Edexcel Level 1/Level 2 Certificate - Longhill High Schoollonghill.org.uk/resources/Maths/Year 11/Exam papers/IGCSE/Sample... · Edexcel Level 1/Level 2 Certificate Mathematics Edexcel

Edexcel Level 1/Level 2 CertificateMathematics

Edexcel Level 1/Level 2 Certificate in Mathematics (KMA0)

First teaching from September 2011

Sample Assessment

Material (SAMs)

UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 2011 1

Contents

General marking guidance 2

Paper 1F 3Sample Assessment Material 3

Sample Mark Scheme 21

Paper 2F 31Sample Assessment Material 31


Paper 3H 59Sample Assessment Material 59


Paper 4H 89Sample Assessment Material 89


UG025980 Edexcel Level 1/Level 2 Certifi cate in Mathematics SAMs © Edexcel Limited 20112

General Marking Guidance

All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last.

Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions.

All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, ie if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme.

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

Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response.

Guidance on the use of codes within this mark scheme M1 – method mark A1 – accuracy mark B1 – working mark oe – or equivalent cao – correct answer only ft – follow through sc - special case


Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper Reference

Turn over

*S39742A0118*

MathematicsPaper 1F

Foundation Tier

Sample Assessment MaterialTime: 2 hours

You must have:

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

KMA0/1F

Instructions

• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answer all questions.• Without sufficient working, correct answers may be awarded no marks.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators may be used.

• You must NOT write anything on the formulae page. Anything you write on the formulae page will gain NO credit.

Information

• The total mark for this paper is 100. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.

Advice

• Read each question carefully before you start to answer it.• Write your answers neatly and in good English.• Check your answers if you have time at the end.

S39742A©2010 Edexcel Limited.

Edexcel Certificate L1/L2


IGCSE MATHEMATICS 4400

FORMULAE SHEET – FOUNDATION TIER

Pythagoras’Theorema2 + b2 = c2

Volume of cylinder = r2h

Curved surface area of cylinder = 2 rh

adj = hyp cosopp = hyp sinopp = adj tan

or

opptanadj

adjcoshyp

oppsinhyp

Circumference of circle = 2 r

Area of circle = r2

Volume of prism = area of cross section length

Area of a trapezium = (a + b)h12

b

a

opp

adj

hyp

b

a

h

lengthsectioncross

r

h

r

c

FORMULA SHEET – FOUNDATION TIER

You must not write on the fomulae page. Anything you do write will gain no credit.


Answer ALL questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1 15 21 23 24 25 27 33 35 39

From the numbers in the box, write down(5)

(i) an even number

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

(ii) a factor of 60

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

(iii) a multiple of 9

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

(iv) a square number

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

(v) a prime number.

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

(Total for Question 1 = 5 marks)


2 The diagram shows a triangle ABC on a centimetre grid.

(a) Write down the coordinates of the point(2)

(i) A, (. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . .)

(ii) B. (. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . .)

(b) Measure the length of the line AB. Give your answer in millimetres.

(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mm

(c) Find the perimeter of triangle ABC.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mm

(d) Write down the special name for triangle ABC.(1)

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

(e) (i) Measure the size of angle B.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°

(ii) Write down the special name for this type of angle.(1)

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


O 1 2 3 4 5 6 7 8 9 10 x

y6

5

4

3

2

1

A C

B


3 (a) Write down the number which is exactly halfway between 0.3 and 0.4

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

(1)

3.7 3.8

(b) What is the reading on the scale?

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

(1)

(c) Write down the value of the 4 in the number 0.746

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

(1)

(d) Here is a list of numbers.

0.3 0.32 0.02 0.23 0.03

Write these numbers in order of size.Start with the smallest number.

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

(1)

(e) Write 34

as a decimal.

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

(1)

(f) Write 0.7 as a percentage.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %(1)

(g) Round 6.84 to the nearest whole number.

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

(1)



4 Here are the first five terms of a number sequence.

1 7 13 19 25

(a) Write down the next term in the sequence.(1)

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

(b) Explain how you worked out your answer.(1)

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

(c) Find the 11th term of the sequence.(1)

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

(d) The 50th term of the sequence is 295 Work out the 49th term of the sequence.

(1)

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

Tamsin says, “Any two terms of this sequence add up to an even number.”

(e) Explain why Tamsin is right.(1)

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

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

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



5 Here are 9 flags.

(a) Write down the letter of the flag which has:(4)

(i) exactly one line of symmetry

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

(ii) rotational symmetry of order 4

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

(iii) 2 lines of symmetry and rotational symmetry of order 2

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

(iv) no lines of symmetry and rotational symmetry of order 2

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

(b) Write down the letter of the flag which has a rhombus on it.(1)

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


A B C

D E F

G H I


6 The bar chart shows information about the number of people, in millions, who speak each of 6 languages.

(a) Write down the number of people who speak Hindi.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . million

(b) Write down the number of people who speak Mandarin Chinese.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . million

(c) Which language is spoken by 190 million people?(1)

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

125 million people speak Japanese.

(d) Draw a bar on the bar chart to show this information.(1)

(e) Find the ratio of the number of people who speak Hindi to the number of people who speak Japanese.

Give your ratio in its simplest form.(2)

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

Bengali Japanese

900800700600500400300200100

0Mandarin Chinese

Spanish English Hindi Arabic

Language

Numberof people(million)


330 million people speak English. 70% of these people live in the USA.

(f) Work out 70% of 330 million.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . million

332 million people speak Spanish. 143 million of these people live in South America.

(g) Work out 143 million as a percentage of 332 million. Give your answer correct to 1 decimal place.

(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %


7 (a) Solve 2x + 9 = 1(2)

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

(b) Solve 5y – 4 = 2y + 7(2)

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



8 The table shows information about the time in each of five cities. For each city, it shows the number of hours time difference from the time in London.

+ shows that the time is ahead of the time in London. shows that the time is behind the time in London.

City

Time difference

from London

(hours)

Cairo +2

Montreal −5

Bangkok +7

Rio de Janeiro −3

Los Angeles −8

Mexico City

(a) When the time in London is 6 a.m., what is the time in:(2)

(i) Bangkok,

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

(ii) Los Angeles.

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

(b) The time in Mexico City is 2 hours ahead of the time in Los Angeles. Complete the table to show the time difference of Mexico City from London.

(1)

(c) Write down the name of the city in which the time is 10 hours behind Bangkok.(1)

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

(d) Work out the time difference between(2)

(i) Cairo and Montreal,

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

(ii) Rio de Janeiro and Los Angeles.

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



9

£1 = 72.5 Indian rupees

(a) Change £86 to Indian rupees.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indian rupees(2)

(b) Change 8700 Indian rupees to pounds (£).

£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)



10

Write down the equation of(3)

(i) line A,

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

(ii) line B,

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

(iii) line C.

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


11 (a) Use your calculator to work out the value of

( . . ). .

3 7 4 62 8 6 3

2

Write down all the figures on your calculator display.(2)

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

(b) Give your answer to part (a) correct to 2 decimal places.(1)

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


8

6

4

2

–2

–2 2 4 6 8O x

y

BC

A


12 Here are five shapes.

Four of the shapes are squares and one of the shapes is a circle. One square is black. Three squares are white. The circle is black.

The five shapes are put in a bag. Alec takes at random a shape from the bag.

(a) Find the probability that he will take the black square.(1)

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

(b) Find the probability that he will take a white square.(2)

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

Jasmine takes a shape at random from the bag 150 times. She replaces the shape each time.

(c) Work out an estimate for the number of times she will take a white square.(2)

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



13 A basketball court is a rectangle, 28 m long and 15 m wide.

(a) Work out the area of the rectangle.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2

(b) In the space below, make an accurate scale drawing of the rectangle. Use 1 cm to represent 5 m.

(2)


14 (a) Work out the value of x2 – 5x when x = –3(2)

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

(b) Factorise x2 – 5x(2)

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



15 Hajra counted the numbers of sweets in 20 packets. The table shows information about her results.

Number of sweets Frequency

46 3

47 6

48 3

49 5

50 2

51 1

(a) What is the mode number of sweets?(1)

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

(b) Work out the range of the number of sweets.(2)

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

(c) Work out the mean number of sweets in the 20 packets.(3)

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



16

P

Q

R

y4

3

2

1

-1

-2

-2 -1 0 1 2 3 4 5 6 7 x

(a) Describe fully the single transformation which maps triangle P onto triangle Q.(2)

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

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

(b) Describe fully the single transformation which maps triangle P onto triangle R.(3)

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

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



17 (a) Simplify, leaving your answers in index form,(2)

(i) 75

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

(ii) 59

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

(b) Solve 9 4

82 2 22n×

=(2)

n = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


18 (a) Expand and simplify 3(4x – 5) – 4(2x + 1)(2)

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

(b) Expand and simplify (y + 8)(y + 3)(2)

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

(c) Expand p(5p2 + 4)(2)

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



19 A tunnel is 38.5 km long.

(a) A train travels the 38.5 km in 21 minutes.

Work out the average speed of the train. Give your answer in km/h.

(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . km/h

(b) To make the tunnel, a cylindrical hole 38.5 km long was drilled. The radius of the cylindrical hole was 4.19 m.

Work out the volume of earth, in m3, which was removed to make the hole. Give your answer correct to 3 significant figures.

(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m3


TOTAL FOR PAPER = 100 MARKS


Sam

ple

Mar

k Sc

hem

e Pa

per

1F

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stio

nN

umbe

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orki

ngAn

swer

Mar

kN

otes

1 (i

) 24

1B1

cao

1

(ii)

15

1B1

cao

1

(iii)

27

1B1

cao

1

(iv)

25

1B1

cao

1

(v)

231

B1 c

ao

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stio

nN

umbe

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orki

ngAn

swer

Mar

kN

otes

2(a)

(i)

(1,5

)1

B12(

a)(i

i)(5

,0)

1B1

2(b)

641

B1 A

llow

+2m

m

2(c)

8(0)

+ 2

x “

64”

204

– 21

2 in

c 2

M1

Also

aw

ard

for

20.4

– 2

1.2

A1 f

t fr

om “

64”

2(d)

isos

cele

s1

B12(

e)(i

) 77

1B1

allo

w +

2

2(e)

(ii)

acut

e1

B1


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swer

Mar

kN

otes

3 (a

) 0.

351

B1 c

ao

3 (b

) 3.

741

B1 c

ao

3 (c

) hu

ndre

dths

1B1

Als

o ac

cept

4 h

undr

edth

s, 10

01,

1004

, 0.

01, 0

.04

3 (d

) 0.

02 0

.03

0.2

3 0

.3 0

.32

1B1

cao

3

(e)

0.75

1B1

cao

3

(f)

701

B1 c

ao

3 (g

) 7

1B1

cao

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orki

ngAn

swer

Mar

kN

otes

4(a)

311

B1 c

ao

4(b)

eg ‘

Add

6’

1B1

4(c)

611

B1 c

ao

4(d)

289

1B1

ft

from

(b)

4(

e)eg

‘Su

m o

f tw

o od

d nu

mbe

rs is

alw

ays

even

’ 1

B1 A

ccep

t if

‘od

d’ u

sed

corr

ectl

y


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orki

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swer

Mar

kN

otes

5(a)

(i)

B1

B1 c

ao

5(a)

(ii)

F1

B1 c

ao

5(a)

(iii)

I1

B1 c

ao

5(a)

(iv)

D1

B1 c

ao

5(b)

H1

B1 c

ao

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stio

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orki

ngAn

swer

Mar

kN

otes

6(a)

300

1B1

cao

6(

b)85

5 -

875

1B1

6(c)

Beng

ali

1B1

6(d)

100

< ba

r <

150

1B1

6(e)

300:

125

12:5

2M

1 f

or 3

00:1

25,

60:2

5 al

so f

or 1

25:3

00,

25:6

0, 5

:12

A1

6(f)

100

70 3

30

231

2M

1 fo

r 10

070

330

A1 f

or 2

31

6(g)

100

332

143

43.1

2M

1 f

or 33

214

3 o

r 0.

4307

22…

A1 f

or 4

3.1

or b

ette

r


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stio

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umbe

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orki

ngAn

swer

Mar

kN

otes

7(a)

x2=

1 9

4

oe

2M

1 fo

r x2

= 1

9 [

sepa

rate

evi

denc

e of

M1

is r

equi

red]

A1

for

4

oe

7(b)

y5y2

= 7

+ 4

311,

332

oe

2M

1 fo

r y5

y2=

7 +

4 [s

epar

ate

evid

ence

of

M1

is r

equi

red]

A1 f

or

311, 3

32 o

e

Also

acc

ept

2 or

mor

e d.

p. r

ound

ed o

r tr

unca

ted

e.g.

3.6

6, 3

.67

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stio

nN

umbe

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orki

ngAn

swer

Mar

kN

otes

8(a)

(i)

1 pm

1

B1 f

or 1

pm

Acce

pt 1

300

8(a)

(ii)

10 p

m

1B1

for

10p

m

Acce

pt 2

200

8(b)

61

B1 c

ao

8(c)

Rio

de J

anei

ro

1B1

for

Rio

de

Jane

iro

Acce

pt R

io

8(d)

(i)

71

B1 f

or 7

Ac

cept

-7

8(d)

(ii)

51

B1 f

or 5

Ac

cept

-5


Que

stio

nN

umbe

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orki

ngAn

swer

Mar

kN

otes

9 (a

) 86

× 7

2.5

6235

2M

1 fo

r 86

× 7

2.5

A1 c

ao

9 (b

) 87

00 ÷

72.

5 12

02

M1

for

8700

÷ 7

2.5

A1 c

ao

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stio

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umbe

rW

orki

ngAn

swer

Mar

kN

otes

10(i

)y

= 3

1B1

cao

10

(ii)

x =

5 1

B1 c

ao

10(i

ii)x

y1

B1 c

ao

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stio

nN

umbe

rW

orki

ngAn

swer

Mar

kN

otes

11(a

) 1.989.

687.

5703

…

2M

1 fo

r 8.

3, 6

8.89

, 9.

1 or

30.

90…

A1

Acc

ept

if f

irst

5 f

igur

es c

orre

ct

Also

acc

ept

791

051

9,

910

6889

11(b

) 7.

571

B1 f

t fr

om (

a) if

non

-tri

vial

ie (

a) m

ust

have

mor

e th

an 2

d.p

.


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stio

nN

umbe

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orki

ngAn

swer

Mar

kN

otes

12(a

) 51

1B1

for

51

Acce

pt 0

.2,

20%

12

(b)

532

M1

for

frac

tion

wit

h de

nom

inat

or 5

A1 f

or 53

, Ac

cept

0.6

, 60

%

12(c

)15

0 x

“53

”90

2M

1 fo

r 15

0 x

“53

”

A1 f

t fr

om “

53”

Do

not

acce

pt 15

090

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orki

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swer

Mar

kN

otes

13(a

) 28

× 1

5 42

02

M1

for

28 ×

15

A1 c

ao

13(b

) Re

ctan

gle

5.6c

m lo

ng a

nd

3cm

wid

e 2

B2 f

or a

n ac

cura

te s

cale

dra

win

g of

the

rec

tang

le/

Allo

w +

2m

m

B1 f

or e

ithe

r le

ngth

or

wid

th.

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orki

ngAn

swer

Mar

kN

otes

14(a

) (-

3)2

5

324

2M

1 fo

r su

bstn

or

9 or

15

seen

A1

cao

14

(b)

)5(xx

2B2

for

)5

(xxB1

for

fac

tors

whi

ch,

whe

n ex

pand

ed a

nd s

impl

ifie

d, g

ive

two

t

erm

s, o

ne o

f w

hich

is c

orre

ct S

C B1

for

x (5

- x

),x

(x -

5x )


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orki

ngAn

swer

Mar

kN

otes

15(a

) 47

1B1

cao

15

(b)

51 4

65

2M

1 f

or 5

1 4

6, 4

6 5

1 et

c

A1 c

ao

15(c

)(4

63)

(47

6)

(48

3) (

49

5)(5

02)

(51

1)

or

13

8 2

82

144

2

45

100

51 o

r 96

0

“960

” 2

0

483

M1

for

fin

ding

at

leas

t 4

prod

ucts

and

add

ing

M1

(dep

on

1st

M1)

for

div

isio

n by

20

A1 c

ao

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stio

nN

umbe

rW

orki

ngAn

swer

Mar

kN

otes

16(a

)

tran

slat

ion

3 sq

uare

s to

th

e ri

ght

and

1 sq

uare

do

wn

2 B2

for

cor

rect

des

crip

tion

of

the

tran

sfor

mat

ion

B1 f

or t

rans

lati

on.

Acce

pt t

rans

late

,

t

rans

late

d et

c

A

ccep

t ‘a

cros

s’ i

nste

ad o

f ‘t

o th

e

rig

ht’

B1 f

or 3

rig

ht a

nd 1

dow

n or

13

but

not

(3,

1)

Thes

e m

arks

are

in

depe

nden

t bu

t aw

ard

no m

arks

if

answ

er is

not

a s

ingl

e tr

ansf

orm

atio

n

16(b

) ro

tati

on o

f 90

° cl

ockw

ise

abou

t (2

, 1)

3

B3 f

or c

orre

ct d

escr

ipti

on o

f th

e tr

ansf

orm

atio

nB1

for

rot

atio

n

A

ccep

t ro

tate

, ro

tate

d et

c B1

for

90°

clo

ckw

ise

or

90°

or 2

70°

B1 f

or (

2,

1)

Thes

e m

arks

are

in

depe

nden

t bu

t aw

ard

no m

arks

if a

nsw

er is

no

t a

sing

le

tran

sfor

mat

ion


Que

stio

nN

umbe

rW

orki

ngAn

swer

Mar

kN

otes

17(a

)(i)

78

1B1

cao

17

(a)(

ii)

561

B1 c

ao

17(b

) 9

4

n =

8 or

13n

= 8

52

M1

for

9 4

n

= 8

or b

ette

r Al

so a

war

d fo

r 2n =

25 ,

2n = 32

or

25 on

answ

er li

ne

A1 c

ao

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umbe

rW

orki

ngAn

swer

Mar

kN

otes

18(a

) 4

815

12x

x19

4x2

M1

for

at le

ast

3 te

rms

corr

ect

inc

sign

s A1

18(b

) 24

83

2y

yy

2411

2y

y2

M1

for

3 te

rms

corr

ect

or

yy

112

seen

A118

(c)

5p3+

4p2

B2 c

ao B

1 fo

r ei

ther

5p3

or f

or+

4p


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stio

nN

umbe

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orki

ngAn

swer

Mar

kN

otes

19(a

) 60

215.

38 o

r 35.0

=6021

;

35.05.

38

110

3M

1 fo

r 21

5.38

or 1

.833

3… o

r 35.05.

38 o

r 18

3.33

3…

or6021

or

0.35

M1

for

“1.8

333…

” 6

0 or

"

35.0"5.

38

A1 c

ao

19(b

) ×

4.1

9² ×

385

00

= 21

2343

3.41

9 m

³2

120

000

3M

2×

4.19

² ×

3850

0

[M1

for

× (

no w

ith

digi

ts 4

19)2 ×

no

wit

h di

gits

385

]

A1 f

or 2

120

000

or

for

answ

er w

hich

rou

nds

to 2

120

000



Turn over

S39745A©2010 Edexcel Limited.

*S39745A0120*



Total Marks

Paper Reference

MathematicsPaper 2F

Foundation Tier

Sample Assessment MaterialTime: 2 hours

You must have:


KMA0/2F

Instructions



Information


Advice




IGCSE MATHEMATICS 4400


Pythagoras’Theorema2 + b2 = c2




or

opptanadj

adjcoshyp

oppsinhyp


Area of circle = r2



b

a

opp

adj

hyp

b

a

h

lengthsectioncross

r

h

r

c


You must not write on the fomulae page. Anything you do write will gain no credit.




You must write down all the stages in your working.

1 (a) Here is a list of numbers.

999 1999 199 9000 1009

(i) Write these numbers in order of size. Start with the smallest.

(3)

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

(ii) From the list, write down an even number.

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

(iii) From the list, write down a number that is a multiple of 9

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

(b) Here are four cards. Each card has a number on it.

3 4 1 2

The four cards are arranged to make the number 3412 The cards can be re-arranged to make other numbers.

(3)

(i) Write down the largest number that can be made.

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

(ii) Write down the smallest odd number that can be made.

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



2 On the probability scale, mark the following with a cross (x).

(i) The probability that the next baby to be born will be a boy. Label this cross A.

(ii) The probability that the day after Saturday will be Sunday. Label this cross B.

(iii) The probability that a person chosen at random has a birthday in May. Label this cross C.


3 O is the centre of the circle.

The line AB touches the circle at T.

(a) Write down the mathematical name for the line(3)

(i) OT,

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

(ii) CT,

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

(iii) AB.

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

(b) Write down the mathematical name for the shaded region.(1)

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


0 0.5 1

C

A

O

T

B


4 (a) Write the number 3969 in words(1)

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

(b) Write a number in the box so that this is a correct calculation.

(1)

189 = 3969

(c) Write down the value of the 3 in the number 3969(1)

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

(d) Write the number 3969 correct to the nearest 10(1)

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

(e) Write the number 3969 correct to the nearest 100(1)

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

(f) Find the cube root of 3969

(i) Write down all the figures on your calculator display.(2)

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

(ii) Give your answer correct to 3 significant figures.

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



5 This formula gives the cost of hiring a bike for a number of days.

cost in pounds = 4 × number of days + 2

(a) Angus hired a bike for 5 days. Calculate the cost.

(2)

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

(b) Jeevan hired a bike. The cost was £30 Calculate the number of days for which Jeevan hired the bike.

(2)

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



6 (a) What fraction of this shape is shaded?(1)

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

(b) Find a fraction that is equivalent to 49 (1)

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

(c) Here is a list of fractions.

720

310

925

1236

Which fraction in the list is the greatest fraction?(3)

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



7 Chocolate bars cost £1.10 each. Cakes cost £1.25 each.

Joshi buys 2 chocolate bars and 3 cakes. He pays with a £10 note.

Work out how much change he should receive.

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



8 Here are the numbers of points scored by 8 teams in a season.

5 3 14 12 4 3 6 9

(a) Find the mode.(1)

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

(b) Work out the mean.(3)

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

(c) Find the median.(2)

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

(d) The team that scored 4 points was The Cheetahs. Later, The Cheetahs had points taken away because of foul play.

(2)

(i) Will the median increase or decrease or stay the same?

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

(ii) Give your reason.

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

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

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

(e) A team is chosen at random from these 8 teams. Find the probability that this team scored more than 10 points.

(2)

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



9 The diagram shows a triangle drawn on a centimeter squared grid.

(a) Work out the area of the triangle.State the units of your answer.

(3)

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

(b)(2)

On the grid, reflect the triangle in the dotted line.



10 Here is a number machine.

Input Add 3 Multiply by 5 Output

(a) Work out the output when the input is 6(2)

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

(b) Work out the input when the output is 70(2)

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

(c) Work out the input when the output is –85(2)

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

(d) Find an expression, in terms of x, for the output when the input is x.(2)

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



11

In the diagram BCD is a straight line.

(a) Work out the size of angle x.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°

(b) (i) Work out the size of angle y.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°

(ii) Give a reason for your answer to part (b)(i).(2)

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

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


A

B DC

y

x50°

Diagram NOTaccurately drawn


12 Michelle has £4800

She gives 52 of the £4800 to a charity.

(a) How much money does Michelle give to the charity?(2)

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

(b) The charity spends 85% of this money on medicines. How much money does the charity spend on medicines?

(2)

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


13 The diagram shows the lengths, in cm, of the sides of a triangle.

The perimeter of the triangle is 17 cm.

(i) Use this information to write an equation in x.

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

(ii) Solve your equation.

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


x (3x – 5)

(2x + 1)


14 Anji mixes sand and cement in the ratio 7 : 2 by weight. The total weight of the mixture is 27 kg.

Calculate the weight of sand in the mixture.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg


15 Solve 5(x – 4) = 35

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



16 Julian has to work out 6 8 47 62 09

. ..

without using a calculator.

(a) Round each number in Julian’s calculation to one significant figure.(2)

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

(b) Use your rounded numbers to work out an estimate for 6 8 47 62 09

. ..

Give your answer correct to one significant figure.(2)

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

(c) Without using your calculator, explain why your answer to part (b) should be greater than the exact answer.

(2)

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

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

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



17 The diagram shows a wall.

(a) Calculate the area of the wall.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2

(b) 1 litre of paint covers an area of 20 m2. Work out the volume of paint needed to cover the wall. Give your answer in cm3.

(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm3


2 m3 m

6 m



18 Solve the simultaneous equations

y = x + 3y = 7x

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

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



19 (a)

Calculate the value of x. Give your answer correct to 3 significant figures.

(3)

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

(b)

Calculate the length of AB. Give your answer correct to 3 significant figures.

(3)

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


5 cm

29°B

A

C

x°4.2 cm

5.1 cm




20 A bag contains some marbles. The colour of each marble is red or blue or green or yellow.

A marble is taken at random from the bag. The table shows the probability that the marble is red or blue or green.

Colour Probability

Red 0.1

Blue 0.2

Green 0.1

Yellow

(a) Work out the probability that the marble is yellow.(2)

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

(b) Work out the probability that the marble is blue or green.(2)

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

The probability that the marble is made of glass is 0.8

(c) Beryl says “The probability that the marble is green or made of glass is 0.1 + 0.8 = 0.9”

(2)

Is Beryl correct? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Give a reason for your answer.

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

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


PLEASE TURN OVER FOR QUESTION 21


21

Calculate the value of h. Give your answer correct to 3 significant figures.

h = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



4 cm h cm

6 cm



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or

5x

15

oe

2B2

for

5(

x 3

) o

r (x

3)

5

or

5x

15

oe

B1 f

or a

nsw

er x

3

5

B0 f

or a

nsw

er 5

x 3

or

x 1

5 ‘x

=’ s

ubtr

act

B1

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stio

nN

umbe

rW

orki

ngAn

swer

Mar

kN

otes

11(a

) 13

01

B1 c

ao

11(b

)(i)

40

1B1

cao

11

(b)(

ii)

angl

e su

m o

f tr

iang

le

1B1

for

cor

rect

rea

son

Do

not

acce

pt 1

80

(90

+ 5

0)

Que

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swer

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kN

otes

12(a

) 52

x 4

800

1920

2M

1 fo

r 52

x 4

800

A1 c

ao

12(b

) 0.

85 ×

“19

20”

oe

1632

2M

1 0.

85 ×

“19

20”

oe

A1 c

ao


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rW

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ngAn

swer

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kN

otes

13(i

)x

2x

1

3x

5

17

1B1

oe

eg 6

x 4

1

7

13(i

i)6

x 2

1 or

6x

21

0

etc

3.5

oe

2M

1 ft

(i)

if 6

xc

A1 f

or 3

.5 o

e, e

g

621

Que

stio

nN

umbe

rW

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swer

Mar

kN

otes

149

seen

97 2

7 or

7

927 o

e

213

B1 f

or 9

see

n

M1

(dep

B1)

for

97 2

7 or

7

927 o

e

A1 c

ao

Que

stio

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umbe

rW

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swer

Mar

kN

otes

155

x–

20

35

5x

= 55

11

3M

1 fo

r 5

x –

20

35

M1

dep

on 1

st M

1 or

M2

for

x 4

7

A1

(de

pend

ent

on b

oth

M m

arks

)


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otes

16(a

) 250×

7or

7,

50,

2 2

B1 f

or 7

and

2

B1 f

or 5

0

16(b

) 17

520

0 or

100

2

M1

ft f

rom

(a)

, (1

75 s

een,

usi

ng

3or

2)

50or

48()7

or6(,

corr

ectl

y

eval

uate

d)A1

for

200

or

100

(if

no w

orki

ng o

ut u

se f

t fr

om (

a))

16

(c)

Num

erat

or in

crea

sing

or

6.8

and

47.6

incr

easi

ng

deno

min

ator

dec

reas

ing

or 2

.09

decr

easi

ng

(b)

roun

ded

up (

not

roun

ded

to 1

sf)

or

‘175

’ ro

unde

d to

200

2B2

any

tw

o of

the

se

B1 a

ny o

ne o

f th

ese

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nore

oth

er

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swer

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17(a

) 6

×2

)3+

2( o

r

2 6

21

6

1 o

e

152

M1

for

6×

2)3

+2(

or

2 6

21

6

1 o

e

A1 c

ao

17(b

) 2015

100

0 oe

75

03

M1

for

‘2015

’ oe

M1

for

‘2015

’ 1

000

oe

A1 c

ao


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rW

orki

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swer

Mar

kN

otes

18x

3 =

7x

(6

x= 3

oe)

x

= 21

,y

= 3

213

M1

for

x 3

= 7

x oe

or

7(y

– 3)

oe

or 0

= 6

x –

3 oe

6x=

3 o

e [s

epar

ate

evid

ence

for

M1

is r

equi

red]

A1

for

x =

21

A1 f

or y

= 3

21

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stio

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rW

orki

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swer

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kN

otes

19(a

) (t

an u

sed)

tan

xº2.41.5

or

tan

x º 1

.214

285…

. oe

50.5

3M

1 (s

in o

r co

s) a

nd (

(4.

22+

5.1

2)

or 6

.6 u

sed

M1

sin

x =

5.1/

( (

4.2

2+

5.1

2)

or c

osx

= 4.

2/(

(4.

22+

5.1

2)

A1 f

or a

nsw

ers

whi

ch r

ound

to

50.5

19(b

) si

n29

AB/

5 or

A

B/si

n29

5/s

in90

A

B 5

sin2

9

2.42

3M

1 si

n29

= A

B/5

or A

B/si

n29

= 5/

sin9

0 M

1A

B 5

sin2

9

OR

M2

for

AB

(5

2 (

5cos

29)2 )

or 5

cos2

9 t

an29

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or a

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ch r

ound

to

2.42


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20(a

) 1

(0.

1 +

0.2

+ 0.

1)

or 1

0

.4 o

e

0.6

2M

1 or

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in t

able

A1

allo

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tab

le if

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) 0.

2 +

0.1

or

1 (

‘0.6

’ +

0.1)

0.

3 oe

2

M1

0.2

+ 0.

1 or

1

(‘0

.6’

+ 0.

1)

A120

(c)

(P

oss)

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or

mut

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l or

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sn’t

wk

for

B or

Y

{No

or p

oss

or p

oss

yes}

2B2

B1

Can’

t te

ll an

d (N

o or

pos

s)

B1 C

orre

ct r

easo

n on

ly

B0 In

corr

ect

reas

on

B0 U

nqua

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d Ye

s

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ngAn

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otes

2142 +

62 (

= 52

)

(42 +

62 )

or“5

2” o

r 2

13

7.21

3M

1 fo

r 42 +

62 (

= 52

)M

1 de

p on

1st

M1

(42 +

62 ) o

r “5

2” o

r 213

A1 f

or a

nsw

ers

whi

ch r

ound

s to

7.2

1




Total Marks

Paper Reference

Turn over

You must have:


Instructions



Information


Advice


MathematicsPaper 3H

Higher Tier

Sample Assessment MaterialTime: 2 hours KMA0/3H

*S39743A0120*S39743A©2010 Edexcel Limited.



IGCSE MATHEMATICS 4400FORMULA SHEET – HIGHER TIER

Pythagoras’Theorem


or

opptanadj

adjcoshyp

oppsinhyp


Area of circle = r2


b

a

opp

adj

hyp

b

a

h

lengthsectioncross

a2 + b2 = c2




h

r

Volume of cone = r2h

Curved surface area of cone = rl

13

r

l

r

h

Volume of sphere = r3

Surface area of sphere = 4 r2

43

r

In any triangle ABC

Sine rule:

Cosine rule: a2 = b2 + c2 – 2bc cos A

Area of triangle = ab sin C12

sin sin sina b c

A B C

C

ab

c BA

The Quadratic EquationThe solutions of ax2 + bx + c = 0,where a 0, are given by

2 42

b b acxa

c

FORMULA SHEET – HIGHER TIERYou must not write on the fomulae page. Anything you do write will gain no credit.




You must write down all stages in your working.

1 (a) Use your calculator to work out the value of

( . . ). .

3 7 4 62 8 6 3

2

Write down all the figures on your calculator display.(2)

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

(b) Give your answer to part (a) correct to 2 decimal places.(1)

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


2 (a) Work out the value of x2 – 5x when x = –3(2)

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

(b) Factorise x2 – 5x(2)

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



3 Hajra counted the numbers of sweets in 20 packets. The table shows information about her results.

Number of sweets Frequency

46 3

47 6

48 3

49 5

50 2

51 1

Work out the mean number of sweets in the 20 packets.

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



4

(a) Describe fully the single transformation which maps triangle P onto triangle Q.(2)

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

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

(b) Describe fully the single transformation which maps triangle P onto triangle R.(3)

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

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


5

4

3

2

–1–2 1 2 3 4O x

y

P

R

Q1

–1 5 6 87

–2

–3


5 (a) Simplify, leaving your answers in index form,(2)

(i) 75

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

(ii) 59

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

(b) Solve 9 4

82 2 22n×

=(2)

n = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


6 (a) Expand and simplify 3(4x – 5) – 4(2x + 1)(2)

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

(b) Expand and simplify (y + 8)(y + 3)(2)

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

(c) Expand p(5p2 + 4)(2)

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



7 A tunnel is 38.5 km long.

(a) A train travels the 38.5 km in 21 minutes.

Work out the average speed of the train. Give your answer in km/h.

(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . km/h

(b) To make the tunnel, a cylindrical hole 38.5 km long was drilled. The radius of the cylindrical hole was 4.19 m.

Work out the volume of earth, in m3, which was removed to make the hole. Give your answer correct to 3 significant figures.

(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m3



8 (a) Shri invested 4500 dollars. After one year, he received 270 dollars interest. Work out 270 as a percentage of 4500.

(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %

(b) Kareena invested an amount of money at an interest rate of 4.5% per year. After one year, she received 117 dollars interest. Work out the amount of money Kareena invested.

(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dollars

(c) Ravi invested an amount of money at an interest rate of 4% per year. At the end of one year, interest was added to his account and the total

amount in his account was then 3328 dollars. Work out the amount of money Ravi invested.

(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dollars



9 (a) Solve 5x – 4 = 2x + 7(2)

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

(b) Solve 7 24

2 3y y(4)

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



10 Here are five shapes.

Four of the shapes are squares and one of the shapes is a circle. One square is black. Three squares are white. The circle is black. The five shapes are put in a bag.

(a) Jasmine takes a shape at random from the bag 150 times. She replaces the shape each time.

Work out an estimate for the number of times she will take a white square.(3)

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

(b) Alec takes a shape at random from the bag and does not replace it. Bashir then takes a shape at random from the bag.

Work out the probability that

(i) they both take a square,(2)

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

(ii) they take shapes of the same colour.(3)

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



11

A and B are points on a circle, centre O. The lines CA and CB are tangents to the circle. CA = 5.7 cm. CO = 6.9 cm.

(a) Give a reason why angle CAO = 90°.(1)

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

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

(b) Calculate the perimeter of the kite CAOB. Give your answer correct to 3 significant figures.

(5)

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


B

O

AC

6.9 cm

5.7 cm



12 The grouped frequency table gives information about the weights of 60 cows.

Weight (w kg) Frequency

100 < w 200 10

200 < w 300 16

300 < w 400 15

400 < w 500 9

500 < w 600 6

600 < w 700 4

(a) Complete the cumulative frequency table.

(1)

Weight (w kg) Cumulativefrequency

100 < w 200

100 < w 300

100 < w 400

100 < w 500

100 < w 600

100 < w 700


(b) On the grid, draw the cumulative frequency graph for your table.(2)

(c) Use your graph to find an estimate for the number of cows that weighed more than 430 kg. Show your method clearly.

(2)

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



13 Show, by shading on the grid, the region which satisfies all three of these inequalities.

y 5 y 2x y x + 1

Label your region R.


y

6

4

2

O 2 4 6 x

–2

–2


14 (a) Make r the subject of the formula A = r2, where r is positive.(2)

r = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The area of a circle is 14 cm2, correct to 2 significant figures.

(b) (i) Work out the lower bound for the radius of the circle. Write down all the figures on your calculator display.

(2)

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

(ii) Give the radius of the circle to an appropriate degree of accuracy. You must show working to explain how you obtained your answer.

(2)

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



15 The frequency, f kilohertz, of a radio wave is inversely proportional to its wavelength, w metres.

When w = 200, f = 1500

(a) (i) Express f in terms of w.(3)

f = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) On the axes, sketch the graph of f against w.(1)

(b) The wavelength of a radio wave is 1250 m. Calculate its frequency.

(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilohertz


f

O w


16 PQR is a triangle.E is the point on PR such that PR = 3PE.F is the point on QR such that QR = 3QF.

PQ = a, PE = b.

(a) Find, in terms of a and b,

(i) PR(1)

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

(ii) QR(1)

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

(iii) PF(1)

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

(b) Show that EF = kPQ where k is a number.(2)


R

F

QP

Eb

a



17 A curve has equation y xx

2 16

The curve has one turning point.

Find ddyx

and use your answer to find the coordinates of this turning point.

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



18

A solid hemisphere A has a radius of 2.8 cm.

(a) Calculate the total surface area of hemisphere A. Give your answer correct to 3 significant figures.

(3)

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

A larger solid hemisphere B has a volume which is 125 times the volume of hemisphere A.

(b) Calculate the total surface area of hemisphere B. Give your answer correct to 3 significant figures.

(3)

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


PLEASE TURN OVER FOR QUESTION 19

A

2.8 cm




y = 3x – 1

x2 + y2 = 5

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




Sam

ple

Mar

k Sc

hem

e Pa

per

3H

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stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

1(a)

1.989.

68

7.57

03…

2

M1

for

8.3,

68.

89,

9.1

or 3

0.90

…

A1 A

ccep

t if

fir

st 5

fig

ures

cor

rect

Also

acc

ept

791

051

9,

910

6889

1(b)

7.

57

1B1

ft

from

(a)

if n

on-t

rivi

al ie

(a)

mus

t ha

ve m

ore

than

2 d

.p.

Q

uest

ion

Num

ber

Wor

king

An

swer

M

ark

Not

es

2(a)

(-3)

2 5

-

3

24

2M

1 fo

r su

bstn

or

9 or

15

seen

A1

cao

2(

b)

)5(xx

2

M1A

1 fo

r )5

(xx

B1 f

or f

acto

rs w

hich

, w

hen

expa

nded

and

sim

plif

ied,

giv

e tw

o

ter

ms,

one

of

whi

ch is

cor

rect

SC

B1 f

or x

(5 -

x ),

x (x

- 5x

)

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k N

otes

346

3

4

7 6

4

8 3

4

9 5

5

0 2

51

1 o

r

138

282

1

44

245

100

51

or 9

60

“960

” 2

0

48

3M

1 f

or f

indi

ng a

t le

ast

4 pr

oduc

ts a

nd a

ddin

g M

1 (d

ep o

n 1s

t M

1) f

or d

ivis

ion

by 2

0 A1

cao


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r W

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k N

otes

4(a)

tr

ansl

atio

n 3

squa

res

to

the

righ

t an

d 1

squa

re

dow

n

2 B2

for

cor

rect

des

crip

tion

of

tran

sfor

mat

ion

B1 f

or t

rans

lati

on.

Acce

pt t

rans

late

,

t

rans

late

d et

c

A

ccep

t ‘a

cros

s’ i

nste

ad o

f ‘t

o th

e

rig

ht’

B1 f

or 3

rig

ht a

nd 1

dow

n or

13

but

not

(3,

-1)

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e m

arks

are

in

depe

nden

t bu

t aw

ard

no m

arks

if

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er is

not

a s

ingl

e tr

ansf

orm

atio

n

4(b)

ro

tati

on o

f 90

° cl

ockw

ise

abou

t (2

, 1)

3

B3 f

or f

or c

orre

ct d

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ipti

on o

f tr

ansf

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atio

n B1

for

rot

atio

n

A

ccep

t ro

tate

, ro

tate

d et

c B1

for

90°

clo

ckw

ise

or

90°

or 2

70°

B1 f

or (

2,

1)

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e m

arks

are

in

depe

nden

t bu

t aw

ard

no m

arks

if a

nsw

er is

no

t a

sing

le

tran

sfor

mat

ion

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otes

5(a)

(i)

78

1B1

cao

5(

a)(i

i)

56 1

B1 c

ao

5(b)

9 4

n

= 8

or

13

n

= 8

5 2

M1

for

9 4

n

= 8

or

13

n =

8 ,

Also

aw

ard

for

2n = 2

5 , 2n =

32 o

r 25 o

n an

swer

line

A1

cao


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6(a)

48

1512

xx

194x

2

M1

for

at le

ast

3 te

rms

corr

ect

inc

sign

s A1

cao

6(

b)24

83

2y

yy

24

112

yy

2

M1

for

3 te

rms

corr

ect

or

yy

112

seen

A1

cao

6(

c)

5p3 +

4p

2B2

cao

B1

for

eith

er 5

p3 or

for

+ 4p

Q

uest

ion

Num

ber

Wor

king

An

swer

M

ark

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es

7(a)

6021

5.38

or

35.0=

6021;

35.05.

38

110

3M

1 fo

r 21

5.38

or 1

.833

3… o

r 35.05.

38 o

r 18

3.33

3…

or 6021

or

0.35

M1

for

“1.8

333…

” 6

0 or

"

35.0"5.

38

A1 c

ao

7(b)

3850

019.4

2

= 21

2343

3.41

9 m

³ 2

120

000

3M

2

× 4

.19²

× 3

8500

= 2

1234

33.4

19 m

³

M1

for

× (

no w

ith

digi

ts 4

19)2 ×

no

wit

h di

gits

385

A1

for

2 1

20 0

00 o

r fo

r an

swer

whi

ch r

ound

s to

2 1

20 0

00


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otes

8(a)

4500

270

100

6

2M

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0027

0 o

r 0.

06 o

r 45

0047

70 o

r 1.

06

A1 c

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8(b)

117

5.4100

26

00

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or 2

6 se

en

A1 c

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8(c)

04.13328

or 3

328

104

100

32

00

3M

2 fo

r 04.13328

or

3328

10

410

0

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for

104

3328

, 10

4% =

332

8 or

32

seen

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ao

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9 (a

) 5

x 2

x 7

4

311

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32 o

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for

corr

ect

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epar

ate

evid

ence

for

M1

is

requ

ired

] A1

als

o ac

cept

2 o

r m

ore

d.p.

rou

nded

or

trun

cate

d eg

3.6

6, 3

.67

9(b)

4 42

7y

or 7

2

y

= 4(

2y

3)

12

82

7y

y o

r si

mpl

er

5-

10y

- 21 o

e

4M

1 fo

r cl

ear

inte

ntio

n to

mul

tipl

y bo

th s

ides

by

4 or

a m

ulti

ple

of

4.

For

exam

ple,

aw

ard

for

4

427

yor

7

2y

4 ×

2y

3 o

r 8

y 3

or

2y

3

4 o

r 2

y 1

2 M

1 fo

r co

rrec

t ex

pans

ion

of b

rack

ets

(usu

ally

12

8y)

or f

or

corr

ect

rear

rang

emen

t of

cor

rect

ter

ms

eg 8

y 2

y 7

1

2 A1

for

red

ucti

on t

o co

rrec

t eq

uati

on o

f fo

rm a

y =

b (d

epen

dent

on

both

M m

arks

)

A1 f

or

21 o

e (d

epen

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on

all p

revi

ous

mar

ks)


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k N

otes

10(a

) 15

0 x

53

90

3Ac

cept

dec

imal

s

B1 f

or 53

see

n

M1

for

150

x 53

A1 c

ao

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not

acce

pt 15

090

10(b

)(i)

43

×54

2012

or

53 o

e 2

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pt d

ecim

als

M1

for

43×

54

A1 f

or 2012

or

53 o

e

10

(b)(

ii)

42×

53+

41×

52

208or

52 o

e 3

Acce

pt d

ecim

als

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for

41×

52 o

r 42

×53

M1

(dep

) fo

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bot

h ab

ove

prod

ucts

A1

for

208 o

r 52

oe

SC M

1 fo

r 52

×52

or

53×

53

SC M

1 (d

ep)

for

addi

ng b

oth

abov

e pr

oduc

ts


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stio

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ng

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Mar

k N

otes

11(a

)

tang

ent

at a

ny p

oint

of

a ci

rcle

and

the

rad

ius

at

that

poi

nt a

re

perp

endi

cula

r

1B1

for

men

tion

of

tang

ent

and

radi

us o

r lin

e fr

om c

entr

e

11(b

) 6.

92 5

.72 o

r 47

.61

32

.49

or 1

5.12

(6

.92

5.7

2 )

3.88

844…

2

5.7

+ 2

“

3.88

844…

”

19.2

5

M1

for

squa

ring

and

sub

trac

ting

M

1 (d

epen

dent

on

1st

M1)

for

squ

are

root

A1

for

3.8

9 or

bet

ter

M1

for

2 5

.7 +

2

“3.

888.

.” o

nly

A1 f

or 1

9.2

or a

nsw

er w

hich

rou

nds

to 1

9.2

(19.

1768

88…

)

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stio

n N

umbe

r W

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ng

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er

Mar

k N

otes

12(a

)

10,

26,

41,

50,

56,

60

1B1

cao

12

(b)

Poin

ts c

orre

ct

Curv

e or

line

seg

men

ts

Corr

ect

grap

h dr

awn

2B1

+ ½

sq

ft f

rom

sen

sibl

e ta

ble

B1

ft

if 4

or

5 po

ints

cor

rect

or

if p

oint

s ar

e pl

otte

d co

nsis

tent

ly

w

ithi

n ea

ch in

terv

al (

inc

end

poin

ts)

at t

he c

orre

ct h

eigh

t 12

(c)

Use

of

w =

430

on

grap

h Ap

prox

16

2M

1 m

ay b

e sh

own

on g

raph

or

impl

ied

by 4

3, 4

4 or

45

stat

ed

A1 if

M1

scor

ed,

ft f

rom

cum

ulat

ive

freq

uenc

y gr

aph

Q

uest

ion

Num

ber

Wor

king

An

swer

M

ark

Not

es

13

Line

s dr

awn

corr

ectl

y Co

rrec

t re

gion

labe

lled

4B3

for

Lin

es d

raw

n co

rrec

tly

[B1

for

each

cor

rect

line

- ig

nore

ad

diti

onal

line

s]

B1 f

or C

orre

ct r

egio

n la

belle

d R


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stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

14(a

) r2 =

A

A

2

M1

for

r2 =

A

or

r2 = A

A1 Ig

nore

±

14(b

)(i)

5.

13

2.07

296…

2

M1

for

13.5

see

n A1

for

ans

wer

whi

ch r

ound

s to

2.0

73

14(b

)(ii)

5.

14 o

r 2.

1483

6…

2.1

2M

1 fo

r 5.

14 o

r va

lue

whi

ch r

ound

s to

2.1

48 o

r 2.

149

cao

A1 d

ep o

n pr

evio

us 3

mar

ks in

(b)

Q

uest

ion

Num

ber

Wor

king

An

swer

M

ark

Not

es

15(a

)(i)

f

= wk

f

= w

3000

00

3M

1 fo

r f

= wk

, (m

ay b

e im

plie

d by

150

0 =

200k

)

M1

for

1500

= 20

0k

A1 A

lso

awar

d if

ans

wer

is f

= wk

but

k is

eva

luat

ed a

s

300

000

in (

a) o

r (b

) 15

(a)(

ii)

f

w

1B1

for

cor

rect

gra

ph

15(b

) f

= 12

5030

0000

24

0 2

M1

for

subs

titu

tion

in f

= wk

A1 f

t fr

om k


Que

stio

n N

umbe

r W

orki

ng

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er

Mar

k N

otes

16(a

)(i)

3 b

1B1

16

(a)(

ii)

3b

a

1

B1

16(a

)(iii

)

32a

+ b

or a

+ 31

(3b

a)

or 3

b 32

(3b

a)

oe

1B1

16(b

) 32

a

or 32

PQ

or k

32

32a

2B2

for

32a

or 32

PQ o

r k

32un

less

cle

arly

obt

aine

d by

non

-vec

tor

met

hod

B1 f

or c

orre

ct v

ecto

r st

atem

ent

wit

h at

leas

t 3

term

s w

hich

in

clud

es E

F (o

r FE

) in

ter

ms

of c

apit

al le

tter

s an

d/or

a,

b eg

PQ

P

E E

F F

Q

PF

PE

EF

a

b +

EF

FQ

Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

17

xy dd2

x

216 x

“2x

± 216 x

” 0

(2,

12)

4

B1 f

or 2

x

B1 f

or ±

216 x

or

± 16

x2

M1

for

“2x

± 216 x

” 0

A1 c

ao

For

answ

er (

2, 1

2) w

ith

no p

rece

ding

mar

ks s

core

d, a

war

d B0

B0

M1

A1


Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

18(a

) 2

28.2

×4

×21

+8.2

×

73.9

3

M2

for

22

8.2×

4×

21+

8.2×

M1

for

each

item

Al

so a

war

d fo

r va

lues

rou

ndin

g to

24.

6 an

d to

49.

2 or

49.

3 A1

for

73.

9 or

ans

wer

whi

ch r

ound

s to

73.

9 18

(b)

312

5 o

r 5

seen

25

7

3.89

…

1850

3

M1

for

find

ing

the

linea

r sc

ale

fact

or 3

125

or

5 M

1 fo

r 25

(

a)

or f

or

(

2.8

× 5)

2 2

(

2.8

5)2

or f

or s

ubst

itut

ing

r =

2.8

5 in

the

exp

ress

ion

used

in (

a)

A1 f

or 1

850

or f

or a

ny v

alue

in r

ange

184

6.3

847

.5

ft f

rom

25

(a)


Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

195

)13(

22

xx

51

33

92

2x

xx

x

or

51

69

22

xx

x

0

46

102

xx

02

22

5x

x

or

01

25

xx

or

01

410

xx

or

20

196

6 o

r 10

493

or

1049103

52 -x

, 51

2-y

1x

, 2

y

52 -x

, 51

2-y

1x

, 2

y

6M

1 fo

r co

rrec

t su

bsti

tuti

on

B1 (

inde

pend

ent)

for

cor

rect

exp

ansi

on o

r (3

x 1

)2 eve

n if

un

sim

plif

ied

B1 f

or c

orre

ct s

impl

ific

atio

n B1

for

cor

rect

fac

tori

sati

on

or f

or c

orre

ct s

ubst

itut

ion

into

the

qua

drat

ic f

orm

ula

and

corr

ect

eval

uati

on o

f ‘b

2 4

ac’

or f

or u

sing

squ

are

com

plet

ion

corr

ectl

y as

far

as

is in

dica

ted

A1 f

or b

oth

valu

es o

f x

A1 f

or c

ompl

ete,

cor

rect

sol

utio

ns




Total Marks

Paper Reference

Turn over

*S39744A0120*S39744A©2010 Edexcel Limited.

MathematicsPaper 4H

Higher Tier

KMA0/4HSample Assessement MaterialTime: 2 hours

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

Instructions



Information


Advice




IGCSE MATHEMATICS 4400FORMULA SHEET – HIGHER TIER

Pythagoras’Theorem


or

opptanadj

adjcoshyp

oppsinhyp


Area of circle = r2


b

a

opp

adj

hyp

b

a

h

lengthsectioncross

a2 + b2 = c2




h

r

Volume of cone = r2h

Curved surface area of cone = rl

13

r

l

r

h

Volume of sphere = r3

Surface area of sphere = 4 r2

43

r

In any triangle ABC

Sine rule:

Cosine rule: a2 = b2 + c2 – 2bc cos A

Area of triangle = ab sin C12

sin sin sina b c

A B C

C

ab

c BA

The Quadratic EquationThe solutions of ax2 + bx + c = 0,where a 0, are given by

2 42

b b acxa

c

FORMULA SHEET – HIGHER TIERYou must not write on the fomulae page. Anything you do write will gain no credit.




You must write down all the stages in your working.

1 The diagram shows the lengths, in cm, of the sides of a triangle.

The perimeter of the triangle is 17 cm.

(i) Use this information to write an equation in x.(1)

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

(ii) Solve your equation.(2)

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


2 Anji mixes sand and cement in the ratio 7 : 2 by weight. The total weight of the mixture is 27 kg.

Calculate the weight of sand in the mixture.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg


x (3x – 5)

(2x + 1)


3 Solve 5(x – 4) = 35

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


4 Julian has to work out 6 8 47 62 09. ..×

without using a calculator.

(a) Round each number in Julian’s calculation to one significant figure.(2)

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

(b) Use your rounded numbers to work out an estimate for 6 8 47 62 09. ..×

Give your answer correct to one significant figure.

(2)

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

(c) Without using your calculator, explain why your answer to part (b) should be larger than the exact answer.

(2)

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

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

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



5 The diagram shows a wall.

(a) Calculate the area of the wall.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2

(b) 1 litre of paint covers an area of 20 m2. Work out the volume of paint needed to cover the wall. Give your answer in cm3.

(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm3


2 m3 m

6 m




y = x + 3y = 7x

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

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



7 (a)


(3)

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

(b)

Calculate the length of AB. Give your answer correct to 3 significant figures.

(3)

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


x°4.2 cm

5.1 cm

5 cm

29°B

A

C




8 A bag contains some marbles. The colour of each marble is red or blue or green or yellow.

A marble is taken at random from the bag. The table shows the probability that the marble is red or blue or green.

Colour Probability

Red 0.1

Blue 0.2

Green 0.1

Yellow

(a) Work out the probability that the marble is yellow.(2)

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

(b) Work out the probability that the marble is blue or green.(2)

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

The probability that the marble is made of glass is 0.8

(c) Beryl says “The probability that the marble is green or made of glass is 0.1 + 0.8 = 0.9”

Is Beryl correct? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

Give a reason for your answer.

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

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



9

Calculate the value of h. Give your answer correct to 3 significant figures.

h = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


4 cm h cm

6 cm



10 (a)

Find the equation of the straight line that passes through the points (0, 1) and (1, 3).(4)

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

(b) Write down the equation of a line parallel to the line whose equation is y = –2x + 5(1)

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

(c) Write down the coordinates of the point of intersection of the two lines whose equations are y = 3x – 4 and y = –2x – 4

(1)

(. . . . . . . . . . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . . . . . . . . . .)


7

6

5

4

–1–2 1 2 3 x

y

3

–1

–2

2

1

O


11 Here are three similar triangles.

Find the value of

(a) w, (1)

w = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) x,(2)

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

(c) y.(2)

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


56°

94°12 cm

10 cm

6 cm

30°

56°

20 cm

x cm

y cm

8 cm

4 cmw°

Diagrams NOTaccurately drawn


12 Simplify

(a) a aa

3 4

2

×

(2)

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

(b) ( )x 6

(1)

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

(c) 3 16 1

2( )( )xx++ (2)

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



13 Here are the marks scored in a maths test by the students in two classes.

Class A 2 13 15 16 4 6 19 10 11 4 5 15 4 16 6

Class B 12 11 2 5 19 14 6 6 10 14 9

(a) Work out the interquartile range of the marks for each class.(4)

Class A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Class B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Use your answers to give one comparison between the marks of Class A and the marks of Class B.

(1)

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

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


14 Solve 5 71

1xx

x

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



15 There are 35 students in a group. 18 students play hockey. 12 students play both hockey and tennis. 15 students play neither hockey nor tennis.

Find the number of students who play tennis.

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


16 A triangle has sides of length 5 cm, 6 cm and 9 cm.


x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


6 cm5 cm

9 cm

x°Diagram NOTaccurately drawn


17 The functions f and g are defined as follows.

f ( )xx

12

g( )x x 1

(a) (i) State which value of x cannot be included in the domain of f.(1)

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

(ii) State which values of x cannot be included in the domain of g.(2)

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

(b) Calculate fg(10)(3)

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

(c) Express the inverse function g–1 in the form g–1(x) = ......(4)

g–1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



18 A fair, 6-sided dice has faces numbered 1, 2, 3, 4, 5 and 6 When the dice is thrown, the number facing up is the score. The dice is thrown three times.

(a) Calculate the probability that the total score is 18(2)

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

(b) Calculate the probability that the score on the third throw is exactly double the total of the scores on the first two throws.

(4)

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



19 (a) Calculate the area of an equilateral triangle of side 5 cm. Give your answer correct to 3 significant figures.

(2)

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

(b) The diagram shows two overlapping circles. The centre of each circle lies on the circumference of the other circle. The radius of each circle is 5 cm. The distance between the centres is 5 cm.

Calculate the area of the shaded region. Give your answer correct to 3 significant figures.

(3)

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


5 cm 5 cm

5 cm

5 cm 5 cm

5 cm




20 The histogram shows information about the heights, h metres, of some trees.

The number of trees with heights in the class 2 < h 3 is 20

Find the number of trees with heights in the class

(a) (i) 4 < h 8 (2)

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

(ii) 3 < h 4

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

(b) Find an estimate for the number of trees with heights in the interval 2.5 < h 3.5(1)

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


Frequencydensity

Height (m)

O 1 2 3 4 5 6 7 8 9


21 (a) Factorise 16x2 – 1(1)

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

(b) Hence express as the product of its prime factors

(i) 1599(3)

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

(ii) 1.599 106 (2)

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




BLANK PAGE


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or

impl

ied

y =

2x

1

4

M1

eg

01

13

not

13

A1fo

r 2

B2 f

t fo

r y

= ‘2

’x

1

(B1f

t fo

r ju

st ‘

2’x

1 o

r y

= x

1 (

m 2

)) (N

o w

orki

ng,

answ

er o

f 2

x 1

: M

1A1

B1)

10(b

)

y =

2x

± c

1

B1

y

2x

± an

y no

. (n

ot 5

) or

lett

er o

r y

2

x

10

(c)

(0

, 4)

1

B1

Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

11(a

)

56

1B1

11

(b)

12620x

or

84 o

e 10

or

10.0

…

2M

1 or

x/s

in30

= 2

0/si

n(18

0 3

0 5

6)

A1

11(c

)64

=10y

or

128 o

e 6.

6 to

6.7

incl

oe

2M

1 or

y=

(42

82

2

4

8

cos

‘56’

)

or

y/s

in56

= 8

/sin

(180

3

0 5

6)

A1 (

a)(b

): f

t (a

) M

-mks

onl

y


Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

12(a

) 27 aa

or

4 aa

or

23

aa

5 a

2M

1 A1

12(b

)

3 x

1B1

12

(c)

Corr

ectl

y ca

ncel

nu

mbe

rs o

r (x

+ 1

)

1 / 2(x

+ 1

) or

0.5

(x+

1)

or

212

or

2

1x

x o

r eq

uiv

2M

1 eg

21 o

r 0.

5 or

den

om =

2

or

6)1

(3x

or

63

3x o

r )1

(xkk

1

A1 N

ot IS

W

Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

13(a

) At

tem

pt a

rran

ge o

ne

set

in o

rder

St

ate

or in

dica

te

corr

ect

15 a

nd 4

or

14

and

6

Clas

s A:

11

Clas

s B:

8 4

M1

M1

NB:

IQR

for

B =

8, c

heck

wor

king

A1

A1

13(b

)

A m

ore

spre

ad o

r gr

eate

r di

sper

sion

or

less

con

sist

ent

than

B

1B1

(B1

if c

onsi

sten

t w

ith

(a).

Igno

re o

ther

.)

Not

: gr

eate

r “r

ange

” or

“di

ffer

ence

”

or “

mor

e co

nsta

nt”

or “

grea

ter

IQR”

or

“gre

ater

var

ianc

e”


Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

145

x 7

= x

2 1

or 5

x 7

=

( x 1

)( x

1

) x2

5x

6 =

0

(x 2

)( x

3

) (=

0)

or

26

4)5

(5

2

x =

2 or

3

4M

1 c

ondo

ne 5

x 7

= x

1

× x

1

M

1 a

llow

dif

fere

nt o

rder

wit

h =

0 M

1 (

x 2

.5)2 +

6

6.2

5 A1

(d

epen

dent

on

all o

ther

M m

arks

)

Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

152

over

lapp

ing

circ

les,

12

in o

verl

ap

6 in

H o

nly

2 in

T o

nly

14

4M

1 M

1 or

6 p

lay

H o

nly

M2

M1

or 2

0 6

, 6

12

x 2

0, 2

0 18

, 35

3

3: M

3 A1

an

s 2:

M3A

0 Q

uest

ion

Num

ber

Wor

king

An

swer

M

ark

Not

es

1692 +

52

2 ×

5 ×

9 ×

co

sx

62

90co

sx

70

or

90

cos

x

70

(cos

x 70

/ 90)

38.9

3

M1

for

92 + 5

2 2

× 5

× 9

× c

osx

62

M1

for

90co

sx

70

or

90co

sx

70

, (c

osx

70/ 9

0)

OR

M2

for

95

26

59

cos

22

2

x

A1 f

or a

nsw

ers

whi

ch r

ound

to

38.9


Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

17(a

)(i)

2 1

B1 o

r 2-

x o

r 2-

x

17(a

)(ii)

x <

1 2

B2 B

1 fo

r x

< 1

or 0

, 1,

2,

3…

17

(b)

9 o

r (1

0 1

) 291

)(x

fg

51 o

r 0.

2

3M

1 fo

r 9

or

(10

1)

M1

for

211

x

A1 ig

nore

ans

= -

1 17

(c)

)1(x

y 2 y=

x 1

x2 y

1

xg

1

)1(

2 xoe

4

M1

1x

y (

y=

)

M1d

ep

1y

x (

x=..

) M

1

2 x

1

y

A1

[SC

xg

1

21

x:

B1]


Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

18(a

) 1 / 6

× 1 / 6

× 1 / 6

al

one

21

61 o

r 0.

0046

…

2M

1 0.

173 o

r 0.

163 o

r be

tter

. N

ot

kA1

18

(b)

1, 1

, 4

or 1

, 2,

6 o

r

2, 1

, 6

seen

or

impl

ied

1, 1

, 4

and

1, 2

, 6(

or 2

, 1,

6)

seen

or

impl

ied

3×

) 61 (3

721 o

r 21

63 o

r 0.

014

or

bett

er

4M

1 ie

one

rou

te

M1

ie t

wo

rout

es in

cl 1

, 1,

4

M1

ie t

hree

rou

tes

and

corr

ect

exp’

n A1

2

×) 61 (3

or

1081

, no

wor

king

: M

0A0

Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

19(a

) ×

5×

5×

21si

n60

10.8

2

M1

1 / 2 ×

5 ×

(

2 5(5 / 2

)2 ) o

r 1 / 2

×

5 ×

4.33

A1

for

ans

wer

s w

hich

rou

nd t

o 10

.8 [

M1A

O f

or

4)3

25(]

19(b

) se

ct =

1 / 6

52

or

13.1

“1

0.8”

2

(1 / 6

5

2 “

10.8

”)

or “

10.8

” 2

2

.26

or 2

1 / 6

5

2 10

.8”

15.4

3

M1

for

sect

= 1 / 6

5

2 o

r 13

.1

M1

for

+ 2

(sec

t

) or

2 ×

sec

t

(al

low

eg

= 1 / 2

5

5

) A1

for

ans

wer

s w

hich

rou

nd t

o 15

.4


Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

20(a

)(i)

20

1B1

cao

20(a

)(ii)

30

1B1

cao

20

(b)

25

1

B1 c

ao

Que

stio

n N

umbe

r W

orki

ng

Answ

er

Mar

k N

otes

21(a

)

(4x

– 1)

(4x

+ 1)

1B1

cao

21(b

)(i)

16

1

02

1 s

een

or

impl

ied

(4

10

1)

(4

1

0 1

) or

39

41

3 1

3 4

1 3

M2

for

fact

ors

3, 1

3, 4

1 (o

r M

1 fo

r 39

, 41

or

13,

123)

A1

cao

21(b

)(ii)

15

99

103

or 1

599

100

0 ‘3

1

3 4

1’

23

53 oe

2

M1

or t

ree

incl

udin

g 10

00 o

r 10

and

100

A1

for

‘3

13

41’

2

3 5

3 oe

f

t (i

) 2

3 5

3

Edexcel, a Pearson company, is the UK's largest awarding body, offering academic and vocational qualifications and testing to more than 25,000 schools, colleges, employers and other places of learning in the UK and in over 100 countries worldwide. Qualifications include GCSE, AS and A Level, NVQ and our BTEC suite of vocational qualifications from entry level to BTEC Higher National Diplomas, recognised by employers and higher education institutions worldwide. We deliver 9.4 million exam scripts each year, with more than 90% of exam papers marked onscreen annually. As part of Pearson, Edexcel continues to invest in cutting-edge technology that has revolutionised the examinations and assessment system. This includes the ability to provide detailed performance data to teachers and students which help to raise attainment.

AcknowledgementsThis document has been produced by Edexcel on the basis of consultation with teachers, examiners, consultants and other interested parties. Edexcel would like to thank all those who contributed their time and expertise to its development.

References to third-party material made in this document are made in good faith. Edexcel does not endorse, approve or accept responsibility for the content of materials, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)

Publications code Authorised by Roger Beard Prepared by Sharon Wood Publications code UG025980 All the material in this publication is copyright © Edexcel Limited 2011

Edexcel, a Pearson company, is the UK's largest awarding body, offering academic and vocational qualifications and testing to more than 25,000 schools, colleges, employers and other places of learning in the UK and in over 100 countries worldwide. Qualifications include GCSE, AS and A Level, NVQ and our BTEC suite of vocational qualifications from entry level to BTEC Higher National Diplomas, recognised by employers and higher education institutions worldwide. We deliver 9.4 million exam scripts each year, with more than 90% of exam papers marked onscreen annually. As part of Pearson, Edexcel continues to invest in cutting-edge technology that has revolutionised the examinations and assessment system. This includes the ability to provide detailed performance data to teachers and students which help to raise attainment.

AcknowledgementsThis document has been produced by Edexcel on the basis of consultation with teachers, examiners, consultants and other interested parties. Edexcel would like to thank all those who contributed their time and expertise to its development.

References to third-party material made in this document are made in good faith. Edexcel does not endorse, approve or accept responsibility for the content of materials, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)

Authorised by Roger Beard Prepared by Sharon Wood Publications code UG025980 All the material in this publication is copyright © Edexcel Limited 2011

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