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Edexcel GCSE in Mathematics B – Modular (2MB01)

Issue oneGCSE Mathematics 2010 Your proven formula for successInside this Sample Assessment Materials pack you’ll find:

Accessible papers to help you and your students prepare for the assessment

Clear and concise mark schemes to let you know what theexaminers are looking for.

One of our hallmarks is the clarity of our papers and we are committedto ensuring that each paper has:

clearly written, topic-focused questions – Our questions teststudents on their mathematical knowledge and not their levels ofcomprehension. Readability tests show that our papers are theclearest available

questions that are ramped – Our questions become moredemanding as the paper progresses, building student confidencebecause they have the chance to show what they can do

a clear layout – We take time to ensure that our questions are clearlyset out with diagrams where necessary. This avoids ambiguities andhelps to reduce mistakes.

Building upon our reputation as the awarding body of choice with themost reliable examination papers, GCSE Maths10 is your provenformula for success.

Edexcel190 High Holborn,London WC1V 7BHTel: 0844 576 0027Fax: 020 7190 5700

www.edexcel.com

Publication code: UG022479

Ed

excel GC

SE in

Ma

them

atics B

(2MB

01)

About EdexcelEdexcel, a Pearson company, is the UK's largest awarding body offering academic and vocational qualifications and testing to schools, colleges,employers and other places of learning here and in over 85 countries worldwide.

Edexcel Limited. Registered in England and Wales No. 4496750Registered office: 190 High Holborn, London WC1V 7BH.BTEC is a registered trademark of Edexcel Ltd.

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For further information, please visit our GCSE Mathematics website – www.maths10.co.uk

Sample Assessment Materials

Contents General Marking Guidance 2

Unit 1: Foundation Tier Sample Assessment Material 3 Sample Mark Scheme 21

Unit 1: Higher Tier Sample Assessment Material 27 Sample Mark Scheme 45

Unit 2: Foundation Tier Sample Assessment Material 51 Sample Mark Scheme 67

Unit 2: Higher Tier Sample Assessment Material 75 Sample Mark Scheme 89

Unit 3: Foundation Tier Sample Assessment Material 97 Sample Mark Schem 117

Unit 3: Higher Tier Sample Assessment Materia 123 Sample Mark Scheme 143

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, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme.

• Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited.

• 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, are 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 sc - special case

Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper Reference

*S37725A0118*

Edexcel GCSE

Mathematics BUnit 1: Statistics and Probability (Calculator)

Foundation Tier

Sample Assessment MaterialTime: 1 hour 15 minutes

You must have:

Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

5MB1/1F

Instructions

• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answer all questions.• 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 60. • 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 with your spelling, punctuation and grammar, as

well as the clarity of expression, on these questions.

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.

S37725A©2010 Edexcel Limited.

3/2/2/2/

Turn over

GCSE Mathematics 2MB01

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

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1 Hannah carried out a survey of 20 people at a Fitness Centre. She asked them which activity they liked best.

Here are her results.

Gym Tennis Squash Swimming Gym

Swimming Gym Tennis Gym Squash

Gym Tennis Squash Tennis Squash

Squash Gym Swimming Gym Swimming

(a) Complete the table to show Hannah’s results.(2)

Activity Tally Frequency

Gym

Tennis

Squash

Swimming

(b) Write down the number of people who liked Squash the best.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) Which activity was liked best by the most people?(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 1 = 4 marks)

2 Mandy lives in Weymouth. She is planning a shopping trip to Bournemouth. She will travel by train.

Here is part of the train timetable from Weymouth to Southampton and from Southampton to Weymouth.

Weymouth to Southampton

Weymouth 0903 1003 1103 1203 1303

Dorchester 0913 1013 1113 1213 1313

Poole 0940 1040 1140 1240 1340

Bournemouth 0953 1053 1153 1253 1353

Brockenhurst 1020 1120 1220 1320 1420

Southampton 1026 1126 1226 1326 1426

Southampton to Weymouth

Southampton 1224 1324 1424 1524 1624

Brockenhurst 1237 1337 1437 1537 1637

Bournemouth 1300 1400 1500 1600 1700

Poole 1335 1435 1535 1635 1735

Dorchester 1344 1444 1544 1644 1744

Weymouth 1355 1455 1555 1655 1755

It takes Mandy 25 minutes to walk from home to the train station at Weymouth. She wants to be in Bournemouth for 3 hours.

Plan a schedule for Mandy’s shopping trip.

Time

Mandy leaves home

Train departs Weymouth

Train arrives Bournemouth

Train leaves Bournemouth (Mandy comes home)

Train arrives Weymouth

Mandy arrives home


3 The bar chart shows the numbers of bikes a shop sold on Wednesday, Thursday, Friday and Saturday.

Wed

Number ofbikes sold

Thurs Fri Sat

Michael started to draw a pictogram to show the same information. He has shown the number of bikes sold on Wednesday.

Complete the pictogram.

Wednesday

Thursday

Friday

Saturday


4 Liam rolls an ordinary dice.

(a) On the probability scale below, mark with a cross ( ) the probability that he gets a number less than 7

(1)

A bag contains 3 blue counters and 1 red counter. Kenneth takes at random one counter from the bag.

(b) On the probability scale below, mark with a cross ( ) the probability that he takes a red counter.

(1)

Terry spins a coloured spinner. The probability that the spinner will land on green is 0.25

The probability that the spinner will land on yellow is 0.35

(c) (i) Write 0.25 as a fraction.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Write 0.35 as a percentage.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A weather forecaster says that the probability it will rain tomorrow is s.

(d) Write down, in terms of s, the probability that it will not rain tomorrow.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*5 The table shows information about some students’ favourite pets.

Cat Dog Rabbit Hamster Goldfish

Boys 6 12 4 10 5

Girls 10 7 6 5 5

On the grid, represent this information in a suitable diagram or chart.


6 Ishmael has four white cards and three grey cards.

A

B

C

D

1

2

3

Ishmael takes at random one white card and one grey card.

(a) Show all the possible outcomes he could get.(2)

Ishmael takes at random one white card and one grey card.

(b) Work out the probability that he will get a C and a 3.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*7 Harry and Edith are planning their holiday. They want to travel by airplane. They can travel with one of three airplane companies, Aireways, King Lingus

or Easy Plane. The tables show the cost per adult and the cost per child to travel with each airplane

company.

Aireways

July August

Week 1 – 8 9 – 15 16 – 22 23 – 31 1 – 12 13 – 19 20 – 26 27 – 31

Adult AM £197 £200 £215 £215 £224 £209 £199 £188

PM £174 £177 £192 £192 £201 £186 £176 £165

Child AM £110 £113 £128 £128 £137 £122 £112 £101

PM £87 £90 £105 £105 £114 £99 £89 £78

King Lingus

July August

Week 1 – 8 9 – 15 16 – 22 23 – 31 1 – 12 13 – 19 20 – 26 27 – 31

Adult AM £193 £195 £197 £211 £220 £213 £208 £204

PM £176 £178 £180 £191 £203 £196 £191 £187

Child AM £119 £121 £123 £134 £146 £139 £134 £130

PM £102 £104 £106 £117 £129 £122 £117 £113

Easy Plane

July August

Week 1 – 8 9 – 15 16 – 22 23 – 31 1 – 12 13 – 19 20 – 26 27 – 31

Adult AM £198 £206 £213 £223 £232 £214 £210 £205

PM £181 £189 £196 £206 £215 £197 £193 £188

Child AM £94 £102 £109 £119 £128 £110 £106 £101

PM £77 £85 £92 £102 £111 £93 £89 £84

Harry and Edith have 3 children. They want to travel on the morning of 27th July.

Work out the cheapest cost.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


8 The pie chart shows some information about the numbers of medals won by Canada in the 2008 Olympic Games.

Bronze

Silver

Gold

120°60°

Canada won 3 gold medals. (a) Work out the total number of medals Canada won.

(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The pie chart below shows some information about the numbers of medals won by Canada in the 2004 Olympic Games.

Bronze Gold

Silver

Maria says “The pie charts show that Canada won the same number of silver medals in 2008

as in 2004”.

(b) Is Maria correct? Yes No

Explain your answer.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*9 Some students did a test. Here are their scores.

Boys’ scores 27 20 12 28 35 28 37

Girls’ scores 29 31 35 15 18 25 35 27 40

Compare fully the scores of these students.


10 Charles wants to find out how much people spend on sweets.

He will use a questionnaire.

(a) Design a suitable question for Charles to use in his questionnaire.(2)

Charles asks the people in his class to do his questionnaire.

(b) Give a reason why this may not be a suitable sample.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*11 Kylie wants to invest £1000 for one year. She considers two investments, Investment A and Investment B.

Investment A

£1000

Earns £2.39 per month

plus

£4.50 bonus for each complete year

Interest paid monthly by cheque.

Investment B

£1000

Earns 3.29% interest per annum

Interest paid yearly by cheque.

Kylie wants to get the greatest return on her investment.

Which of these investments should she choose?

(Total for Question 11= 5 marks)

12 Nadine asked 50 people which of the newspapers the Times, the Guardian and the Telegraph they like best.

Here is information about her results.

19 out of the 25 males said they like the Telegraph best. 5 females said they like the Guardian best. 4 out of the 7 people who said they like the Times best were female.

Work out the number of people who like the Telegraph best.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


13 The scatter graph shows some information about a random sample of ten male players at a basketball club.

For each player it shows his height and his weight.

60180 190 200 210 220

70

80

90

100

110

120

Weight (kg)

Height (cm)

(a) (i) On the scatter graph, draw a line of best fit.

(ii) Work out the gradient of your line of best fit.(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Estimate the proportion of male players in the club whose weight is greater than 99 kg and whose height is less than 200 cm.

(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


14 Jenny uses her mother’s recipe to make cheese scones. Her recipe uses a mixture of self-raising flour, butter and cheese in the ratio 6 : 2 : 1 by

weight.

In her kitchen, Jenny has: 2 kg of self-raising flour, 500 grams of butter, 200 grams of cheese.

When Jenny makes cheese scones each scone needs about 45 grams of mixture.

Work out the largest number of cheese scones that Jenny can make.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


TOTAL FOR PAPER: 60 MARKS)

Uni

t 1

Foun

dati

on T

ier:

Sta

tist

ics

and

Prob

abili

ty

5M

B1F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

1.

(a)

Gym

II

II II

7

Te

nnis

IIII

4

Sq

uash

IIII

5 Sw

imm

ing

IIII

4

7, 4

, 5,

4

2

B2 f

or a

ll fr

eque

ncie

s co

rrec

t (B

1 fo

r 2

freq

uenc

ies

or 2

tal

lies

corr

ect

or o

ne t

ally

wit

h it

s fr

eque

ncy

corr

ect)

(b

)

5 1

B1 f

or 5

or

‘5’

ft f

rom

tab

le

(c

)

Gym

1

B1 f

or g

ym o

r ‘g

ym’

ft f

rom

tab

le

To

tal f

or Q

uest

ion:

4 m

arks

2.

FE

e.g.

090

3 –

25 m

inut

es =

08

38

0903

09

53

0953

+ 3

hou

rs =

125

3 13

00

1355

13

55 +

25

min

utes

= 1

420

e.g.

08

38

0903

09

53

1300

13

55

1420

5 B1

for

a c

orre

ct t

ime

25 m

inut

es (

or m

ore)

bef

ore

the

trai

n de

part

s e.

g.

0838

, 09

38 …

or

earl

ier

B1 f

or a

cor

rect

dep

artu

re t

ime,

e.g

. 09

03,

1003

… w

ith

the

asso

ciat

ed

corr

ect

arri

val t

ime

0953

, 10

53…

B1

for

a c

orre

ct d

epar

ture

tim

e (3

hou

rs a

fter

arr

ival

) e.

g. 1

300,

140

0…

B1 f

or a

cor

rect

arr

ival

tim

e co

rres

pond

ing

to t

he d

epar

ture

tim

e, e

.g.

1355

, 14

55…

B1

for

a c

orre

ct a

rriv

al t

ime

at h

ome,

e.g

. 14

20,

1520

…

To

tal f

or Q

uest

ion:

5 m

arks

3.

Key

repr

esen

ts 8

bi

kes

3 B2

for

all

3 da

ys c

orre

ct

(B1

for

at le

ast

one

day

corr

ect,

i.e.

o

ne c

ircl

e fo

r Th

ursd

ay

or

one

and

a ha

lf c

ircl

es o

r ft

1 21

× ‘

Thur

sday

’ fo

r Fr

iday

or

two

and

a qu

arte

r ci

rcle

s or

ft

2 41

× ‘

Thur

sday

’ fo

r Sa

turd

ay)

B1 f

or a

cor

rect

key

Tota

l for

Que

stio

n: 3

mar

ks

5M

B1F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

4.

(a)

Cr

oss

at 1

1

B1 f

or c

ross

at

1 (a

llow

±2

mm

tol

eran

ce)

(b

)

Cros

s at

41

1 B1

for

cro

ss a

t 41

(al

low

±5

mm

tol

eran

ce)

(c)(

i)

(i

i)

41 35

2 B1

for

41 o

e fr

acti

on

B1 f

or 3

5 or

35.

0

(d

)

1 —

s

1

B1 c

ao

To

tal f

or Q

uest

ion:

5 m

arks

5M

B1F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

5.

QW

C (i

)

Dia

gram

or

char

t 4

B1 f

or a

key

or

suit

able

labe

ls t

o id

enti

fy b

oys

and

girl

s B1

for

5 c

orre

ct a

nim

al la

bels

B1

for

a d

iagr

am o

r ch

art

(com

bine

d or

sep

arat

e) s

et u

p fo

r co

mpa

riso

n, e

.g.

dual

bar

cha

rt,

back

-to-

back

ste

m a

nd le

af d

iagr

ams,

pi

e ch

arts

, pi

ctog

ram

s, v

erti

cal (

stic

k) d

iagr

ams,

etc

C1

ful

ly c

orre

ct d

iagr

am o

r ch

art

QW

C: F

ully

cor

rect

dia

gram

or

char

t an

d al

l lab

ellin

g is

cor

rect

and

cle

ar

To

tal f

or Q

uest

ion:

4 m

arks

6.

(a

)

(A,1

), (

A,2)

, (A

,3),

(B,

1),

(B,2

), (

B,3)

, (C

,1),

(C,

2),

(C,3

), (

D,1

),

(D,2

), (

D,3

)

2 B2

for

list

ing

all 1

2 ou

tcom

es

(B1

for

listi

ng 6

out

com

es,

igno

re r

epea

ts)

(b

)

121

1 B1

ft

for

'12'1

Tota

l for

Que

stio

n: 3

mar

ks

7.

QW

C (i

, ii,

iii

) FE

2(

215)

+ 3

(128

) =

814

2(21

1) +

3(1

34)

= 82

4 2(

223)

+ 3

(119

) =

803

Easy

Pla

ne

£8

03

6 M

1 fo

r 2

× Ad

ult

+ 3

× Ch

ild

M1

for

usin

g co

rrec

t Ad

ult

and

Child

, i.

e. (

215,

128

) or

(21

1, 1

34)

or

(223

, 11

9)

A2 f

or 8

14,

824

and

803

(A1

for

one

or t

wo

corr

ect

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2×’

Adul

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’)

B1 f

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, i.

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or

poun

ds

C1 f

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asy

Plan

e id

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QW

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mus

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sta

ted

and

tota

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mus

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att

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e

Tota

l for

Que

stio

n: 6

mar

ks

8.

(a)

3 ×

6 18

2

M1

for

360

÷ 60

or

6 se

en o

r 1

gold

= 2

0 A1

cao

(b)

N

o an

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prop

riat

e ex

plan

atio

n

1 C1

for

‘N

o’ a

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th

e pi

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the

prop

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the

sam

e

OR

expl

ains

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uld

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the

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ar

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Tota

l for

Que

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mar

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5M

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, iii

)

12

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, 7,

28,

28,

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15,

18,

25,

27,

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35,

40

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pare

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2.

rang

es

6 B2

for

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(boy

s) =

28

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med

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(gir

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29

OR

mea

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26.7

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bett

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(gir

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= 28

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mea

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or r

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(bo

ys)

= 25

and

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ge (

girl

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25

(B1

for

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ect

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OR

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ully

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stic

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tc

(B1

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diag

ram

cha

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ith

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r in

pre

sent

atio

n)

C1 f

or m

edia

n (g

irls

) >

med

ian

(boy

s) o

e or

mea

n (g

irls

) >

mea

n (b

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oe

or f

or r

ange

(bo

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= ra

nge

(gir

ls)

oe

C1 f

or c

omm

ents

rel

atin

g to

all

wor

king

(ie

ra

nge/

mea

n/m

edia

n/ch

arts

dep

on

B4)

QW

C: D

ecis

ions

sho

uld

be

just

ifie

d, a

nd c

alcu

lati

ons

attr

ibut

able

SC

If n

o m

arks

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red

B1 f

or a

cor

rect

com

pari

son

To

tal f

or Q

uest

ion:

6 m

arks

10

. (a

)

Que

stio

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resp

onse

box

es

2 B2

for

a s

uita

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ques

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wit

h at

leas

t 3

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t in

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riod

) (B

1 fo

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suit

able

que

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tim

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es)

(b)

Re

ason

1

B1 f

or b

iase

d or

all

the

stud

ents

the

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e or

stu

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mor

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, et

c To

tal f

or Q

uest

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3 m

arks

11

. Q

WC

(ii,

iii

) FE

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5 3.

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100

0

33.1

8

32.9

0

5 M

1 fo

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× 12

’ +

4.5

or d

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how

ing

2.39

, 4.

78,

7.17

, …

, 28

.68

oe (

cond

one

one

erro

r)

A1 c

ao

M1

for

3.29

/100

× 1

000

oe

A1 c

ao

C1 f

or In

vest

men

t A

iden

tifi

ed Q

WC:

Dec

isio

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ust

be s

tate

d, w

ith

calc

ulat

ions

cle

arly

att

ribu

tabl

e

Tota

l for

Que

stio

n: 5

mar

ks

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B1F

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Ans

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Add

itio

nal G

uida

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e.

g.

Mal

e

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G

u..

Te.

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e

19

25

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4

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two-

way

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nn d

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and

mal

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belle

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4,

5, 7

, 19

and

25

M1

for

atte

mpt

to

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16

(con

done

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err

or)

A1 c

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[NB

Two-

way

tab

le/V

enn

diag

ram

nee

d no

t co

ntai

n al

l num

bers

]

Tota

l for

Que

stio

n: 4

mar

ks

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(a)(

i)

(i

i)

Li

ne o

f be

st f

it

1.

25

3

B1 f

or li

ne d

raw

n be

twee

n (1

90,

80),

(19

0, 9

5) a

nd (

210,

105

), (

210,

12

0)

M1

for

diff

. y

/ di

ff.

x A1

for

0.5

— 2

or

ft t

heir

line

of

best

fit

(b

)

20%

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1 fo

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al li

ne a

t 99

and

a v

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cal l

ine

at 2

00 o

r 2

seen

A1 f

or 2

0% o

r 102

or 0

.2 o

e

Tota

l for

Que

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mar

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5

19

4

G

Te

Ti 25

25

5M

B1F

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Ans

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M

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Add

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nal G

uida

nce

14.

FE

Sc

one

30g:

10g:

5g

200

÷ 5

= 40

50

0 ÷

10 =

50

2000

÷ 3

0 =

66.7

40

4 M

1 fo

r 45

÷(6+

2+1)

A1

for

SRF

= 3

0, B

= 1

0, C

= 5

M

1 fo

r 20

0÷5

or 5

00÷1

0 or

200

0÷30

A1

cao

O

R M

1 fo

r 6×

200

or 2

×200

or

1×20

0 or

6×5

00 o

r 2×

500

or 1

×500

or

6×20

00

or 2

×200

0 or

1×2

000

A1

for

SRF

, B,

C =

120

0, 4

00,

200

or 1

500,

500

, 25

0 or

200

0, 6

66.7

, 33

.3

M1

for

(120

0 +

400

+ 20

0)/4

5 A1

cao

.

Tota

l for

Que

stio

n: 4

mar

ks


Write your name here

Surname Other names

Total Marks

Paper Reference

*S37724A0117*

Edexcel GCSE

Mathematics BUnit 1: Statistics and Probability (Calculator)

Higher Tier


You must have:


5MB1/1H

Instructions



Information

• The total mark for this paper is 60. • 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



2/3/3/2

Turn over


Formulae – Higher Tier


Volume of 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




1 The table shows some information about the ages, in years, of 80 people.

Age (a years) Frequency

20 a < 30 19

30 a < 40 22

40 a < 50 24

50 a < 60 10

60 a < 70 5

(a) Find the class interval that contains the median.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Draw a frequency polygon to show this information.(2)


200

10

20

30

Frequency

30 40Age (a years)

50 60 70

*2 Harry and Edith are planning their holiday.

They want to travel by airplane.

They can travel with one of three airplane companies, Aireways, King Lingus or Easy Plane.

The tables show the cost per adult and the cost per child to travel with each airplane company.

Aireways

July AugustWeek 1 – 8 9 – 15 16 – 22 23 – 31 1 – 12 13 – 19 20 – 26 27 – 31

Adult AM £197 £200 £215 £215 £224 £209 £199 £188PM £174 £177 £192 £192 £201 £186 £176 £165

Child AM £110 £113 £128 £128 £137 £122 £112 £101PM £87 £90 £105 £105 £114 £99 £89 £78

King Lingus

July AugustWeek 1 – 8 9 – 15 16 – 22 23 – 31 1 – 12 13 – 19 20 – 26 27 – 31

Adult AM £193 £195 £197 £211 £220 £213 £208 £204PM £176 £178 £180 £191 £203 £196 £191 £187

Child AM £119 £121 £123 £134 £146 £139 £134 £130PM £102 £104 £106 £117 £129 £122 £117 £113

Easy Plane

July AugustWeek 1 – 8 9 – 15 16 – 22 23 – 31 1 – 12 13 – 19 20 – 26 27 – 31

Adult AM £198 £206 £213 £223 £232 £214 £210 £205PM £181 £189 £196 £206 £215 £197 £193 £188

Child AM £94 £102 £109 £119 £128 £110 £106 £101PM £77 £85 £92 £102 £111 £93 £89 £84

Harry and Edith have 3 children. They want to travel on the morning of 27th July.

Work out the cheapest cost.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*3 Some students did a test.

This back-to-back stem and leaf diagram shows information about their scores.

Boys’ scores Girls’ scores

8 2 2 7 8

9 6 5 2 3 0 4 7 8

9 5 4 3 2 1 0 4 3 5 5 7 8

7 7 7 6 5 4 5 0 1 3 5 7 7 7 9 9

5 3 2 1 6 0 3 6

Compare and contrast the scores of these students.


Key for boys’ scores8 | 2 means 28

Key for girls’ scores2 | 7 means 27

4 Charles wants to find out how much people spend on sweets.

He will use a questionnaire.

(a) Design a suitable question for Charles to use in his questionnaire.(2)

Charles asks the people in his class to do his questionnaire.

(b) Give a reason why this may not be a suitable sample.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


5 The scatter graph shows some information about a random sample of ten male players at a basketball club.

For each player it shows his height and his weight.

(a) (i) On the scatter graph, draw a line of best fit.(1)

(ii) Work out the gradient of your line of best fit.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) Write down a practical interpretation of this gradient.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18060

70

80

90

100

110

120

190 200Height (cm)

Weight (kg)

210 220

Some of the male players at the basketball club have a weight greater than 99 kg.

(b) Estimate the proportion of these players who have a height less than 200 cm.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


6 Jenny uses her mother’s recipe to make cheese scones.

Her recipe uses a mixture of self-raising flour, butter and cheese in the ratio 6 : 2 : 1 by weight.

In her kitchen, Jenny has 2 kg of self-raising flour 500 grams of butter 200 grams of cheese

When Jenny makes cheese scones each scone weighs about 45 grams.

Work out the largest number of cheese scones that Jenny can make.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


7 A bag contains only red counters, blue counters, green counters and yellow counters. Rachel is going to take at random a counter from the bag.

The table shows each of the probabilities that Rachel will take a red counter or a blue counter or a green counter or a yellow counter.

Colour Red Blue Green Yellow

Probability 0.15 2x x 0.1

(a) Work out the probability that Rachel will take a green counter.(2)

……….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .……………….

Rachel says that there are exactly 9 blue counters in the bag. Rachel is wrong.

(b) Explain why there cannot be exactly 9 blue counters in the bag.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


8 A book has 120 pages.

The mean number of words per page for the whole book is 231 The mean number of words per page for the first 20 pages is 236

Calculate the mean number of words per page for the other 100 pages.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*9 Kylie wants to invest £20 000 for 3 years. She considers two investments, Investment A and Investment B.

Kylie wants to get the greatest return on her investment.

Which of these investments should she choose?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Investment A

£20 000

Earns 3.02% interest per annum

Interest paid yearly by cheque

Investment B

£20 000

Earns 2.98% compound interest per annum

10 The table gives some information about the lengths of time, in hours, that some batteries lasted.

Time (h hours) Frequency

0 h < 10 5

10 h < 20 18

20 h < 25 15

25 h < 40 12

40 h < 60 10

Draw a histogram for the information in the table.


0 10 20 30

Time (h hours)

40 50 60 70

11 (a) Explain what is meant by

(i) a random sample,(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) a stratified sample.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A Sixth Form College has 850 students. The table shows some information about these students.

Number of female students

Number of male students

Year 12 184 241

Year 13 222 203

Linda is going to do a survey of the students in the college. She uses a sample of 50 students stratified by year group and by gender.

(b) Work out the number of Year 12 female students in her sample.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


12

Bert has a game at a fair.

In the game players pay to spin a wheel.

When the wheel stops, the amount shown by the arrow is given to the player. The table shows the probabilities that the wheel will stop on 5p, on 10p, on 20p and on 50p.

5p 10p 20p 50p

Probability 0.5 0.25 0.15 0.1

Bert wants to make a profit from the game.

Work out the minimum he can charge players to spin the wheel.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


5p

10p

20p

50p

Spin the wheel

13 In a bag there are 5 red counters and 4 blue counters.

Suki takes at random two counters from the bag.

Work out the probability that the counters will each have a different colour.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*14

A scientist wants to estimate the number of fish in a lake. He catches 50 fish from the lake and marks them with a dye. The fish are then returned to the lake. The next day the scientist catches another 50 fish. 4 of these fish are marked with the dye.

Work out an estimate for the total number of fish in the lake. You must write down any assumptions you have made.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


TOTAL FOR PAPER = 60 MARKS

Angling Chronicle

Anglers dismayed at falling fi sh numbers!

Uni

t 1

Hig

her

Tier

: St

atis

tics

and

Pro

babi

lity

5M

B1H

Q

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Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

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(a

)

30 ≤

a <

40

1 B1

cao

(b)

Po

ints

plo

tted

at

(25

, 16

),

(35,

20)

, (4

5,

23),

(55

, 9)

, (6

5, 2

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d jo

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25 o

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the

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or

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ting

but

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jo

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) Pl

otti

ng t

oler

ance

: 1

(2 m

m)

squa

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poin

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o be

joi

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by li

nes

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or h

and

draw

n, b

ut n

ot c

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Tota

l for

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mar

ks

2.

QW

C (i

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iii

) FE

2(

215)

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(128

) =

814

2(21

1) +

3(1

34)

= 82

4 2(

223)

+ 3

(119

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803

Easy

Pla

ne

£8

03

6 M

1 fo

r 2

× Ad

ult

+ 3

× Ch

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M1

for

usin

g co

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ult

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Child

, i.

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215,

128

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(21

1, 1

34)

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9)

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14,

824

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e id

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sta

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tota

l co

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mus

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att

ribu

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Tota

l for

Que

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mar

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5M

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Wor

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Q

WC

(i,

iii)

M

edia

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= 4

5 M

edia

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irls

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50

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= 6

5 –

22 =

43

Rang

e (g

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) =

66 –

27

= 39

IQ

R (b

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= 5

7 –

39 =

18

IQR

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– 3

8 =

19

Com

pare

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med

ians

2.

ran

ge/I

QR

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for

med

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45

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= 43

and

ran

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girl

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IQR

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IQR

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= 19

(B

1 fo

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IQR)

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for

ful

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trib

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SC If

no

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d B1

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a c

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l for

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a s

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Wor

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Mar

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(ii)

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kg

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for

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To

tal f

or Q

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7 m

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6.

FE

Sc

one

30g:

10g:

5g

200

÷ 5

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50

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50

2000

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66.7

40

4 M

1 fo

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÷ (

6 +

2 +

1)

A1 f

or S

RF =

30,

B =

10,

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5

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for

200÷

5 or

500

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30

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ao

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6 ×

200

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× 2

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6 ×

500

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2 ×

500

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× 5

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2000

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2 ×

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1 ×

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for

SRF

, B,

C =

120

0, 4

00,

200

or 1

500,

500

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0 or

200

0, 6

66.7

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for

(120

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400

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5 A1

cao

Tota

l for

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mar

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(a)

1 –

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ap

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plan

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1 C1

for

an

appr

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corr

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expl

anat

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e.g

. yo

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4.5

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coun

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9÷5

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1.8

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ount

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Tota

l for

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stio

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mar

ks

5M

B1H

Q

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Wor

king

A

nsw

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Mar

k A

ddit

iona

l Gui

danc

e 8.

(120

× 2

31 –

20

× 23

6) ÷

100

23

0 3

M1

for

120

× 23

1 or

20

× 23

6 or

277

20 o

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20 s

een

M1

for

(‘12

0 ×

231’

– ‘

20 ×

236

’) ÷

100

oe

A1

cao

To

tal f

or Q

uest

ion:

3 m

arks

9.

Q

WC

(ii,

iii)

FE

3.

02/1

00 ×

200

00 ×

3

2000

0 ×

(1.0

298)

3

(£)1

812

(£

)184

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stm

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3

A1 f

or 1

812

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1812

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2 fo

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oces

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.g.

(1.0

298)

3 × 2

0000

(M

1 fo

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0298

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0000

oe

or 2

0596

see

n)

A1 f

or 1

841.

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C1 f

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ting

the

gre

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of

'181

2' a

nd '1

841.

81' o

r '2

1812

' and

'2

1841

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QW

C: D

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ion

mus

t be

sta

ted

wit

h al

l cal

cula

tion

s at

trib

utab

le

To

tal f

or Q

uest

ion:

6 m

arks

10

.

0 ≤

d <

10

fd

0.5

10 ≤

d <

20

fd

1.8

20 ≤

d <

25

fd

3.0

25 ≤

d <

40

fd

0.8

40 ≤

d <

60

fd

0.5

Corr

ect

hist

ogra

m

3 B2

for

5 c

orre

ct h

isto

gram

bar

s ±

½ s

quar

e (B

1 fo

r 3

hist

ogra

m b

ars

corr

ect)

B1

for

fre

quen

cy d

ensi

ty la

bel o

r ke

y an

d co

nsis

tent

sca

ling

Tota

l for

Que

stio

n: 3

mar

ks

11.

(a)

(i)

(ii)

Co

rrec

t ex

plan

atio

n 1 1

C1 f

or a

ll ha

ve e

qual

cha

nce

of b

eing

sel

ecte

d C1

for

gro

ups

in t

he s

ampl

e ar

e in

the

sam

e pr

opor

tion

as

they

are

in t

he

popu

lati

on

(b)

850

184

× 50

11

2

M1

for

850

184

× 5

0 or

1718

4

A1 c

ao

To

tal f

or Q

uest

ion:

4 m

arks

5M

B1H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 12

.

0.5×

5 +

0.25

×10

+ 0.

15×2

0 +

0.1×

50 =

13

14p

4 M

2 fo

r 0.

5×5

+ 0.

25×1

0 +

0.15

×20

+ 0.

1×50

oe

or f

or a

con

sist

ent

calc

ulat

ion

for

n sp

ins,

e.g

. 50

×5 +

25×

10 +

15×

20 +

10×

50 w

here

n =

100

(c

ondo

ne o

ne e

rror

)

(M1

for

0.5

×5 o

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25×1

0 or

0.1

5×20

or

0.1×

50 o

e)

A1 f

or 1

3 or

14

A1 f

or 1

4p

To

tal f

or Q

uest

ion:

4 m

arks

13

.

95 ×

84+

94 ×

85=

7220+

7220

OR

1 –

[95

× 84

+ 94

× 83

]

=1 –

7232

7240

4 M

1 fo

r tr

ee d

iagr

am w

ith

at m

ost

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rors

or

one

of 95

× 84

or

94 ×

85or

94×

83or

7220or

7212or

185or

183oe

M1

for

any

two

of 95

× 84

, 94

× 85

, 94

× 83

or 7220

, 7220

, 7212

or 185

,

185,

183oe

M1

for

95 ×

84+

94 ×

85oe

or

1 –

[95

× 84

+ 94

× 83

] oe

A1 f

or 7240

oe

SC B

2 fo

r 8140

Tota

l for

Que

stio

n: 4

mar

ks

14.

QW

C (i

i,

iii)

504

= N50

(4 ×

12.

5)/(

50 ×

12.

5) =

50

/625

625

Assu

mpt

ion

4 M

1 fo

r 504

oe o

r N50

or 1

2.5

seen

M1

for

(4 ×

12.

5)/(

50 ×

12.

5) o

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att

empt

to

scal

e, i.

e. 4

×k/5

0×k

A1

for

625

C1

for

a c

orre

ct a

ssum

ptio

n, e

.g.

the

popu

lati

on h

as n

ot c

hang

ed o

ver

nigh

t or

the

dye

has

not

was

hed

off

or t

he r

etur

ned

sam

ple

has

thor

ough

ly m

ixed

wit

h th

e po

pula

tion

or

the

sam

ple

is r

ando

m,

etc

QW

C: A

ssum

ptio

n m

ust

be s

tate

d cl

earl

y, in

line

wit

h su

ppor

ting

ca

lcul

atio

ns

To

tal f

or Q

uest

ion:

4 m

arks



Total Marks

Paper Reference

*S37726A0113*

Edexcel GCSE

Mathematics BUnit 2: Number, Algebra, Geometry 1

(Non-Calculator)Foundation Tier


You must have:

Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.

5MB2/2F

Instructions

• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answer all questions.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators must not be used.

Information



Advice



2/2/3/3/2

Turn over

GCSE Mathematics 2544





b

a

h

length

crosssection

12





1 This is part of a list of TV programmes for one evening.

(a) Which TV programme lasts for 10 minutes?(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…………………………….

Brian turned on his TV set at 19 40

(b) How many minutes did Brian have to wait for the start of Arthur?(1)

………………….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…. minutes

Richard Hammond’s Blast Lab lasts for 45 minutes.

(c) At what time did Richard Hammond’s Blast Lab end?(1)

…………….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…………..


18 00 Tikkabilla18 30 Teletubbies19 00 Lunar Jim19 10 Kerwhizz19 35 Lazy Town20 00 ChuckleVision20 15 Arthur20 30 Richard Hammond’s Blast Lab

2 (a) Simplify y + y + y + y + y(1)

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…………….

(b) Simplify x + 5 + 2x – 7(2)

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….


3 The table gives information about the temperatures at midnight on New Year’s Eve in 5 capital cities.

City Temperature

London –3o C

Madrid 7o C

Oslo –11o C

Washington DC 1o C

Wellington 14o C

In Oslo, the temperature dropped by 8 degrees from midday to midnight.

(a) What was the temperature in Oslo at midday?(1)

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….

At midnight on New Year’s Eve in Paris, the temperature was halfway between the temperature in London and the temperature in Madrid.

(b) What was the temperature in Paris?

You must show your working.(2)

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….


4 The diagrams show three different size packets of Brew Tea Bags (BTB).

Tommy buys 200 bags of Brew Tea Bags (BTB). Tommy pays with a £10 note.

* (a) Which packets should Tommy buy to leave him with the most change from £10?


A supermarket shelf has room for just 72 small packets of Brew Tea Bags (BTB). On Tuesday morning, when the supermarket opens, there are 57 packets on the shelf. During the day, 125 packets are sold and 2 cartons, each containing 48 packets, are used to keep the shelf stocked up.

(b) Is there any space on the shelf to unpack another carton of 48 packets?



BTB

40 bags 125 g £0.85

BTB

80 bags 250 g £1.65

BTB

160 bags500 g £3.40

Diagrams NOTaccurately drawn

5 This is an accurately drawn quadrilateral.

(a) Write down the mathematical name of this quadrilateral.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………………………………………..

(b) Which line is perpendicular to the line CD?(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………………………………………

(c) Measure the length of the line AC.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………………………………………

(d) Measure the size of the angle ABD.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………………………………………


A B

C D

6 Here is a list of numbers.

From the list, write down all the numbers which are not factors of 32

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….


7 (a) Draw all the lines of symmetry of this shape.(1)

(b) Which of these shapes has rotational symmetry?(1)

(c) In the space below, draw a shape that has line symmetry and rotational symmetry order 3.

(2)


2 4 8 12 16 20 32 40

A B C

8 On the grid, draw the graph of y = 5x + 1 from x = –1 to x = 3


O 1 2 3 –1

2

4

6

8

10

12

14

16

18

–2

–4

–6

x

y

BLANK PAGE

9 This is a graph that can be used to convert between £ (pounds) and € (euros).

£ (pounds)

€ (euros)

O

10

10 20

20

30

30 40

40

50

60

50

This is part of a clipping from a newspaper showing the exchange rates for some countries.

(a) The exchange rate for the euro has been smudged. Find an estimate for the exchange rate for the euro.

(2)

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….

Ali wishes to buy a villa in Spain. She has a budget of £150 000 In a brochure she sees these three villas.

(b) Which of these three villas can Ali afford to buy? You must show your working.

(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .……………………………………………


UK £1 = Australia ....................... 1.91 dollarsBrazil ............................ 3.01 rialsChina ............................. 11.16 yenCanada .......................... 1.76 dollarsEuro .............................. Hong Kong ................... Japan .............................

Villa A Villa B Villa C

€155 000 €170 000 €200 000

*10 The table shows the membership and annual fees of a local golf club.

Full members

Weekday members

Lady members

Junior members

Number of members 243 64 77 36

Annual Fee £600 £300 £250 £120

The club needs to raise £7200 to refurbish the clubhouse next year.

In the committee meeting, the club Captain suggests that the fee for each full member next year should be increased by 5%.

The club President says that next year each member should pay an extra £18

Which is the better suggestion? You must show all your working.


11 p = 34 22 ×

q = 25

Work out the value of qp

You must show your working.

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….


*12 The diagram shows a wall in Jenny’s kitchen.

Jenny wishes to tile this wall in her kitchen. She chooses between the two types of tile shown below.

Which tiles should Jenny use to spend the least amount of money on tiling the wall? You must show all of your working.


Units Units

Units Units

Cooker

Hood

30 cm 90 cm

3.3 m

40 cm WALL

10 cm

Type A

× 10 cm 20 tiles per box

£9.99

Type B

15 cm × 15 cm

12 tiles per box

£11.49

Diagram NOTaccurately drawn

13 (a) Factorise fully 8p2q + 12p(2)

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….. . . . . . . . . . . . . . . . . . . . . . . . .

(b) Expand and simplify 5 – 2(m – 3)(2)

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….. . . . . . . . . . . . . . . . . . . . . . . . .


14 Here are the first 5 terms of an arithmetic sequence.

5 8 11 14 17

(a) Write down an expression, in terms of n, for the nth term of this sequence.(2)

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….. . . . . . . . . . . . . . . . . . . . . . . . .

The expression 3n2 + 2 is the nth term of another sequence.

(b) Find the 4th term of this sequence.(2)

…….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .………….. . . . . . . . . . . . . . . . . . . . . . . . .


*15

PQR is a straight line parallel to ST. QT = UT Angle STQ = 100°. Prove that angle QTU = (2x – 20)°.



P RQ

T

U

100°

x°

S

Uni

t 2

Foun

dati

on T

ier:

Num

ber,

Alg

ebra

, an

d G

eom

etry

1

5M

B2F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

1.

FE

(a)

Lu

nar

Jim

1 B1

cao

(b

) 20

15

– 19

40

= 20

+ 1

5

35

1 B1

cao

(c

) 20

30

+ 45

= 2

1 00

+ 1

5 21

15

1 B1

cao

Tota

l for

Que

stio

n: 3

mar

ks

2.

(a)

5y

1

B1 f

or 5

y or

5 ×

y

(b)

x

+ 2x

+ 5

– 7

3x

– 2

2

B2 c

ao

[B1

for

eith

er 3

x or

– 2

] To

tal f

or Q

uest

ion:

3 m

arks

3.

(a

) −1

1 +

8 O

R us

e a

num

ber

line

and

coun

t ba

ck

Eg:

–1

1 –

10 –

9 –

8 –

7 –

6 –

4

–3 –

2 –

1 0

1

Co

unt

8 pl

aces

−3o C

1 B1

cao

(b

)

2o C 2

M1

for

27

3+−

or

evid

ence

of

a nu

mbe

r lin

e fr

om –

3 to

7

A1 c

ao

Tota

l for

Que

stio

n: 3

mar

ks

5M

B2F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

4. FE

(a)

200

bags

= 4

0 ×

5, c

ost

= £0

.85

× 5

= £4

.25

or 8

0 ×

2 +

40 ×

1,

cost

=

£1.6

5 ×

2 +

£0.8

5 =

£3.3

0 +

£0

.85

= £

4.15

or

160

× 1

+ 4

0 ×

1, c

ost

= £3

.40

+ £0

.85

= £4

.25

OR

Usi

ng t

he 8

0 ba

g pa

cket

is

leas

t ex

pens

ive

sinc

e:

£1.6

5 <

£0.8

5 ×

2 (£

1.70

) an

d

£1.6

5× 2

= £

3.30

< £

3.40

Th

eref

ore

2 80

bag

pac

kets

+

1 40

bag

pac

ket

will

be

need

ed t

o ge

t th

e le

ast

expe

nsiv

e to

tal c

ost.

80 ×

2 +

40

× 1

is t

he le

ast

expe

nsiv

e

4 B1

for

at

leas

t 2

alte

rnat

ive

way

s of

get

ting

200

bag

s M

1 fo

r a

corr

ect

proc

ess

to w

ork

out

the

cost

of

1 w

ay

A1 f

or t

he 3

cor

rect

tot

al c

osts

C1

for

jus

tifi

cati

on t

hat

80 ×

2 +

40

× 1

is t

he le

ast

expe

nsiv

e, t

here

fore

gi

ving

Tom

my

the

grea

test

cha

nge

O

R M

1 fo

r co

mpa

ring

the

cos

t of

2 4

0 ba

g pa

cket

s w

ith

1 80

bag

pac

ket

or 2

80

bag

pac

kets

wit

h 1

1600

bag

pac

ket

A1

for

cor

rect

ari

thm

etic

giv

ing

accu

rate

cos

ts

C1 f

or j

usti

fica

tion

tha

t us

ing

80 b

ag p

acke

ts g

ives

thy

leas

t ex

pens

ive

way

B1

for

80

bags

× 2

+ 4

0 ba

g ×

1

(b

) 57

+ 4

8 ×

2 –

125

= 15

3 –

125

= 28

pkt

s on

she

lf

72 –

28

= 44

pkt

s on

she

lf a

t en

d of

day

O

R 57

+ 4

8 +

48 =

105

+ 4

8 =

153

153

– 12

5 =

28 p

kts

on s

helf

72

– 2

8 =

44 p

kts

on s

helf

at

end

of d

ay

OR

Whe

n th

ere

are

72 –

48

= 24

pk

ts o

n sh

elf,

a c

arto

n ca

n op

ened

. Af

ter

selli

ng 5

7 –

24 =

33,

1st

cart

on o

f 48

is o

pene

d to

fill

th

e sh

elf

to 7

2.

Afte

r se

lling

a f

urth

er 4

8, 2

nd

cart

on o

f 48

add

ed.

33 +

48

= 81

pkt

s so

ld.

125

– 81

= 4

4 pk

ts o

n sh

elf

at

end

of d

ay

Not

roo

m f

or

the

full

cart

on

3 M

1 fo

r 57

+ 4

8 ×

2 –

125

oe

M1

for

72 –

“57

+ 4

8 ×

2 –

125

“ =

44

C1 f

or j

usti

fica

tion

for

ope

ning

ano

ther

car

ton

or n

ot

OR

M1

for

a co

rrec

t pr

oces

s th

at in

clud

es t

he r

emov

ing

of 1

25 p

kts

M1

for

calc

ulat

ion

lead

ing

to t

he n

umbe

r of

spa

ces

rem

aini

ng a

t th

e en

d of

the

day

C1

for

jus

tifi

cati

on f

or o

peni

ng a

noth

er c

arto

n or

not

Tota

l for

Que

stio

n: 7

mar

ks

5M

B2F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

5.

(a)

Tr

apez

ium

1 B1

cao

(b

)

AC

1 B1

cao

(c

)

4.

5cm

or

45m

m

1

B1 f

or B

1 ca

o

(d

)

56.3

o 1

B1 f

or a

n an

gle

in t

he r

ange

55

to 5

8 in

c. To

tal f

or Q

uest

ion:

4 m

arks

6.

12

, 20

and

40

2 B2

cao

(–

1 fo

r ea

ch e

xtra

num

ber

give

n)

[B1

for

1 or

2 c

orre

ct n

umbe

rs (

– 1

for

each

ext

ra n

umbe

r gi

ven)

Tota

l for

Que

stio

n: 2

mar

ks

7.

(a)

Ve

rtic

al a

nd

hori

zont

al li

nes

of s

ymm

etry

on

ly

1 B1

cao

(–

1 fo

r ex

tra

lines

dra

wn)

(b

)

B 1

B1 c

ao

(c)

Eg

. Eq

uila

tera

l tr

iang

le

2 B2

for

any

sha

pe s

atis

fyin

g bo

th c

rite

ria

[B1

for

a sh

ape

wit

h ro

tati

on a

l sym

met

ry o

f or

der

3 w

ith

no li

ne

sym

met

ry]

Tota

l for

Que

stio

n: 4

mar

ks

8.

Ta

ble

of v

alue

s

x =

– 1

0

1

2

3

y =

– 4

1

6

11

16

OR

Usi

ng y

= m

x +

c,

grad

ient

= 5

, y-

inte

rcep

t =

1

Sing

le li

ne f

rom

(–

1,

– 4)

to

(3

, 16

)

3 B3

for

a c

orre

ct s

ingl

e lin

e fr

om (

–1,

– 4)

to

(3,

16)

[B2

for

at le

ast

3 co

rrec

t po

ints

plo

tted

and

joi

ned

wit

h lin

e se

gmen

ts

OR

3 co

rrec

t po

ints

plo

tted

tw

o of

whi

ch m

ust

be t

he e

xtre

mes

wit

h no

jo

inin

g O

R a

sing

le li

ne o

f gr

adie

nt 5

pas

sing

thr

ough

(0,

1)

B1 f

or 2

cor

rect

ly p

lott

ed p

oint

s O

R a

sing

le li

e of

gra

dien

t 5

OR

a si

ngle

line

pas

sing

thr

ough

(0,

1)

Tota

l for

Que

stio

n: 3

mar

ks

5M

B2F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

9.

(a)

£1

= 1

.15

euro

s 2

M1

for

read

ing

off

one

of s

ay £

10,

£20,

£50

, et

c an

d di

vidi

ng t

heir

res

ult

by 1

0, 2

0, 5

0, e

tc

A1 f

or a

n an

swer

in t

he r

ange

1.0

5 to

1.2

5 in

c.

FE

(b)

From

gra

ph,

£15

= €1

7.25

£1

5000

0 =

€172

500

A –

yes

B -

yes

C

- n

o O

R Fr

om g

raph

, €1

5.5

= £1

3.5,

so

€155

000

= £1

3500

0 Fr

om g

raph

, €1

7 =

£14.

8, s

o €1

7000

0 =

£148

000

From

gra

ph,

€20

= £1

7.4,

so

€200

000

= £1

7400

0

OR

£150

000

× “a

nsw

er t

o (a

)”

= €1

7250

0

A –

yes

B -

yes

C

- n

o

Wit

hout

the

use

of

a ca

lcul

ator

, di

visi

on b

y “(

a)”

is n

ot li

kely

A –

yes

B -

yes

or

no

C -

no

3 M

1 fo

r a

suit

able

rea

ding

fro

m t

he g

raph

A1

for

con

vert

ing

to e

uros

(€1

7250

0 ±

€250

0)

C1 f

or c

orre

ct c

ompa

riso

n to

pri

ce o

f th

e vi

llas

OR

M1

for

a su

itab

le r

eadi

ng f

rom

the

gra

ph f

or t

he p

rice

of

one

of t

he

villa

s A1

for

con

vert

ing

to p

ound

s (±

£200

0)

C1 f

or c

orre

ct c

ompa

riso

n to

pri

ce o

f th

e vi

llas

for

thei

r ‘c

orre

ct’

conv

ersi

ons

OR

M1

for

£150

000

× “a

nsw

er t

o (a

)”

A1 f

or €

1725

00 ±

€25

00

C1 f

or c

orre

ct c

ompa

riso

n to

pri

ce o

f th

e vi

llas

Tota

l for

Que

stio

n: 5

mar

ks

5MB2

F Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 10

. Q

WC

(ii,

iii

) FE

5%

of

£600

= 6

× 5

= 3

0 24

3 ×

30 =

729

0 (2

43 +

64

+ 77

+ 3

6) ×

18

= 42

0 ×

18

Met

hod

1: 4

20 ×

10

= 42

00

420

× 8

= 3

360

+

7

560

Met

hod

2:

4000

+ 2

00 +

320

0 +

160

= 75

60

Met

hod

3:

4 2

0

0 4

0 2

0 0

1

3 2

1 6

0

0

8

× 40

0 20

10

40

00

200

8 32

00

160

£18

per

mem

ber

5 M

1 fo

r 60

010

05×

or

equi

vale

nt

A1 f

or 7

290

M1

for

a co

mpl

ete

met

hod,

con

doni

ng o

ne m

ulti

plic

atio

n er

ror

A1 f

or 7

560

C1 f

or c

ompa

ring

the

tw

o re

sult

s an

d cl

earl

y in

dica

ting

, w

ith

reas

on,

the

sugg

esti

on w

hich

is b

ette

r. F

or e

xam

ple,

£18

per

mem

ber

rais

es t

he

mos

t m

oney

and

the

ref

urbi

shm

ent

is s

hare

d by

all

mem

bers

[A

ccep

t th

e 5%

levy

sin

ce it

rai

ses

enou

gh m

oney

and

the

clu

bhou

se is

lik

ely

to b

e us

ed m

ore

by f

ull m

embe

rs t

han

any

othe

r] Q

WC:

Dec

isio

n an

d ju

stif

icat

ion

shou

ld b

e cl

ear,

wit

h w

orki

ng f

or 1

st a

nd 2

nd M

1 cl

earl

y pr

esen

ted

and

attr

ibut

ed

Tota

l for

Que

stio

n: 5

mar

ks

5M

B2F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

11.

5

34 2

22

×

57

534

5

34

222

22

2−

+

==

×

O

R

22

22

22

22

22

22

22

×=

××

××

××

××

××

OR

4 2 =

16,

3 2 =

8 S

O p

= 1

6 ×

8 =

128

5 2=

32 =

q 32

128÷

=qp

2 2or

4

2 M

1 fo

r ad

ding

the

indi

ces

in p

and

the

n su

btra

ctin

g th

e in

dice

s in

the

qu

otie

nt

A1 f

or

2 2 o

r 4

OR

M1

for

22

22

22

22

22

22

22

×=

××

××

××

××

××

wit

h an

att

empt

to

canc

el

A1 f

or

2 2or

4

OR

M1

for

128

and

32 s

een

A1 f

or

2 2 o

r 4

Tota

l for

Que

stio

n: 2

mar

ks

5M

B2F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

12.

QW

C (i

, ii,

iii

) FE

330

÷ 10

= 3

3 A

tile

s pe

r lo

ng r

ow

40 ÷

10

= 4

long

row

s 33

× 4

= 1

32 t

iles

90 ÷

10

= 9

tile

s pe

r sh

ort

row

30

÷ 1

0 =

3 sh

ort

row

s 9

× 3

= 27

tile

s 13

2 +

27 =

159

tile

s

No

of b

oxes

nee

ded

= 8

(20

× 8

= 16

0 ti

les)

£9

.99

× 8

= £7

9.92

33

0 ÷

15 =

22

B ti

les

per

long

row

40

÷ 1

5 =

3 lo

ng r

ows

(1 r

ow o

f ti

les

will

be

cut

) 22

× 3

= 6

6 A

tile

s 90

÷ 1

5 =

6 ti

les

per

shor

t ro

w

30 ÷

15

= 2

shor

t ro

ws

6 ×

2 =

12 t

iles

66 +

12

= 78

tile

s

No

of b

oxes

nee

ded

= 7

(12

× 7

= 84

ti

les)

£1

1.49

× 7

= £

80.4

3 OR

Wal

l are

a =

330

× 40

+ 9

0 ×

30 =

132

00

+ 27

00 =

159

00 c

m2

Tile

A a

rea

= 10

× 1

0 =

100

cm2

No

of t

iles

= 15

900

÷ 10

0 =

159

No

of b

oxes

nee

ded

= 8

(20

× 8

= 16

0 ti

les)

£9

.99

× 8

= £7

9.92

Ti

le B

are

a =

15 ×

15

= 22

5 cm

2

No

of t

iles

= 15

900

÷ 22

5 =

70(2

25 ×

70

= 15

700)

+ 1

N

o of

box

es n

eede

d =

6 (1

2 ×

6 =

72

tile

s)

but

som

e ti

les

will

nee

d to

be

cut,

so

7 bo

xes

need

ed

£11.

49 ×

7 =

£80

.43

Tile

A is

th

e m

ost

econ

omic

al

6 M

1 fo

r 33

0 ÷

10 o

r 9

0 ÷

10 o

r 3

30 ÷

15

or 9

0 ÷

15

A1 f

or (

33 a

nd 9

) or

(22

and

6)

M1

for

33 ×

4 +

9 ×

3 o

r 22

× 3

+ 6

× 2

A1

ft

for

10 A

box

es n

eede

d (‘

33 ×

4’

÷ ‘9

× 3

’) ÷

20

roun

ded

up t

o ne

ares

t w

hole

num

ber)

or

for

7A b

oxes

nee

ded

(‘22

× 3

’ ÷

‘6 ×

2’)

÷ 1

2 ro

unde

d up

to

near

est

who

le n

umbe

r)

B1 f

or a

nsw

ers

or £

79.9

2 an

d £8

0.43

to

just

ify

the

choi

ce

C1 f

or c

omm

ent

on t

he n

eed

to c

ut s

ome

Type

B t

iles

QW

C: D

ecis

ion

mus

t be

sta

ted,

wit

h al

l cal

cula

tion

s at

trib

utab

le

OR

M1

for

eith

er 3

30 ×

40

or 9

0 ×

30 o

r 10

× 1

0 or

15

× 15

A1

for

159

00 a

nd (

100

or 2

25)

M1

for

1590

0 ÷

100

or 1

5900

÷ 2

25

A1 f

t fo

r 10

A b

oxes

nee

ded

(‘15

900’

÷ ‘

100’

) ÷

20 r

ound

ed u

p to

nea

rest

w

hole

num

ber)

or

7 B

boxe

s ne

eded

(‘1

5900

’ ÷

‘225

’) ÷

12

roun

ded

up t

o ne

ares

t w

hole

num

ber)

B1

for

ans

wer

s or

£79

.92

and

£80.

43 t

o ju

stif

y th

e ch

oice

C1

for

com

men

t on

the

nee

d to

cut

som

e Ty

pe B

tile

s Q

WC:

Dec

isio

n m

ust

be s

tate

d, w

ith

all c

alcu

lati

ons

attr

ibut

able

Tota

l for

Que

stio

n: 6

mar

ks

5M

B2F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

13.

(a

)

4p(2

pq +

3)

2

B2 f

or 4

p(2p

q +

3)

[B1

for

2p(2

pq +

6) o

r 4

(p2 q

+ 3p

) or

p(4p

q +

12) o

r 2(

2p2 q

+ 6p

)]

(b)

5 –

2(m

– 3

) = 5

– 2

m +

6

11

– 2

m

2 M

1 fo

r 5

– 2

m +

6

A1 c

ao

Tota

l for

Que

stio

n: 4

mar

ks

14.

(a)

3n

+ 2

2

B2 f

or 3

n +

2 or

equ

ival

ent

[B1

for

3n +

k w

here

k ≠

2]

(b)

3 ×

2 4 +

2 =

3 ×

16

+ 2

= 48

+ 2

50

2

M1

for

3 ×

2 4 +

2 w

ith

a cl

ear

inte

ntio

n to

squ

are

the

4 in

depe

nden

t of

th

e sc

alar

3

A1 c

ao

To

tal f

or Q

uest

ion:

4 m

arks

15

. Q

WC

(i,

ii,

iii)

An

gle

RQT=

100

° (a

lter

nate

ang

les

are

equa

l)

Angl

e TQ

U =

100

– x

An

gle

QU

T =

100

– x

(bas

e an

gles

of

isos

tri

angl

e)

Angl

e Q

TU =

180

– (

100

– x

+ 10

0 –

x) (

angl

es in

a t

rian

gle)

Proo

f

5 B1

for

ang

le R

QT

= 10

0°

B1 f

or a

ngle

TQ

U =

100

– x

or

angl

e Q

UT

= 10

0 –

x

B1 f

or c

ompl

etin

g th

e pr

oof

C2

for

all

3 re

ason

s gi

ven

QW

C: P

roof

sho

uld

be c

lear

ly la

id o

ut w

ith

tech

nica

l lan

guag

e co

rrec

t, e

g al

tern

ate

angl

es a

re e

qual

[C

1 fo

r ju

st 1

or

2 re

ason

s gi

ven]

QW

C: P

roof

sho

uld

be c

lear

ly la

id o

ut

wit

h te

chni

cal l

angu

age

corr

ect,

eg

alte

rnat

e an

gles

are

equ

al

To

tal f

or Q

uest

ion:

5 m

arks



Total Marks

Paper Reference

*S37722A0113*

Edexcel GCSE

Mathematics BUnit 2: Number, Algebra, Geometry 1

(Non-Calculator)Higher Tier


You must have:

Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.

5MB2/2H

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



Advice



2/3/3/2

Turn over




Volume of a prism = area of cross section × length Area of trapezium = (a + b)h




Sine Rule



length

crosssection

rh

r

l

C

ab

c BA

13


xb b ac

a=

− ± −( )2 42

43

12

b

a

h

12




1 (a) Express 84 as a product of its prime factors.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Sally is a patient in a hospital. She has to take a red pill every 4 hours, a blue pill every 6 hours and a white pill

every 8 hours. She takes a pill of each colour at midday.

(b) When will she next take a pill of each colour at the same time?(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


2 Anwar, Bethany and Colin each earn the same weekly wage.

Each week, Anwar saves 12% of his wage and spends the rest.

Each week, Bethany spends 78

of her wage and saves the rest.

The ratio of the money Colin saves each week to what he spends is 1 : 9

Which of Anwar, Bethany and Colin, saves the most money each week? You must show each stage of your working.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


3 Here are the first 5 terms of an arithmetic sequence.

5 8 11 14 17

(a) Write down an expression, in terms of n, for the nth term of this sequence.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The expression 3n2 + 2 is the nth term of another sequence.

(b) Find the 4th term of this sequence.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


4

Q Rx°

T

SP

PQ, QR and RS are 3 sides of a regular decagon. PRT is a straight line. Angle TRS = x°

Work out the value of x

x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



5 The diagram shows a wall in Jenny’s kitchen.

Units Units

Units Units

Cooker

Hood

30 cm 90 cm

3.3 m

40 cm WALL

Jenny wishes to tile this wall in her kitchen. She chooses between the two types of tile shown below.

10 cm

Type A

× 10 cm 20 tiles per box

£9.99

Type B

15 cm × 15 cm

12 tiles per box

£11.49

* (a) Which tiles should Jenny use to spend the least amount of money on tiling the wall?

You must show all of your working.(6)


A Box of Type A tiles has dimensions 10.5 cm × 10.5 cm × 21 cm. Readypac wants to produce cartons which hold 12 boxes of Type A tiles, when full.

(b) On the grid below, design a net of a carton that Readypac could use. (3)


6 (a) Factorise fully 8p2q + 12p(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Expand and simplify 5 – 2(m – 3)(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


7 (a) On the grid, draw the graph of y = 5x + 1 from x = –1 to x = 3(3)

O 1 2 3 –1

2

4

6

8

10

12

14

16

18

–2

–4

–6

x

y

(b) Which of the following is the equation of a line parallel to y = 5x + 1?(1)

A B C D E y = x + 1 5y = x + 1 y + 5x = 3 y – 5x + 1 = 0 y

x= − +5

1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) Find the equation of line which is perpendicular to y = 5x + 1 and passes through the point (0, 0).

(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


8 The diagram shows a cross-section of Rafa’s new swimming pool.

Ground Ground 1.1 m

2.1 m

12 m

Deep end

Shallow end

The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.

The length of the pool is 12 m. The width of the pool is 4 m. The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.

Rafa fills the pool up with water from a hosepipe. The surface of the water is to be 10 cm from the top of the pool.

Rafa turns on the hosepipe at 09 00 on Monday and water fills at a rate of 200 ml per second.

When the pool is full, Rafa turns off the tap. At what time will this be?Show your working.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


9 Find the value of

(i) 80

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) 13

2⎛⎝⎜

⎞⎠⎟

−

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) 16 234− −( )

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


10 Simplify fully x x+ + −34

53

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*11

S

P

Q

R T

Q and R are two points on the circumference of a circle. S and T are two points on the circumference of another circle.

QT and SR are tangents to both circles. P is the point of intersection of the two tangents.

Prove that QR is parallel to ST.


12

3(x + 1)

2x + 7x + 1

AB

x – 4

The diagram shows two shapes. In shape A, all of the angles are right angles.

Shape B is a rectangle. All the measurements are in centimetres.

The area of shape A is equal to the area of shape B.

Find an expression, in terms of x, for the length and an expression, in terms of x, for the width of shape B.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



Diagrams NOT accurately drawn

Uni

t 2

Hig

her

Tier

: N

umbe

r, A

lgeb

ra,

Geo

met

ry 1

5MB2

H

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

1.

(a)

84 =

2 ×

42

=

2 ×

2 ×

21

=

2 ×

2 ×

3 ×

7

OR

Use

of

fact

or t

rees

2 ×

2 ×

3 ×

7 2

M1

for

a sy

stem

atic

met

hod

of a

t le

ast

2 co

rrec

t di

visi

ons

by a

pri

me

num

ber

or a

n eq

uiva

lent

fac

tor

tree

or

a fu

ll pr

oces

s w

ith

one

calc

ulat

ion

erro

r A1

for

2 ×

2 ×

3 ×

7 o

r 22 ×

3 ×

7

(b

) LC

M o

f 4,

6 a

nd 8

is 2

4 O

R Re

d =

afte

r

4,

8,

12

,

16,

20,

2

4,

28,

……

..

Blue

= a

fter

6,

12,

18

,

24,

30

, 3

6, …

…..

W

hite

= a

fter

8

, 1

6,

24

, 3

2,

40,

……

. O

R Ta

ble

of t

imes

fro

m m

idda

y on

war

ds in

to t

he n

ext

day,

w

ith

indi

cati

on w

hen

a re

d,

blue

and

whi

te p

ill a

re t

o be

ta

ken.

Mid

day

on t

he

follo

win

g da

y 2

M1

for

an a

ttem

pt t

o fi

nd t

he L

CM

A1 f

or m

idda

y (o

r eq

uiva

lent

) th

e ne

xt d

ay

OR

M1

for

listi

ng m

ulti

ples

of

4, 6

and

8

A1 f

or m

idda

y (o

r eq

uiva

lent

) th

e ne

xt d

ay

O

R M

1 fo

r a

corr

ect

tim

etab

le s

how

ing

whe

n pi

lls a

re t

aken

A1

for

mid

day

(or

equi

vale

nt)

the

next

day

Tota

l for

Que

stio

n: 4

mar

ks

5M

B2H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 2.

Co

lin s

aves

9

11 +

= 101

of h

is w

age

Anw

ar s

aves

12%

,

Beth

any

save

s 1

– 87

= 81

of h

er

wag

e

101 =

0.1

, 12

% =

0.12

, 81

=0.

125

OR 101

= 1

0%,

12%,

81 =

12.

5%

OR

Let

the

wee

kly

wag

e be

£10

0 sa

y

Colin

sav

es

91

1 + =

101of

his

wag

e An

war

sav

es 1

2%,

Beth

any

save

s

1 –

87 =

81of

her

wag

e

101of

£10

0 =

101 ×

100

= 1

0

12%

of £

100

= 10

012

× 1

00 =

12

81 o

f £1

00 =

81 ×

100

= 1

2.5

Beth

any

4 B1

for

9

11 +

= 101

B1 f

or 1

– 87

= 81

M1

for

conv

ersi

on t

o a

deci

mal

or

0.1

or 0

.12

or 0

.125

see

n A1

cao

for

Bet

hany

O

R M

1 fo

r co

nver

sion

to

a pe

rcen

tage

or

10%

or 1

2.5%

see

n A1

cao

for

Bet

hany

O

R B1

for

9

11 +

= 101

[or

M1

for

100

÷ (1

+9)]

B1 f

or 1

– 87

= 81

{or

A1

ft f

or £

100

– “£

87.5

0” (

= £1

2.50

)}

M1

for

101 ×

100

(=1

0) [

or A

1 fo

r 10

]

or 10

012

× 1

00 (

=12)

or 81

× 1

00 (

=12.

5) {

or 87

× 1

00 (

=87.

5)}

A1 c

ao f

or B

etha

ny

Tota

l for

Que

stio

n: 4

mar

ks

5M

B2H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e

3.

(a)

3n

+ 2

2

B2 f

or 3

n +

2 or

equ

ival

ent

[B1

for

3n +

k w

here

k ≠

2]

(b

) 3

× 42

+ 2

= 3

× 1

6 +

2 =

48 +

2

50

2 M

1 fo

r 3

× 42

+ 2

wit

h a

clea

r in

tent

ion

to s

quar

e th

e 4

inde

pend

ent

of

the

scal

ar 3

. A1

cao

To

tal f

or Q

uest

ion:

4 m

arks

4.

Angl

e PQ

R =

angl

e Q

RS =

1018

0)2

10(×

−=

144°

(int

erio

r an

gle

of a

n n-

side

d po

lygo

n)

Angl

e Q

PR =

ang

le Q

RP

=

214

418

0−

= 18

° (b

ase

angl

es o

f is

os

tria

ngle

) An

gle

PRS

=

144

– 18

= 1

26°

x

= 18

0 –

126

= 54

° (a

ngle

s on

a s

trai

ght

line)

54°

5 M

1 fo

r 10

180

)210(

×−

oe

A1 f

or in

teri

or a

ngle

= 1

44

M1

for

214

418

0−

or

18°

seen

M1

(dep

) fo

r “1

80 –

(‘1

44’

– ‘1

8’)”

A1

cao

Tota

l for

Que

stio

n: 5

mar

ks

5M

B2H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 5.

Q

WC

(i,

ii,

iii) FE

(a)

Wal

l are

a =

330

× 40

+ 9

0 ×

30 =

132

00

+ 27

00 =

159

00 c

m2

Tile

A a

rea

= 10

× 1

0 =

100

cm2

No

of t

iles

= 15

900

÷ 10

0 =

159

No

of b

oxes

nee

ded

= 8

(20

× 8

= 16

0 ti

les)

£9

.99

× 8

= £7

9.92

Ti

le B

are

a =

15 ×

15

= 22

5 cm

2 N

o of

tile

s =

1590

0 ÷

225

= 70

(225

× 7

0 =

1570

0) +

1

No

of b

oxes

nee

ded

= 6

(12

× 6

= 72

ti

les)

bu

t so

me

tile

s w

ill n

eed

to b

e cu

t, s

o 7

boxe

s ne

eded

£1

1.49

× 7

= £

80.4

3 O

R 33

0 ÷

10 =

33

A ti

les

per

long

row

40

÷ 1

0 =

4 lo

ng r

ows

33 ×

4 =

132

tile

s 90

÷ 1

0 =

9 ti

les

per

shor

t ro

w

30 ÷

10

= 3

shor

t ro

ws

9 ×

3 =

27 t

iles

132

+ 27

= 1

59 t

iles

N

o of

box

es n

eede

d =

8 (2

0 ×

8 =

160

tile

s)

£9.9

9 ×

8 =

£79.

92

330

÷ 15

= 2

2 B

tile

s pe

r lo

ng r

ow

40 ÷

15

= 3

long

row

s (1

row

of

tile

s w

ill b

e cu

t)

22 ×

3 =

66

A ti

les

90 ÷

15

= 6

tile

s pe

r sh

ort

row

30

÷ 1

5 =

2 sh

ort

row

s 6

× 2

= 12

tile

s 66

+ 1

2 =

78 t

iles

N

o of

box

es n

eede

d =

7 (1

2× 7

= 8

4 ti

les)

£1

1.49

× 7

= £

80.4

3

Tile

A is

th

e m

ost

econ

omic

al

6 M

1 fo

r ei

ther

330

× 4

0 or

90

× 30

or

10 ×

10

or 1

5 ×

15

A1 f

or 1

5900

and

(10

0 or

225

) M

1 fo

r 15

900

÷ 10

0 or

159

00 ÷

225

A1

ft

for

10 A

box

es n

eede

d (‘

1590

0’ ÷

‘10

0’)

÷ 20

rou

nded

up

to

near

est

who

le n

umbe

r) o

r 7

B bo

xes

need

ed (

‘159

00’

÷ ‘2

25’)

÷ 1

2 ro

unde

d up

to

near

est

who

le n

umbe

r)

B1 f

or a

nsw

ers

or £

79.9

2 an

d £8

0.43

to

just

ify

the

choi

ce

C1 f

or c

omm

ent

on t

he n

eed

to c

ut s

ome

Type

B t

iles

QW

C: D

ecis

ion

mus

t be

sta

ted,

wit

h al

l cal

cula

tion

s at

trib

utab

le

OR

M1

for

330

÷ 10

or

90

÷ 10

or

330

÷ 1

5 or

90

÷ 15

A1

for

(33

and

9)

or (

22 a

nd 6

) M

1 fo

r 33

× 4

+ 9

× 3

or

22 ×

3 +

6 ×

2

A1 f

t fo

r 10

A b

oxes

nee

ded

(‘33

× 4

’ ÷

‘9 ×

3’)

÷ 2

0 ro

unde

d up

to

near

est

who

le n

umbe

r) o

r fo

r 7A

box

es n

eede

d (‘

22 ×

3’

÷ ‘6

× 2

’) ÷

12

rou

nded

up

to n

eare

st w

hole

num

ber)

B1

for

ans

wer

s or

£79

.92

and

£80.

43 t

o ju

stif

y th

e ch

oice

C1

for

com

men

t on

the

nee

d to

cut

som

e Ty

pe B

tile

s Q

WC:

Dec

isio

n m

ust

be s

tate

d, w

ith

all c

alcu

lati

ons

attr

ibut

able

5M

B2H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 5.

(b

) Th

e ca

rton

can

hav

e di

men

sion

s 42

cm

× 3

1.5

cm ×

21

cm o

r 63

cm

× 2

1 cm

× 2

1 cm

or

84 c

m ×

31.

5 cm

× 1

0.5

cm o

r 63

cm

× 4

2 cm

× 1

0.5

cm o

r 12

6 cm

× 2

1 cm

× 1

0.5

cm

Net

3

B1 f

or q

uoti

ng a

cor

rect

set

of

dim

ensi

ons

(cou

ld b

e si

mpl

y on

the

di

agra

m)

M1

for

a ne

t sh

owin

g 6

rect

angl

es t

hat

coul

d fo

rm a

cub

oid

A1 f

or a

n ac

cura

te s

cale

dra

win

g or

leng

ths

labe

led

accu

rate

ly

Tota

l for

Que

stio

n: 9

mar

ks

6.

(a)

4p

(2pq

+ 3

)

2 B2

for

4p(

2pq

+ 3)

[B

1 fo

r 2p

(2pq

+ 6

) or

4 (p

2 q +

3p)

or p

(4pq

+ 1

2) o

r 2(

2p2 q

+ 6p

)]

(b)

5 –

2(m

– 3

) = 5

– 2

m +

6

11

– 2

m

2 M

1 fo

r 5

– 2m

+ 6

A1

cao

To

tal f

or Q

uest

ion:

4 m

arks

7.

(a

) Ta

ble

of v

alue

s

x =

–1

0

1

2

3

y =

–4

1

6

11

16

OR

Usi

ng y

= m

x +

c, g

radi

ent

= 5,

y-

inte

rcep

t =

1

Sing

le li

ne

from

(–

1, –

4) t

o

(3,

16)

3 B3

for

a c

orre

ct s

ingl

e lin

e fr

om (

–1,

–4)

to (

3, 1

6)

[B2

for

at le

ast

3 co

rrec

t po

ints

plo

tted

and

joi

ned

wit

h lin

e se

gmen

ts

OR

3 co

rrec

t po

ints

plo

tted

tw

o of

whi

ch m

ust

be t

he e

xtre

mes

wit

h no

jo

inin

g O

R a

sing

le li

ne o

f gr

adie

nt 5

pas

sing

thr

ough

(0,

1)]

B1

for

2 c

orre

ctly

plo

tted

poi

nts

OR

a si

ngle

lie

of g

radi

ent

5 O

R a

sing

le li

ne p

assi

ng t

hrou

gh (

0, 1

)

(b

)

D

1 B1

cao

(c

) G

radi

ent

= –

51,

c =

0 y

= –

51x

2 M

1 fo

r y

= –

51x

+ c

A1 c

ao

Tota

l for

Que

stio

n: 6

mar

ks

5M

B2H

Q

uest

ion

Wor

king

A

nsw

er

Mar k

Add

itio

nal G

uida

nce

8.

Vo

lum

e of

wat

er in

poo

l whe

n fu

ll

= 2

)12(+

× 12

× 4

= 7

2 m

3

= 72

000

000

cm

3 (m

l)

Tim

e to

fill

poo

l =

72 0

00 0

00 ÷

200

=

360

000

seco

nds

= 36

0 00

0 ÷

60 =

600

0 m

ins

=

100

hour

s

100

hour

s or

4

days

and

4

hour

s, F

rida

y 13

00

6 M

1 fo

r 2

)12(+

× 12

A1 f

or 7

2 m

3 B1

for

72

000

000

cm3 (

ml)

or

mul

tipl

ying

vol

ume

by 1

000

000

M

1 fo

r “7

2 00

0 00

0” ÷

200

M

1 fo

r “3

60 0

00”

÷ 36

00

A1 f

or 1

00 h

ours

or

4 da

ys a

nd 4

hou

rs,

Frid

ay a

t 13

00

[B1

for

an a

nsw

er le

ft a

s 36

0 00

0 se

cond

s, if

the

last

M1

not

awar

ded]

Tota

l for

Que

stio

n: 6

mar

ks

9.

(i)

(ii)

(iii)

2

13 ⎟ ⎠⎞⎜ ⎝⎛

or

1

91− ⎟ ⎠⎞

⎜ ⎝⎛

23 )16(

= (

)316

1 9 64

4 B1

cao

B1

cao

B2

cao

[B1

for

23 )16(

or e

quiv

alen

t]

Tota

l for

Que

stio

n: 4

mar

ks

10.

3

54

3x

x+

−+

=12

)5(

)3(3

−+

+x

x

711

12x−

3 M

1 re

solu

tion

of

deno

min

ator

to

12

M1

expa

nsio

n an

d si

mpl

ific

atio

n of

bra

cket

s A1

cao

Tota

l for

Que

stio

n: 3

mar

ks

5M

B2H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 11

. Q

WC,

(i

, ii,

iii

)

PS

= P

T a

nd P

Q =

PR

(equ

al

tgts

fro

m a

poi

nt)

Let

angl

e SP

T =

x

Angl

e PS

T =

angl

e PT

S =

218

0x

−

(bas

e an

gles

of

isos

tr

iang

le)

Angl

e Q

PR =

x (

vert

ical

ly

oppo

site

ang

les)

An

gle

PQR

= an

gle

PRQ

=

218

0x

−

(ba

se a

ngle

s of

isos

tr

iang

le)

Ther

efor

e an

gle

PQR

= an

gle

PTS

whi

ch a

re a

lter

nate

an

gles

. H

ence

QR

is p

aral

lel t

o ST

Proo

f 5

B1 f

or P

S =

PT o

r PQ

= P

R B1

for

equ

al t

ange

nts

from

a p

oint

B1

for

ang

le P

ST =

ang

le P

TS =

2

180

x−

or

angl

e PQ

R =

angl

e PR

Q =

218

0x

−

C1

for

bas

e an

gles

of

isos

tri

angl

e ar

e eq

ual o

r ve

rtic

ally

opp

osit

e an

gles

ar

e eq

ual Q

WC:

Wor

king

sho

uld

be c

lear

ly la

id o

ut in

a lo

gica

l se

quen

ce,

wit

h ca

lcul

atio

ns a

trib

utab

le

C1 f

or a

lter

nate

ang

les

impl

ying

par

alle

l QW

C: A

ny t

echn

ical

lang

uage

sh

ould

be

corr

ect

Tota

l for

Que

stio

n: 5

mar

ks

5M

B2H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 12

.

A

= 3(

x +

1)(2

x +

7) –

(x −

4)(

x +1

) =

3(2

2 x +

9x

+ 7)

– (

2 x−

3x −

4)

= 5

2 x+

30x

+ 25

Fa

ctor

isin

g gi

ves

5(

x +

1)(x

+ 5

) O

R Sp

litti

ng s

hape

A in

to r

ecta

ngle

s,

area

to

be a

dded

: e.

g.

3(x

+ 1)

(x +

11)

+ (x

– 4

)(2x

+ 2

) =

3(

2 x +

12x

+ 1

1) +

(2

2 x–

6x −

8)

= 5

2 x +

30x

+ 2

5 Fa

ctor

isin

g gi

ves

5(x

+ 1)

(x +

5)

5x +

5 b

y x

+ 5 or

5x

+ 2

5 by

x

+ 1

6 M

1 fo

r at

tem

ptin

g to

sub

trac

t th

e ar

ea o

f sm

all r

ecta

ngle

fro

m a

rea

of

larg

e re

ctan

gle

in A

M

1 fo

r 3

(x +

1)(

2x +

7) –

(x −

4)(

x +

1)

A1 f

or 3

(22 x

+ 9

x +

7) a

nd (

2 x −

3x −4

) A1

for

52 x

+ 3

0x +

25

M1

for

atte

mpt

ing

to f

acto

rise

“5

2 x +

30x

+ 2

5” t

o ge

t di

men

sion

s of

B

A1 f

or 5

x +

5 by

x +

5 o

r 5x

+ 2

5 by

x +

1

O

R M

1 fo

r at

tem

ptin

g to

add

the

are

a of

tw

o (o

r m

ore)

rec

tang

les

that

m

ake

up t

he s

hape

A

M1

for

3(x

+ 1)

(x +

11)

+ (

x −

4)(2

x +

2) o

e eq

uiva

lent

A1 f

or 3

(2 x +

12x

+ 1

1) a

nd (

22 x −

6x −8

)

A1 f

or 5

2 x +

30x

+ 2

5

M1

for

atte

mpt

ing

to f

acto

rise

“5

2 x +

30x

+ 2

5” t

o ge

t di

men

sion

s of

B

A1 f

or 5

x +

5 by

x +

5 o

r 5x

+ 2

5 by

x +

1

Tota

l for

Que

stio

n: 6

mar

ks



Total Marks

Paper Reference

*S37723A0120*

Edexcel GCSE

Mathematics BUnit 3: Number, Algebra, Geometry 2 (Calculator)

Foundation Tier


You must have:


5MB3/3F

Instructions



Information



Advice



2/2/3/2

Turn over

GCSE Mathematics 2544





b

a

h

length

crosssection

12



Write all your answers in the spaces provided.


1 Here are 8 polygons.

(a) Write down the mathematical name for shape A.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Write down the letter of the shape that is an octagon.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) Write down the letters of the pair of congruent shapes.(1)

. . . . . . . . . . . . . . . . and . . . . . . . . . . . . . . . .


E

A B

F

C

G

D

H

2 Jan bought 3 boxes of Salt ‘n’ Vinegar crisps and 2 boxes of Ready Salted crisps to sell at the Year 11 disco.

There are 48 bags of crisps in each box.

At the end of the disco there were 25 bags of crisps left.

How many bags of crisps were sold at the disco?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bags


Crisps48 bags

3 Tom wants to clean the upstairs windows of his house.

He decides to buy a ladder.

The ladder has to reach exactly 3.8 metres up the wall of the house.

To be safe, the ladder has to be at an angle of 72° to the ground.

What length of ladder should Tom buy?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*4 Ben buys 10 trays of bottled water for £5.99 a tray.

Each tray holds 12 bottles of water.

Ben goes to a car boot sale to sell his water.

In the morning he sells 80 bottles at 99p each.

In the afternoon he reduces the price and he sells all the bottles he has left for 75p each.

How much profit or loss does he make?

£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


12 bottles £5.99 a tray

5 (a) Reflect the shaded shape in the mirror line.(1)

(b) Describe the single transformation that moves shape P to shape Q.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


1

2

3

4

5

–1

–2

–3

– 4

–5

3 4 5–1–2–3– 4 –5 O x

y

P

Q

21

6 Jemilla goes swimming.

She swims 64 lengths of a swimming pool.

Each length is 25 m long.

(a) Work out how far Jemilla swims.

Give your answer in kilometres.(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilometres

The swimming pool is 25 m long by 10 m wide by 2.5 m deep.

(b) How many litres of water does it contain?(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l


7 Erica and Luke use this rule to work out their pay.

Pay = number of hours worked × rate of pay per hour

Erica worked for 32 hours. Her rate of pay per hour was £5.20

(a) What was Erica’s pay?(2)

£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Luke’s pay was £172.50 His rate of pay per hour was £5.75

(b) How many hours did Luke work?(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hours


8 This is the meter reading card for Mr Hassan’s use of electricity.

Here is part of Mr Hassan’s bill.

Find the total cost of Mr Hassan’s electricity bill.

£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Electricity Meter Lightning Electric Co

Reading

Date of meter reading Reading in units

3 April 2012 0 8 9 6 3

30 June 2012 1 0 6 2 5

Electricity Bill Lightning Electric Co

2 July 2012

Current rates

Standing charge 15.07p for each day

Cost per unit 11.85p

9 Harry buys some tiles so that he can tile his bathroom floor. One of the tiles is drawn on the grid below.

On the grid below show how the tiles will tessellate. You should draw at least 6 tiles.


10 (a) Solve 4x = 12(1)

x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Solve y – 7 = 11(1)

y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


11 In a school there are 220 pupils in Year 9. 120 of these pupils are girls.

What fraction of the 220 pupils are boys?

Give your fraction in its simplest form.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


12 Here are the plan and front elevation of a prism. The front elevation shows the cross section of the prism.

On the grid below draw a side elevation of the prism.


Plan

Front Elevation

13 The graph shows the cost of buying gas from the North Eastern Gas Company.

Here are the costs for buying gas from three Gas Companies.

North Eastern Basic cost £30 First 200 units free then each unit costs 5p

Pacific Every unit costs 20p

East Anglian Basic cost £10 Every unit costs 10p

Erica uses between 100 and 200 units each month.

Explain which would be the cheapest for her to use. Show clearly how you got your answer.

60

50

40

30Costin £s

NorthEastern

Gas units used

20

10

0 50 100 150 200 250 300

*

14 Mrs White wants to buy a new washing machine.

Three shops sell the washing machine she wants.

Clean Machines Electrics Wash ‘n’ Go

Washing machine Washing machine Washing machine

Buy now pay later!

£50 deposit plus

10 equal payments of £27

14 off the usual price

of

£420

£280

plus

VAT at 1712%

Mrs White wants to buy the cheapest one. She decides to buy her washing machine from one of these 3 shops.

From which of these shops should she buy her washing machine? You must show how you decided on your answer.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*

15 The perimeter of this shape is 22 cm.

Find the area.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm²


16 Use your calculator to work out

71.56.338.26700

2

2

+−

You must give your answer as a decimal. Give your answer to three significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


2x + 7

x

3x

All measurements are in centimetres

x

17 Jason earns £50 000 a year.

He has to pay income tax.

He is allowed to earn £6500 before paying tax. He pays 20% tax on the next £37 400. He then pays 40% tax on the rest.

His employer deducts the income tax each month.

How much income tax does Jason get deducted each month?

£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


18 The shaded isosceles right angled triangle is cut out of a large square of side 200 mm.

The squares are cut out of an A0 sized rectangular piece of paper which has dimensions 1189 mm by 841 mm.

More triangles are cut from the paper that is left after the squares have been cut out.

What is the greatest total number of these triangles that can be cut out of the large, rectangular sheet of paper?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . triangles


200 mm 200 mm

200 mm 200 mm

19 P = 3a + 2b²

(a) Find the value of P when a = 5 and b = – 4 (2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Make a the subject of the formula.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


20 –3 n < 2

n is an integer.

(a) Write down all the possible values of n.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Write down the inequalities represented on the number line.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



– 4 – 3 – 2 – 1 0 1 2 3 4 x

Uni

t 3

Foun

dati

on T

ier:

Num

ber,

Alg

ebra

, G

eom

etry

2

5M

B3F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

1.

(a)

Re

gula

r he

xago

n 1

B1 (

acce

pt h

exag

on)

(b

)

C 1

B1 c

ao

D

and

G

1 B1

for

bot

h, in

any

ord

er

Tota

l for

Que

stio

n: 3

mar

ks

2.

(3

+ 2

) ×

48 =

240

24

0 –

35

215

3 M

1 fo

r at

tem

pt t

o fi

nd t

otal

num

ber

of b

ags

of c

risp

s M

1 fo

r at

tem

pt t

o su

btra

ct 2

5 A1

cao

3

Tota

l for

Que

stio

n: 3

mar

ks

3. FE

4.0

m ±

0.1

m

4 M

2 fo

r dr

awin

g a

righ

t an

gled

tri

angl

e (M

1 fo

r a

sket

ch o

f a

righ

t an

gled

tri

angl

e)

M1

for

draw

ing

an a

ngle

of

72º

± 2º

A1

for

ans

wer

of

4.0

m ±

0.1

m

Tota

l for

Que

stio

n: 4

mar

ks

4.

QW

C (i

, ii,

iii

) FE

10

× £

5.99

= £

59.9

0 10

× 1

20 –

80

= 40

80

× £

0.99

= £

79.2

0 40

× £

0.75

= £

30

£79.

20 +

£30

– £

59.9

0 O

R 5.

99 ÷

12

= 50

p (a

ppro

x)

10 ×

12

– 80

= 4

0 80

× (

“99

– 50

”)=

£39.

20

40 ×

(“7

5 –

50”)

= £

10

£49.

30 p

rofi

t 5

M1

for

atte

mpt

to

find

ori

gina

l cos

t of

wat

er

M1

for

atte

mpt

to

find

cos

t of

sal

e of

fir

st 8

0 bo

ttle

s

M1

for

atte

mpt

to

find

num

ber

of r

emai

ning

bot

tles

10

× 12

– 8

0 oe

M

1 fo

r at

tem

pt t

o fi

nd c

ost

of c

ost

of s

ale

of r

emai

ning

bot

tles

A1

cao

QW

C: D

ecis

ion

mus

t be

sta

ted

wit

h cl

ear

wor

king

att

ribu

ted

corr

ectl

y O

R M

1 fo

r 5.

99 ÷

12

= ap

prox

50p

M

1 fo

r at

tem

pt t

o fi

nd p

rofi

t on

sal

e of

fir

st 8

0 bo

ttle

s

M1

for

atte

mpt

to

find

num

ber

of r

emai

ning

bot

tles

M

1 fo

r at

tem

pt t

o fi

nd p

rofi

t on

sal

e of

rem

aini

ng b

ottl

es

A1 c

ao Q

WC:

Dec

isio

n m

ust

be s

tate

d w

ith

clea

r w

orki

ng a

ttri

bute

d co

rrec

tly

To

tal f

or Q

uest

ion:

5 m

arks

5M

B3F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

5.

(a)

Co

rrec

t re

flec

tion

1

B1 c

ao

(b

)

Rota

tion

180

º ce

ntre

(–0

.5,

1)

2 B2

for

all

3 at

trib

utes

B1

for

any

tw

o of

the

thr

ee a

ttri

bute

s To

tal f

or Q

uest

ion:

3 m

arks

6.

(a

) 64

× 7

5m =

480

0m

4800

÷ 1

000

4.8

km

3 M

1 fo

r 64

× 7

5 M

1 fo

r “6

4 ×

75”

÷ 10

00

A1 c

ao

(b

) Vo

l = 2

5 ×

10 ×

2.5

= 6

25m

³ 62

5 ×

1000

62

5 00

0 3

M1

for

atte

mpt

at

find

ing

the

volu

me

M1

for

atte

mpt

to

find

the

num

ber

of l

in 1

m³ o

r 1m

³ = 1

000l

A1

cao

To

tal f

or Q

uest

ion:

6 m

arks

7.

(a

) 32

× £

5.20

£1

66.4

0 2

M1

for

32 ×

£5.

20

A1 c

ao

(b

) £1

72.5

0 ÷

£5.7

5 30

hou

rs

2 M

1 fo

r 17

2.50

÷ 5

.75

A1 c

ao

Tota

l for

Que

stio

n: 4

mar

ks

8. FE

D

ays

3rd A

pr t

o 30

th J

un is

28

+ 3

1 +

30 =

89

days

Co

st o

f da

ys

=”89

” ×

15.0

7p =

£13

.41

Uni

ts u

sed

1062

5 –

8963

=

1662

Co

st o

f un

its

= 16

62 ×

11.

85

= £1

96.9

5 19

6.95

+ 1

3.41

£210

.36

6 M

1 fo

r at

tem

pt t

o fi

nd t

he n

umbe

r of

day

s M

1 fo

r st

andi

ng c

harg

e =

“89”

× 1

5.07

p M

1 fo

r at

tem

pt t

o fi

nd t

he n

umbe

r of

uni

ts u

sed

M1

for

atte

mpt

to

find

cos

t of

uni

ts “

1662

” ×

11.8

5p

A1 f

or s

tand

ing

char

ge =

“13

.41”

or

unit

cos

t =

£196

.95

A1

for

£21

0.36

cao

Tota

l for

Que

stio

n: 6

mar

ks

5M

B3F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

9.

Corr

ect

te

ssel

lati

on

2 M

1 fo

r ex

tra

hexa

gons

in v

erti

cal p

lane

or

at p

oint

s in

hor

izon

tal p

lane

or

1 h

exag

on m

eets

ano

ther

on

a di

agon

al p

lane

A1

for

at

leas

t 6

hexa

gons

tes

sella

ting

cor

rect

ly

Tota

l for

Que

stio

n: 2

mar

ks

10.

(a)

3

1 B1

cao

(b)

18

1

B1 c

ao

Tota

l for

Que

stio

n: 2

mar

ks

11.

22

0 –

120

220

100

115

2 M

1 fo

r 22

0120

220−

oe

A1 c

ao

OR

M1

for

1 –

12

02

20

(=1

00

22

0)

A1 c

ao

Tota

l for

Que

stio

n: 2

mar

ks

5M

B3F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

12.

Corr

ect

fron

t el

evat

ion

3 B1

for

rec

tang

le o

f w

idth

3 c

m

B1 f

or r

ecta

ngle

of

heig

ht 4

cm

B1

for

hid

den

line

show

n do

tted

To

tal f

or Q

uest

ion:

3 m

arks

13

. Q

WC

(ii,

iii

) FE

Fo

r 10

0 un

its:

N

Eas

tern

= £

30

Paci

fic

= £2

0 Ea

st A

nglia

n =

£20

For

200

unit

s:

N E

aste

rn =

£30

Pa

cifi

c =

£40

East

Ang

lian

= £3

0 O

R G

raph

s pl

otte

d co

rrec

tly

Corr

ect

conc

lusi

on

wit

h ju

stif

ying

w

orki

ng

5 B1

for

cal

cula

ting

2 c

orre

ct p

oint

s fo

r Pa

cifi

c

M1

for

atte

mpt

fin

d 2

corr

ect

poin

ts o

n Ea

st A

nglia

n

A1 f

or t

wo

corr

ect

poin

ts o

n Ea

st A

nglia

n

M1

for

calc

ulat

ing

a po

int

that

allo

ws

a co

mpa

riso

n to

be

mad

e be

twee

n 10

0 an

d 20

0 un

its

C1

for

cor

rect

con

clus

ion

QW

C: D

ecis

ion

mus

t be

sta

ted,

and

all

com

men

ts s

houl

d be

cle

ar a

nd f

ollo

w t

hrou

gh f

rom

wor

king

out

Tota

l for

Que

stio

n: 5

mar

ks

14.

QW

C (i

i,

iii) FE

28

0 ×

0.17

5 +

280

(= 3

29)

420 ÷

4 (=

315

) 50

+ 1

0 ×

27 (

= 32

0)

£315

, El

ectr

ics

6 M

1 fo

r 50

+ 1

0 ×

27

M1

for

41 ×

420

or

420

÷ 4

oe

M1

for

280 ×

0.17

5 +

280

or 2

80 ×

1.1

75 o

e A2

for

320

, 31

5 an

d 32

9

(A1

for

any

2 co

rrec

t of

320

, 31

5 an

d 32

9)

C1(d

ep o

n M

2 A2

) fo

r ‘E

lect

rics

’ as

fin

al a

nsw

er Q

WC:

Dec

isio

n m

ust

be

stat

ed,

wit

h al

l cal

cula

tion

s at

trib

utab

le To

tal f

or Q

uest

ion:

6 m

arks

15

.

2(3x

+ 2

x +

7) =

22

OR

3x +

2x

+ 7

+ x+

x +

2x

+ x

+ 7

= 22

10

x +

14 =

22

10x

= 8

x =

0.8

Area

= 2

.4 ×

8.6

– 1

.6 ×

0.8

O

R 0.

8 ×

08 +

2.4

× 7

.8

19.3

6 cm

² 5

M1

for

atte

mpt

to

find

an

expr

essi

on o

f th

e pe

rim

eter

A1

for

10x

+ 1

4 =

22

A1 f

or x

= 0

.8

M1

for

atte

mpt

to

find

are

a A1

for

19.

36

Tota

l for

Que

stio

n: 5

mar

ks

5MB3

F Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 16

.

4.

08

3 B1

for

5.6

644

or 8

1.85

35(2

772…

) or

76.

1(89

1277

2…)

or 1

8.67

B1

for

4.0

8(08

3169

4)

B1 c

ao

Tota

l for

Que

stio

n: 3

mar

ks

17.

20

% of

£37

400

= £

7480

50

000

– 3

7 40

0 –

6500

=

£610

0 40

% of

610

0 =

£244

0 (“

7480

” +

“244

0”)

÷ 1

2

£826

.67

5 M

1 fo

r at

tem

pt t

o fi

nd 2

0% o

f £3

7 40

0 M

1 fo

r at

tem

pt t

o fi

nd h

ow m

uch

is t

axed

at

40%

50 0

00 –

37

400

– 65

00

M1

for

atte

mpt

to

find

40%

of

“610

0”

M1

for

mon

thly

tax

bill

is (

“748

0” +

“24

40”)

÷ 1

2

A1 f

or £

826.

67 c

ao

To

tal f

or Q

uest

ion:

5 m

arks

18

.

11

89 ÷

200

or

891

÷ 20

0 =

5 an

d 4

or 2

0 sq

uare

s 20

0² ÷

2

= √(

200²

÷ 2

) =

141.

4 Re

alis

ing

that

ano

ther

row

of

squa

res

of s

ide

141.

4 fi

ts o

r 89

1 ÷

141.

4 =

5 sq

uare

s

90

5 M

1 fo

r at

tem

pt t

o di

vide

118

9 ÷

200

or 8

91 ÷

200

M

1 fo

r 20

0² ÷

2

M1

for √(

200²

÷ 2

) M

1 fo

r re

alis

ing

that

ano

ther

row

of

squa

res

of s

ide

141.

4 fi

ts o

r 89

1 ÷

141.

4

A1 c

ao f

or 9

0 tr

iang

les

Tota

l for

Que

stio

n: 5

mar

ks

19.

(a)

3 ×

5 +

2 ×

(–4)

² 15

+ 2

× 1

6 15

+ 3

2

47

2 M

1 fo

r 3

× 5

+ 2

× (–

4)²

A1 f

or 4

7

(b

) P

–2b²

= 3

a a

= (P

– 2

b²) ÷

3

322

bP

a−

=

2 M

1 fo

r P

– 2b

² = 3

a A1

cao

To

tal f

or Q

uest

ion:

4 m

arks

5M

B3F

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

20.

(a)

–3

, –2,

–1,

0,

1

2 B2

for

–3,

–2,

–1,

0, 1

(B

1 fo

r –2

, –1,

0,

1 or

–2,

–1,

0,

1, 2

)

(b)

–1

< x

≤ 3

2

B2 f

or –

1 <

x ≤

3 (B

1 fo

r –1

≤ x

≤ 3

or

–1 <

x <

3

Tota

l for

Que

stio

n: 4

mar

ks



Total Marks

Paper Reference

*S37719A0120*

Edexcel GCSE

Mathematics BUnit 3: Number, Algebra, Geometry 2 (Calculator)

Higher Tier


You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

5MB3/3H

Instructions



Information



Advice



2/3/3/2

Turn over




Volume of a prism = area of cross section × length Area of trapezium = (a + b)h




Sine Rule



length

crosssection

rh

r

l

C

ab

c BA

13


xb b ac

a=

− ± −( )2 42

43

12

b

a

h

12


Write all your answers in the spaces provided.


1

A Large tub of popcorn costs £3.80 and holds 200g. A Regular tub of popcorn costs £3.50 and holds 175g.

Which is the better value for money?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Large Regular

200g 175g

£3.80£3.50

2 Use your calculator to work out

You must give your answer as a decimal. Give your answer to three significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Queston 2 = 3 marks)

6700 2 383 6 5 71

2

2

−+

.. .

3 The perimeter of this shape is 22 cm.

Find the area.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm²


4 –3 n < 2

n is an integer.

(a) Write down all the possible values of n.(2)

……………………….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .……………….

(b) Write down the inequalities represented on the number line.(2)

……………………….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .……………….


2x + 7

x

3x x

All measurements are incentimetres

0 1 2 3 4– 4 – 3 –2 – 1 x

*5 The graph shows the cost of buying gas from the North Eastern Gas Company.

Here are the costs for buying gas from three Gas Companies.

North Eastern Basic cost £30 First 200 units free then each unit costs 5p

Pacific Every unit costs 20pEast Anglian Basic cost £10 Every unit costs 10p

Erica uses between 100 and 200 units each month.

Explain which Company would be the cheapest for her to use. Show clearly how you got your answer.

0

10

20

30

40

Costin £s

50

60

50 100 150 200 250 300

NorthEastern

Gas units used

6

Ben’s Tyre Shop

Mini prices for Tyres

Tyres for Minis Price

Goodweek £65

Dunlap £62

Bridgearth £75

Pirello £69

Valves 50p per tyre

Balancing £1 per tyre

Des buys two Dunlap tyres with valves and balancing and has to pay VAT at 15%.

(a) Work out the total amount Des pays for the tyres.(3)

£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Ben sees Dunlap tyres offered for sale in a different garage. He wants to compare the prices before VAT was added.

(b) What is the price of these tyres before VAT was added?(2)

£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In 2010 the VAT rate is to be increased from 15% to 17½%.

(c) By what number will Ben have to multiply the old prices by to give the new prices including VAT?

(2)

£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Tyre Sale

Dunlap tyres for Minis (including valves and balancing)

£71.30 including VAT at 15%

7 The shaded isosceles right angled triangle is cut out of a large square of side 200 mm.

The squares are cut out of an A0 sized rectangular piece of paper which has dimensions 1189 mm by 841 mm.

More triangles are cut from the paper that is left after the squares have been cut out.

What is the greatest total number of these triangles that can be cut out of the large, rectangular sheet of paper?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . triangles


200 mm

200 mm 200 mm

200 mm

8 Tom wants to clean the upstairs windows of his house.

He decides to buy a ladder.

The ladder has to reach exactly 3.8 metres up the wall of the house.

To be safe, the ladder has to be at an angle of 72° to the ground.

What length of ladder should Tom buy?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


9 The time it takes for the pendulum of a clock to swing from one end of its arc to the other and back again is given by the formula

(a) Find the value of l, when

T = 2, π = 3.14 and g = 9.81(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Make l the subject of the formula. (3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


T lg

= 2π

10 Solve

(4)

x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


xx

xx+

= ++4

73

11

Steve is working out the height of a tall vertical building CD. The building is standing on horizontal ground.

Steve measures the angle of elevation of the top, D, of the building from two different points A and B.

The angle of elevation of D from A is 65° The angle of elevation of D from B is 78° AB = 50 m. ABC is a straight line.

Calculate the height of the building. Give your answer correct to 3 significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m


A B C 65° 78°50m

D


12 Solve the simultaneous equations

3x + 2y = 11

2x – 5y = 20

x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Queston 12 = 4 marks)

13 Solve 3x2 + 2x – 4 = 0

Give your answer correct to three significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


14 Gerry has an ingot of steel that he is going to turn into ball bearings.

The ingot is in the shape of a cuboid and it cost him £50.

The dimensions of the cuboid are 30 cm, by 15 cm by 8 cm to the nearest mm. The ball bearings are spheres of diameter 5 mm to the nearest tenth of a millimetre.

Gerry melts the ingot and recasts the metal without losing any of the steel. He sells all the ball bearings he makes at 10 ball bearings for 1 pence.

Work out the least profit Gerry could make if he sells all of the ball bearings.

£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


*15

A, B and C are points on the circle with centre O.

Prove that the angle subtended by arc BC at the centre of the circle is twice the angle subtended by arc BC at point A.


A

Diagramaccurately drawn

NOT

O

BC

16

The diagram shows a regular hexagon OABCDE.

(a) Find BC , in terms of a and b.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

X is the midpoint of CD.

Y is the point on BC extended, such that BC : CY = 3 : 2

* (b) Prove that O, X and Y lie on the same straight line.(4)


B C

6b

6a

X

A 12b D

O E

OA = DC = 6a, OC = 12b

17

The diagram shows the graph of y = f(x).

The only vertex of the graph is A at (1, 2).

Write down the coordinates of the vertex of the curve with equation.

(a) (i) y = f(x) + 3(1)

. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . .

(ii) y = f(x – 2)(1)

. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . .

The curve with equation y = f(x) is transformed to give the curve with equation y = – f(x)

(b) Describe the transformation.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


–2 2

2

4

6

4O

A

x

y = f(x)

y

18

The diagram shows a net. The net is a sector of a circle. The radius of the circle is 10.3 cm and the angle at the centre of the circle is 120º.

The net is used to make a cone.

Calculate the vertical height of the cone. Give your answer correct to 3 significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm



Diagram NOT accurately drawn

10.3 cm

120°

Uni

t 3

Hig

her

Tier

: N

umbe

r, A

lgeb

ra,

Geo

met

ry 2

5MB3

H

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

1.

FE

38

0 ÷

200

= 1.

9 35

0 ÷

175

= 2

Regu

lar

by 0

.1p

per

gram

3

M1

for

380

÷ 20

0 (=

1.9

) or

200

÷ 3

80 (

= 0.

526)

M

1 fo

r 35

0 ÷

175

(= 2

) oe

or

175

÷ 35

0 (=

0.5

) oe

C1

for

Reg

ular

wit

h co

rrec

t ca

lcul

atio

ns To

tal f

or Q

uest

ion:

3 m

arks

2.

(a

)(i)

(i

i)

4.

08

3 B1

for

5.6

644

or 8

1.85

35(2

772…

) or

76.

1(89

1277

2…)

or 1

8.67

B1

for

4.0

8(08

3169

4)

B1 c

ao

Tota

l for

Que

stio

n: 3

mar

ks

3.

2(

3x +

2x

+ 7)

= 2

2 O

R 3x

+ 2

x +

7 +

x +

x +

2x +

x +

7

= 22

10

x +

14

= 22

10

x =

8 x

= 0.

8 Ar

ea =

2.4

× 8

.6 –

1.6

× 0

.8

OR

0.8

× 08

+ 2

.4 ×

7.8

19.3

6 cm

² 5

M1

for

atte

mpt

to

find

an

expr

essi

on o

f th

e pe

rim

eter

A1

for

10x

+ 1

4 =

22

A1 f

or x

= 0

.8

M1

for

atte

mpt

to

find

are

a A1

for

19.

36

Tota

l for

Que

stio

n: 5

mar

ks

4.

(a)

–3

, –2,

–1,

0,

1 2

B2 f

or –

3, –

2, –

1, 0

, 1

(B1

for

–2, –

1, 0

, 1

or –

2, –

1, 0

, 1,

2)

(b

)

–1 <

x ≤

3

2 B2

for

–1

< x ≤

3 (B

1 fo

r –1

≤ x

≤ 3

or –

1 <

x <

3

Tota

l for

Que

stio

n: 4

mar

ks

5M

B3H

Q

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ion

Wor

king

A

nsw

er

Mar

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ddit

iona

l Gui

danc

e 5.

Q

WC

(ii,

iii

) FE

Fo

r 10

0 un

its:

N

Eas

tern

= £

30

Paci

fic

= £2

0 Ea

st A

nglia

n =

£20

For

200

unit

s:

N E

aste

rn =

£30

Pa

cifi

c =

£40

East

Ang

lian

= £3

0 O

R G

raph

s pl

otte

d co

rrec

tly

Corr

ect

conc

lusi

on w

ith

just

ifyi

ng

wor

king

5 B1

for

cal

cula

ting

2 c

orre

ct p

oint

s fo

r Pa

cifi

c

M1

for

atte

mpt

fin

d 2

corr

ect

poin

ts o

n Ea

st A

nglia

n

A1 f

or t

wo

corr

ect

poin

ts o

n Ea

st A

nglia

n

M1

for

calc

ulat

ing

a po

int

that

allo

ws

a co

mpa

riso

n to

be

mad

e be

twee

n 10

0 an

d 20

0 un

its

C1

for

cor

rect

con

clus

ion

QW

C: D

ecis

ion

mus

t be

sta

ted,

and

all

com

men

ts s

houl

d be

cle

ar a

nd f

ollo

w t

hrou

gh f

rom

wor

king

out

Tota

l for

Que

stio

n: 5

mar

ks

6. FE

(a)

2 ×

(62

+ 0.

50+

1)

“127

” ×

1.15

£1

46.0

5 3

M2

for

atte

mpt

to

find

cos

t in

clud

ing

VAT

e.g.

“12

7” ×

1.1

5

(M1

for

VAT

= “

127”

× 0

.175

or

127

100

15×

or

12.7

0 +

6.35

)

A1 c

ao

(b

) 71

.30

÷ 1.

15

£62

2 M

1 fo

r 71

.30

÷ 1.

15 o

r 71

.30

÷ 11

5 ×

100

A1 c

ao

(c

)

1.02

(173

913)

2

M1

for

÷ 1.

15 o

r ×

1.17

5 A1

for

1.0

2(17

3913

) To

tal f

or Q

uest

ion:

7 m

arks

7.

1189

÷ 2

00 o

r 89

1 ÷

200

= 5

and

4 or

20

squa

res

200²

÷ 2

= √(

200²

÷ 2

) =

141.

4 Re

alis

ing

that

ano

ther

row

of

squa

res

of s

ide

141.

4 fi

ts o

r 89

1 ÷

141.

4 =

5 sq

uare

s

90

5 M

1 fo

r at

tem

pt t

o di

vide

118

9 ÷

200

or 8

91 ÷

200

M

1 fo

r 20

0² ÷

2

M1

for √(

200²

÷ 2

) M

1 fo

r re

alis

ing

that

ano

ther

row

of

squa

res

of s

ide

141.

4 fi

ts o

r 89

1 ÷

141.

4 A1

cao

for

90

tria

ngle

s

Tota

l for

Que

stio

n: 5

mar

ks

5M

B3H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 8.

FE

h

3.8

7

2º

sin

72 =

h8.3

h =

72si

n8.3

4 m

4

M1

for

draw

ing

sket

ch o

f sc

enar

io s

how

ing

all i

nfor

mat

ion

M1

for

sin

72 =

h8.3

or

for

atte

mpt

at

scal

e dr

awin

g

M1

for

h =

72si

n8.3

C1 a

ny la

dder

ove

r 4.

66 m

lon

g pr

ovid

ing

M3

earn

ed

NB

scal

e dr

awin

g at

tem

pt s

core

s a

max

imum

of

2 m

arks

Tota

l for

Que

stio

n: 4

mar

ks

9.

(a)

2 =

2 ×

3.14

×

81.9l

81.9l

=

14.32

2×

81.9l

=

2

14.32

2⎟ ⎠⎞

⎜ ⎝⎛×

l = 9

.81

× 2

14.32

2⎟ ⎠⎞

⎜ ⎝⎛×

0.99

5 2

M1

for

divi

ding

2 b

y 2

× 3.

14 a

nd s

quar

ing

A1 f

or 0

.994

(969

37)

cao

(b)

T2 = 4π2

gl

22

4πT =

gl

l =

2

2

4πg

T

3 M

1 fo

r sq

uari

ng b

oth

side

s M

1 fo

r di

vidi

ng b

y 4π

² or

mul

tipl

ying

by

g

A1 f

or l

= 2

2

4πg

T o

e

Tota

l for

Que

stio

n: 5

mar

ks

5M

B3H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 10

.

x(x

+ 3)

= (

x +

7)(x

+ 4

)

-3.

5 4

M1

for

mul

tipl

ying

thr

ough

by

LCD

= (

x +

4)(x

+ 3

)

A1 f

or

2811

32

2+

+=

+x

xx

x

B1 f

or –

28 =

8

A1 c

ao

Tota

l for

Que

stio

n: 4

mar

ks

11.

(a)

78 –

65

= 1

3 50si

n65

sin"

13"

DB

=

50si

n65

sin"

13"

DB=

×

(=20

1..)

“2

01” ×

sin

78

197

m

6 B1

for

13o

M1

for

50si

n65

sin"

13"

DB

=

M1

for

50si

n65

sin"

13"

DB=

×

A1 f

or 2

01 –

201

.5

M1

for

“201

” ×

sin

78

A1 f

or 1

96.6

– 1

97.1

O

R B1

for

13o

M1

for

50si

n102

sin"

13"

AD=

M1

for

50si

n102

sin"

13"

AD=

×

A1 f

or 2

17 –

217

.42

M

1 fo

r “2

17” ×

sin

65

A1 f

or 1

96.6

– 1

97.1

Tota

l for

Que

stio

n: 6

mar

ks

5M

B3H

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

ddit

iona

l Gui

danc

e 14

. FE

()3

3

255

.034

)95.7

95.14

95.29(

π

××

=8

0694

5590

11.0

6323

75.

3559

£462

.25

6 B1

for

usi

ng t

he le

ast

valu

e of

1 d

imen

sion

of

the

cubo

id

M1

for

29.9

5 ×

14.9

5 ×

7.95

oe

B1

for

usi

ng g

reat

est

radi

us o

f sp

here

as

0.25

cm +

0.0

05 c

m

M1

for

divi

ding

leas

t vo

lum

e of

lead

“35

59.6

3237

5” b

y gr

eate

st v

olum

e of

sph

ere

“0.0

6945

59”

A1

for

512

50 o

r Se

lling

pri

ce =

£51

.25

A1 f

or P

rofi

t =

£1.2

5 ca

o

To

tal f

or Q

uest

ion:

6 m

arks

5MB3

H

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

15.

QW

C (i

,ii,

iii

)

Jo

in A

O a

nd p

rodu

ce t

o P

Mar

k eq

ual a

ngle

s in

isos

cele

s tr

iang

le A

OC

or A

OB

M

ark

angl

e CO

P as

tw

ice

angl

e CA

O o

r m

ark

angl

e BO

P as

tw

ice

angl

e BA

O

Iden

tify

ang

le A

as

half

ang

le

BOC

4 M

1 fo

r Jo

inin

g A

O a

nd p

rodu

cing

to

“P”

M1

for

mar

king

equ

al a

ngle

s in

isos

cele

s tr

iang

le A

OC

or A

OB

givi

ng r

easo

n th

at

tria

ngle

s ar

e is

osce

les

beca

use

radi

i are

equ

al

M1

for

mar

king

ang

le C

OP

as t

wic

e an

gle

CAO

or

mar

king

Ang

le B

OP

as t

wic

e an

gle

BAO

giv

ing

reas

on t

hat

exte

rior

ang

le o

f a

tria

ngle

is e

qual

to

the

inte

rior

and

op

posi

te a

ngle

s o.

e. Q

WC:

Wor

king

sho

uld

be lo

gica

l and

seq

uent

ial i

n st

ruct

ure;

fo

llow

ing

on f

rom

labe

lling

the

ext

ende

d lin

e

A1 f

or Id

enti

fyin

g an

gle

A a

s ha

lf a

ngle

BO

C if

M3

awar

ded

QW

C: A

ll la

belli

ng a

nd

angl

e no

tati

on s

houl

d be

con

sist

ent

To

tal f

or Q

uest

ion:

4 m

arks

16

. (a

) –

6b –

6a

+ 12

b 6b

– 6

a 1

B1 c

ao

QW

C (i

i,

iii)

(b)

BC =

–6b

– 6

b +

12b

=

6b –

6a

CY=

4b –

4a

OX

= 12

b –

3a

OY

= 12

b +

4b–4

a =

16b

– 4a

O

X :

OY

= 3

: 4

4

M1

for

atte

mpt

to

find

CY

or

sigh

t of

⅔(6

b –

6a)

M1

for

atte

mpt

to

find

OX

or s

ight

of

12b

– 3a

M

1 fo

r at

tem

pt t

o fi

nd O

Y or

sig

ht o

f 12

b +

4b –

4a

A1

for

OX

: O

Y =

3 :

4 sh

ows

that

OX

and

OY

are

co-

linea

r Q

WC:

labe

lling

mus

t be

co

nsis

tent

and

cor

rect

Tota

l for

Que

stio

n: 5

mar

ks

17.

(a

) (i

) (i

i)

(1

, 5)

(3

, 2)

2

B1

cao

B1

cao

(b

)

Refl

ecti

on in

x

axis

1

B1 c

ao

Tota

l for

Que

stio

n: 3

mar

ks

5MB3

H

Que

stio

n W

orki

ng

Ans

wer

M

ark

Add

itio

nal G

uida

nce

18.

360

120

× 2π

× 10

.3 =

21.

572

“21

.572

”÷ 2π

= 3.

4333

√(

10.3

² – 3

.433

²)

9.71

4

M1

for

Len

gth

of a

rc =

360

120

× 2π

× 10

.3

M1

for

Rad

ius

of c

ircl

e =

“21.

572”

÷ 2π

M

1 fo

r √(

10.3

² – 3

.433

²)

A1 c

ao

To

tal f

or Q

uest

ion:

4 m

arks

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