GCSE (9-1) Mathematics - MathsGeeksmathsgeeks.co.uk/allpapers/GCSE/Edexcel/9-1EdexcelSet2.pdf · GCSE (9-1) Mathematics ... P v 1v 2 91 i i i 2 2015 i ii 2015 4 7 Ignoring subsequent

GCSE (9-1) Mathematics

SPECIMEN PAPERS SET 2Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1)

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics -Specimen Papers Set 2 - September 2015 © Pearson Education Limited 2015

ii

Contents

Introduction 1

General marking guidance 3

Paper 1F – specimen paper and mark scheme 7



Paper 1H – specimen paper and mark scheme 97



References to third party materials in these specimen papers are made in good faith.

Pearson 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.)

All information in this document is correct at time of publication.


iii


iv

Introduction

These specimen papers have been produced to complement the sample assessment materials for Pearson Edexcel Level 1/ Level 2 GCSE (9-1) in Mathematics and are designed to provide extra practice for your students. The specimen papers are part of a suite of support materials offered by Pearson.

The specimen papers do not form part of the accredited materials for this qualification.


11Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics -Specimen Papers Set 2 - September 2015 © Pearson Education Limited 2015


22 Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics -Specimen Papers Set 2 - September 2015 © Pearson Education Limited 2015



General marking guidance These notes offer general guidance, but the specific notes for examiners appertaining to individual questions take precedence. 1 All candidates must receive the same treatment. Examiners must mark the last

candidate in exactly the same way as they mark the first.

Where some judgement is required, mark schemes will provide the principles by which marks will be awarded; exemplification/indicative content will not be exhaustive.

2 All the marks on the mark scheme are designed to be awarded; mark schemes

should be applied positively. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme. If there is a wrong answer (or no answer) indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme.

Questions where working is not required: In general, the correct answer should be given full marks. Questions that specifically require working: In general, candidates who do not show working on this type of question will get no marks – full details will be given in the mark scheme for each individual question.

3 Crossed out work

This should be marked unless the candidate has replaced it with an alternative response.

4 Choice of method If there is a choice of methods shown, mark the method that leads to the answer given on the answer line.

If no answer appears on the answer line, mark both methods then award the lower number of marks.

5 Incorrect method

If it is clear from the working that the “correct” answer has been obtained from incorrect working, award 0 marks. Send the response to review for your Team Leader to check.

6 Follow through marks

Follow through marks which involve a single stage calculation can be awarded without working as you can check the answer, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given.



7 Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question or its context. (eg. an incorrectly cancelled fraction when the unsimplified fraction would gain full marks). It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect (eg. incorrect algebraic simplification).

8 Probability

Probability answers must be given as a fraction, percentage or decimal. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability answer is given on the answer line using both incorrect and correct notation, award the marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer.

9 Linear equations

Unless indicated otherwise in the mark scheme, full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously identified in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded (embedded answers).

10 Range of answers

Unless otherwise stated, when an answer is given as a range (e.g 3.5 – 4.2) then this is inclusive of the end points (e.g 3.5, 4.2) and all numbers within the range.



Guidance on the use of abbreviations within this mark scheme

M method mark awarded for a correct method or partial method P process mark awarded for a correct process as part of a problem solving question A accuracy mark (awarded after a correct method or process; if no method or

process is seen then full marks for the question are implied but see individual mark schemes for more details)

C communication mark B unconditional accuracy mark (no method needed) oe or equivalent cao correct answer only ft follow through (when appropriate as per mark scheme) sc special case dep dependent (on a previous mark) indep independent awrt answer which rounds to isw ignore subsequent working



Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper Reference

Turn over

S50155A©2015 Pearson Education Ltd.

6/6/4/

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MathematicsPaper 1 (Non-Calculator)

Foundation TierSpecimen Papers Set 2

Time: 1 hour 30 minutes 1MA1/1FYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser.

Instructions

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

– there may be more space than you need.• Calculators may not be used.• Diagrams are NOT accurately drawn, unless otherwise indicated.• You must show all your working out.

Information

• The total mark for this paper is 80• 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.• Keep an eye on the time.• Try to answer every question.• Check your answers if you have time at the end.

Pearson Edexcel Level 1/Level 2 GCSE (9 - 1)



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Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1 Find 10% of £320

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

(Total for Question 1 is 1 mark)

2 Write 0.8 as a percentage.

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


3 (a) Work out 84 ÷ 3

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

(1)

(b) Work out 0.17 × 6000

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

(1)

(c)Workout(−2)3

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

(1)

(Total for Question 3 is 3 marks)

4 Here is a square-based pyramid.

(i) How many faces does the pyramid have?

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

(ii) How many edges does the pyramid have?

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




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1 Find 10% of £320

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


2 Write 0.8 as a percentage.

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


3 (a) Work out 84 ÷ 3

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

(1)

(b) Work out 0.17 × 6000

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

(1)

(c)Workout(−2)3

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

(1)


4 Here is a square-based pyramid.

(i) How many faces does the pyramid have?

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

(ii) How many edges does the pyramid have?

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


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5

6

5

4

3

2

1

O

–1

–2

–3

–4

–6 –5 –4 –3 –2 –1 1 2 3 4 5 6

A

B

x

y

(a) Write down the coordinates of point B.

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . .)(1)

(b) Find the coordinates of the midpoint of AB.

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . .)(1)

(c) On the grid, draw the line with equation y=−3(1)




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6 Here are the instructions for making a drink.

Add 100 ml of juiceto 2 litres of water

Dev uses 5 litres of water to make the drink.

How much drink has he made?

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


7 In a box there are three types of chocolates.

There are 6 plain chocolates, 8 milk chocolates and 10 white chocolates.

Ben takes at random a chocolate from the box.

(a) Write down the probability that Ben takes a plain chocolate.

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

(2)

Deon takes 2 chocolates from the box.

(b) Write down all the possible combinations of types of chocolates that Deon can take.

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

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(2)




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6 Here are the instructions for making a drink.

Add 100 ml of juiceto 2 litres of water

Dev uses 5 litres of water to make the drink.

How much drink has he made?

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


7 In a box there are three types of chocolates.

There are 6 plain chocolates, 8 milk chocolates and 10 white chocolates.

Ben takes at random a chocolate from the box.

(a) Write down the probability that Ben takes a plain chocolate.

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

(2)

Deon takes 2 chocolates from the box.

(b) Write down all the possible combinations of types of chocolates that Deon can take.

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

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(2)


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8 8 identical pens cost £12 Work out the cost of 10 of these pens.

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


9 Here are five fractions.

28

1040

1248

524

2080

One of these fractions is not equivalent to 14

(a) Write down this fraction.

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

(1)

(b) Work out 27

114

+

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

(2)

(c) Work out 45

310

÷

Give your answer in its simplest form.

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

(2)




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10 (a) Solve 3x + 7 = 1

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

(2)

(b) f = 6 g = 5

Work out the value of 3f – 2g

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

(2)


11 Write down three different multiples of 4 that add up to 40

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




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10 (a) Solve 3x + 7 = 1

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

(2)

(b) f = 6 g = 5

Work out the value of 3f – 2g

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

(2)


11 Write down three different multiples of 4 that add up to 40

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


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12 Helen has 80 books to sell.

Each book is Fiction or Non-fiction. The ratio of the number of Fiction books to the number of Non-fiction books is 3:1

Each book has a normal price of £10 Helen reduces the price of all the Non-fiction books.

Non-fiction

All books normal price

Helen sells all 80 books.

Work out the total amount of money Helen will receive.

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


13 Ryan and Carl each get paid a basic pay of £60 per day.

One day, Ryan also gets a bonus of 25% of his basic pay. Carl also gets £20 in tips from customers.

Work out the difference between the total amounts of money that Ryan and Carl each get.

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


All books½ price



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14 Some people were asked if they liked swimming or cycling or running.

The table shows the results for the males and the results for the females.

Swimming Cycling Running

Male 2 6 4

Female 8 5 5

(a) On the grid, draw a bar chart to show this information.

(4)

(b) Work out the percentage of the 30 people that are female.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %(2)




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14 Some people were asked if they liked swimming or cycling or running.

The table shows the results for the males and the results for the females.

Swimming Cycling Running

Male 2 6 4

Female 8 5 5

(a) On the grid, draw a bar chart to show this information.

(4)

(b) Work out the percentage of the 30 people that are female.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %(2)


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15 The table shows information about the ages of all the people at a party.

Age (years) Frequency

11−20 6

21−30 16

31−40 10

41−50 8

(a) Work out the total number of these people who were aged 40 or less.

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

(1)

Andy says that the range of ages is 39 years because 50 – 11 = 39

(b) The range may not be 39 years. Explain why.

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

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(1)




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16 The diagram shows a quadrilateral ABCD.

120° 57°B

D

A

C

Is AB parallel to DC? You must give your reasoning.


17 Irena sells ice creams. One day she sells 80 ice creams. The next day she sells 108 ice creams.

Work out the percentage increase in the number of ice creams she sells.

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




10

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16 The diagram shows a quadrilateral ABCD.

120° 57°B

D

A

C

Is AB parallel to DC? You must give your reasoning.


17 Irena sells ice creams. One day she sells 80 ice creams. The next day she sells 108 ice creams.

Work out the percentage increase in the number of ice creams she sells.

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


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18 Dimitar has 20 sweets. Pip also has 20 sweets.

Dimitar gives Pip x sweets.

Dimitar then eats 5 of his sweets. Pip then eats half of her sweets.

Write expressions for the number of sweets Dimitar and Pip now have.

Dimitar .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pip .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


19 (a) Factorise y2 + 27y

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

(1)

(b) Simplify (t3)2

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

(1)

(c) Simplify ww

9

4

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

(1)




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20 The diagram shows a square with perimeter 16 cm.

3 cm

2 cm

Work out the proportion of the area inside the square that is shaded.

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




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3 cm

2 cm


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21 David has designed a game. He uses a fair 6-sided dice and a fair 5-sided spinner. The dice is numbered 1 to 6 The spinner is numbered 1 to 5

Each player rolls the dice once and spins the spinner once. A player can win £5 or win £2

Win £2

roll a 1or

spin a 1or

both

Win £5

roll a 5and

spin a 5

David expects 30 people will play his game. Each person will pay David £1 to play the game.

(a) Work out how much profit David can expect to make.

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

(4)

(b) Give a reason why David’s actual profit may be different to the profit he expects to make.

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

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

(1)




14

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22 Triangle ABC has perimeter 20 cm.

AB = 7 cm. BC = 4 cm.

By calculation, deduce whether triangle ABC is a right-angled triangle.


23 One sheet of A3 card has area 18

m2.

The card has a mass of 160 g per m2.

Work out the total mass of 25 sheets of A3 card.

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




14

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AB = 7 cm. BC = 4 cm.




m2.



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


15

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24 Here are the first five terms of a sequence.

2 8 18 32 50

(a) Find the next term of this sequence.

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

(1)

The nth term of a different sequence is 3n2 – 10

(b) Work out the 5th term of this sequence.

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

(1)


25 Write 504 as a product of powers of its prime factors.

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


TOTAL FOR PAPER IS 80 MARKS



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Total Marks

Paper Reference

Turn over


6/6/4/

*S50157A0128*

Mathematics Paper 2 (Calculator)


Time: 1 hour 30 minutes 1MA1/2FYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator.

Instructions


– there may be more space than you need.• Calculators may be used.• If your calculator does not have a π button, take the value of π to be 3.142

unless the question instructs otherwise.• Diagrams are NOT accurately drawn, unless otherwise indicated.• You must show all your working out.

Information



Advice







Total Marks

Paper Reference

Turn over


6/6/4/

*S50157A0128*




Instructions




Information



Advice





3


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5Living to 100 years old

1 in 3 babies born last year

are expected to live to 100 years old

720 000 babies were born last year.

How many of these babies are expected to live to 100 years old?

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


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1 Write 6819 to the nearest 1000

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


2 Write these temperatures in order. Start with the lowest temperature.

7°C –2°C 10°C –5°C 3°C

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


3 Write 0.075 as a fraction. Give your fraction in its simplest form.

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


4 Find the value of 54

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




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5Living to 100 years old

1 in 3 babies born last year

are expected to live to 100 years old

720 000 babies were born last year.

How many of these babies are expected to live to 100 years old?

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


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1 Write 6819 to the nearest 1000

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


2 Write these temperatures in order. Start with the lowest temperature.

7°C –2°C 10°C –5°C 3°C

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


3 Write 0.075 as a fraction. Give your fraction in its simplest form.

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


4 Find the value of 54

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




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7 Tracy buys

2 coffees at £1.10 each 3 teas at 95p each 5 sandwiches at £2.15 each

Tracy shares the total cost equally between 5 people.

How much does each person pay?

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


4

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6 Here is part of a train timetable from Swindon to London.

Swindon to London

Swindon 06 10 06 27 06 41 06 58 07 01 07 17 07 28

Didcot 06 27 06 45 06 58 – 07 18 – 07 45

Reading 06 41 06 59 07 13 07 28 07 33 07 43 08 00

London 07 16 07 32 07 44 08 02 08 07 08 14 08 33

(a) How long should the 06 58 train from Swindon take to get to London?

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

(1)

Clare says,

“All these trains take more than one hour to get from Swindon to London.”

(b) Is Clare correct? You must give a reason for your answer.

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7 Tracy buys

2 coffees at £1.10 each 3 teas at 95p each 5 sandwiches at £2.15 each

Tracy shares the total cost equally between 5 people.

How much does each person pay?

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


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6 Here is part of a train timetable from Swindon to London.

Swindon to London

Swindon 06 10 06 27 06 41 06 58 07 01 07 17 07 28

Didcot 06 27 06 45 06 58 – 07 18 – 07 45

Reading 06 41 06 59 07 13 07 28 07 33 07 43 08 00

London 07 16 07 32 07 44 08 02 08 07 08 14 08 33

(a) How long should the 06 58 train from Swindon take to get to London?

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

(1)

Clare says,

“All these trains take more than one hour to get from Swindon to London.”

(b) Is Clare correct? You must give a reason for your answer.

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Pete also carried out a survey to find out the type of fruit people like best. He asked 30 people which type of fruit they like best.

He drew this pie chart for his results.

banana

Diagram accurately drawn

orangeapple

A smaller proportion of people like bananas best in Pete’s survey than in Rachel’s survey.

(c) Explain how Pete’s pie chart and Rachel’s table show this.

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(2)


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8 Rachel carried out a survey of 10 people to find out the type of fruit they like best.

The table gives information about her results.

Type of fruit Number of people

apple 2

banana 5

orange 3

(a) Which type of fruit is the mode?

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

(1)

In Rachel’s survey, 2 out of 10 people like apples best.

(b) Write 2 out of 10 as a percentage.

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Pete also carried out a survey to find out the type of fruit people like best. He asked 30 people which type of fruit they like best.

He drew this pie chart for his results.

banana

Diagram accurately drawn

orangeapple

A smaller proportion of people like bananas best in Pete’s survey than in Rachel’s survey.

(c) Explain how Pete’s pie chart and Rachel’s table show this.

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(2)


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8 Rachel carried out a survey of 10 people to find out the type of fruit they like best.

The table gives information about her results.

Type of fruit Number of people

apple 2

banana 5

orange 3

(a) Which type of fruit is the mode?

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

(1)

In Rachel’s survey, 2 out of 10 people like apples best.

(b) Write 2 out of 10 as a percentage.

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



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10 Karol ran in a race.

The graph shows her speed, in metres per second, t seconds after the start of the race.

(a) Write down Karol’s speed 3 seconds after the start of the race.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .m/s(1)

(b) Write down Karol’s greatest speed.

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There were two times when Karol’s speed was 9 m/s.

(c) Write down these two times.

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0 2 4 6 8 10Time (t seconds)

Speed (m/s)

10

8

6

4

2

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9 The smallest angle of a triangle is 25° The triangle is enlarged by scale factor 3

Ben says,

“The smallest angle of the enlarged triangle is 75° because 25 × 3 = 75”

Is Ben right? Explain your answer.

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10 Karol ran in a race.


(a) Write down Karol’s speed 3 seconds after the start of the race.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .m/s(1)

(b) Write down Karol’s greatest speed.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .m/s(1)

There were two times when Karol’s speed was 9 m/s.

(c) Write down these two times.

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Speed (m/s)

10

8

6

4

2

0

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9 The smallest angle of a triangle is 25° The triangle is enlarged by scale factor 3

Ben says,

“The smallest angle of the enlarged triangle is 75° because 25 × 3 = 75”

Is Ben right? Explain your answer.

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12 Martin has 8 pints of soup in a pan. He also has 24 soup bowls. He puts 0.3 pints of soup into each bowl.

How much soup has Martin left over?

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13 Abi invests £500 for 4 years in a bank account. The account pays simple interest at a rate of 2.3% per year.

Work out the total amount of interest Abi has got at the end of 4 years.

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


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11 The first three terms of a number pattern are 1 2 4

Hester says the first five terms of this number pattern are 1 2 4 8 16

(a) Write down the rule Hester could have used to get the 4th and 5th terms.

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(1)

(b) Write down the 6th term of Hester’s number pattern.

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(1)

Jack uses a different rule.

He says the first six terms of the number pattern are 1 2 4 7 11 16

(c) Write down the 7th and 8th terms of Jack’s number pattern.

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12 Martin has 8 pints of soup in a pan. He also has 24 soup bowls. He puts 0.3 pints of soup into each bowl.

How much soup has Martin left over?

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13 Abi invests £500 for 4 years in a bank account. The account pays simple interest at a rate of 2.3% per year.

Work out the total amount of interest Abi has got at the end of 4 years.

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


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11 The first three terms of a number pattern are 1 2 4

Hester says the first five terms of this number pattern are 1 2 4 8 16

(a) Write down the rule Hester could have used to get the 4th and 5th terms.

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(1)

(b) Write down the 6th term of Hester’s number pattern.

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(1)

Jack uses a different rule.

He says the first six terms of the number pattern are 1 2 4 7 11 16

(c) Write down the 7th and 8th terms of Jack’s number pattern.

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(1)




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Turn over

15 Here is a list of ingredients for making chocolate mousse for 2 people.

Chocolate moussefor 2 people

40 grams sugar110 grams dark chocolate 2 eggs

14

teaspoon lemon juice

Ellie has 250 grams of sugar and 550 grams of dark chocolate. She assumes that she has plenty of lemon juice and plenty of eggs.

(a) What is the greatest number of people Ellie can make chocolate mousse for? You must justify your answer.

(3)

Ellie only has 6 eggs.

(b) What effect would this have on the greatest number of people Ellie can make chocolate mousse for?

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(1)


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14 The graph shows the cost of using a mobile phone for one month for different numbers of minutes of calls made.

The cost includes a fixed rental charge of £20 and a charge for each minute of calls made.

Work out the charge for each minute of calls made.

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0 100 200 300 400 500Number of minutes

Cost (£)

40

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Turn over

15 Here is a list of ingredients for making chocolate mousse for 2 people.

Chocolate moussefor 2 people

40 grams sugar110 grams dark chocolate 2 eggs

14

teaspoon lemon juice

Ellie has 250 grams of sugar and 550 grams of dark chocolate. She assumes that she has plenty of lemon juice and plenty of eggs.

(a) What is the greatest number of people Ellie can make chocolate mousse for? You must justify your answer.

(3)

Ellie only has 6 eggs.

(b) What effect would this have on the greatest number of people Ellie can make chocolate mousse for?

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(1)


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14 The graph shows the cost of using a mobile phone for one month for different numbers of minutes of calls made.

The cost includes a fixed rental charge of £20 and a charge for each minute of calls made.

Work out the charge for each minute of calls made.

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0 100 200 300 400 500Number of minutes

Cost (£)

40

30

20

10

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18 There are 64 cards in a pack. Each card is either red or black. The ratio of the number of red cards to the number of black cards is 1 : 1

8 red cards are removed from the pack.

Find the ratio of the number of red cards now in the pack to the number of black cards now in the pack.


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16 A sprinter runs a distance of 200 metres in 25 seconds.

Work out the average speed of the sprinter.

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17 (a) Simplify 7x + 2y – 3x + 4y

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(2)

(b) Factorise 10x – 15

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(1)

(c) Solve 5p = 3p + 8

p = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)




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18 There are 64 cards in a pack. Each card is either red or black. The ratio of the number of red cards to the number of black cards is 1 : 1

8 red cards are removed from the pack.

Find the ratio of the number of red cards now in the pack to the number of black cards now in the pack.


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16 A sprinter runs a distance of 200 metres in 25 seconds.

Work out the average speed of the sprinter.

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17 (a) Simplify 7x + 2y – 3x + 4y

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(2)

(b) Factorise 10x – 15

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(1)

(c) Solve 5p = 3p + 8

p = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)




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(ii) a score of 5 or more.

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(2)


20 Water flows through a pipe at a rate of 20 gallons per minute.

1 gallon = 4.55 litres.

Change 20 gallons per minute to litres per second. Give your answer correct to 3 significant figures.

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19 Here are a 4-sided spinner and a 5-sided spinner.

The spinners are fair.

2 1

4

3

2 43

51

Jeff is going to spin each spinner once. Each spinner will land on a number. Jeff will get his score by adding these two numbers together.

(a) Complete the possibility space diagram for each possible score.

5-sided spinner

1 2 3 4 5

4-sided spinner

1 2 3 4 5 6

2 3

3 4

4 5

(1)

Jeff spins each spinner once.

(b) Find the probability that Jeff gets

(i) a score of 3

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(ii) a score of 5 or more.

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(2)


20 Water flows through a pipe at a rate of 20 gallons per minute.

1 gallon = 4.55 litres.

Change 20 gallons per minute to litres per second. Give your answer correct to 3 significant figures.

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19 Here are a 4-sided spinner and a 5-sided spinner.

The spinners are fair.

2 1

4

3

2 43

51

Jeff is going to spin each spinner once. Each spinner will land on a number. Jeff will get his score by adding these two numbers together.

(a) Complete the possibility space diagram for each possible score.

5-sided spinner

1 2 3 4 5

4-sided spinner

1 2 3 4 5 6

2 3

3 4

4 5

(1)

Jeff spins each spinner once.

(b) Find the probability that Jeff gets

(i) a score of 3

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Turn over

23 The time series graph shows information about the percentages of the people in a village that used the village shop for the years between 1980 and 2010

(a) Describe the trend in the percentage of the people in the village who used the shop for this period.

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(1)

(b) (i) Use the graph to predict the percentage of the people in the village likely to use the shop in the year 2020

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(ii) Is your prediction reliable? Explain your answer.

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(3)


1980 1990 2000 2010 2020

Year

Percentage

40

35

30

25

20

15

10

5

0

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21 Find the highest common factor (HCF) of 32, 48 and 72

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22

A

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4

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1 2 3 4–1

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–4 –3 –2 –1 O

Describe the single transformation that maps shape A onto shape B.

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




19

*S50157A01928*

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Turn over



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

(1)


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


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

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

(3)


1980 1990 2000 2010 2020

Year

Percentage

40

35

30

25

20

15

10

5

0

18

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21 Find the highest common factor (HCF) of 32, 48 and 72

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


22

A

y

B

x

4

3

2

1

1 2 3 4–1

–2

–3

–4

–4 –3 –2 –1 O


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

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




21


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D

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TE IN

TH

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25

x

The diagram shows a regular octagon and a regular hexagon.

Find the size of the angle marked x You must show all your working.

x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °


x

20

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TE IN

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24 (a) Expand and simplify 3(y − 2) + 5(2y + 1)

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

(2)

(b) Simplify 5u2w4 × 7uw3

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

(2)




21


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25

x



x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °


x

20

*S50157A02028*

D

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

(2)


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

(2)




23


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27 On a farm

the number of cows and the number of sheep are in the ratio 6 : 5 the number of sheep and the number of pigs are in the ratio 2 : 1

The total number of cows, sheep and pigs on the farm is 189

How many sheep are there on the farm?

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


22

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TH

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26 Here is a Venn diagram.

BA15 12

18

10

1416

11 13 17 19

(a) Write down the numbers that are in set

(i) A È B

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

(ii) A Ç B

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

(2)

One of the numbers in the diagram is chosen at random.

(b) Find the probability that the number is in set Aʹ

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

(2)




23


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TE IN

TH

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27 On a farm




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


22

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D

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D

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BA15 12

18

10

1416

11 13 17 19


(i) A È B

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

(ii) A Ç B

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

(2)



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

(2)




25

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TH

IS A

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TH

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29

A

B

C

72°

D

ABC is an isosceles triangle with BA = BC.

D lies on AC. ABD is an isosceles triangle with AB = AD.

Angle ABD = 72°

Show that the triangle BCD is isosceles. You must give a reason for each stage of your working.



24

*S50157A02428*

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28 A

O

B

C4.8 cm

The arc ABC is a quarter of a circle with centre O and radius 4.8 cm. AC is a chord of the circle.

Work out the area of the shaded segment. Give your answer correct to 3 significant figures.

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




25

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29

A

B

C

72°

D

ABC is an isosceles triangle with BA = BC.

D lies on AC. ABD is an isosceles triangle with AB = AD.

Angle ABD = 72°

Show that the triangle BCD is isosceles. You must give a reason for each stage of your working.



24

*S50157A02428*

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28 A

O

B

C4.8 cm



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




27

*S50157A02728*

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IS AREA

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TH

IS A

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BLANK PAGE

26

*S50157A02628*

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D

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TE IN

TH

IS A

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D

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TH

IS A

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BLANK PAGE



27

*S50157A02728*

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D

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TE IN

TH

IS A

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D

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BLANK PAGE

26

*S50157A02628*

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IS AREA

D

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TE IN

TH

IS A

REA

D

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TH

IS A

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D

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BLANK PAGE



28

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BLANK PAGE



28

*S50157A02828*

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BLANK PAGE



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e m

ouss

e fo

r usi

ng th

e su

gar a

vaila

ble

P1fo

r pro

cess

to fi

nd n

umbe

r of p

eopl

e th

at E

llie

can

mak

e m

ouss

e fo

r usi

ng th

e ch

ocol

ate

avai

labl

e A

1fo

r cor

rect

ans

wer

with

supp

ortiv

e w

orki

ng

(b)

corr

ect

expl

anat

ion

C1

for “

can

only

mak

e m

ouss

e fo

r 6 p

eopl

e” o

e

168

B1

cao

17(a

)4x

+ 6y

M1

for 4

xor

6y

A1

for 4

x+

6yor

2(2

x+

3y)

(b)

5(2x

–3)

B1

cao

(c)

4M

1fo

r met

hod

to is

olat

e te

rms i

n p

on o

ne si

de a

nd

cons

tant

s on

the

othe

r sid

eA

1ca

o

183

: 4M

1fo

r 32

–8

(= 2

4)M

1(d

ep) f

or “

24”

: 32

A1

cao



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

19(a

)Ta

ble

com

plet

eB

1ca

o

(bi)

1 10B

1fo

r 1 10

oe o

r ft f

rom

tabl

e

(bii)

7 10B

1fo

r 7 10

oe o

r ft f

rom

tabl

e

201.

52M

1fo

r 20

× 4.

55 ÷

60

A1

for 1

.52

or 1

.516

(....)

218

M1

for f

indi

ng th

e H

CF

of a

ny tw

o of

the

thre

e nu

mbe

rs o

rfo

r 25

and

3 ×

24 an

d 23

× 32

A1

cao

22Tr

ansl

atio

n by�4 −3�

B1

for t

rans

latio

n

B1

�4 −3�



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

23(a

)Tr

end

desc

ribed

C1

for “

perc

enta

ge o

f peo

ple

who

use

the

shop

de

crea

ses”

oe

(bi)

13-1

7P1

for p

roce

ss to

dra

w tr

end

line

on g

raph

A1

for 1

3 -1

7

(bii)

No

+ re

ason

C1

for c

omm

ent,

eg “

no, b

ecau

se 2

020

is b

eyon

d th

e tim

e pe

riod

cove

red

by th

e gi

ven

data

”

24(a

)13

y−

1M

1fo

r exp

ansi

on o

f one

bra

cket

A1

for f

ull

sim

plifi

catio

n

(b)

35u3 w

7B

1fo

r 2 o

f 35,

u3an

dw

7co

rrec

tB

1ca

o

2510

5P1

for p

roce

ss to

find

the

exte

rior a

ngle

or i

nter

ior

angl

e of

a h

exag

on o

r oct

agon

P1fo

r pro

cess

to fi

nd th

e bo

th e

xter

ior a

ngle

s or

bo

th in

terio

r ang

les

A1

for 1

05 f

rom

cor

rect

wor

king



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

26(a

)(i)

10, 1

2, 1

4, 1

5, 1

6,

18B

1ca

o

(ii)

12, 1

8B

1ca

o

(b)

7 10M

1fo

r 7 o

r ind

icat

ing

corr

ect r

egio

n or

for 1

0, 1

4,

16, 1

1, 1

3, 1

7, 1

9 lis

ted

A1

for 7 10

oe

276

:5 =

12

:10

2 : 1

= 1

0 : 5

70P1

for s

trate

gy to

star

t to

solv

e th

e pr

oble

m

eg 1

2 : 1

0 an

d 10

: 5

C :

S : P

= 1

2 : 1

0 : 5

P1fo

r pro

cess

to so

lve

the

prob

lem

eg 10 27 ×

189

10 27 ×

189

A1

cao

281 4

× π

× 4.

8²6.

58B

1fo

r use

of f

orm

ula

for a

rea

of a

circ

le

1 2×

4.8

× 4.

8P1

for c

ompl

ete

proc

ess t

o fin

d ar

ea o

f sha

ded

regi

on1 4

× π

× 4.

8² −

1 2×

4.8

× 4.

8A

1fo

r 6.5

6 –

6.58



Total Marks

Paper Reference

Turn over


6/6/4/

*S50159A0124*




Instructions




Information



Advice





Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

29⦟

ADB

= 72

° (ba

se a

ngle

s of

isos

cele

s tria

ngle

ABD

)R

esul

t sho

wn

M1

for ⦟

ADB

= 72

° an

d ⦟

BAD

= 18

0° −

2 ×

72°

⦟BA

D=

180°

− 2

× 7

2°

(ang

le su

m o

f a tr

iang

le is

18

0°)

M1

for ⦟

BCA

= “3

6°”

⦟BC

A=

36° (

base

ang

les

of is

osce

les t

riang

le A

BC)

M1

for ⦟

BDC

= 18

0° −

72°

⦟BD

C=

180°

− 7

2° (a

ngle

s on

a st

raig

ht li

ne su

m to

18

0°)

C1

for c

ompl

ete

chai

n of

reas

onin

g to

find

ang

le

DBC

= 36

° an

d on

e co

rrec

t rea

son

⦟D

BC=

180°

− 3

6° −

108

° (a

ngle

sum

of a

tria

ngle

is

180°

)

C1

C1

depe

nden

t on

all p

revi

ous m

arks

for c

orre

ct

dedu

ctio

n an

d fu

ll re

ason

s.



Total Marks

Paper Reference

Turn over


6/6/4/

*S50159A0124*




Instructions




Information



Advice





3


D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

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TE IN

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REA

6 Coffee is sold in jars. There are 200g of coffee in each jar.

Ben makes 8 cups of coffee each day. He thinks he uses 2g of coffee to make each cup of coffee.

Ben wants to buy enough coffee for 28 days.

(a) How many jars of coffee does Ben need to buy?

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

(3)

Ben finds that he uses 2.5 g of coffee to make each cup of coffee.

(b) How does this affect the number of jars of coffee he needs to buy? You must give a reason for your answer.

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

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

(2)


7 Write down three different factors of 18 that add together to give a prime number.

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


2

*S50159A0224*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




1 Change 4500g to kg.

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


2 Write 0.19 as a fraction.

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


3 Write down an even number that is a multiple of 7

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


4 On the grid, draw a parallelogram.


5 Write 35

as a percentage.

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




3


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

6 Coffee is sold in jars. There are 200g of coffee in each jar.

Ben makes 8 cups of coffee each day. He thinks he uses 2g of coffee to make each cup of coffee.

Ben wants to buy enough coffee for 28 days.

(a) How many jars of coffee does Ben need to buy?

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

(3)

Ben finds that he uses 2.5 g of coffee to make each cup of coffee.

(b) How does this affect the number of jars of coffee he needs to buy? You must give a reason for your answer.

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

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

(2)


7 Write down three different factors of 18 that add together to give a prime number.

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


2

*S50159A0224*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




1 Change 4500g to kg.

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


2 Write 0.19 as a fraction.

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


3 Write down an even number that is a multiple of 7

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


4 On the grid, draw a parallelogram.


5 Write 35

as a percentage.

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




5


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

10 The stem and leaf diagram gives information about the speeds of 27 cars.

Key:3 8 means 38 miles per hour

3 8

4 1 3 4 6 7 8 8 9 9

5 2 2 4 6 7 7 8 8 9

6 1 1 2 2 2 2 3

7 0

(a) Find the median speed.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . miles per hour(1)

(b) Work out the range.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . miles per hour(1)

One of the cars is chosen at random.

Jack says,

“The probability that the speed of this car is more than 60 miles per hour is 13

”

(c) Jack is wrong. Explain why.

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

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

(2)


4

*S50159A0424*

D

O N

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IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

8 A model plane has a length of 17cm.

The scale of the model is 1:200

Work out the length of the real plane. Give your answer in metres.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . metres


9 (a) Find the value of 3 97 336.

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

(1)

(b) Find the value of 7 29 2 3 0 85 2. ( . . )+ −

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

(2)




5


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

10 The stem and leaf diagram gives information about the speeds of 27 cars.

Key:3 8 means 38 miles per hour

3 8

4 1 3 4 6 7 8 8 9 9

5 2 2 4 6 7 7 8 8 9

6 1 1 2 2 2 2 3

7 0

(a) Find the median speed.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . miles per hour(1)

(b) Work out the range.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . miles per hour(1)

One of the cars is chosen at random.

Jack says,

“The probability that the speed of this car is more than 60 miles per hour is 13

”

(c) Jack is wrong. Explain why.

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

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

(2)


4

*S50159A0424*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

8 A model plane has a length of 17cm.

The scale of the model is 1:200

Work out the length of the real plane. Give your answer in metres.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . metres


9 (a) Find the value of 3 97 336.

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

(1)

(b) Find the value of 7 29 2 3 0 85 2. ( . . )+ −

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

(2)




7


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

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12 Ibrar buys 3kg of apples. He also buys 0.4kg of mushrooms. The total cost is £6.93

1kg of apples cost £1.95

Work out the cost of 1kg of mushrooms.

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


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11 You can use this graph to change between litres and gallons.

0 10 20 30 400

1

2

3

4

5

6

7

8

9

10

Gallons

Litres

Which is the greater, 60litres or 12gallons? You must show how you get your answer.

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12 Ibrar buys 3kg of apples. He also buys 0.4kg of mushrooms. The total cost is £6.93

1kg of apples cost £1.95

Work out the cost of 1kg of mushrooms.

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


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11 You can use this graph to change between litres and gallons.

0 10 20 30 400

1

2

3

4

5

6

7

8

9

10

Gallons

Litres

Which is the greater, 60litres or 12gallons? You must show how you get your answer.

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14 You can use this rule to work out the total cost, in pounds, of hiring a carpet cleaner.

Multiply the number of days by 7.8 and then add 12

Andy hires a carpet cleaner. The total cost is £82.20

(a) Work out the number of days Andy hires the carpet cleaner for.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .days(2)

Chloe hires a carpet cleaner for y days. The total cost is £T.

(b) Write down a formula for T in terms of y.

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

(2)


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13

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30°95°

y° x°

y°

ABC is a straight line. BCD is a triangle. ABDE is a quadrilateral.

(a) (i) Work out the value of x.

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

(ii) Give a reason for your answer.

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

(2)

(b) Work out the value of y.

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(2)




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14 You can use this rule to work out the total cost, in pounds, of hiring a carpet cleaner.

Multiply the number of days by 7.8 and then add 12

Andy hires a carpet cleaner. The total cost is £82.20

(a) Work out the number of days Andy hires the carpet cleaner for.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .days(2)

Chloe hires a carpet cleaner for y days. The total cost is £T.

(b) Write down a formula for T in terms of y.

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

(2)


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13

E

D

BA C35°

30°95°

y° x°

y°

ABC is a straight line. BCD is a triangle. ABDE is a quadrilateral.

(a) (i) Work out the value of x.

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

(ii) Give a reason for your answer.

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(2)

(b) Work out the value of y.

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(2)




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16 Ross rolled an ordinary dice 30 times.

The frequency table gives information about his results.

Score Frequency

1 7

2 5

3 4

4 4

5 6

6 4

Ross worked out the mean score as 8

(a) Explain why it is impossible for the mean score to be 8

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(1)

Graham also worked out the mean score.

Here is his working.

1 × 7 + 2 × 5 + 3 × 4 + 4 × 4 + 5 × 6 + 6 × 4 = 99

99 ÷ 6 = 16.5

The mean score is 16.5

(b) Describe the mistake Graham made in his method to work out the mean score.

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(1)


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15 There are 35 pens in a box. 15 of the pens are green. The rest of the pens are red.

(a) What fraction of the pens in the box are red?

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(1)

(b) Write down the ratio of the number of green pens to the number of red pens. Give your ratio in its simplest form.

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(2)




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16 Ross rolled an ordinary dice 30 times.

The frequency table gives information about his results.

Score Frequency

1 7

2 5

3 4

4 4

5 6

6 4

Ross worked out the mean score as 8

(a) Explain why it is impossible for the mean score to be 8

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

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

(1)

Graham also worked out the mean score.

Here is his working.

1 × 7 + 2 × 5 + 3 × 4 + 4 × 4 + 5 × 6 + 6 × 4 = 99

99 ÷ 6 = 16.5

The mean score is 16.5

(b) Describe the mistake Graham made in his method to work out the mean score.

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

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(1)


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15 There are 35 pens in a box. 15 of the pens are green. The rest of the pens are red.

(a) What fraction of the pens in the box are red?

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

(1)

(b) Write down the ratio of the number of green pens to the number of red pens. Give your ratio in its simplest form.

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

(2)




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Turn over

18 The diagram shows the positions of two churches, A and B.

N

N

A

B

25°

Amber says,

“The bearing of church B from church A is 025°”

Amber is wrong. Explain why.

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12

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17 Amelia, Hayden and Sophie did a test. The total for the test was 75 marks.

Amelia got 56% of the 75 marks.

Hayden got 815

of the 75 marks.

Sophie got 43 out of 75

Who got the highest mark? You must show all your working.




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Turn over

18 The diagram shows the positions of two churches, A and B.

N

N

A

B

25°

Amber says,

“The bearing of church B from church A is 025°”

Amber is wrong. Explain why.

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17 Amelia, Hayden and Sophie did a test. The total for the test was 75 marks.

Amelia got 56% of the 75 marks.

Hayden got 815

of the 75 marks.

Sophie got 43 out of 75

Who got the highest mark? You must show all your working.




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21 Here are the first five terms of an arithmetic sequence.

– 3 1 5 9 13

Find an expression, in terms of n, for the nth term of this sequence.

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22 The ratio of the number of boys to the number of girls in a school is 4:5 There are 95 girls in the school.

Work out the total number of students in the school.

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19 There are only blue counters, green counters, red counters and yellow counters in a bag. George is going to take at random a counter from the bag.

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

Colour blue green red yellow

Probability 0.5 0.2 0.25

(a) Work out the probability that George will take a red counter.

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(1)

There are 120 counters in the bag.

(b) Work out the number of green counters in the bag.

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(2)


20 (a) Show the inequality –2 x < 3 on the number line below.

–4 –3 –2 –1 0 1 2 3 4 5 x

(2)

(b) Solve the inequality 4y + 7 < 16

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

(2)




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21 Here are the first five terms of an arithmetic sequence.

– 3 1 5 9 13

Find an expression, in terms of n, for the nth term of this sequence.

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19 There are only blue counters, green counters, red counters and yellow counters in a bag. George is going to take at random a counter from the bag.

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

Colour blue green red yellow

Probability 0.5 0.2 0.25

(a) Work out the probability that George will take a red counter.

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(1)

There are 120 counters in the bag.

(b) Work out the number of green counters in the bag.

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(2)


20 (a) Show the inequality –2 x < 3 on the number line below.

–4 –3 –2 –1 0 1 2 3 4 5 x

(2)

(b) Solve the inequality 4y + 7 < 16

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

(2)




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24 Make t the subject of the formula y = t3

– 2a

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25 Jim rounds a number, x, to one decimal place. The result is 7.2

Write down the error interval for x.

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23 The diagram represents a solid made from seven centimetre cubes.

On the centimetre grid below, draw a plan of the solid.




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– 2a

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27 At a depth of x metres, the temperature of the water in an ocean is T °C. At depths below 900 metres, T is inversely proportional to x.

T is given by

Tx

= 4500

(a) Work out the difference in the temperature of the water at a depth of 1200 metres and the temperature of the water at a depth of 2500 metres.

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Here are four graphs.

T

O x

A T

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B

T

O x

C T

O x

D

One of the graphs could show that T is inversely proportional to x.

(b) Write down the letter of this graph.

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(1)


26 Katie measured the length and the width of each of 10 pine cones from the same tree.

She used her results to draw this scatter graph.

0 1 2 3 4 50

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Width (cm)

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(a) Describe one improvement Katie can make to her scatter graph.

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(1)

The point representing the results for one of the pine cones is an outlier.

(b) Explain how the results for this pine cone differ from the results for the other pine cones.

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(1)


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(1)



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Turn over


T is given by

Tx

= 4500


.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°C (3)


T

O x

A T

O x

B

T

O x

C T

O x

D



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(1)




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(1)



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(1)


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Length (cm)


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

(1)



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

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

(1)




21


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29 The diagram shows an oil tank in the shape of a prism. The cross section of the prism is a trapezium.

3m

2.5m1.4m

2.4m

Only fill to85%

of capacity

The tank is empty.

Oil flows into the tank. After one minute there are 300 litres of oil in the tank.

Assume that oil continues to flow into the tank at this rate.

(a) Work out how many more minutes it takes for the tank to be 85% full of oil. (1 m3 = 1000 litres)

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minutes(5)

The assumption about the rate of flow of the oil could be wrong.

(b) Explain how this could affect your answer to part (a).

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

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

(1)


20

*S50159A02024*

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28 Here is a right-angled triangle.

xy

Four of these triangles are joined to enclose the square ABCD as shown below.

A

B

C

D

Show that the area of the square ABCD is x2 + y2




21


D

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TH

IS A

REA

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TH

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D

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TH

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REA


3m

2.5m1.4m

2.4m

Only fill to85%

of capacity

The tank is empty.




.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minutes(5)



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

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

(1)


20

*S50159A02024*

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D

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IS AREA

D

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

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D

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xy


A

B

C

D





23

*S50159A02324*

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IS AREA

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TE IN

TH

IS A

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TH

IS A

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IS A

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BLANK PAGE

22

*S50159A02224*

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IS AREA

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IS AREA

D

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TE IN

TH

IS A

REA

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IS A

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30

2x

3x

2x – 1

x – 3 x + 3 5

x + 3

In the diagram all measurements are in centimetres.

The perimeter of the quadrilateral is twice the perimeter of the triangle.

Work out the perimeter of the quadrilateral.

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





23

*S50159A02324*

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IS AREA

D

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

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D

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IS A

REA

BLANK PAGE

22

*S50159A02224*

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IS AREA

D

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IS AREA

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RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

REA

30

2x

3x

2x – 1

x – 3 x + 3 5

x + 3

In the diagram all measurements are in centimetres.

The perimeter of the quadrilateral is twice the perimeter of the triangle.

Work out the perimeter of the quadrilateral.

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





24

*S50159A02424*

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IS AREA

BLANK PAGE



24

*S50159A02424*

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BLANK PAGE



Pape

r 1M

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)



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(=42

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19(a

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(b)

24M

1fo

r 120

× 0

.2 o

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Pape

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20(a

)di

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from

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7.25

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Total Marks

Paper Reference

Turn over


6/6/4/

*S50156A0116*


Higher TierSpecimen Papers Set 2

Time: 1 hour 30 minutes 1MA1/1HYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser.

Instructions



Information



Advice





Pape

r 1M

A1:

3F

Que

stio

nW

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ngA

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otes

29(a

)36

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1000

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ume

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4 or

36

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the

aver

age

rate

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slow

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w

ould

take

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e tim

e, if

the

aver

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was

fa

ster

it w

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3048

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for x

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5 oe

B1

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ep P

1) fo

r cor

rect

per

imet

er fo

r the

ir x



Total Marks

Paper Reference

Turn over


6/6/4/

*S50156A0116*



Time: 1 hour 30 minutes 1MA1/1HYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser.

Instructions



Information



Advice





3


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


3 cm

2 cm


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


2

*S50156A0216*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA





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

(1)

(b) Simplify (t3)2

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

(1)

(c) Simplify ww

9

4

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(1)




3


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3 cm

2 cm


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2

*S50156A0216*

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

(1)

(b) Simplify (t3)2

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

(1)

(c) Simplify ww

9

4

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(1)




5


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AB = 7 cm. BC = 4 cm.




m2.



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4

*S50156A0416*

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Win £2

roll a 1or

spin a 1or

both

Win £5

roll a 5and

spin a 5



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

(4)


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

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

(1)




5


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AB = 7 cm. BC = 4 cm.




m2.



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4

*S50156A0416*

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Win £2

roll a 1or

spin a 1or

both

Win £5

roll a 5and

spin a 5



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

(4)


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

(1)




7


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7 A shop has a sale.

Microwave ovens

13

off normal price

Combination ovens

40% off normal price

A microwave oven has a sale price of £90 A combination oven has a sale price of £84

Which of these ovens has the greater normal price? You must show all your working.


8 Work out an estimate for 4 98 2 16 7 35. . .+ ×

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


6

*S50156A0616*

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6 (a) Work out 2 14

313

×

Give your answer as a mixed number in its simplest form.

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(3)

(b) Write the numbers 3, 4, 5 and 6 in the boxes to give the greatest possible total. You may write each number only once.

1 +

2

(1)




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7 A shop has a sale.

Microwave ovens

13

off normal price

Combination ovens

40% off normal price

A microwave oven has a sale price of £90 A combination oven has a sale price of £84

Which of these ovens has the greater normal price? You must show all your working.


8 Work out an estimate for 4 98 2 16 7 35. . .+ ×

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


6

*S50156A0616*

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6 (a) Work out 2 14

313

×

Give your answer as a mixed number in its simplest form.

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

(3)

(b) Write the numbers 3, 4, 5 and 6 in the boxes to give the greatest possible total. You may write each number only once.

1 +

2

(1)




9


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11 A solid is made by putting a hemisphere on top of a cone.

x

5x

The total height of the solid is 5x The radius of the base of the cone is x The radius of the hemisphere is x

2x

h

A cylinder has the same volume as the solid. The cylinder has radius 2x and height h All measurements are in centimetres.

Find a formula for h in terms of x Give your answer in its simplest form.

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


Volume of cone = 13πr 2h

r

h

Volume of sphere = 43πr 3

r

8

*S50156A0816*

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9 Here is a cuboid.

x

3x2x

All measurements are in centimetres. x is an integer. The total volume of the cuboid is less than 900 cm3

Show that x 5


10 y is inversely proportional to x When x = 1.5, y = 36

Find the value of y when x = 6

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




9


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11 A solid is made by putting a hemisphere on top of a cone.

x

5x

The total height of the solid is 5x The radius of the base of the cone is x The radius of the hemisphere is x

2x

h

A cylinder has the same volume as the solid. The cylinder has radius 2x and height h All measurements are in centimetres.

Find a formula for h in terms of x Give your answer in its simplest form.

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


Volume of cone = 13πr 2h

r

h

Volume of sphere = 43πr 3

r

8

*S50156A0816*

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9 Here is a cuboid.

x

3x2x

All measurements are in centimetres. x is an integer. The total volume of the cuboid is less than 900 cm3

Show that x 5


10 y is inversely proportional to x When x = 1.5, y = 36

Find the value of y when x = 6

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




11


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13 Mr Brown gives his class a test. The 10 girls in the class get a mean mark of 70% The 15 boys in the class get a mean mark of 80%

Nick says that because the mean of 70 and 80 is 75 then the mean mark for the whole class in the test is 75%

Nick is not correct. Is the correct mean mark less than or greater than 75%? You must justify your answer.

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

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

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


14 Show that 4 3 4 3

13

−( ) +( ) simplifies to 13


10

*S50156A01016*

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IS AREA

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IS A

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12 ABCD is a parallelogram.

A D

CB

E

E is the point where the diagonals AC and BD meet.

Prove that triangle ABE is congruent to triangle CDE.




11


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13 Mr Brown gives his class a test. The 10 girls in the class get a mean mark of 70% The 15 boys in the class get a mean mark of 80%

Nick says that because the mean of 70 and 80 is 75 then the mean mark for the whole class in the test is 75%

Nick is not correct. Is the correct mean mark less than or greater than 75%? You must justify your answer.

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

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

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


14 Show that 4 3 4 3

13

−( ) +( ) simplifies to 13


10

*S50156A01016*

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TH

IS A

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12 ABCD is a parallelogram.

A D

CB

E

E is the point where the diagonals AC and BD meet.

Prove that triangle ABE is congruent to triangle CDE.




13


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17 Solve x2 – 6x – 8 = 0

Write your answer in the form a ± b where a and b are integers.

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


18 LMN is a right-angled triangle.

N

QP

L M

Angle NLM = 90° PQ is parallel to LM.

The area of triangle PNQ is 8 cm2

The area of triangle LPQ is 16 cm2

Work out the area of triangle LQM.

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


12

*S50156A01216*

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O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

15 (a) Find the value of 8 1063 ×

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

(1)

(b) Find the value of 144 6412

13×

−

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

(2)

(c) Solve 3 181

2x =

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

(2)


16 The probability that Sanay is late for school tomorrow is 0.05 The probability that Jaden is late for school tomorrow is 0.15

Alfie says that the probability that Sanay and Jaden will both be late for school tomorrow is 0.0075 because 0.05 × 0.15 = 0.0075

What assumption has Alfie made?

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

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




13


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

17 Solve x2 – 6x – 8 = 0

Write your answer in the form a ± b where a and b are integers.

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


18 LMN is a right-angled triangle.

N

QP

L M

Angle NLM = 90° PQ is parallel to LM.

The area of triangle PNQ is 8 cm2

The area of triangle LPQ is 16 cm2

Work out the area of triangle LQM.

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


12

*S50156A01216*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

15 (a) Find the value of 8 1063 ×

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

(1)

(b) Find the value of 144 6412

13×

−

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

(2)

(c) Solve 3 181

2x =

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

(2)


16 The probability that Sanay is late for school tomorrow is 0.05 The probability that Jaden is late for school tomorrow is 0.15

Alfie says that the probability that Sanay and Jaden will both be late for school tomorrow is 0.0075 because 0.05 × 0.15 = 0.0075

What assumption has Alfie made?

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

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




15


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

20 Show that 3 63 10

5252 3

xx x

xx x

+− −

÷ +−

simplifies to ax where a is an integer.


21 Solve the inequality x2 > 3(x + 6)

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


14

*S50156A01416*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

19 The histogram shows information about the time taken by cyclists to finish a cycle race.

70 80 90 100 110 120Time (t minutes)

Frequency density

7 cyclists took 80 minutes or less to finish the race.

(i) Work out an estimate for the number of cyclists who took more than 105 minutes to finish the race.

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

(ii) Explain why your answer to part (i) is only an estimate.

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

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




15


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

20 Show that 3 63 10

5252 3

xx x

xx x

+− −

÷ +−

simplifies to ax where a is an integer.


21 Solve the inequality x2 > 3(x + 6)

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


14

*S50156A01416*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

19 The histogram shows information about the time taken by cyclists to finish a cycle race.

70 80 90 100 110 120Time (t minutes)

Frequency density

7 cyclists took 80 minutes or less to finish the race.

(i) Work out an estimate for the number of cyclists who took more than 105 minutes to finish the race.

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

(ii) Explain why your answer to part (i) is only an estimate.

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

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




16

*S50156A01616*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

22 The line l is a tangent to the circle x2 + y2 = 40 at the point A. A is the point (2, 6).

The line l crosses the x-axis at the point P.

Work out the area of triangle OAP.

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





16

*S50156A01616*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

22 The line l is a tangent to the circle x2 + y2 = 40 at the point A. A is the point (2, 6).

The line l crosses the x-axis at the point P.

Work out the area of triangle OAP.

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





Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

1a

y(y

+ 27

)B

1

bt6

B1

cw

5B

1

216

÷ 4

5 8P1

Usi

ng si

de le

ngth

s of 4

1×4 2 =

2 or

1 2×1 4 =1 8

2×4 2 =

4 or

1 2×1 2 =1 4

P1M

etho

d to

find

frac

tion

or a

rea

for o

ne u

nsha

ded

trian

gle

1×4 2

+ 2×

4 2=

6 or

1 2×1 4 +1 2×1 2 =

3 8 P1

Met

hod

to c

ompl

ete

frac

tion

or a

rea

for t

otal

un

shad

ed re

gion

16–

6 =

10 o

r 1 −

3 8=5 8

P1

Met

hod

to fi

nd to

tal f

ract

ion

or a

rea

for s

hade

d re

gion

A1

for 5 8

oe o

r 0.6

25



Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

3a

1 6×1 5

× 30

×5

= 5

(5 6×1 5

+1 6

×4 5

+ 1 6

×1 5

)×30

×230

–5

–20

5P1 P1 P1 A

1

for i

dent

ifyin

g co

rrec

t pro

cess

to fi

nd

prob

abili

ties f

or w

innn

g sc

ores

. May

incl

ude

use

of tr

ee d

iagr

am o

r sam

ple

spac

efo

r cor

rect

pro

cess

to fi

nd p

rize

mon

eyfo

r com

plet

ing

corr

ect p

roce

ss to

find

pro

fit

bEx

plan

atio

nC

1fo

r app

ropr

iate

com

men

t to

inte

rpre

tres

ult e

g pr

obab

ility

so o

nly

likel

ihoo

d no

t cer

tain

ty, o

ther

th

an 3

0 m

ay p

lay,

£5

is sm

all d

iffer

ence

.

4N

o w

ith

reas

onin

gM

1M

1D

eriv

eAC

=9 c

man

d id

entif

y as

hyp

oten

use

42+

72

A1

for u

sing

eg

AC =

√42

+72

or 6

5 an

d 81

C

1fo

r con

clud

ing

expl

anat

ion

that

ABC

is n

ot a

rig

ht-a

ngle

d tri

angl

e w

ith e

vide

nce.

550

0gP1

1 8×

160

(=20

)P1

‘20’

× 2

5A

150

0 (o

r 0.5

)B

1C

orre

ct u

nits

g (o

r kg)



Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

6a

71 2M

19 4×1

0 3oe

M1

90 12oe

A1

71 2

b51 4

+ 62 3

or

52 3+

61 4

B1

51 4+

62 3or

52 3

+ 61 4

790 2

× 3

=135

Com

bina

tion

with

reas

onP1

Link

s eith

er 2 3

with

90

and

60%

with

84

84 60×

100

=140

P1Pr

oces

s to

find

orig

inal

pric

e of

mic

row

ave

oven

eg

90 2

× 3

(=13

5)P1

Proc

ess t

o fin

d or

igin

al p

rice

of c

ombi

natio

n ov

en e

g 84 60

× 10

0 (=

140)

A1

Cor

rect

orig

inal

pric

es £

135

and

£140

with

in

terp

reta

tion

of re

sults

to c

oncl

ude

that

co

mbi

natio

n ov

en h

ad g

reat

er n

orm

al p

rice.

84

-4.5

B1

Rou

nds a

ppro

pria

tely

usi

ng tw

o of

5, 2

or 7

M1

√19

A1

4-4

.5



Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

9x×

2x×3

x=R

easo

ning

to

reac

h x

≤5

M1

Star

ts re

ason

ing

to fi

nd v

olum

e in

term

s of x

M1

Giv

es in

equa

lity

6x3

≤90

0or

subs

titut

es 5

and

6 in

to 6

x3

M1

Com

plet

es re

ason

ing

to sh

ow x

≤ 5

109

M1

Find

s con

stan

t 36

× 1.

5 (=

54) o

r 6 1.5=4

M1

54 ÷

6 o

r 36

÷ 4

A1

9 ca

o

114 3×2𝜋𝜋𝑥𝑥

3 +4 3𝜋𝜋𝑥𝑥

3 =2 𝜋𝜋𝑥𝑥

3h

=𝑥𝑥 2

P1Pr

oces

s to

find

volu

me

of c

one

or h

emis

pher

e

P1Pr

oces

s to

tota

l vol

ume

of so

lid(2

x)2 𝜋𝜋ℎ

= 4x

2 𝜋𝜋ℎ

P1Pr

oces

s to

find

volu

me

ofcy

linde

r4x

2 𝜋𝜋ℎ

= 2 𝜋𝜋𝑥𝑥

3P1

Equa

tes 2

vol

umes

A1

Rea

ches

h=𝑥𝑥 2

12C

ompl

ete

proo

fM

1B

egin

s pro

of B

AE=A

CD

and

ABE=

EDC

M

1AB

=D

C b

ecau

se o

ppos

ite si

des o

f a

para

llelo

gram

are

equ

alC

1C

ompl

etes

pro

of w

ith a

ll re

ason

s eg

alte

rnat

e an

gles

are

equ

alan

d re

fere

nce

to A

SA



Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

13m

ore

than

C1

Mak

es re

fere

nce

to d

iffer

ent n

umbe

rs o

f girl

s an

d bo

ys

C1

Com

plet

es re

ason

ing

eg th

ere

are

mor

e (b

oys)

w

ith 8

0% th

an (g

irls)

with

70%

or c

orre

ct m

ean

(700

+120

0)÷2

5 =

76

14C

ompl

etes

re

ason

ing

M1

Expa

nsio

n of

(4−√3

)(4

+√3

)with

at l

east

3

term

s out

of 4

cor

rect

or 4

2− √3

×√3

C1

for

13fr

om c

orre

ct w

orki

ng

15a

200

B1

200

or 2

× 1

02

b3

B1

12 a

nd 1 4

A1

3ca

o

c−2

M1

81 =

34

or

41

381

−=

A1

cao

16Ev

ents

in

depe

nden

tC

1St

atem

ent t

hat e

vent

s are

inde

pend

ent



Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

173

± √1

7M

1Fo

r (x

−3)

2–

9–

8 (=

0) o

r

(𝑥𝑥=

)−(−6)

±�

(−6)2 −

4(1)

(−8)

2(1)

allo

w si

gn e

rror

for b

M1

For x

–3

= ± √1

7or

𝑥𝑥=

6±√68

2A

1ca

o

1848

P1Id

entif

ies t

hat 1

6 ÷

8 =

2 so

PL=

2NP

P1Pr

oces

s to

find

area

of L

MN

8×

(2+1

)2(=

72)

P1C

ompl

etes

pro

cess

to fi

nd a

rea

of L

QM

‘72’

−16

− 8

A1

48 c

ao

19i

18M

1 U

ses f

requ

ency

dens

ity fo

r und

er 8

0 ba

r eg

7÷10

M

1C

ompl

etes

met

hod

to fi

nd o

ver 1

05 m

inut

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Total Marks

Paper Reference

Turn over


6/6/4/1/

*S50158A0124*



Time: 1 hour 30 minutes 1MA1/2HYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator.

Instructions




Information



Advice





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1980 1990 2000 2010 2020Year

Percentage

40

35

30

25

20

15

10

5

0



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x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °




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BA15 12

18

10

1416

11 13 17 19


(i) A È B

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(ii) A Ç B

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6 On a farm




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7 A

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C4.8 cm



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8 Steve is asked to solve the equation 5(x + 2) = 47

Here is his working. 5(x + 2) = 47 5x + 2 = 47 5x = 45 x = 94

Steve’s answer is wrong.

(a) What mistake did he make?

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(1)

Liz is asked to solve the equation 3x2 + 8 = 83

Here is her working.3x2 + 8 = 83

3x2 = 75x2 = 25x = 54

(b) Explain what is wrong with Liz’s answer.

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9 The functions f and g are such that

f (x) = 3(x – 4) and g(x) = x5

+ 1

(a) Find the value of f (10)

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(1)

(b) Find g–1(x)

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

(2)

(c) Show that ff (x) = 9x – 48

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10 The population of a city increased by 5.2% for the year 2014

At the beginning of 2015 the population of the city was 1560000

Lin assumes that the population will continue to increase at a constant rate of 5.2% each year.

(a) Use Lin’s assumption to estimate the population of the city at the beginning of 2017 Give your answer correct to 3 significant figures.

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(3)

(b) (i) Use Lin’s assumption to work out the year in which the population of the city will reach 2000000

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(ii) If Lin’s assumption about the rate of increase of the population is too low, how might this affect your answer to (b)(i)?

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(3)




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11 The cumulative frequency graphs show information about the times taken by 100 male runners and by 100 female runners to finish the London marathon.

A male runner is chosen at random.

(a) Find an estimate for the probability that this runner took less than 4 hours to finish the London marathon.

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(2)

120 180 240 300 360 420Time (minutes)

Cumulativefrequency

80

60

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0480

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female



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Turn over

(b) Use medians and interquartile ranges to compare the distribution of the times taken by the male runners with the distribution of the times taken by the female runners.

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

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

(4)




14

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12 Marie has 25 cards. Each card has a different symbol on it.

Marie gives one card to Shelley and one card to Pauline.

(a) In how many different ways can Marie do this?

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

(2)

There are 12 boys and 10 girls in David’s class. David is going to pick three different students from his class and write their names in a

list in order.

The order will be

boygirlboy

or girlboygirl

(b) How many different lists can David write?

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

(3)




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13 The number of slugs in a garden t days from now is pt where

p0 = 100

pt + 1 = 1.06pt

Work out the number of slugs in the garden 3 days from now.

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


14 D is directly proportional to the cube of n.

Mary says that when n is doubled, the value of D is multiplied by 6

Mary is wrong. Explain why.

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

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(1)




16

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15 Karol runs in a race.


(a) Calculate an estimate for the gradient of the graph when t = 4 You must show how you get your answer.

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

(3)


Speed (m/s)

10

8

6

4

2

0



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(b) Describe fully what your answer to part (a) represents.

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(2)

(c) Explain why your answer to part (a) is only an estimate.

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

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

(1)


16 (i) Find the value of 3 2 10115 . ×

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

(ii) Find the value of 1034

Give your answer correct to 1 decimal place.

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




18

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17

b

ca

a is 8.3 cm correct to the nearest mm b is 6.1 cm correct to the nearest mm

Calculate the upper bound for c. You must show your working.

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




19

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Turn over

18 Simplify fully ( )( )a b a b+ −4 2

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




20

*S50158A02024*

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19 (a) Sketch the graph of y = cos x° for 0 x 360

y

xO 90 180 270 360

(2)



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y

x

4

2

2 4

–2

–4

–4 –2 O

6

6–6

y

x

4

2

2 4

–2

–4

–4 –2 O

6

6–6

(b) The graph of y = f(x) is shown on both grids below.

(i) On this grid, draw the graph of y = –f(x)

(ii) On the grid below, draw the graph of y = f(x − 3)

(2)




22

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20

Q

R

S

U

TP

O

PQRST is a regular pentagon. R, U and T are points on a circle, centre O. QR and PT are tangents to the circle. RSU is a straight line.

Prove that ST = UT.




23

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21 Given that

2x − 1 : x − 4 = 16x + 1 : 2x − 1

find the possible values of x.

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24

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BLANK PAGE





Pape

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B1

for t

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for “

perc

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ses”

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(bi)

13-1

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for 1

3 -1

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(bii)

No

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omm

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eg “

no, b

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is b

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3(a

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410

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for p

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find

the

exte

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or i

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ior

angl

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a h

exag

on o

r oct

agon

P1fo

r pro

cess

to fi

nd th

e bo

th e

xter

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ngle

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bo

th in

terio

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A1

for 1

05 f

rom

cor

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wor

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Pape

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5(a

)(i)

10, 1

2, 1

4, 1

5, 1

6,

18B

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(ii)

12, 1

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o

(b)

7 10M

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r ind

icat

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corr

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egio

n or

for 1

0, 1

4,

16, 1

1, 1

3, 1

7, 1

9 lis

ted

A1

for 7 10

oe

66

:5 =

12

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2 : 1

= 1

0 : 5

70P1

P1 fo

r stra

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to st

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o so

lve

the

prob

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eg

12

: 10

and

10: 5

C :

S : P

= 1

2 : 1

0 : 5

P1P1

for p

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solv

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e pr

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10 27 ×

189

10 27 ×

189

A1

A1

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71 4

× π

× 4.

8²6.

58B

1fo

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of f

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ula

for a

rea

of a

circ

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1 2×

4.8

× 4.

8P1

for c

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proc

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o fin

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f sha

ded

regi

on1 4

× π

× 4.

8² −

1 2×

4.8

× 4.

8A

1fo

r 6.5

6 –

6.58



Pape

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8(a

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(b)

expl

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C1

for “

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both

solu

tions

” oe

9(a

)18

B1

cao

(b)

5(x

–1)

M1

for m

etho

d to

find

inve

rse

func

tion

A1

for 5

(x–

1) o

r 5x

− 5

(c)

9x–

48 sh

own

M1

for m

etho

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find

com

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1fo

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lead

ing

to 9

x–

48

10(a

)15

6000

0 ×

(1.0

52)2

1730

000

P1fo

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to fi

nd p

opul

atio

n in

201

6P1

for c

ompl

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proc

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o fin

d po

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tion

in 2

017

A1

for 1

7250

00 -

1730

000

(b)(

i)20

20P1

for p

roce

ss to

find

whe

n po

pula

tion

will

exc

eed

2 00

0 00

0A

1fo

r 202

0

(ii)

C1

for c

orre

ct c

omm

ent o

n ho

w a

ssum

ptio

n w

ill

affe

ct th

e an

swer

, eg

if th

e pe

rcen

tage

gro

wth

is

high

er th

e po

pula

tion

may

exc

eed

2 00

0 00

0 ea

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.



Pape

r 1M

A1:

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11(a

)0.

43M

1fo

r use

of g

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at 2

40 m

inut

esA

1fo

r 0.4

2 –

0.44

oe

(b)

com

paris

on

B1

for a

t lea

st o

ne m

edia

n (2

49 –

252

or 2

73 –

276)

B1

for l

east

one

inte

rqua

rtile

rang

e (6

9 –

73 o

r 67

-71)

C1

for c

omm

ent c

ompa

ring

aver

age

times

eg

fem

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take

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ales

oe

C1

for c

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spre

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spre

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es is

abo

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e sa

me

(NB

–at

leas

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of t

he c

omm

ents

mus

t be

in

cont

ext)

12(a

)25

× 2

460

0P1

for p

roce

ss to

find

num

ber o

f way

sA

1ca

o

(b)

12 ×

10

× 11

10

× 1

2 ×

913

20 +

108

0

2400

P1fo

r pro

cess

to fi

nd n

umbe

r of l

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with

boy

then

gi

rl th

en b

oy o

rthe

num

ber o

f lis

ts w

ith g

irl

then

boy

then

girl

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plet

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find

the

tota

l num

ber o

f lis

tsA

1ca

o



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

1311

9M

1fo

r 1.0

6 ×

100

oe

M1

for 1

.063

× 10

0oe

A1

acce

pt 1

19.1

016

14ex

plan

atio

nC

1fo

r a c

orre

ct e

valu

atio

n, e

g th

e va

lue

of D

shou

ld b

e m

ultip

lied

by 8

, she

has

use

d 2

× 3

inst

ead

of 2

³

15(a

)1.

0–

1.3

M1

for f

indi

ng g

radi

ent b

y dr

awin

g ta

ngen

tM

1fo

r met

hod

to c

alcu

late

gra

dien

tA

1Fo

r 1.0

–1.

3

(b)

C1

for a

ccel

erat

ion

C1

for e

g“

4 se

cond

afte

r the

star

t of t

he ra

ce”,

“w

hen

the

spee

d is

7.6

m/s

”, “

in m

/s2 ”

(c)

limita

tion

C1

for c

omm

ent,

eg d

epen

dent

on

accu

racy

of

cons

truct

ing

a ta

ngen

t

16(i)

200

B1

cao

(ii)

5.6

B1

For 5

.6(2

...)



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

17�

8.35

²−6.

05²

5.75

4997

828

B1

for f

indi

ng b

ound

s of o

ne m

easu

rem

ent,8

.25

8.35

, 6.0

5 or

6.1

5P1

for p

roce

ss o

f cho

osin

g an

d us

ing

corr

ect

boun

dsP1

for p

roce

ss o

f Pyt

hago

ras’

rule

with

cor

rect

bo

unds

A

1fo

r 5.7

54(9

97…

)

18( √𝑎𝑎

+2 √𝑏𝑏)

( √𝑎𝑎−

2 √𝑏𝑏)

a–

4bM

1fo

r exp

ansi

on o

f bra

cket

s or

42

bb

=

√𝑎𝑎× √𝑎𝑎

−2 √𝑎𝑎 √𝑏𝑏

+2 √𝑏𝑏 √𝑎𝑎−

2 √𝑏𝑏

×2 √𝑏𝑏

M1

for a

or (–

4b)

A1

cao

19(a

)sk

etch

B1

for c

orre

ct sh

ape

for 0

⩽x⩽

360

B1

for f

ully

cor

rect

sket

ch w

ith la

bels

(b)(

i)sk

etch

B1

cao

(ii)

sket

chB

1ca

o



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

20⦟

TSU

= 36

0 ÷

5 (=

72)

Exte

rior a

ngle

s of a

pol

ygon

ad

d up

to 3

60o

proo

fM

1fo

r met

hod

to fi

nd in

terio

r or e

xter

ior a

ngle

of

regu

lar p

enta

gon

⦟Q

RO=⦟

OTP

= 90

The

tang

entt

o a

circ

le is

pe

rpen

dicu

lar (

90o )to

the

radi

us(d

iam

eter

)

M1

for u

sing

ang

le b

etw

een

tang

ent a

nd ra

dius

⦟RO

T=

540

–2

× 90

–2

× 10

8 (=

144

)M

1fo

r met

hod

to fi

nd a

ngle

RO

T

⦟RU

T=

144

÷ 2

(= 7

2)Th

e an

gle

at th

e ce

ntre

of a

ci

rcle

is tw

ice

the

angl

e at

th

e ci

rcum

fere

nce

C1

for m

etho

d to

find

ang

le R

UT

with

reas

on

Bas

e an

gles

of a

n is

osce

les

trian

gle

are

equa

lC

1fo

r ded

uctio

n th

at S

T=

UT

with

reas

ons

212𝑥𝑥

− 1

𝑥𝑥 −

4

=16𝑥𝑥 +

1

2𝑥𝑥 −

1–1 12

, 5P1

for p

roce

ss to

writ

e as

an

equa

tion

(2x

–1)

² = (1

6x+

1)(x

–4)

P1fo

r pro

cess

to c

lear

the

frac

tions

12x²

–59

x–

5 =

0P1

for p

roce

ss to

writ

e eq

uatio

n in

form

ax

² + b

x+

c =

0(1

2x+

1)(x

–5)

= 0

P1fo

r pro

cess

to so

lve

the

equa

tion

A1

cao



Total Marks

Paper Reference

Turn over


6/6/4/

*S50160A0124*




Instructions




Information



Advice







Total Marks

Paper Reference

Turn over


6/6/4/

*S50160A0124*




Instructions




Information



Advice





3


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


– 2a

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




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


2

*S50160A0224*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA






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







3


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


– 2a

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




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


2

*S50160A0224*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA






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







5


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


T is given by

Tx

= 4500


.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°C (3)


T

O x

A T

O x

B

T

O x

C T

O x

D



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

(1)




1 2 3 4 50

1

2

3

4

5

60

Width (cm)

Length (cm)


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

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

(1)



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

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

(1)


4

*S50160A0424*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA



1 2 3 4 50

1

2

3

4

5

60

Width (cm)

Length (cm)


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

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

(1)



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

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

(1)




5


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


T is given by

Tx

= 4500


.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°C (3)


T

O x

A T

O x

B

T

O x

C T

O x

D



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

(1)




1 2 3 4 50

1

2

3

4

5

60

Width (cm)

Length (cm)


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

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

(1)



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

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

(1)


4

*S50160A0424*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA



1 2 3 4 50

1

2

3

4

5

60

Width (cm)

Length (cm)


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

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

(1)



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

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(1)




7


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3m

2.5m1.4m

2.4m

Only fill to85%

of capacity

The tank is empty.




.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minutes(5)



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

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

(1)


6

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xy


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7


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3m

2.5m1.4m

2.4m

Only fill to85%

of capacity

The tank is empty.




.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minutes(5)



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

(1)


6

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xy


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9


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10 The surface gravity of a planet can be worked out using the formula

g mr

= 6.67 × 10 11

2

−

where

m kilograms is the mass of the planet r metres is the radius of the planet

For the Earth and Jupiter here are the values of m and r.

Jupiter

m = 1.90 × 1027

r = 7.149 × 107

Earth

m = 5.98 × 1024

r = 6.378 × 106

Work out the ratio of the surface gravity of Earth to the surface gravity of Jupiter. Write your answer in the form 1: n

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


8

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9 Ibrar bought a house for £145 000

The value of the house depreciated by 4% in the first year. The value of the house depreciated by 2.5% in the second year.

Ibrar says,

“4 + 2.5 = 6.5 so in two years the value of my house depreciated by 6.5%”

(a) Is Ibrar right? You must give a reason for your answer.

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

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

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

(2)

The value of Ibrar’s house increases by x% in the third year. At the end of the third year the value of Ibrar’s house is £140 000

(b) Work out the value of x. Give your answer correct to 3 significant figures.

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

(3)




9


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10 The surface gravity of a planet can be worked out using the formula

g mr

= 6.67 × 10 11

2

−

where

m kilograms is the mass of the planet r metres is the radius of the planet

For the Earth and Jupiter here are the values of m and r.

Jupiter

m = 1.90 × 1027

r = 7.149 × 107

Earth

m = 5.98 × 1024

r = 6.378 × 106

Work out the ratio of the surface gravity of Earth to the surface gravity of Jupiter. Write your answer in the form 1: n

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


8

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9 Ibrar bought a house for £145 000

The value of the house depreciated by 4% in the first year. The value of the house depreciated by 2.5% in the second year.

Ibrar says,

“4 + 2.5 = 6.5 so in two years the value of my house depreciated by 6.5%”

(a) Is Ibrar right? You must give a reason for your answer.

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

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

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

(2)

The value of Ibrar’s house increases by x% in the third year. At the end of the third year the value of Ibrar’s house is £140 000

(b) Work out the value of x. Give your answer correct to 3 significant figures.

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

(3)




11


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12 Zahra mixes 150g of metal A and 150g of metal B to make 300g of an alloy.

Metal A has a density of 19.3g/cm3. Metal B has a density of 8.9g/cm3.

Work out the density of the alloy.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g/cm3


10

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11 Solve the simultaneous equations

2x – 4y = 193x + 5y = 1

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

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




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12 Zahra mixes 150g of metal A and 150g of metal B to make 300g of an alloy.

Metal A has a density of 19.3g/cm3. Metal B has a density of 8.9g/cm3.

Work out the density of the alloy.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g/cm3


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11 Solve the simultaneous equations

2x – 4y = 193x + 5y = 1

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

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




13

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Turn over

14 The table gives information about the speeds, in km/h, of 81 cars.

Speed (s km/h) Frequency

90 < s 100 13

100 < s 105 16

105 < s 110 18

110 < s 120 22

120 < s 140 12

(a) On the grid, draw a histogram for the information in the table.

(3)

(b) Find an estimate for the median.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .km/h(2)


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13y7

6

5

4

3

2

1

O

–1

–2

–3

–4

–5

–6

–7

–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x

On the grid, enlarge the triangle by scale factor −112

, centre (0, 2)




13

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Turn over

14 The table gives information about the speeds, in km/h, of 81 cars.

Speed (s km/h) Frequency

90 < s 100 13

100 < s 105 16

105 < s 110 18

110 < s 120 22

120 < s 140 12

(a) On the grid, draw a histogram for the information in the table.

(3)

(b) Find an estimate for the median.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .km/h(2)


12

*S50160A01224*

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13y7

6

5

4

3

2

1

O

–1

–2

–3

–4

–5

–6

–7

–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x

On the grid, enlarge the triangle by scale factor −112

, centre (0, 2)




15


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17 The product of two consecutive positive integers is added to the larger of the two integers.

Prove that the result is always a square number.


14

*S50160A01424*

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15 Show that ab

ab+

−+1 1 2( )

can be written as abb( )+ 1 2


16 The diagram shows a sector of a circle of radius 4 cm.

B

A C

O

100° 4cm

Work out the length of the arc ABC. Give your answer correct to 3 significant figures.

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




15


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17 The product of two consecutive positive integers is added to the larger of the two integers.

Prove that the result is always a square number.


14

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15 Show that ab

ab+

−+1 1 2( )

can be written as abb( )+ 1 2


16 The diagram shows a sector of a circle of radius 4 cm.

B

A C

O

100° 4cm

Work out the length of the arc ABC. Give your answer correct to 3 significant figures.

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




17


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19 Prove algebraically that the recurring decimal 0.31̇8̇ can be written as 722


16

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18 Here is a speed-time graph for a car.

0 2 4 6 8 10 120

5

10

15

20

25

30

Time (s)

Speed (m/s)

(a) Work out an estimate for the distance the car travelled in the first 10 seconds. Use 5 strips of equal width.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .m(3)

(b) Is your answer to (a) an underestimate or an overestimate of the actual distance? Give a reason for your answer.

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

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

(1)




17


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19 Prove algebraically that the recurring decimal 0.31̇8̇ can be written as 722


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18 Here is a speed-time graph for a car.

0 2 4 6 8 10 120

5

10

15

20

25

30

Time (s)

Speed (m/s)

(a) Work out an estimate for the distance the car travelled in the first 10 seconds. Use 5 strips of equal width.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .m(3)

(b) Is your answer to (a) an underestimate or an overestimate of the actual distance? Give a reason for your answer.

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

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

(1)




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Turn over

21C

BDA

25°

4.9cm

80°3.8cm

ABC is a triangle. D is a point on AB.

Work out the area of triangle BCD. Give your answer correct to 3 significant figures.

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


18

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20

2a

A

P

BO 2b

OAB is a triangle. P is the point on AB such that AP : PB = 5:3

OA→

= 2a

OB→

= 2b

→OP = k(3a + 5b) where k is a scalar quantity.

Find the value of k.

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




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Turn over

21C

BDA

25°

4.9cm

80°3.8cm

ABC is a triangle. D is a point on AB.

Work out the area of triangle BCD. Give your answer correct to 3 significant figures.

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


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20

2a

A

P

BO 2b

OAB is a triangle. P is the point on AB such that AP : PB = 5:3

OA→

= 2a

OB→

= 2b

→OP = k(3a + 5b) where k is a scalar quantity.

Find the value of k.

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




21

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23 (a) Write 2x2 + 16x + 35 in the form a(x + b)2 + c where a, b, and c are integers.

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

(3)

(b) Hence, or otherwise, write down the coordinates of the turning point of the graph of y = 2x2 + 16x + 35

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

(1)



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22 There are y black socks and 5 white socks in a drawer.

Joshua takes at random two socks from the drawer.

The probability that Joshua takes one white sock and one black sock is 611

(a) Show that 3y2 – 28y + 60 = 0

(4)

(b) Find the probability that Joshua takes two black socks.

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

(3)




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23 (a) Write 2x2 + 16x + 35 in the form a(x + b)2 + c where a, b, and c are integers.

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

(3)

(b) Hence, or otherwise, write down the coordinates of the turning point of the graph of y = 2x2 + 16x + 35

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

(1)



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22 There are y black socks and 5 white socks in a drawer.

Joshua takes at random two socks from the drawer.

The probability that Joshua takes one white sock and one black sock is 611

(a) Show that 3y2 – 28y + 60 = 0

(4)

(b) Find the probability that Joshua takes two black socks.

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

(3)




23

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24

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Pape

r 1M

A1:

3H

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stio

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ngA

nsw

erN

otes

117

1P1

for p

roce

ss to

find

one

shar

eP1

for p

roce

ss to

find

tota

lA

1ca

o

2pl

anC

1a

parti

ally

cor

rect

pla

nC

1co

rrec

t pla

n

3t=

3(y

+ 2a

)M

1ad

ding

2a

to b

oth

side

s or m

ultip

lyin

g ea

ch te

rm

by 3

A1

t= 3

(y+

2a) o

r t=

3y+

6a

47.

15 ≤

x<

7.25

B1

for 7

.15

and

7.25

B1

cao

5(a

)im

prov

emen

tC

1ap

prop

riate

impr

ovem

ent e

g do

not

hav

e ax

es

star

ting

at (0

, 0)

(b)

expl

anat

ion

C1

expl

anat

ion

egpi

ne c

one

has a

ver

y sh

ort w

idth

fo

r its

leng

th

6(a

)1.

95M

1m

etho

d to

find

one

tem

pera

ture

eg 4

500

÷ 12

00M

1fo

r com

plet

e m

etho

dA

1ca

o

(b)

DB

1ca

o



Pape

r 1M

A1:

3H

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stio

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orki

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nsw

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otes

7co

mpl

ete

chai

n of

reas

onin

gC

1st

arts

cha

in o

f rea

soni

ng e

g fin

ds a

rea

of la

rge

squa

re a

nd a

rea

of tr

iang

le o

r use

of P

ytha

gora

s C

1fo

r (x

+y)

2–

4× (x

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) oe

or

22

yx

+×

22

yx

+C

1co

mpl

ete

chai

n of

reas

onin

g w

ith c

orre

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lgeb

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8(a

)36

.4P1

star

t pro

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met

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to fi

nd a

rea

of tr

apez

ium

P1co

mpl

ete

proc

ess t

o fin

d vo

lum

e of

tank

P1pr

oces

s to

find

time

eg v

olum

e ×

1000

÷ 3

00P1

proc

ess t

o fin

d 85

% o

f vol

ume

or o

f tim

eA

1fo

r 36.

4 or

36

min

s 24

secs

(b)

C1

expl

anat

ion

eg if

the

aver

age

rate

was

slow

er it

w

ould

take

mor

e tim

e, if

the

aver

age

rate

was

fa

ster

it w

ould

take

less

tim

e

9(a

)N

o w

ith re

ason

C1

parti

al e

xpla

natio

n, e

g 0.

96 ×

0.9

75C

1N

o w

ith fu

ll ex

plan

atio

n, e

g0.

96 ×

0.9

75 =

0.

936

so o

nly

a 6.

4% re

duct

ion

(b)

3.15

P1co

mpl

ete

proc

ess t

o fin

d va

lue

afte

r 2 y

ears

eg

(145

000

–‘5

800’

) × 2

.5/1

00 o

e or

145

000

× 0.

96

× 0.

975

(= 1

3572

0)P1

(140

000

–‘1

3572

0’) ÷

‘135

720’

× 1

00 o

eA

1fo

r 3.1

5 –

3.15

4



Pape

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A1:

3H

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stio

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nsw

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otes

101

: 2.5

3P1

for s

ubst

itutin

g va

lues

to fi

nd su

rfac

e gr

avity

of

eith

er E

arth

(= 9

.805

..) o

r Jup

iter (

= 24

.796

..)P1

for c

ompl

ete

proc

ess

A1

for 1

: 2.

528

to 2

.53

11x

= 4.

5y

=–2

.5M

1fo

r a c

orre

ct p

roce

ss to

elim

inat

e on

e va

riabl

e (c

ondo

neon

e ar

ithm

etic

err

or)

A1

cao

for e

ither

xor

yM

1(d

ep) f

or su

bstit

utin

g fo

und

valu

e in

toon

e of

the

equa

tions

or a

ppro

pria

te m

etho

d af

ter s

tarti

ng

agai

n (c

ondo

ne o

ne a

rithm

etic

err

or)

A1

cao

1212

.2P1

begi

ns p

roce

ss e

g15

0÷19

.3 (=

7.7

7..)

or 1

50÷8

.9

(= 1

6.85

..)P1

com

plet

e pr

oces

s to

find

tota

l vol

ume

P1co

mpl

ete

proc

esst

o fin

d th

e de

nsity

of t

he a

lloy

A1

for a

nsw

er in

rang

e 12

.1 to

12.

2

13Tr

iang

le

(–6,

2),

(–6,

–1),

M1

for c

orre

ct sh

ape

and

the

corr

ect o

rient

atio

n in

th

e w

rong

pos

ition

or t

wo

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ces c

orre

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(–3,

–1)

A1

cao



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orki

ngA

nsw

erN

otes

14(a

)hi

stog

ram

C1

for 2

cor

rect

bar

s of d

iffer

ent w

idth

s or a

t lea

st 3

co

rrec

t fre

quen

cy d

ensi

ties

C1

all b

ars i

n co

rrec

t pro

porti

ons o

r 4 c

orre

ct b

ars

with

axe

s sca

led

and

labe

lled

C1

fully

cor

rect

his

togr

am w

ith a

xes s

cale

d an

d la

belle

d

(b)

81 ÷

2 =

40.

510

8.2

C1

for 8

1 ÷

2 =

40.5

and

11.

5 ÷

18 ×

5 (=

3.1

9..)

90 to

105

is 2

9C

1Fo

r ans

wer

in ra

nge

108

to 1

09

15sh

own

C1

for

2 )1(

)1(

+−

+ ba

ba

or

3

2

)1(

)1(

)1(

++

−+

bb

ab

aoe

C1

com

plet

e ch

ain

of re

ason

ing

1618

.2M

1fo

r 36

026

0×

π ×8

oe

or 36

010

0×

π ×8

oe

A1

for 1

8.1

to 1

8.2

17pr

oof

C1

star

ts p

roof

eg

n(n+

1) o

r (n

–1)

×nC

1n(

n+1)

+ n

+1 o

r (n

–1)

×n+

nC

1fo

r con

vinc

ing

proo

f inc

ludi

ng (n

+1)2

or n

2



Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

18(a

)va

lues

0, 2

, 5, 9

, 15,

24

86M

1fo

r sta

rting

to fi

nd a

rea

unde

r cur

veM

1fo

r met

hod

to fi

nd th

e ar

ea u

nder

the

curv

e be

twee

n t=

0an

d t=

10(a

nd a

t lea

st 2

are

as)

A1

(b)

over

estim

ate

with

reas

onC

1fo

r ove

rest

imat

e an

d ap

prop

riate

reas

on li

nked

to

met

hod

eg a

rea

betw

een

trape

zium

s and

cur

veal

so in

clud

ed

19pr

oof

lead

ing

to 227

M1

for f

indi

ng tw

o co

rrec

t rec

urrin

g de

cim

als t

hat

whe

n su

btra

cted

wou

ld re

sult

in a

term

inat

ing

deci

mal

or i

nteg

er w

ith in

tent

ion

to su

btra

cteg

x=

0.31

818.

.., 1

00x

= 31

.818

18...

A1

fully

cor

rect

pro

of

2041

P1st

arts

pro

cess

eg

=AB

2b–

2a

P1pr

oces

s to

find

APor

BP

P1co

mpl

ete

proc

ess t

o fin

d O

PA

1fo

r 41

oe



Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

2110

.4P1

star

ts p

roce

ss b

y us

ing

cosi

ne ru

le to

find

CD

eg (C

D)2

= 4.

92 +3.8

2 –2×

4.9×

3.8×

cos8

0 (=

31

.98.

.)P1

uses

sine

rule

to fi

nd a

ngle

AC

Dor

ang

le A

DC

eg

'65

5.5'

80sin

8.3sin=

Cor

'

655

.5'80

sin9.4sin

=D

P1us

es si

ne ru

le to

find

BC

or B

D

eg

'6.33

sin'

'65

5.5'

25sin

=BD

P1pr

oces

s to

find

area

eg

1/2

absi

nCA

1fo

r 10.

4 to

10.

43



Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

22(a

)ch

ain

of

reas

onin

gC

1fo

r a re

leva

nt p

rodu

ct e

g 5

+yy

×4

5 +yC

1fo

r a

corr

ect e

quat

ion

eg 2

×

+

×+

45

5y

yy

=116

C1

for m

etho

d to

elim

inat

e fr

actio

ns fr

om a

lgeb

raic

ex

pres

sion

C1

com

plet

e ch

ain

of re

ason

ing

(b)

113M

1m

etho

d to

solv

e eq

uatio

n eg

(ax

+b)

(cx

+d) w

ith

ac=

3 an

d bd

= ±6

0A

1fo

r sel

ectin

g y

= 6

A1

for

113oe

232(

x+

4)2

+ 3

P1pr

oces

s to

find

a, e

g 2x

2+

16x

+ 35

= 2

(x2

+ …

) or

a=

2P1

for 2

((x

+ 4)

2+

…))

or b

= 4

A1

for 2

(x+

4)2

+ 3

or a

= 2,

b=

4, c

= 3

(–4,

3)

B1

ft fr

om a

nsw

er o

f for

m a

(x+

b)2

+c

Documents

GCSE (9-1) Mathematics - MathsGeeksmathsgeeks.co.uk/allpapers/GCSE/Edexcel/9-1EdexcelSet2.pdf · GCSE (9-1) Mathematics ... P v 1v 2 91 i i i 2 2015 i ii 2015 4 7 Ignoring subsequent