B1
for
2a
or 7
b co
rrec
t
(c
)
–xy
1
(d)
2a
+ 7b
+ 8
2To
tal f
or Q
uest
ion:
5 m
arks
12
. (a
)
Pat
wit
h re
ason
1 C1
for
Pat
and
exp
lana
tion
tha
t yo
u do
5 ×
3 f
irst
, th
en d
o 20
– “
15”
(b
)
7 1
B1 c
ao
(c
) 5
+ 8
× (3
4
+ 2
) = 1
3 Br
acke
ts in
co
rrec
t pl
ace
1 B1
cao
Tota
l for
Que
stio
n: 3
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201032
=5M
M1F
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
13.
15 a
nd 1
6 pa
rts
shad
ed
OR
75.043
=,
8.054
=
OR
201543
=,
201654
=
54 w
ith
reas
on
3M
1 fo
r co
rrec
tly
shad
ing
15 o
ut o
f 20
for
43
M1
for
corr
ectl
y sh
adin
g 16
out
of
20 f
or 54
A1 (
depe
nden
t on
M1,
M1)
for
sel
ecti
on o
f 54
OR
M1
for
75.043
=
M1
for
8.054
=
A1 (
depe
nden
t on
M1,
M1)
for
sel
ecti
on o
f 0.
8 oe
O
R
M1
for
201543
=
M1
for
201654
=
A1 (
depe
nden
t on
M1,
M1)
for
sel
ecti
on o
f 2016
oe
Tota
l for
Que
stio
n: 3
mar
ks
14.
Le
t g
be t
he p
roba
bilit
y th
at
the
bead
will
be
gree
n Pr
obab
ility
blu
e =
2g,
prob
abili
ty y
ello
w
=g
+ 0.
11
1.02
=+
++
gg
g
41.0
1−
=g
= 0
.225
403
M1
for
sigh
t of
g +
2g
+ g
+ 0.
1 =
1 M
1 fo
r so
luti
on
A1 f
or 4
0
Tota
l for
Que
stio
n: 3
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 33
5MM
1FQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 15
. (a
)
Corr
ect
enla
rgem
ent
2 B2
cao
(B
1 co
rrec
t sc
ale
fact
or b
ut in
the
wro
ng p
osit
ion)
(b)
Re
flec
tion
in
the
line
x =
–2
2 M
1 fo
r re
flec
tion
wit
h th
e eq
uati
on o
f a
line
give
n or
sho
wn
on t
he
diag
ram
A1 f
or x
= –
2
(c)
A ro
tati
on o
f 18
0o abo
ut
(a,b
) fo
llow
ed b
y a
tran
slat
ion
of
−−−
ba22
4
Corr
ect
rota
tion
and
tr
ansl
atio
n
2 M
1 fo
r a
rota
tion
of
180o a
bout
a s
tate
d po
int
and
a tr
ansl
atio
n co
nsis
tent
wit
h th
e ce
ntre
of
rota
tion
. Th
e tr
ansl
atio
n m
ay b
e po
orly
de
scri
bed
A1 f
or a
ful
ly c
orre
ct d
escr
ipti
on,
such
as
rota
tion
of
180° a
bout
O
follo
wed
by
a tr
ansl
atio
n of
− 04
Tota
l for
Que
stio
n: 6
mar
ks
16.
(a)
200
52=–= 20
023
== 0
.145=
Yes,
as
the
diff
eren
cebe
twee
n th
e re
lati
vefr
eque
ncie
sis
so
larg
e
2 M
1 at
tem
pts
to c
alcu
late
at
leas
t tw
o re
lati
ve f
requ
enci
es
A1 c
oncl
usio
n
(b
) 25
0 ×
0.7
175
2 M
1 25
0 ×
0.7
A1
cao
To
tal f
or Q
uest
ion:
4 m
arks
17
.
Area
of
rect
angl
e =
60
Area
of
trap
eziu
m =
63
612
72+
×=
63
123
cm2
4 M
1 ar
ea o
f re
ctan
gle
= 5
× 12
M1
area
of
trap
eziu
m =
6
12 2h
+×
B1h
= 7
A1 c
ao
Tota
l for
Que
stio
n: 4
mar
ks
18.
(a)
4t=
19 –
1
4t=
–18
4.5
2 M
1 fo
r co
rrec
tly
mov
ing
the
num
ber
term
eg
4t=
19 –
1
A1 4
.5 o
e
(b)
4w–
2w=
7 –
8 2w
= –
1 -0
.5
2 M
1 fo
r m
ovin
g te
rms
corr
ectl
y eg
4w
– 2w
= 7
– 8
A1–0
.5 o
e
(c)
x +
2x +
2x
+ 5
= 7x
x =
2.50
£1
0 2
M1
for
x +
2x +
2x
+ 5
= 7x
A1 c
ao
Tota
l for
Que
stio
n: 6
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201034
5MM
1FQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 19
. (i
) 15
.8 ×
6.8
= 1
07.4
4 0.
158
× 6.
8 1.
0744
1
B1 c
ao
(i
i)
1074
.4 ÷
0.1
58
6800
1
B1 c
ao
Tota
l for
Que
stio
n: 2
mar
ks
20.
(a)
Sam
ple
spac
e is
(1,
1) t
o (6
,6)
Even
t co
nsis
ts o
f th
e 6
pair
s.
(1,1
) to
(6,
6)
3663
M1
for
iden
tify
ing
sam
ple
spac
e an
d at
tem
ptin
g to
list
all
pair
s M
1 fo
r id
enti
fyin
g th
e do
uble
s
A1366
oe
(b
)
1 2
3 4
56
11
1B
1 1B
1
1B
21B
B
BB
B B
31
B
B
B
41B
B
BB
B B
51
B
B
B
61B
B
B B
B B
36323
M1
iden
tifi
es e
ithe
r th
e ou
tcom
es w
ith
a 1
or w
ith
a bl
ue
M1
(dep
) id
enti
fies
the
out
com
es w
hich
are
nei
ther
(or
the
ir
com
plem
ent)
A13632
Tota
l for
Que
stio
n: 6
mar
ks
21.
3243
− =
128
129−
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Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 35
=5M
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Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201036
==
==
==
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=
==
==
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Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 37
= 15
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Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201038
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 39
Centre Number Candidate Number
Write your name hereSurname Other names
Total Marks
Paper Reference
Turn over
*S38371A0121*
Edexcel GCSE
Methods in MathematicsUnit 1: Methods 1 For Approved Pilot Centres ONLY
Higher Tier
Sample Assessment MaterialTime: 1 hour 45 minutes
You must have:
Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.
5MM1H/01
S38371A©2010 Edexcel Limited.
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.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators must not be used.
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.• Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed – you should take particular care on these questions with your spelling, punctuation
and grammar, as well as the clarity of expression.
Advice
• Read each question carefully before you start to answer it.• Keep an eye on the time.• Try to answer every question.• Check your answers if you have time at the end.
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201040
Formulae – Higher Tier
You must not write on this formulae page.Anything you write on this formulae page will gain NO credit.
Volume of a prism = area of cross section × length Area of trapezium = (a + b)h
Volume of sphere = r3 Volume of cone = r2h
Surface area of sphere = 4 r2 Curved surface area of cone = rl
In any triangle ABC The Quadratic Equation The solutions of ax2+ bx + c = 0 where a 0, are given by
Sine Rule
Cosine Rule a2= b2+ c2– 2bc cos A
Area of triangle = ab sin C
length
crosssection
rh
r
l
C
ab
c BA
13
a b csin A sin B sin C
xb b ac
a=
− ± −( )2 42
43
12
b
a
h
12
GCSE Mathematics 2MM01
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 41
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
You must NOT use a calculator.
1 Work out 1920
340×
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 1 = 2 marks)
2 (a) Write 120 as a product of its prime factors.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Find the Highest Common Factor (HCF) of 120 and 96(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 2 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201042
3 Here are the first four terms in an arithmetic sequence.
7 11 15 19
Is the number 203 a term in this arithmetic sequence? You must give a reason for your answer.
(Total for Question 3 = 3 marks)
4 (a) Expand and simplify 2(x + 2y) + 3(x – y)(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Solve 6 = – 4(x – 1)(3)
x =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 43
(c) Solve 3(y + 2) + 2y = y + 9(4)
y =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 4 = 9 marks)
5 Simplify
(i) 26 × 27
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) 48 ÷ 42
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(iii) 3 33
8
6
×(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 5 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201044
6 Jim has two ordinary dice. On both dice the even numbers are coloured blue and the odd numbers are coloured red.
Each dice is thrown once.
(a) Work out the probability that the numbers on the two dice are the same.(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Work out the probability of getting a blue number or the number 1(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 45
7 Here is a sequence of patterns made from centimetre squares
Pattern Number 1 Pattern Number 2 Pattern Number 3
(a) Write down the number of centimetre squares in Pattern Number 4(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Find an expression, in terms of n, for the number of centimetre squares in Pattern Number n.
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) Can the number of centimetre squares in a pattern ever be a square number? Explain your answer.
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 7 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201046
8 (a) On the grid, plot the graph of y + 2x = 10 for values of x from –1 to 5(3)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
–1
–2
1 2 3 4 5 6–1–2 O x
y
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 47
(b) Work out the equation of the graph that is perpendicular to y + 2x = 10 and passes through the point (1, 8).
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201048
9 This is some information about a class. There are 35 students in the class. 17 of the students study History. 20 of the students study Geography. 8 of the students study both History and Geography.
(a) Draw a suitable diagram that shows all this information.(4)
A student is chosen at random from the class.
(b) Find the probability that this student studies neither History nor Geography.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 49
10
A
B
C D
E
F12 cm
6 cm
12 cm
5 cm
ABCDEF is a hexagon with one line of symmetry. CD is parallel to AF. The distance between CD and AF is 12 cm. The interior angles at A and F are right angles. EF = 5 cm AF = 12 cm Calculate the area of the hexagon.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .cm2
(Total for Question 10 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201050
11
2
4
6
8
10
–2
–4
–6
–8
2 4 6 8 10–2–4–6–8–10 O x
y
ST
U
(a) Enlarge shape S, scale factor 2, centre (0, 2).(2)
(b) Describe fully the single transformation that maps shape S onto shape T.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shape S can be transformed to shape U by a rotation followed by a translation.
(c) Describe the rotation and the translation fully. (2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 11 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 51
12 Hiroshi has two boxes, A and B.
In box A are 6 green and 4 red counters. In box B are 3 green and 7 red counters.
Hiroshi takes a counter at random from box A and a counter at random from box B.
(a) Work out the probability that Hiroshi takes 2 red counters.(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Work out the probability that Hiroshi takes 1 red counter and 1 green counter.(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201052
13 Put the following numbers in order. Start with the smallest number.
6.0 × 108 3.2 × 10–2 46 × 107 0.43 × 10–3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 13 = 2 marks)
14 Prove, using algebra, that the sum of two consecutive whole numbers is always an odd number.
(Total for Question 14 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 53
15 A
B C
Diagram NOTaccurately drawn
DE
F
ABC is a triangle. D is the midpoint of AC. E is the point on AB such that DE is parallel CB. F is the point on BC such that DF is parallel to AB.
* (a) Prove that triangles AED and DFC are congruent.(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Show that the area of the parallelogram EDFB is one half of the area of the triangle ABC.
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 15 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201054
16
T
Diagram NOTaccurately drawn
S
Q
O
R36°P
PT is a tangent to the circle, centre O at T.
R, S and Q are points on the circle. PSO is a straight line.
* (a) Work out the size of angle SRT. Give reasons for your answer.
(4)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 55
x°48°
2x°
Diagram NOTaccurately drawn
AB
C
D
B, C and D are three points on a circle. AB is the tangent to the circle at B. Angle ABC = x° Angle CBD = 48° Angle BCD = 2x°
(b) Find the value of x(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 = 7 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201056
17 Diagram NOTaccurately drawn
Y
X
O
P3a
6b
OX = 3a and OY = 6b.
P lies on XY such that XP: PY = 2:1
(a) Find OP, the position vector of P. Give your answer in terms of a and b.(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
G is the point such that YG is parallel to OP and the length of YG = length of OP.
(b) Find OG, the position vector of the point G. Give your answer in terms of a and b in its simplest form.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 17 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 57
18 (a) Rationalise the denominator of 37 (2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Expand ( )( )2 6 3 12+ +
Give your answer in the form p q2 3+ where p and q are integers.(4)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 18 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201058
19 Prove that the answer to every line of the pattern below is 8.
3 × 5 – 1 × 7 4 × 6 – 2 × 8 5 × 7 – 3 × 9
(4)
(Total for Question 19 = 4 marks)
*
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 59
20 (a) Simplify 2 5 24 16
2
2
x xx− +
− (3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Complete the square for the expression
12x2 – 12x(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) Find the nth term of the quadratic sequence
1, 7, 17, 31, ...(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 20 = 9 marks)
TOTAL FOR PAPER = 100 MARKS
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201060
Uni
t 1
Hig
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Met
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1
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2 ×
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Que
stio
n: 9
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 61
=5M
M1H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
5(i
)(i
i)(i
ii)=
213 6 4 3 3
4B1
cao
B1
cao
M
1 fo
r 38
× 31 =
39an
d at
tem
pt t
o di
vide
A1
cao
To
tal f
or Q
uest
ion:
4 m
arks
6
(a)
Sam
ple
spac
e is
(1,
1) t
o (6
,6)
Even
t co
nsis
ts o
f th
e 6
pair
s.
(1,1
) to
(6,
6)
3663
M1
iden
tfyi
ng s
ampl
e sp
ace
an a
ttem
ptin
g to
list
all
pair
s M
1 fo
r id
entf
ying
the
dou
bles
A1366
oe
(b)
12
34
56
11
1B1
1B1
1B
21B
BB
BB
B
31
BB
B
41B
BB
BB
B
51
BB
B
61B
BB
BB
B
36323
M1
iden
tifi
es e
ithe
r th
e ou
tcom
es w
ith
a 1
or w
ith
a bl
ue
M1
(dep
) id
enti
fies
the
out
com
es w
hich
are
nei
ther
(or
the
ir
com
plem
ent)
A13632
Tota
l for
Que
stio
n: 6
mar
ks
7.(a
)20
1B1
cao
(b)
nn
+2
2B2
cao
(B
1 fo
r an
y qu
adra
tic
star
ting
n2 )
(c)
Reas
on1
C1 is
alw
ays
n m
ore
than
a s
quar
e, if
you
put
the
sm
all s
quar
es
toge
ther
you
get
a r
ecta
ngle
oe
nn
+2
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201062
=5M
M1H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
8.(a
)Co
rrec
t gr
aph
3B3
for
a f
ully
cor
rect
gra
ph
M1
for
an a
ttem
pt t
o re
arra
nge
the
equa
tion
to
y =
or t
o su
bsti
tute
a
valu
e of
x(i
n th
e ra
nge
–1 t
o 5)
into
the
equ
atio
n .
M1
for
then
sub
stit
utin
g x
in t
he r
ange
–1
to 5
into
the
equ
atio
n
y =
10 –
2x o
r in
to t
he o
rigi
nal e
quat
ion
and
atte
mpt
ing
to f
ind
yA1
cor
rect
line
dra
wn
from
–1
to 5
(b
)m
= 21
8 =
21(1
) +
c
217
21+
=x
y2
B2 c
ao
B1 f
or e
ithe
r m
= 21
or
c =
217
Tota
l for
Que
stio
n: 5
mar
ks
9.
OR X
X/
/ *
XX
/ /
*X
/ /
/ /
*X
/ /
/ /
*X
/ /
/ /
*X
/ /
/ /
*X
/ /
/ /
**
Key:
one
sq
per
stud
ent
X H
isto
ry o
nly,
/ /
for
ge
ogra
phy
only
, *
for
His
tory
an
d G
eogr
aphy
and
bla
nk f
or
neit
her
3565
M1
two
over
lapp
ing
oval
s w
ith
corr
ect
labe
ls
M1
wit
h 8
in t
he in
ters
ecti
on
A1 9
and
12
in t
he c
orre
ct p
lace
s A1
6 in
the
cor
rect
pla
ce
B1356
cao
OR
M1
for
draw
ing
grid
75
oe
×M
1 fo
r 17
– 8
= 9
, 20
– 8
= 1
2 A1
for
9 H
isto
ry/1
2 G
eogr
aphy
A1
for
6 n
eith
er
B1 f
or 356
cao
Tota
l for
Que
stio
n: 5
mar
ks
89
12
6H
G
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 63
=5M
M1H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
10.
Area
of
rect
angl
e =
60
123
cm2
4M
1 Ar
ea o
f re
ctan
gle
= 5
× 12
M1
area
of
trap
eziu
m =
6
12 2h
+×
B1h
= 7
A1 c
ao
Area
of
trap
eziu
m =
63
612
72+
× =
63
Tota
l for
Que
stio
n: 4
mar
ks
11.
(a)
Corr
ect
enla
rgem
ent
2B2
cao
(B
1 co
rrec
t sc
ale
fact
or b
ut in
the
wro
ng p
osit
ion)
(b
)Re
flec
tion
in
the
line
x =
–22
M1
for
refl
ecti
on w
ith
the
equa
tion
of
a lin
e gi
ven
or s
how
n on
the
di
agra
mA1
for
x =
–2
(c)
A ro
tati
on o
f 18
0o abo
ut(a
, b)
follo
wed
by
a
tran
slat
ion
of
−−
−b
a2
24
Corr
ect
rota
tion
and
tr
ansl
atio
n
M1
for
a ro
tati
on o
f 18
0o abo
ut a
sta
ted
poin
t an
d a
tran
slat
ion
cons
iste
nt w
ith
the
cent
re o
f ro
tati
on.
The
tran
slat
ion
may
be
poor
ly
desc
ribe
d
2
A1 f
or a
ful
ly c
orre
ct d
escr
ipti
on,
such
as
rota
tion
of
180o a
bout
O
follo
wed
by
a tr
ansl
atio
n of
− 04
Tota
l for
Que
stio
n: 6
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201064
=5M
M1H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
12.
(a)
107104
×10
028
3B1
sig
ht o
f tw
o of
107
,106
,103
,104
M1
107104
×
A1 f
or 10
028
oe
(b)
103104
107106
×+
×10
054
3M
1 107
106×
or
103104
×
M1
adds
tog
ethe
r pr
obab
iliti
es f
or G
R an
d RG
A1
oe
Tota
l for
Que
stio
n: 6
mar
ks
NPK=
0.43
×10-3
,3.
2×10
-2,
46×1
07 ,6×
108
2M
1 (n
umbe
rs p
ut in
com
mon
for
m a
t le
ast
in p
airs
acc
ordi
ng t
o si
gn o
f in
dex)
A1 c
orre
ct o
rder
Tota
l for
Que
stio
n: 2
mar
ks
14.
Proo
f 3
M1
atte
mpt
to
arri
ve a
t n
and
n +
1 (o
e)
M1
sigh
t of
2n
+ 1
(oe)
A1
exp
lana
tion
of
2n +
1To
tal f
or Q
uest
ion:
3 m
arks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 65
=5M
M1H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
15.
(a)
QW
Cii
AD
= D
C(g
iven
)A
DE
= FC
D(c
orre
spon
ding
an
gles
for
ED
and
FC)
EAD
= F
DC
(co
rres
pond
ing
angl
es f
or B
A a
nd F
D)
Hen
ceA
ED�
DFC
(2 a
ngle
s an
d th
e co
rres
pond
ing
side
)
Proo
f 3
M1
any
3 co
rrec
t st
atem
ents
whi
ch w
ould
lead
to
a co
ngru
ence
pro
of
M1
all t
hree
sta
tem
ents
jus
tifi
ed
M1
corr
ect
reas
on f
or c
ongr
uenc
e Q
WC:
Sta
tem
ent
supp
orte
d by
co
rrec
t pr
evio
us w
orki
ng a
nd j
usti
fica
tion
(b)
Area
of
DFC
= a
rea
AED
(con
grue
nt)
FC =
ED
= B
F (c
ongr
uenc
y an
d op
posi
te s
ides
of
a pa
ralle
logr
am a
re e
qual
)
So a
rea
of p
aral
lelo
gram
ED
FB =
2 ×
are
a D
FC=
2 ×
area
AED
But
area
A
ED =
41×
area
ABC
Proo
f 2
Hen
ce s
how
n
M1
area
of
DFC
= a
rea
AED
(co
ngru
ent)
FC
= E
D =
BF
(c
ongr
uenc
y an
d op
posi
te s
ides
of
a pa
ralle
logr
am a
re
equa
l)so
are
a of
par
alle
logr
am E
DFB
= 2
× a
rea
DFC
= 2
× ar
ea
AED
A1 b
ut a
rea
AED
=41
× ar
ea
ABC
and
conc
lusi
on
Tota
l for
Que
stio
n: 5
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201066
5MM
1HQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e
16.
(a)
QW
C
SOT
= 90
o–
36 o
SQT
= 27
o15
3oM
1 SO
T =
90 o
– 36
ow
ith
angl
e be
twee
n ta
ngen
t an
d ra
dius
= 9
0 o4
C1 S
QT
= SO
T ÷
2 w
ith
angl
e at
cen
tre
2 a
ngle
at
circ
umfe
renc
e.
QW
C: C
orre
ct a
ttri
buta
ble
wor
king
sho
wn
wit
h re
ason
sta
ted
×SR
T =
73o
C1 S
RT =
180
– S
QT
wit
h op
posi
te a
ngle
s of
a c
yclic
qua
drila
tera
l are
su
pple
men
tary
QW
C: C
orre
ct a
ttri
buta
ble
wor
king
sho
wn
wit
h re
ason
sta
ted
A1 f
or 1
53o ca
o
(b)
BDC
= x
44o
3B1
BD
C =
xx
x+
+M
1 0
248
182
4818
0x
x+
+=
=A1
cao
To
tal f
or Q
uest
ion:
7 m
arks
17
.(a
)→
→=
OX
OP
+
→ XP =
3a+
32(6
b–
3a)
= 4b
+a
4b+
a3
M1
→ XY =
6b
– 3a
M1
→ XP =
32(6
b–
3a)
A1 c
ao
(b)
→ OG
=
=
→→
+YG
OY
6b+
a+
4b =
a +
10b
a +
10b
3M
1
=(p
aral
lelo
gram
) → OP
→ YG
M1
= 6b
+ ‘
a +
4b’
→ OG
A1 f
t on
(a)
Tota
l for
Que
stio
n: 6
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 67
=5M
M1H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
18.
(a)
7773
×77
32
M1
7773
×
A1 c
ao
(b)
23
212
1872
++
+
26
23
34
32
++
+
29
36
+4
M1
corr
ect
exp
or 3
out
of
4 te
rms
corr
ect
M
1 72
362
=×
B12
672
= o
r 3
212
=A1
cao
Tota
l for
Que
stio
n:6
mar
ks
19.
QW
C(i
ii)
The
nth
line
of t
he
patt
ern
is:
(n+
2)(n
+ 4)
–n(
n+
6)
Proo
f su
ppor
ted
by
attr
ibut
able
wor
king
. 4
M1
for
(n +
2)(
n +
4)M
1 fo
r –n
(n +
6)
A1 f
or c
orre
ct s
impl
ific
atio
n B1
con
clus
ion
QW
C: A
ppro
pria
te c
oncl
usio
n su
ppor
ted
by
attr
ibut
able
wor
king
.To
tal f
or Q
uest
ion:
4 m
arks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201068
5MM
1H/X
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 20
.(a
)B1
)2)(1
2(−
−x
x)2
)(12(
25
22
−−
=+
−x
xx
x
)2)(2
(4)4
(416
42
2+
−=
−=
−x
xx
x)2
(41
2+−
xx3
B1 o
r )2
)(2(4
+−
xx
)42
)(42(
+−
xx
B1
cao
M1
for
12x2 –
12x
= 2
(x2 –
6x)
2(x
– 3)
2 – 9
(b)
12x2 –
12x
= 2
(x2 –
6x)
3
=
2[(
x –
3)2 –
(3)2 ]
M1
for
Z=2
[(x
– 3)
2 – (3
)2 ]
= 2
(x –
3)2 –
9
A1 f
or ===================Z
=2(x
– 3
)2 – 9
2n2 –
1
(c)
1
7
1
7
31
3
M1
for
usin
g m
etho
d of
dif
fere
nces
(oe
)
6
10
14
4
4
A1 f
or s
ight
of
2n2
2nd
diff
eren
ce is
4,
so u
se
2n2
= =
n =
1
2
=
n =
2
8
n =
3
18
n =
4
32
nth
term
is 2
n2 – 1
A1 c
orre
ct g
ener
alis
atio
n To
tal f
or Q
uest
ion:
9 m
arks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 69
Unit 2: Methods 2
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201070
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 71
Centre Number Candidate Number
Write your name hereSurname Other names
Total Marks
Paper Reference
Turn over
*S38370A0122*
Edexcel GCSE
Methods in MathematicsUnit 2: Method 2For Approved Pilot Centres ONLY
Foundation Tier
Sample Assessment MaterialTime: 1 hour 45 minutes
You must have:
Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
5MM2F/01
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.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators may be used.
• If your calculator does not have a π button, take the value of π to be 3.142 unless the question instructs otherwise.
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.• Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed – you should take particular care on these questions with your spelling, punctuation
and grammar, as well as the clarity of expression.
Advice• Read each question carefully before you start to answer it.• Keep an eye on the time.• Try to answer every question.• Check your answers if you have time at the end.
S38370A©2010 Edexcel Limited.
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201072
GCSE Mathematics 2MM01
Formulae: Foundation Tier
You must not write on this formulae page.Anything you write on this formulae page will gain NO credit.
Area of trapezium = (a + b)h
Volume of prism = area of cross section × length
b
a
h
length
crosssection
12
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 73
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
1
The arrow points to a number.
(a) What has to be added to the number to make 6?(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Write down the number that is 1000 times the number the arrow points to.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 1 = 3 marks)
2 Find the number that should be written in the empty boxes.
(i)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 2 = 4 marks)
0 1 2 3 4 5 6
+ – =38 64 77
× ÷ =2.3 0.765.75
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201074
3
This shape has been drawn on a grid of centimetre squares.
(a) Find the area of this shape.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) On the grid, draw a rectangle that has the same area as this shape.(2)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 75
(c) Work out the area of this triangle.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 3 = 6 marks)
Diagram NOTaccurately drawn
13 cm5 cm
12 cm
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201076
4 Anisha has four cards, with a number written on each card.
Anisha puts all four cards on the table to make a number.
(a) (i) Write the numbers on the cards to show the smallest number Anisha can make with the four cards.
(ii) Write the numbers on the cards to show the largest number Anisha can make with the four cards.
(2)
Anisha uses the cards to make a true statement.
(b) Write the number on the cards to make this true. Use each of Anisha’s cards once.
(1)
A fifth card is needed to show the result of the multiplication 4915 × 10 She needs a fifth card.
(c) Write the number that should be on the fifth card.(1)
(Total for Question 4 = 4 marks)
4 9 1 5
+ =
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 77
5 Crystal wrote down the temperature at different times on 1st January 2009.
Time Temperature
4 am – 10°C
8 am – 4°C
noon 7°C
3 pm 6°C
7 pm – 2°C
midnight – 6°C
(a) Write down(2)
(i) the highest temperature
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °C
(ii) the lowest temperature.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °C
(b) Work out the difference in the temperature between(2)
(i) 4 am and 8 am
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °C
(ii) 3 pm and 7 pm.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °C
(Total for Question 5 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201078
6 Imran thinks of a number. He multiplies the number by 3 He then adds 19 His answer is 61
What number did Imran first think of?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 = 2 marks)
7 Find the reciprocal of:
(i) 0.2(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) 0.2 × 1
5 (2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 7 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 79
8
Arthur, Beth and Charlie each have some marbles. They keep their marbles in boxes each with their own name on.
Arthur has a marbles, Beth has b marbles and Charlie has c marbles.
(a) Write down an expression, in terms of a, b and c, for the total number of marbles that they have altogether.
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Beth puts 4 of her marbles and Charlie puts 2 of her marbles into Arthur’s box. Charlie also puts 1 of her marbles into Beth’s box.
*(b) Complete the diagram to show expressions for the number of marbles in each box. Give your answers in their simplest forms.
(4)
After this has been done the number of marbles in Arthur’s box is the same as the number of marbles in Beth’s box and is the same as the number of marbles in Charlie’s box.
(c) Find an expression, in terms of a, for the total number of marbles that they have.(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 = 8 marks)
Arthur
a
Beth
b
Charlie
c
Arthur Beth Charlie
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201080
9 (a) Find two square numbers which have a sum which is also a square number.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Find two cube numbers which have a difference which is a prime number.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 = 4 marks)
10 (a) Shade1
4of this shape.
(1)
(b) Work out the number that is half way between(3)
(i) 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
(ii) 6.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6
(iii) 1
4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
(c) Find the point on the line AB that is 1
3of the way along the line from A.
Mark this point with a cross (×).(1)
(Total for Question 10 = 5 marks)
A B
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 81
11
Work out the size of the angle marked x. You must show clearly how you obtained your answer.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(Total for Question 11 = 4 marks)
Diagram NOT260°accurately drawn
130°
70° x
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201082
12 The diagram shows a mathematical rule.
It multiplies the input by 3 and then subtracts 3 to get the output.
(a) Complete the diagram.(1)
(b) Complete the diagram.(1)
In this diagram the input and the output have the same value, t
(c) Work out the value of t.(2)
t = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
input × 3 – 3 output
10 × 3 – 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
117× 3 – 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
t× 3 – 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .t
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 83
In this diagram the input is x and the output is y
(d) Write x in terms of y(2)
(Total for Question 12 = 6 marks)
y× 2 + 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201084
13 (a) Write1
20as a decimal.
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Find7
25 as a percentage.
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Danny shares a bag of sweets with his friends.
He gives Mary3
5of the sweets.
He gives Ann1
10of the sweets.
He has 12 sweets left.
(c) How many sweets does Danny give to Mary?(4)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 13 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 85
14
(a) What special name is given to this polygon?(1)
………………………….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………..
One of the polygons below is congruent to the polygon shown in part (a).
(b) Draw a circle around this polygon.(1)
(c) On the grid, show how the shape below will tessellate. You should draw at least 8 shapes.
(2)
(Total for Question 14 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201086
15
XYZ is an isosceles triangle. PQRS is a square.
PQ = XY
XZ = YZ
XZ is 14 cm longer than PQ.
The perimeter of both shapes is the same.
Find the length of XZ.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm
(Total for Question 15 = 3 marks)
Diagram NOTaccurately drawn
X Y
Z
P Q
RS
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 87
16 Here is a triangular prism.
(a) Calculate the volume of the triangular prism.(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm3
A cube has the same volume as this triangular prism.
(b) Calculate the surface area of the cube. Give your answer correct to the nearest whole number.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question 16 = 5 marks)
Diagram NOTaccurately drawn
8 cm
9 cm
14 cm
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201088
17
In the diagram, AD = BD = BE.
ADEC is a straight line. Angle DBA = 28° Angle CBF = 32°
BF is parallel to AC.
Find the size of the angle marked y You must show clearly how you obtained your answer.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(Total for Question 17 = 4 marks)
D E C
BF
32°y
Diagram NOTaccurately drawn
28°
A
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 89
18
The diagram shows a circle enclosed by a square. Work out the area of the region shaded in the diagram. Give your answer correct to one decimal place.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question 18 = 4 marks)
Diagram NOTaccurately drawn
12 cm
12 cm
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201090
19 (a) Solve 3y + 4 = 2 – 2y(2)
y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Solve 3(2x – 4) + x = 2x – 25(4)
x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 19 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 91
20 There were 800 students at Prestwick School at the start of the year.
48% of these 800 students were girls.
(a) What is the number of girls attending the school?(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
There are 176 students in Year 10.
(b) What percentage of the students at the school are Year 10 students?(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %
By the end of the year1
6of the girls had left and 12
1
2% of the boys had left.
(c) Work out the number of students at Prestwick School at the end of the year.(4)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 20 = 8 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201092
21
ABCDP is a regular pentagon.QPEX is part of a regular octagon.PARQ is a parallelogram.
Calculate the size of angle PAR.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(Total for Question 21 = 7 marks)
TOTAL FOR PAPER = 100 MARKS
R
A
B
D E
P
Q
X
Diagram NOTaccurately drawn
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 93
Uni
t 2
Foun
dati
on:
Met
hods
2
5MM
2FQ
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kA
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2.8
2M
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2 or
6 –
3.4
A1
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00
1B1
cao
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l for
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stio
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mar
ks
2.(i
)
(ii)
38 +
64
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25
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75 =
0.4
0.
76 ÷
0.4
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.9
25 1.9
2 2
M1
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64
and
‘102
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77
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M1
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nd 0
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A1 c
ao
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l for
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stio
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mar
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3.(a
)18
cm
22
M1
show
s cl
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at is
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25
12×
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m2
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512
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A1 c
ao
Tota
l for
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n: 6
mar
ks
4.(a
) (i
)
(ii)
14
59
9541
2
B1 c
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B1 c
ao t
rans
pose
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swer
s aw
ard
one
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k (b
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1
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+ 5
= 1
4 or
5 +
9 =
14
(c)
01
B1 c
ao
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201094
5MM
2FQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 5.
(a)(
i)
(ii)
7 −10
2B1
cao
B1
cao
(b
)(i)
(i
i)
6 82
B1 a
ccep
t −
6 B1
acc
ept
− 8
Tota
l for
Que
stio
n: 4
mar
ks
6.61
– 19
= 4
2 42
÷ 3
= 1
4 14
2M
1 fo
r –1
9 an
d ÷
3 or
42
seen
A1
cao
To
tal f
or Q
uest
ion:
2 m
arks
7.
(i)
(ii)
5 253
A1 c
ao
M1
0.04
oe
A1 c
ao
Tota
l for
Que
stio
n: 3
mar
ks
8.(a
)a
+ b
+ c
1
B1 c
ao
QW
C(i
i)(b
)a
+ 6
b –
3 c
– 3
4B4
all
corr
ect
QW
C: c
orre
ct n
otat
ion
and
sim
plif
ied
expr
essi
ons
(B3
all c
orre
ct b
ut u
nsim
plif
ied)
(B
2 an
y 2
corr
ect)
(B
1 an
y 1
corr
ect)
(c
)b
= a
+ 9
c =
a +
93a
+ 1
8 3
M1
for
b =
a +
9 o
r c
= a
+ 9
for
a s
tate
men
t th
at A
rthu
r ha
d 9
less
tha
n Be
th (
or C
harl
ie)
A1 f
or a
cor
rect
alg
ebra
ic e
xpre
ssio
n fo
r b
or c
in t
erm
s of
aA1
any
exp
ress
ion
that
wou
ld s
impl
ify
to 3
a +
18To
tal f
or Q
uest
ion:
8 m
arks
9.
(a)
List
s sq
uare
num
bers
1,
4, 9
, 16
, 25
9
+ 16
2M
1 lis
ts s
quar
e nu
mbe
rs (
at
leas
t 4)
A1
9 a
nd 1
6 (b
)Li
sts
cube
num
bers
1 8
1
and
8 2
M1
for
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A1 1
and
8 a
nd c
omm
ent
that
7 is
pri
me
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 95
=5M
M2F
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
10.
(a)
2sq
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aded
1B1
2 s
quar
es s
hade
d
(b)(
i) (
ii)
(iii)
40 6.55
83
3B1
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B1
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B1 0
.375
, 83 o
e
(c)
Mar
k 2.
1-2.
5 cm
fro
m A
1
B1 f
or m
ark
2.1-
2.5
cm f
rom
A
Tota
l for
Que
stio
n: 5
mar
ks
1136
0 –
260
= 10
0 10
0 +
70 +
130
= 3
00
360
– 30
0 =
60
180
– 60
= 1
20
120o
4B1
for
100
cle
arly
sho
wn
in t
he c
orre
ct p
lace
M
1 fo
r 36
0 –
(100
+ 7
0 +
130)
M
1 fo
r 18
0 –
‘60’
A1
cao
Tota
l for
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stio
n: 4
mar
ks
12.
(a)
271
B1 c
ao
(b)
401
B1 c
ao
(c)
3t–
3 =
t1.
52
M1
3t–
3 =
tA1
cao
(d
)y
x=
+4
24
2−
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x2
4−
=y
x2
M1
for
a cl
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he d
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am o
r fr
om
24
÷−
=y
xA1
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To
tal f
or Q
uest
ion:
6 m
arks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201096
5MM
2FQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 13
.(a
)0.
05
1B1
cao
(b
)
10028
44257
=×
28%
1B1
cao
(c)
107101
53=
+
103107
1=
− 103 o
f th
e to
tal =
12
103
12×
÷ =
40
244
B1107
M1
1071
− o
f th
e to
tal i
s 12
sw
eets
M1
'10
3'12
×÷
A1 2
4
Tota
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n: 6
mar
ks
14.
(a)
Hex
agon
1
B1 c
ao
(b)
The
one
on
the
far
righ
t 1
B1 c
ao
(c)
Tess
ella
tion
2
B2 f
or a
t le
ast
7 ad
diti
onal
sha
pes
draw
n (B
1 fo
r at
leas
t 5
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tion
al s
hape
s dr
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or
shap
es o
nly
on o
ne li
ne,
or in
com
plet
e te
ssel
lati
on)
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 97
5MM
2FQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 15
.Le
tX
Y =
xx
xx
x4
1414
=+
++
+28
=x
423
B1 o
r 14
14+
++
+x
xx
x4M
1 x
xx
x4
1414
=+
++
+A1
cao
Tota
l for
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stio
n: 3
mar
ks
16.
(a)
89
362×
=
3614
504
×=
504
2M
1 8
936
2×=
, o
r '3
6'14×
214
98
÷×
×
A1 c
ao
(b)
350
4x
=x
= 7.
958(
1..)
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rfac
e ar
ea =
6 ×
7.9
58(1
..)2
380
3M
1 x
=3
504
M1
6 ×
‘7.9
58(1
..)2 ’
A1 c
ao
Tota
l for
Que
stio
n: 5
mar
ks
17.
(a)
BAD
= 28
°
BDE
= 56
°
BED
= 5
6°
EBF
= 56
°
y =
56° –
32°
OR BA
D =
28°
BDE
= 56
°
DBE
= 6
8°
ECB
= 32
°
y =
180°
– 2
8° – 28
° – 6
8° – 3
2°
24o
4B1
BAD
= 2
8°
M1
BDE
= 56
°
M1
EBF
= 56
°
A1 c
ao
OR
B1BA
D =
28°
M1
BDE
= 56
°
M1
ECB
= 32
°
A1 c
ao
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 201098
5MM
2FQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 18
.Ci
rcle
:×
6 ×
6 =
113.
097.
. 14
4 –
113.
097…
= 3
0.90
3 30
.903
÷ 4
7.73
4
M1
for
× 6
× 6
B1
for
144
M
1 14
4 –
‘113
.097
’…
A1 a
nsw
ers
in r
ange
7.7
– 7
.8
Tota
l for
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mar
ks
19.
(a)
5y =
– 2
y
= –
522
M1
corr
ect
proc
ess
of is
olat
ing
the
term
s in
y
A1–
52oe
(b)
252
126
−=
+−
xx
x12
252
6+
−=
−+
xx
x
513−
=x
513−
=x
4B1
2512
6−
=−
xx
M1
corr
ect
proc
ess
of is
olat
ing
the
term
s in
xfr
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4 o
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term
eq
uati
onM
1 co
llect
ter
ms
in x
on
one
side
A1513
−=
x o
e
Tota
l for
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stio
n: 6
mar
ks
20.
(a)
800
100
48×
= 38
438
4 2
M1
80
010
048×
A1 c
ao
(b)
100
800
176
×22
2M
110
080
017
6×
A1 c
ao
(c)
384
÷6 =
64
1005.
12)
384
800
(×
− =
52
800
– 64
– 5
2 =
684
684
4M
1 38
4 ÷6
M1
1005.
12)'
384
'80
0(
×−
M1
800
– ‘6
4’ –
‘52
’A1
cao
Tota
l for
Que
stio
n: 8
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 99
5MM
2FQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 21
.Ex
t an
gle
of a
pen
tago
n is
72
o
Ext
angl
e of
oct
agon
is 4
5o
APQ
= 72
+ 4
5= 1
17o
PAR
= 1
80 –
117
= 6
3
OR
APE
= 1
08o
QPE
= 1
35o
APQ
= 36
0 –
108
– 13
5 =
117o
PAR
= 18
0 –
117
= 63
63o
7M
1 fo
r 5360
or
8360
A1,
A1 f
or 7
2 an
d 45
M
1 fo
r ‘7
2’ +
’45
’ A1
for
117
M
1 fo
r 18
0 –
‘117
’ A1
cao
O
R
M1
905
410
×−
or
908
416
×−
A1,
A1 f
or 1
08 a
nd 1
35
M1
for
360
– 10
8 –
135
A1 f
or 1
17
M1
for
180
– ‘1
17’
A1 c
ao
Tota
l for
Que
stio
n: 7
mar
ks
= = =
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010100
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 101
Centre Number Candidate Number
Write your name hereSurname Other names
Total Marks
Paper Reference
Turn over
*S38372A0122*
Edexcel GCSE
Methods in MathematicsUnit 2: Methods 2 For Approved Pilot Centres ONLY
Higher Tier
Sample Assessment MaterialTime: 1 hour 45 minutes
You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
5MM2H/01
S38372A©2010 Edexcel Limited.
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.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators may be used.• If your calculator does not have a π button, take the value of π to be
3.142 unless the question instructs otherwise.
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.• Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed – you should take particular care on these questions with your spelling, punctuation
and grammar, as well as the clarity of expression.
Advice• Read each question carefully before you start to answer it.• Keep an eye on the time.• Try to answer every question.• Check your answers if you have time at the end.
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010102
GCSE Mathematics 2MM01
Formulae – Higher Tier
You must not write on this formulae page.Anything you write on this formulae page will gain NO credit.
Volume of a prism = area of cross section × length Area of trapezium = (a + b)h
Volume of sphere = r3 Volume of cone = r2h
Surface area of sphere = 4 r2 Curved surface area of cone = rl
In any triangle ABC The Quadratic Equation The solutions of ax2+ bx + c = 0 where a 0, are given by
Sine Rule
Cosine Rule a2= b2+ c2– 2bc cos A
Area of triangle = ab sin C
length
crosssection
rh
r
l
C
ab
c BA
13
a b csin A sin B sin C
xb b ac
a=
− ± −( )2 42
43
12
b
a
h
12
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 103
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
1 Divide £60 in the ratio 2:3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 1 = 3 marks)
2 The diameter of a circle is 15 cm.
Find its circumference. Give the units of your answer. Give your answer correct to 1 decimal place.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 2 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010104
3 Here is a triangular prism
(a) Calculate the volume of the triangular prism.(2)
Diagram NOTaccurately drawn
8 cm
9 cm
14 cm
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm3
A cube has the same volume as this triangular prism.
(b) Calculate the surface area of the cube. Give your answer correct to the nearest whole number.
(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question 3 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 105
4 (a) n is an integer and –3 < n 2
Write down all the possible values of n(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Here is a number line.
(b) Display the inequality –3 < x 2 on the number line.(2)
(Total for Question 4 = 4 marks)
1 2 3 4–1–2 –3–4 0 x
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010106
5
d
l
The diagram is a shape made up of a rectangle of width d and length l together with a semicircle of diameter d.
The perimeter P of the shape is given by P d l d= + +22
π
(a) Work out the perimeter of the shape when the width is 8.4 cm and the length is 11.7 cm.
(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm
(b) Rearrange the formula to make d the subject. (3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 5 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 107
6
A D E C
B F
32°28° y
Diagram NOTaccurately drawn
In the diagram, AD = BD = BE
ADEC is a straight line. Angle DBA = 28° Angle CBF = 32° BF is parallel to AC.
Find the size of the angle marked y. You must show clearly how you obtained your answer.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(Total for Question 6 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010108
7
A
R
B
D E
P
Q
X
Diagram NOTaccurately drawn
ABDEP is a regular pentagon. QPEX is part of a regular octagon. PARQ is a parallelogram.
Calculate the size of angle PAR.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(Total for Question 7 = 7 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 109
8 The quadratic curve with equation y = x2 + bx + c passes throughthe points (2, – 4) and (–1, 2)
Find the values of b and c
b = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
c = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010110
9 Here are four graphs.
x
y
x
y
x
y
x
y
A B
C D
Here are five equations of graphs.
P y = sin x Q y = cos x
R y = 2xS y =
x1
T y = x2
Match each graph with an equation.
A with equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B with equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C with equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D with equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 111
10 y is directly proportional to the square root of x and y = 8 when x = 25
(a) Find a formula for y in terms of x(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
y = 36
(b) Find the value of x(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010112
11
Diagram NOTaccurately drawn
5 cm
34 cm
30 cm
28 cm
AB
C D
E
Here is the design for a logo, ABCD. The design is made from two right-angled triangles.
(a) Work out the perimeter of the logo.(4)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 113
Diagram NOTaccurately drawn
5 cm
34 cm
30 cm
28 cm
A
B
C
D
E
The logo is turned to rest on the ground at the corners A and D.
(b) Calculate the size of angle BAD.(4)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(Total for Question 11 = 8 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010114
12 On a farm, 38
of the land area is used to keep sheep.
Half of the rest of the land area on the farm is used to grow crops.
The land area of the farm used to grow crops is 600 000 m2.
Work out the land area of the farm used to keep sheep.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2
(Total for Question 12 = 3 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 115
13 (a) Prove that the recurring decimal 0 124 41330
• •=
(3)
(b) Hence or otherwise, express as a fraction, the recurring decimal 0 0621.• •
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 13 = 4 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010116
14
2
x + 4
x
Diagram NOTaccurately drawn
x + 3
The diagram shows a hexagon. All the angles are right angles. All the measurements are in centimetres.
The area of the hexagon is 50 cm2.
(a) Show that x2 + 4x – 44 = 0(3)
(b) (i) Solve the equation x2 + 4x – 44 = 0(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) Write down the length of the longest side.(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .cm
(Total for Question 14 = 7 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 117
15 (a) Find the set of values of x for which 3x – 5 < x + 8(2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Hence or otherwise, find the set of values of x for which
3x – 5 < x + 8 and 5x > x – 8(3)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 15 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010118
16 Find two numbers which have a difference of 3 and have a product of 88(5)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 119
17 Solve x2 + y2 = 34
y – x = 8(5)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 17 = 5 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010120
18
2
4
6
8
10
12
14
16
1 2 3 4 5–1–2 0 x
y
Here is the graph of y = f(x) = x2 − 4x + 7 for values of x from −2 to 4
(a) On the grid draw the graph of y = f(x+1) for values of x from −2 to 3(2)
The algebraic equation of another graph is y = g(x) = x2 − 3
y = f(x) can be mapped onto y = g(x) by a transformation.
* (b) Describe fully this transformation. You must show clearly how you obtained your answer.
(4)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 18 = 6 marks)
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 121
19 (a) Show that (mn – 1)2 + (m + n)2 = (m2 + 1)(n2 + 1)(3)
The two shorter sides of a right-angled triangle are 2m and m2 – 1 where m is a positive integer.
(b) Show that the hypotenuse is always a positive integer.(2)
(c) Find two square numbers which have a sum equal to 50005(2)
(Total for Question 19 = 7 marks)
*
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010122
20
70o
A
B
C
D
Diagram NOTaccurately drawn
9 cm
10.5 cm
7.5 cm
80o
In the quadrilateral ABCD, AD = 10.5 cm AB = 9 cm CD = 7.5 cm Angle BAD = 70° Angle BCD = 80°
Calculate the size of angle DBC.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °
(Total for Question 20 = 6 marks)
TOTAL FOR PAPER = 100 MARKSEND
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 123
Uni
t 2
Hig
her:
Met
hods
2
5MM
2HQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 1.
)32(
60+
÷ =
12
12×
3
12×
4
24,
36
3 M
1 )3
2(60
+÷
A1 c
ao
A1 c
ao
Tota
l for
Que
stio
n: 3
mar
ks
2.
15
π×
=47.
1(2…
) 47
.1 c
m
3 M
1 15
π×
=47.
1(2…
) A1
cao
B1
(in
dep)
cm
To
tal f
or Q
uest
ion:
3 m
arks
3.
(a
) 8
936
2×=
3614
504
×=
504
2 M
1 8
936
2×=
,'3
6'14×
or
214
98
÷×
×
A1 c
ao
(b
) 3
504
x=
x =
7.95
8(1.
.)
Surf
ace
area
= 6
× 7
.958
(1..
)2
380
3 M
1 x
=3
504
M1
6 ×
‘7.9
58(1
..)2 ’
A1 c
ao
Tota
l for
Que
stio
n: 5
mar
ks
4.
(a)
–2
,–1
, 0,
1,
2
2 B2
cao
(B
1–1
, 0,
1,
2 or
–2,
–1,
0, 1
)
(b)
Co
rrec
t nu
mbe
rlin
e
2M
1 lin
e fr
om (
–3 t
o +2
) A1
wit
h op
en c
ircl
e at
−3
and
clos
ed c
ircl
e at
2
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010124
=5M
M2H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
5.
(a)
P =
8.4
+ 2
× 11
.7 +
×
8.4
÷ 2
45
.0
2 M
1 fo
r 8.
4 +
2 ×
11.7
+
× 8.
4 ÷
2 A1
44.
9 –
45.0
(b
) 2
2d
dl
Pπ
+=
−
)2
1(2
π+
=−
dl
P2
1
2 π+−
=l
Pd
3M
1 fo
r 2
2d
dl
Pπ
+=
−
M1
for
)
21(
2π
+=
−d
lP
A1
21
2 π+−
=l
Pd
oe
SC If
is
tak
en t
o be
3.1
4 th
en a
llow
1 m
ark
for
57.22l
Pd
−=
oe
Tota
l for
Que
stio
n: 5
mar
ks
6.
BA
D =
28°
BDE
= 56
°
BED
= 5
6°
EBF
= 56
°
y =
56°
– 32
°
OR
BAD
= 2
8°
BDE
= 56
°
DBE
= 6
8°
ECB
= 32
°
y =
180°
– 2
8°–
28°
– 68
°–
32°
24°
4 B1
BA
D =
28°
M1
BDE
= 56
°
M1
EBF
= 56
°
A1 c
ao
OR
B1BA
D =
28°
M1
BDE
= 56
°
M1
ECB
= 32
°
A1 c
ao
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 125
=5M
M2H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
7.
Ext
angl
e of
a p
enta
gon
is 7
2o
Ext
angl
e of
oct
agon
is 4
5o
APQ
= 72
+ 4
5 =
117o
PAR
= 1
80 –
117
= 6
3
OR
APE
= 1
08o
QPE
= 1
35o
APQ
= 36
0 –
108
– 13
5 =
117o
PAR
= 18
0 –
117
= 63
63o
7M
1 fo
r 5360
or
8360
A1,
A1 f
or 7
2 an
d 45
M
1 fo
r ‘7
2’+’
45’
A1 f
or 1
17
M1
for
180
– ‘1
17’
A1 c
ao
OR
M1
905
410
×−
or
908
416
×−
A1,
A1 f
or 1
08 a
nd 1
35
M1
for
360
– 10
8 –
135
A1 f
or 1
17
M1
for
180
– ‘1
17’
A1 c
aoTo
tal f
or Q
uest
ion:
7 m
arks
8.
42
22−
=+
+c
b8
2−
=+
cb
2)1
()1
(2
=+
−+
−c
b 3=
+−
cb
3−=
b2−
=c
5C1
42
22−
=+
+c
bM
1 3
=+
−c
bM
1 co
rrec
t m
etho
d to
elim
inat
e b
or c
A13−
=b
A12−
=c
Tota
l for
Que
stio
n: 5
mar
ks
9.
AS
BP
C R
D T
3 B3
all
corr
ect
(B2
3 co
rrec
t)
(B1
2 co
rrec
t)
Tota
l for
Que
stio
n: 3
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010126
=5M
M2H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
10
a x
ky
=25
8×
=k 58
=k
xy
6.1=
3M
1 x
ky
=M
1 25
8×
=k
A158
=k
b
x×
=6.1
36
2
6.136=
x
506.
25
2 M
1 x
×=
6.136
A1 c
ao
Tota
l for
Que
stio
n: 5
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 127
=5M
M2H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
11.
(a)
256
900
1156
3034
22
=−
=−
1625
6=
EC=
28
– 16
= 1
2
169
144
2512
52
2=
+=
+13
169
=
30 +
28
+ 5
+ 13
+ 3
4
110
4 M
1 2
230
34−
M1
(dep
) EC
= 2
8 –
‘16’
M1
16
914
425
'12'
52
2=
+=
+A1
110
OR
M1
for
34si
nBE
A=
,BE
= 3
4 ×
sin
28.
07
A1 f
or B
E =
16,
CE =
26
–BE
= 1
2, D
E =
13)
125(
22
=+
M1
for
22
125
+=
169
A1 1
10
(b
)
285
30ta
n−
=BA
D
12.1ta
n1−
=BA
D
48.2
°4
M1
reco
gnit
ion
of a
rig
ht-a
ngle
d tr
iang
le w
ith
side
s 30
– 5
and
28
M1
285
30ta
n−
=BA
D
M1
12.1ta
n1−
=BA
DA1
48.
2 or
bet
ter
O
R
Angl
e CE
D =
125
tan
1−=
22.6
2º
Angl
e BE
A =
1630ta
n1−
= 61
.93º
Angl
e D
EA =
180
º –
22.6
2º –
61.9
3º
AD =
54.
3745.
95co
s34.
13.213
342
2=
−+
Angl
e D
AE =
20.
17º
Angl
e BA
E =
28.0
7º
Angl
e BA
D =
48.
2º
Tota
l for
Que
stio
n: 8
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010128
=5M
M2H
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
12.
8583
1=
− 5 16of
the
land
are
a =
6000
00
Land
are
a =
1660
0000
5×
= 19
2000
0
Shee
p ar
ea =
3
1920
000
8×
7200
00
3 M
1 5 16
of t
he la
nd a
rea
= 60
0000
M1
land
are
a =
16'6
0000
0'5
×
A1 c
ao
Tota
l for
Que
stio
n: 3
mar
ks
13.
(a)
x =
0.12
4242
4…
10x
= 1.
2424
…
1000
x =1
24.2
424…
99
0x =
123
(o
e)
123
4199
033
0x
==
(oe)
3 M
1 x
= 0.
1242
424…
M
1 10
xan
d 10
00x
wit
h su
btra
ct (
or x
and
100
x w
ith
subt
ract
)
A1 c
orre
ct
33041
990
123
=
(b
) 41
233
0÷
41 660
1 B1
cao
Tota
l for
Que
stio
n: 4
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 129
5MM
2HQ
uest
ion
Wor
king
Ans
wer
Mar k
Add
itio
nal G
uida
nce
14.
(a)
)4(
+xx
+2
3× =
50
506
42
=+
+x
x OR
50)2
()3
(2=
++
+x
xx
502
62
2=
++
+x
xx
AG
3 M
1 sp
lit a
rea
into
rec
tang
les
wit
h co
rrec
t ex
pres
sion
s fo
r ar
eas
A1 e
xpan
d co
rrec
tly
A1 s
et =
50
and
conc
lude
(b
)(i)
(ii)
2)
44(
14
44
2−
××
−±
−=
x
219
24
±−
=x OR
442
)2(
22
−−
+x48
)2(
±=
+x
4.93
or
–8.9
3
8.93
4M
1 )
)((
bx
ax
++
wit
h ab
= -
45
A1)5
)(9(
−+
xx
A1 c
ao
OR
M1
2)
44(
14
44
2−
××
−±
−=
x a
llow
sig
n er
rors
in b
and
c
M1
219
24
±−
=x
A1 OR
M1
442
)2(
22
−−
+x
M1
48)2
(±
=+x
A1x
= 4
.93
or
– 8.
93 (
both
‘or
bet
ter’
)
B1 c
ao
Tota
l for
Que
stio
n: 7
mar
ks
15.
(a)
3x–
x<
8 +
5 2x
< 5
x
<
213
or
6.5
x<
6.5
2 M
1
A1
(b
) 5x
> x
– 8
4x>
8
x>
2
Corr
ect
ineq
ualit
y di
agra
m
–2 <
x <
6.5
–2 <
x <
6.5
3
B1 f
or c
orre
ct s
olut
ion
of in
equa
lity
M1
for
corr
ect
ineq
ualit
y di
agra
m
A1 c
ao
Tota
l for
Que
stio
n: 5
mar
ks
=
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010130
5MM
2H/X
Q
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 16
.
88)3
(=
−xx
088
32
=−
−x
x0
)11
)(8(
=−
+x
x,8−
=x
11=
x
OR
88)3
(=
−xx
088
32
=−
−x
x
2)
88)(1(4
93
−−
±=
x
2193
±=
x
–8,
11
5 M
1 fo
r se
ttin
g up
equ
atio
n A1
for
cor
rect
sim
plif
icat
ion
M1
for
corr
ect
fact
oris
atio
n A1
cao
A1
cao
OR
M1
for
sett
ing
up e
quat
ion
A1 f
or c
orre
ct s
impl
ific
atio
n
M1
for
corr
ect
subs
titu
tion
into
for
mul
a A1
cao
A1
cao
Tota
l for
Que
stio
n: 5
mar
ks
17.
x
y+
=8
0)5
)(3(
030
162
034
)8(
34
2
222
=+
+=
++
+−
++
=+
xx
xx
xx
yx
3,5
5,3
=−
==
−=
yx
yx
5M
1 fo
r re
arra
ngin
g8
=−
xy
and
for
subs
titu
ting
into
342
2=
+y
xA1
for
cor
rect
sim
plif
icat
ion
M1
for
corr
ect
fact
oris
atio
n A2
cao
for
tw
o co
rrec
t pa
irs
of v
alue
s
A1 c
ao f
or e
ithe
r bo
th x
val
ues
corr
ect
or b
oth
y va
lues
cor
rect
Tota
l for
Que
stio
n: 5
mar
ks
=
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 131
=5M
M2H
/X
Que
stio
nW
orki
ngA
nsw
erM
ark
Add
itio
nal G
uida
nce
18.
(a)
Co
rrec
t gr
aph
2 M
1 tr
ansl
atio
n pa
ralle
l to
the
x-ax
isA1
by
-1 u
nits
Q
WC
ii,
iii
(b)
7)
(4)
(2
++
−+
ax
ax
44
22
2+
−−
++
ax
aax
x2
=a
Tran
slat
ion
by
−−62
4 M
1 re
plac
e x
by x
+ a
in f(
x +
a)M
1 ex
pand
cor
rect
ly
A1a
= 2
A1 c
ao Q
WC:
All
calc
ulat
ions
are
att
ribu
tabl
e, w
ith
wor
king
cle
arly
la
id o
ut in
a c
lear
pro
gres
sion
of
proc
ess To
tal f
or Q
uest
ion:
6 m
arks
19
.Q
WC
ii,
iii
(a)
12
)1(
22
2+
−=
−m
nn
mm
n
mn
mn
m2
)(
22
2+
+=
+Ad
ding
2
22
21
nm
nm
++
+1
22
22
++
+n
mn
m)1
(1)1
(2
22
++
+n
nm
Proo
f3
B11
2)1
(2
22
+−
=−
mn
nm
mn
and
m
nn
mn
m2
)(
22
2+
+=
+B1
22
22
1n
mn
m+
++
B1 c
onvi
ncin
g fa
ctor
isat
ion
to g
ive
)1)(1
(2
2+
+n
mQ
WC:
All
calc
ulat
ions
are
att
ribu
tabl
e, w
ith
wor
king
cle
arly
laid
out
in a
cle
ar
prog
ress
ion
of p
roce
ss
(b
) Se
tm
=n
in t
he a
bove
an
d ge
t
=+
−2
22
)2(
)1(
mm
22
)1(
+m From
Pyt
hago
ras,
the
th
ird
side
is )1(
2+
m
Proo
f 2
M1
Set
m =
n in
the
abo
ve a
nd g
et:
=+
−2
22
)2(
)1(
mm
22
)1(
+m
C1 F
rom
Pyt
hago
ras,
the
thi
rd s
ide
is)1
(2
+m
(c
) 5
× 10
001
m=
2, n
= 1
00
1992 an
d 10
222
M1
set
m =
2,
n =
100
in (
a)A1
992 a
nd 1
022
Tota
l for
Que
stio
n: 7
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010132
5MM
2HQ
uest
ion
Wor
king
Ans
wer
Mar
kA
ddit
iona
l Gui
danc
e 20
.70
cos
5.10
92
5.10
92
2×
×−
+=
(BD
2 )19
1.25
– 6
4.64
= 1
26.6
'25.
11'80
sin
5.7si
n=
DBC
×=
−
'25.
11'80
sin
5.7si
n1
DBC
= 41
.0(3
…)
41.0
6
M1
70co
s5.
109
25.
109
22
××
−+
M1
corr
ect
orde
r of
eva
luat
ion
to g
et (
BD2 )
A1 1
1.3
or b
ette
r (1
1.25
2…)
M1
'25.
11'80
sin
5.7si
n=
DBC
M1
×=
−
'25.
11'80
sin
5.7si
n1
DBC
A1 4
1.0
or b
ette
r
Tota
l for
Que
stio
n: 6
mar
ks
Edexcel GCSE in Methods in Mathematics Sample Assessment Materials © Edexcel Limited 2010 133
= = = = = = OMK==
= = = = = =
OQSUNMNONQNS
OQ=
JOM
ñ
ó
================================================================================March 2010
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