CCEA GCSE Specimen Assessment Materials for Mathematicsbrownlowcollege.co.uk/wp-content/uploads/2018/01/... · 2018. 1. 16. · CCEA has developed new specifications which comply

CCEA GCSE SpecimenAssessment Materials for

Mathematics

GCSE

For first teaching from September 2017For first assessment in Summer 2018For first award in Summer 2019Subject Code: 2210

ForewordCCEA has developed new specifications which comply with criteria for GCSE qualifications. The specimen assessment materials accompanying new specifications are provided to give centres guidance on the structure and character of the planned assessments in advance of the first assessment. It is intended that the specimen assessment materials contained in this booklet will help teachers and students to understand, as fully as possible, the markers’ expectations of candidates’ responses to the types of tasks and questions set at GCSE level. These specimen assessment materials should be used in conjunction with CCEA’s GCSE Mathematics specification.

GCSE MathematicsSpecimen Assessment Materials

Contents

Specimen Papers 3

Unit M1: Calculator Paper 3Unit M5.1: Non-Calculator Paper 29Unit M5.2: Calculator Paper 43




Mark Schemes 199

General Marking Instructions 201





Subject Code 2210

QAN 603/1688/3

A CCEA Publication © 2017

You may download further copies of this publication from www.ccea.org.uk

SPECIMEN PAPERS

Centre Number

Candidate Number

General Certificate of Secondary Education2018

For Examiner’s use only

Question Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

TotalMarks

TIME1 hour 45 minutes.

INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided.Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all thirty questions.

INFORMATION FOR CANDIDATESFunctional Mathematics is assessed in this unit.The total mark for this paper is 100Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question.You may use a calculator.The Formula Sheet is on page 4.

Mathematics

[CODE]

SPECIMEN PAPER

M1

Calculator Paper

Foundation Tier

3

4

Formula Sheet

Area of trapezium = 1–2 (a + b)h

Volume of prism = area of cross section × length

a

h

b

crosssection

length

Formula Sheet

Examiner Only

Marks Re-mark

5

1 Julie is a car-parking attendant.

(a) Julie is paid £5.00 an hour. Last month she worked 36 hours. How much did Julie earn last month?

Answer £ [1]

(b) Julie saves £15 each week towards a holiday. How many weeks will it take to save £300?

Answer [1]

(c) Last week there were one thousand, three hundred and seven cars in the car park.

Write this number in figures.

Answer [1]

(d) In June, 9271 people used the car park. What is this number rounded to the nearest hundred?

Answer [1]

Examiner Only

Marks Re-mark

6

2 Ryan owns a shop in Dungannon.

Ryan lives in Strabane. The table below shows distances in miles between towns.

(a) How far does Ryan have to travel to his shop?

Augher Dromore Dungannon Pomeroy Strabane

Augher 20 14 17 40

Dromore 20 28 24 23

Dungannon 14 28 9 42

Pomeroy 17 24 9 22

Strabane 40 23 42 22

Answer miles [1]

(b) (i) On Friday, Ryan made a profit of one hundred and eight pounds and forty seven pence.

Write this amount in figures.

Answer £ [1]

(ii) On Saturday, Ryan increased his Friday profit by 10%.

What profit did he make on Saturday?

Answer £ [3]

Examiner Only

Marks Re-mark

7

3 Frank is going on a holiday.

Frank’s suitcase measures 120 cm 60 cm 35.5 cm. Write these measurements in metres.

Answer [2]

4 Frank leaves home at 5.45 am and drives to the airport. He arrives at 7.00 am. How long did his journey take?

Answer [1]

5 The chart below shows the number of cars arriving at Dublin airport, to the nearest 100

Times of arrival

0

100

200

300

400

500

600

Time

7am 8am 9am 10am 11am noon

Num

ber o

f car

s

Approximately how many cars arrived between 7 am and 12 noon?

Answer [2]

Examiner Only

Marks Re-mark

8

6 The bar chart below shows the number of stalls each week in June and July at a summer fair.

Number of stalls in June and July

0

10

20

30

40

50

60

Key: June July

Week 1 Week 2 Week 3 Week 4

Num

ber o

f Sta

lls

(a) Which week in July had the lowest number of stalls?

Answer [1]

(b) In June how many more stalls were there in Week 3 than in Week 4?

Answer [2]

(c) What was the mean number of stalls in July?

Answer [3]

Examiner Only

Marks Re-mark

9

7 Amy uses triangular tiles to tile her kitchen floor. She has two types of tile: light tiles and dark tiles.

What fraction of the floor is covered in dark tiles?

Write your answer in its simplest form.

Answer [2]

9310

*28GMT1104*

*28GMT1104*

2 (a)

What fraction of the diagram is shaded?

Give your answer in its simplest form.

Answer [2]

(b) Write 5672 to the nearest 100

Answer [1]

(c) Write down in figures the number forty-nine thousand and twenty-five.

Answer [1]

Examiner Only

Marks Re-mark

10

8 What type of triangle is this?

Circle your answer

equilateral isosceles right-angled scalene

[1]

Examiner Only

Marks Re-mark

11

9 (a) Josh is designing a logo for a sports company.

He draws the logo on a 1 cm grid.

Calculate the perimeter of the logo.

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

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

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

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

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

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

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

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

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

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

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

Answer cm [2]

(b) This net is folded to make a cube.

Which letter will be opposite X?

B EA X C

DAnswer [1]

Examiner Only

Marks Re-mark

12

10 Mary is baking scones. She compares the amount of milk required in 4 recipes.

Recipe Amount of milk required

Recipe A

Recipe B

Recipe C

Recipe D

12

cup

58

cup

34

cup

14

cup

Write the recipes in order, starting with the recipe that requires the least amount of milk.

Recipe Recipe Recipe Recipe [2]

Examiner Only

Marks Re-mark

13

11 Lynn is drawing a pictogram to show the number of cakes she sells.

Type of cake Number of cakes

Chocolate

Carrot

Coffee

Sponge

Key

= 4 cakes

(a) How many chocolate cakes did Lynn sell?

Answer [1]

(b) How many more carrot cakes than coffee cakes did Lynn sell?

Answer [1]

(c) Lynn sold 12 sponge cakes. Complete the pictogram to show this information. [1]

(d) Give one advantage of using a circle to represent 4 cakes.

[1]

Examiner Only

Marks Re-mark

14

12 (a) Write down the value of 2.32 Answer [1]

(b) Show that 5 is the highest common factor of 10 and 15

[2]

(c) Show that 23 is not a square number.

[2]

13 Here is a sign in a car park.

CAR PARK

Pay machine takes these coins

£2 £1 50p 20p 10p 5p

Lucy paid exactly £2.85

She used six coins. She did not use any £1 coins.

Show three different ways she could have paid.

[3]

Examiner Only

Marks Re-mark

15

14 The Ulster Rugby Club ticket prices for their match against Munster are:

Adult £16 Child £6 Senior Citizen £9

A family spends £53 on tickets. They buy at least one of each type of ticket. How many of each ticket do they buy?

Answer Adult

Answer Child

Answer Senior Citizen [3]

Examiner Only

Marks Re-mark

16

15 Three friends buy a restaurant.

Gordon’s share is 35%

Jay’s share is 14

Gino pays £36 000

How much does the restaurant cost?

Answer £ [4]

16 Solve the equations

(a) 6x = 24

Answer x = [1]

(b) y – 8 = 12

Answer y = [1]

Examiner Only

Marks Re-mark

17

17 Calculate the volume of this cereal box. Include the correct units in your answer.

6 cm

26 cm

19 cm

Cereal

Answer [3]

Examiner Only

Marks Re-mark

18

18 The chart below shows the types of stalls at the fair.

STALLS

Household

Food

Clothes

New goods

(a) Which is the most common type of stall?

Answer [1]

(b) Jane estimates that there are twice as many clothes stalls as food stalls.

Explain why Jane is correct.

[1]

Examiner Only

Marks Re-mark

19

19 Seven people spent the following amounts of money on their lunch.

£5, £7, £4, £3, £9, £6, £7

(a) Find the modal amount spent.

Answer £ [1]

(b) Find the median amount spent.

Answer £ [2]

20 A clothes shop has a sale.

John buys a pair of jeans and a shirt in the sale. Before the sale the jeans were £54 and the shirt was £28 How much in total did John pay?

Answer £ [5]

© CCEA

Jeans – 1/3 off Shirts – 20% off

Examiner Only

Marks Re-mark

20

21 Gareth has applied for a loan of £3,000 which has an APR of 6%.

On application to the loan company, the APR he is offered is 8%. If Gareth pays back his loan at the end of one year, how much extra does

the APR of 8% cost than the APR of 6%?

Answer [3]

22 The diagram shows two identical squares. Find the size of the angle x.

x

70°

Diagram not drawn to scale

Answer x = [4]

Examiner Only

Marks Re-mark

21

23 Farrah’s mobile phone passcode is a four digit number.

All four digits are different. The first digit is an even prime. The second and third digits have a sum of 8 and a product of 15 The fourth digit is double the third digit. What is Farrah’s passcode?

Answer [3]

24 (a) Expand and simplify 7(2a + 3) + 3(4a – 2)

Answer [2]

(b) Factorise 20d – 35

Answer [1]

Examiner Only

Marks Re-mark

22

25 The volumes of these boxes are the same.

6 cm 4 cm

6 cm 6 cm

6 cm L cm

Calculate the length of the side marked L.

Answer L = cm [3]

Examiner Only

Marks Re-mark

23

26 50 people take a driving test.

The two-way table shows the results.

Pass Fail

Male 12 10

Female 20

(a) Complete the two-way table. [1]

(b) Complete the frequency tree from the two-way table.

Fail

Fail

Pass

Pass

50

Female

Male

[2]

Examiner Only

Marks Re-mark

24

27 (a) James wants to install a swimming pool in his garden.

F

G

centre

FG is the diameter of the swimming pool. FG is 9 m. Calculate the area of the swimming pool. Give your answer correct to the nearest whole number.

Answer m2 [4]

(b) Calculate the perimeter of the swimming pool. Give your answer correct to 1 decimal place.

Answer m [3]

Examiner Only

Marks Re-mark

25

28 The cost, £C, of booking a party at a hotel can be calculated using the formula

C = 45N + 200

N = number of guests at the party. Rosie is planning to book a party at the hotel. She has a budget of £1,100

Rosie wants to spend all her money.

How many guests can she invite?

Answer guests [4]

Examiner Only

Marks Re-mark

26

29 25 pupils took part in a computer quiz.

The times, to the nearest minute, that the pupils took to complete the quiz are:

27 33 29 24 34

22 26 28 22 31

19 38 36 18 30

23 35 27 21 37

24 26 25 28 21

(a) Use this information to complete the grouped frequency table:

Time taken (min) Tally (if required) Frequency

15–19

20–24

25–29

30–34

35–39

[2]

(b) (i) Which type of diagram would you use to display this information?

[1]

(ii) Give a reason for your answer.

[1]

Examiner Only

Marks Re-mark

27

30

Diagram notdrawn accurately

B

A C

D

ABCD is a kite. The length of AB is 2 cm less than the length of AD. The perimeter of the kite is 30 cm. Let the length of AD = x Work out the length of AB.

Answer AB = cm [4]

THIS IS THE END OF THE QUESTION PAPER

28

Centre Number

Candidate Number



Question Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

TotalMarks

TIME1 hour.

INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided.Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all twenty questions.

INFORMATION FOR CANDIDATESThe total mark for this paper is 50Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question You must not use a calculator for this paper.The Formula Sheet is on page 30.

Mathematics

[CODE]

SPECIMEN PAPER

M5.1

Non-Calculator Paper

Foundation Tier

29

30 [Turn over

Formula Sheet



a

h

b

crosssection

length

Examiner Only

Marks Re-mark

31

1 The probability that it will rain on Saturday is 0.7

Write this as a fraction.

Answer [1]

2 A roll of material is 15 metres long.

Sally buys 8.5 metres of the material. How much material is left on the roll?

Answer m [2]

3 Jack buys a pack of crisps for £1.50

There are 6 bags of crisps in the pack. How much does each bag cost?

Answer £ [2]

Examiner Only

Marks Re-mark

32

4 Kate estimates that 120 is 12

Is she correct?

Give a reason for your answer.

Answer because [2]

5 The formula for calculating the perimeter of a rectangle can be written as:

P = 2(l + b)

where l is the length and b is the breadth of the rectangle.

This formula can also be written as:

P = 2l + 2b

P = 2l + b

P = l + l + b + b

P = 2 l b Tick the correct answer or answers. [2]

Examiner Only

Marks Re-mark

33

6 Use the train timetable below to answer the questions that follow.

Train Timetable

Bangor 0816 0825 0848 0907 0922

Carnalea | 0829 0852 | 0926

Helen’s Bay | 0833 0856 | 0930

Seahill | 0836 0859 | 0933

Cultra | 0839 0902 | 0936

Marino | 0841 0904 | 0938

Holywood 0829 0844 0907 0920 0941

(a) Brian takes the 0930 train from Helen’s Bay.

What time should he arrive in Holywood?

Answer [1]

(b) Clare takes the 0848 train from Bangor.

She is travelling to Holywood. How long should the journey take?

Answer min [2]

Examiner Only

Marks Re-mark

34

7 John works in a multi-storey car park.

(a) By 9.30 am, the car park was 75% full. What fraction of the car park was full?

Answer [1]

(b) John says that 13 of the drivers had passengers. What is 13 of 1500?

Answer [1]

(c) One hundred cars (to the nearest 10), arrived between 11.00 and 12.00

What is the smallest possible number of cars that arrived in this time?

Answer [1]

8

Day 1 2 3 4 5 6 7 8 9 10

Sun: Rain:

John kept a record of the weather for ten days. It was either sunny or raining. What is the probability that it was raining?

Answer [1]

© CCEA

Examiner Only

Marks Re-mark

35

9 The time is twenty-five past two in the afternoon.

Write this time using the 24-hour clock.

Answer [1]

10 A normal six sided dice is rolled 240 times.

It lands on six a total of 20 times. Do you think the dice is fair?


Answer because [2]

11 Given that a = 5, b = 10 and c = 12, work out

2a – b + 4c

Answer [2]

Examiner Only

Marks Re-mark

36

12 Jess has a large wooden chest in the shape of a cuboid. The inside of the chest is 130 cm long, 40 cm wide and 20 cm tall.

Jess has a collection of one hundred 10 cm cubes.

Can all of her cubes fit into the chest? Justify your answer.

Answer because [3]

© Patrick Cleiren / Hemera /Thinkstock

Examiner Only

Marks Re-mark

37

13 Elsie travels to Belfast to go to St George’s Market. The distance she travels is 105 miles each way. Elsie’s car goes 35 miles for every gallon of petrol it uses. Elsie says ‘To travel to Belfast and back, my car needs 6 gallons of petrol’. Is she correct?

You must show your working

Answer Elsie is [3]

14 A recipe uses 6 eggs to make 12 buns.

Eve only wants to make 4 buns. How many eggs does she need?

Answer eggs [2]

Examiner Only

Marks Re-mark

38

15 This is a plan of part of a field.

27 m

8 m

What is the maximum number of plots measuring 4 m 3 m that could fit into this space?

Answer [2]

16 Mary ran 50 km last week. She ran 30 miles this week. She says she ran at least 100 km over the 2 weeks. Is she right?

Explain your answer

Answer because [3]

Examiner Only

Marks Re-mark

39

17 Pablo is an artist. He paints on canvas. He uses different sizes of canvas but they all have their width and height in

the ratio 4:3

(a) Which of the following canvas sizes could he use?

32 cm by 24 cm 60 cm by 45 cm 100 cm by 70 cm 120 cm by 90 cm

Circle the correct answers [3]

(b) Write down another canvas size that he could use that is not given in the list above.

Answer [1]

Examiner Only

Marks Re-mark

40

18

10987654321–1–2–3–4–5–6–7–8–9–10

1

2

3

4

5

–6

6

–5

7

–4

8

–3

9

–2

10

–1

y

x

A

(a) How many lines of symmetry has shape A?

Answer [1]

(b) Translate the shape A, 5 right, 4 down. Label it B. [1]

(c) Draw the image of shape A after a reflection in the y axis.

Label it C. [2]

40

Examiner Only

Marks Re-mark

41

19 The word lengths of the first 60 words in a book were recorded.

The table shows the probability of some of these word lengths.

Number of letters Probability

1 – 2 0.1

3 – 4 0.25

5 – 6 0.45

7 – 8 0.15

9 or more

The first chapter contains 7500 words. How many words of 9 or more letters would you expect in the first chapter?

Answer words [4]

20

W

V

Z

Y X

p

Diagram not drawn accurately

VWXYZ is a regular pentagon. The angle p = 36º Work out the sum of the interior angles of this regular pentagon.

Answer ° [4]


42

Centre Number

Candidate Number


For Examiner’s

use onlyQuestion

Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

TotalMarks

TIME1 hour.

INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided. Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all nineteen questions.

INFORMATION FOR CANDIDATESThe total mark for this paper is 50Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question.You may use a calculator.The Formula Sheet is on page 44.

Mathematics

[CODE]

SPECIMEN PAPER

M5.2

Calculator Paper

Foundation Tier

43

44

Formula Sheet



a

h

b

crosssection

length

Formula Sheet

Examiner Only

Marks Re-mark

45

1 This circle is drawn on a centimetre grid.

–2

5

4

3

2

1

0

–1

–3

–4

–5

–5 –4 –3 –2 –1 1 2 3 4 5

y

x

What is the length of the radius of the circle?

Answer cm [1]

Examiner Only

Marks Re-mark

46

2 Ryan has a market stall.

Last Saturday he sold £126.60 worth of goods. From this amount he paid £8.00 to rent his stall and £8.50 for petrol.

How much is left from the sale of the goods?

Answer £ [2]

3 The fuel tank of a car holds 52 litres of petrol.

The car goes 11 miles on each litre of petrol. How far can the car go on a full tank of petrol?

Answer miles [2]

Examiner Only

Marks Re-mark

47

4 Some “U” shapes are made with matches.

Shape 1 Shape 2 Shape 3

(a) Draw shape 4 in the space above. [1]

(b) Complete the table below for shapes 4 and 5 [1]

Shape Number 1 2 3 4 5

Number of Matches 5 8 11

(c) What pattern do you notice in the ‘number of matches’ row?

Answer [1]

Shape 4

Examiner Only

Marks Re-mark

48

5 (a) A bag contains cards numbered from 1 to 20 A card is taken at random from the bag.

Which type of number, from odd, even or square, is least likely to be taken?

Explain your answer.

Answer [1]

because [1]

(b) Impossible Unlikely Evens Likely Certain

Choose a word from the box above which best describes the likelihood of each of these events:

(i) The next baby to be born in the world will be a girl.

Answer [1]

(ii) February follows March in the same year.

Answer [1]

6 Kevin buys 3 oranges priced at 75 pence each.

How much change does he get from £5?

Answer £ [2]

Examiner Only

Marks Re-mark

49

7 13

of all babies born in Northern Ireland last year can expect to live to

90 years of age. Last year, 24 393 babies were born in Northern Ireland.

How many are expected to live to 90 years of age?

Answer [2]

8 (a) Write 1 12

million in figures.

Answer [1]

(b) Write down a percentage between 13

and 25

Answer [1]

9 A manager wishes to buy new uniforms for his 30 staff.

A shirt costs £8.15 and trousers cost £19.95 A uniform consists of a shirt and trousers.

Estimate the total cost of the uniforms.

Show all steps of your working clearly.

Answer £ [2]

Examiner Only

Marks Re-mark

50

10 Tom buys three shirts.

Each shirt costs £5 correct to the nearest pound (£).

What is the most that Tom could have paid in total for three shirts?

Answer £ [2]

11 There are 60 pupils in Year 8.

A pupil is chosen at random.

What is the probability that a boy is chosen?

Tick a box and give a reason for your answer.

exactly 0.5 about 0.5 cannot say

Reason

[2]

12 Jewellery boxes cost £3.25 each. Beth has £15 She estimates she can buy 5 of these jewellery boxes.

Explain why Beth is wrong.

[2]

Examiner Only

Marks Re-mark

51

13 (a) The probability that a bus is on time is 0.7 Mark with an X on the scale below, the probability that the bus is not

on time.

[1]

(b) A fair dice is thrown once.

Explain why the probability of getting a prime number is greater than the probability of getting a factor of 5

[3]

14 Mick owns a shop.

A plan of the shop is drawn using a scale of 1:10 The height of the shop is 3.75 metres.

(a) What length on the plan represents the height of the shop?

Answer [1]

(b) Mick has a display unit that is 0.9 m wide and 1.7 m tall. On the plan there is a space that is 10 cm wide and 15 cm tall. Will the display unit fit into this space?

Show your working.

Answer [2]

0 1

Examiner Only

Marks Re-mark

52

15 The cost, £C, of a taxi journey can be calculated using the formula

C = 2.50 + 1.25 M

£2.50 is the initial charge, M = number of miles. Julie has £10 and Kate has £20 Kate says she can travel exactly twice the number of miles that Julie can by

taxi.

Is Kate correct?


Answer because [3]

16 Alice wants to buy 6 pens.

She sees these offers in two shops.

NIBS BOOKENDS

pens 20p eachpens 32p each

buy 2 pens, get one free

Alice thinks Bookends will be cheaper.

Is Alice correct?

Show your working.

[4]

Examiner Only

Marks Re-mark

53

17 Mark writes the first five terms of the sequence with the nth term rule

5n – 3

as 2, 7, 12, 18, 22

Is he correct?


Answer because [2]

Examiner Only

Marks Re-mark

54

18 Oil is sold in litres or gallons.

Litres 0 500 1000

Gallons 0 110 220

(a) Use the numbers in the table to draw the conversion graph on the grid.

[2]

(b) Use your graph to convert 100 gallons to litres.

Answer [2]

0

50

100

150

200

250

Litres

200 400 600 800 1000

Gal

lons

Examiner Only

Marks Re-mark

55

19 Matthew changes £500 into euro.

The exchange rate is £1 = 1.23 euro. Matthew spends 480 euro on his holiday. He changes the remainder of his euro into pounds (£) when he gets home. The exchange rate is now £1 = 1.18 euro.

How much, in pounds, does he get?

Answer £ [4]


56

Centre Number

Candidate Number


For Examiner’s

use onlyQuestion

Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

TotalMarks


INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided. Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all twenty-six questions.

INFORMATION FOR CANDIDATESFunctional Mathematics is assessed in this unit.The total mark for this paper is 100Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question.You may use a calculator.The Formula Sheet is on page 58.

Mathematics

[CODE]

SPECIMEN PAPER

M2

Calculator Paper

Foundation Tier

57

58

Formula Sheet



a

h

b

crosssection

length

Formula Sheet

Examiner Only

Marks Re-mark

59

1 The foundation of a child’s playground is laid in the form of a cuboid.

The foundation is made of concrete.

l = 40 m


w = 20 m

d = 0.75 m

What is the volume of concrete required?

Answer m3 [2]

Examiner Only

Marks Re-mark

60

2 Coffee mornings are held twice a week for ten weeks to raise money.

The amounts raised on Tuesdays and Saturdays are shown in the bar charts below.

Amounts Raised at Tuesday Coffee Mornings

1 2 3 4 5 6 7 8 9 10Am

ount

Rai

sed

(£) 15

10

5

0

Week

Amounts Raised at Saturday Coffee Mornings

1 2 3 4 5 6 7 8 9 10

Am

ount

Rai

sed

(£)

15

20

10

5

0

Week

(a) What is the mean amount raised on Tuesdays?

Answer £ [2]

(b) The mean amount raised on Saturdays is £12.50

(i) How would you explain the difference in this amount and the mean amount raised on Tuesdays?

[1]

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61

(ii) How much more is raised on Saturdays than on Tuesdays?

Answer £ [1]

3 The table below shows how much electricity was used in Max’s home each quarter over 4 years.

Year 2008 2009 2010 2011

Quarter 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

Electricity Usage(Units)

300 270 325 350 295 265 315 340 305 275 340 360 310 280 350 375

(a) What is the median number of units used in 2009?

Answer [3]

(b) What is the range of the number of units used in 2010?

Answer [2]

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62

4 A questionnaire was given to pupils in a school.

5 out of every 8 pupils returned the questionnaire. What percentage returned the questionnaire?

Answer % [1]

5 A window cleaner charges a call out fee of £3 plus 25p per square metre of glass cleaned.

(a) A front window in a butcher’s shop measures 3.5 m by 6 m.

How much does it cost to get 2 of these windows cleaned?

Answer £ [4]

(b) The owner of a bakery pays £8 for his windows to be cleaned.

Each window in the bakery has an area of 5 m2

How many windows did he get cleaned?

Answer [3]

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63

6 Insert one of <, > or = to make each statement true.

(a) 12.5% 18

[1]

(b) 0.16 g 0.2 g [1]

(c) –2°c –3°c [1]

(d) 34

45

[1]

7 Here is a sign in a car park.

Car ParkPay machine takes these coins

£2 £1 50p 20p 10p 5p

Lucy paid exactly £2.85

She used six coins. She did not use any £1 coins.

Show three different ways she could have paid.

Answer

[3]

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64



A family spends £53 on tickets. They buy at least one of each type of ticket.

How many of each ticket do they buy?

Answer Adult

Answer Child




Jay’s share is 14

Gino pays £36 000


Answer £ [4]

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65

10 Solve these equations:

(a) 24 = 6q

Answer q = [1]

(b) r – 8 = 12

Answer r = [1]

11 (a) Stephanie designed a badge for her youth club.

It has four sides. None of the sides are parallel. It has one pair of equal angles. It has 2 pairs of equal sides. Its diagonals cross at right angles. What shape is the badge?

Answer [2]

(b) Marie designed two badges. She says that they are quadrilaterals. Both badges have rotational symmetry of order 2 What shapes are Marie’s badges?

Answer , [2]

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66

12 The diagram shows two identical squares.

Find the size of the angle x.

x

70°


Answer x = [4]


All four digits are different. The first digit is an even prime. The second and third digits have a sum of 8 and a product of 15 The fourth digit is double the third digit. What is Farrah’s passcode?

Answer [3]

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67


Answer [2]


Answer [1]


6 cm 4 cm

6 cm 6 cm

6 cm L cm


Answer L= cm [3]

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68


The two-way table below shows the results.

Pass Fail

Male 12 10

Female 20



Fail

Fail

Pass

Pass

Female

Male

[2]

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69

17

24° 3x°

56°4x°

To calculate the value of x, Julie uses the equation

24 + 4x + 56 + 3x = 180

(a) Explain why Julie’s equation is incorrect.

[1]

(b) Calculate the correct value for x.

Answer x = [4]

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70

18 At each end of a sports pitch there is a semi circular goal area which requires special turf.

The radius of the goal area is 8 m.

Calculate the total area of special turf required for the goal areas.

Answer m2 [2]

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71

19

John has £160 to spend and wants to buy 10 footballs and 6 rugby balls. The price tag on a football is £8.40 The price tag on a rugby ball is £16 John gets a discount as shown above.

How much change will John have from his £160?

Answer £ [5]

© adekvat/iStock/Thinkstock

Footballs13 off the tag price

Rugby balls18% off the tag price

© Nik01ay/iStock/Thinkstock

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72

20 William’s town council rates are £1500 per year.

He can pay his rates by making 12 equal monthly payments by direct debit. William is given a 3% charge for paying monthly.

How much is William’s monthly payment?

Answer £ [3]

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73

21


B

A C

D

ABCD is a kite. The length of AB is 2 cm less than the length of AD. The perimeter of the kite is 30 cm. Let the length of AD = x

Work out the length of AB.

Answer cm [4]

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74

22 Joe wants to put a straight pipe from corner A to corner C in his garden.

Work out how much longer the pipe is if he puts it along the edges from A to B to C rather than across the diagonal AC.

Answer m [4]

A 8 m B

D C

6 m

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75

23 The Post Office, the Greengrocers and the Butchers are three shops in town.

100 people were asked which shops they had used in the past week. 31 had been to the Post Office; 54 had been to the Greengrocers; and 36 had been to the Butchers.

Of these, 8 had been in the Post Office and Greengrocers only; 12 had been in the Butchers and Greengrocers only; 3 had been to all the shops; and 15 had been to the Butchers only.

(a) Complete the Venn diagram to represent the number of people in each shop.

Post Office Greengrocer

Butcher

[3]

(b) Calculate how many people did not use any of the shops in the past week.

Answer [2]

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76



27 33 29 24 34

22 26 28 22 31

19 38 36 18 30

23 35 27 21 37

24 26 25 28 21

(a) Use this information to complete the grouped frequency table below.


15–19

20–24

25–29

30–34

35–39

[2]

(b) (i) Use the table in part (a) to calculate an estimate of the mean time.

Answer min [4]

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

[1]

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77

25

3x – 1

x + 3

4

The perimeter of the rectangle is equal to the perimeter of the square.

Calculate x.

Answer x = [4]

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78

26 The graph shows the cost, C (£), of hiring a car for d days from Roy’s Rentals.

(a) Calculate the gradient of the straight line.

Answer [2]

(b) Give a meaning to the value you found in part (a).

Answer [1]

0

20

10

30

50

70

90

100

40

60

80

Number of days, d

21 3 5 74 6 8

Cos

t, C

(£)

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79

(c) Rachel owns a car rental company.

She charges £40 to rent a car plus £5 for each day the car is rented.

Draw a graph for Rachel’s car company on the grid provided for Roy’s Rentals on the previous page. [2]

(d) Using information from your graphs, what advice would you give to someone who is planning to rent a car?

[1]


80

Centre Number

Candidate Number



Question Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

TotalMarks

TIME1 hour.

INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided. Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all sixteen questions.

INFORMATION FOR CANDIDATESThe total mark for this paper is 50Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question.You must not use a calculator for this paper.The Formula Sheet is on page 82.

Mathematics

[CODE]

SPECIMEN PAPER

M6.1


Foundation Tier

8181

82 [Turn over

Formula Sheet



a

h

b

crosssection

length

Formula Sheet

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83

1 A normal six sided dice is rolled 240 times.

It lands on six a total of 20 times.

Do you think the dice is fair?


Answer because [2]

2 Jess has a large wooden chest in the shape of a cuboid.

The inside of the chest is 130 cm long, 40 cm wide and 20 cm tall.

‘

Jess has a collection of one hundred 10 cm cubes.

Can all of her cubes fit into the chest? Justify your answer.

Answer because [3]

© Patrick Cleiren / Hemera /Thinkstock

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84

3 (a) Write down the name of the sequence of numbers below:

1, 3, 6, 10, 15, 21…

Answer [1]

(b) What is the largest number less than 70 that belongs to this sequence?

Answer [1]

4 Given that a = 5, b = 10 and c = 12, work out 2a – b + 4c

Answer [2]

5 (a) Estimate 385

Answer [2]

(b) Is your estimate greater than or less than the actual value of 385?

Answer [1]

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85

6

(a) What is the order of rotational symmetry of shape A?

Answer [1]

(b) How many lines of symmetry has shape A?

Answer [1]

(c) Draw the image of shape A after a reflection in the line

y = 2 [2]

10987654321–1–2–3–4–5–6–7–8–9–10

1

2

3

4

5

–6

6

–5

7

–4

8

–3

9

–2

10

–1

y

x

A

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86

7 Lewis is visiting a friend who lives 80 miles away.

He leaves home at 10 am and drives 40 miles at 60 mph. He then stops for 20 minutes at a petrol station. Lewis continues his journey at 45 mph.

(a) Draw Lewis’ journey on the travel graph below. [3]

0

20

10

30

50

70

90

40

60

80

Time

LEWIS’ JOURNEY

10:20 10:40 11:00 11:20 11:40 12:00 12:20 12:4010:00

Dis

tanc

e (m

iles)

(b) How far from home was Lewis at 11:30?

Answer miles [1]

09:40

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87

8 In a school, 38 of the teachers are male.

What percentage of the teachers are male?

Answer % [1]

9 Sean is making plans to build a shed with a rectangular floor.

The floor has length 4 m and width 3 m. He thinks the area of the floor is too small. He wants to have exactly double the floor area. He writes down 3 ideas:

Idea 1 Add 2 m to the length and add 2 m to the width. Idea 2 Double the length and double the width. Idea 3 Double the length only.

Which idea will work?


Idea

[4]

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88

10 The plan below shows a Hall and the surrounding area.

Housing Estate School

Playing FieldsHall

Car ParkB

Car ParkA

The scale of the plan is 1 : 1000

For parts (a) to (c), measure to the nearest centimetre.

(a) What is the length and the width of the Hall in metres?

Answer m, m [2]

(b) What is the area of the playing fields in square metres?

Answer [4]

(c) What is the ratio of the total car park area to the playing fields area in its simplest form?

Answer [3]

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89

11 A car parking space is 2.5 m by 5.0 m.

Below is a scale drawing of part of the car park.

Mark on the drawing the maximum number of parking spaces that will fit in this park and number them.

Scale 1 : 250 [2]


The table below shows the probability of some of these word lengths.


1 – 2 0.1

3 – 4 0.25

5 – 6 0.45

7 – 8 0.15

9 or more

The first chapter contains 7500 words. How many words of 9 or more letters would you expect in the first chapter?

Answer words [4]

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90

13 Jack is feeding the grass on his lawn. He uses the ratio 1 part fertiliser to 24 parts water.

He needs three litres in total.

How much fertiliser should he use (in ml)?

Answer ml [3]

14 Write the binary number 1101

as a decimal number.

Answer [1]

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91

15 Tiles measure 50 cm by 30 cm.

Each tile costs £2.09

Estimate the cost of tiling a room which measures 4.18 m by 2.72 m.

Answer £ [4]

16 The bearing of B from A is 075° What is the bearing of A from B?

Answer ° [2]


9292

Centre Number

Candidate Number



Question Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

TotalMarks

TIME1 hour.

INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided. Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all twenty questions


Mathematics

[CODE]

SPECIMEN PAPER

M6.2

Calculator Paper

Foundation Tier

93

94

Formula Sheet



a

h

b

crosssection

length

Formula Sheet

Examiner Only

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95

1 The distance from a school to the town centre is 1.5 miles. Use 1 mile = 1.609 kilometres to work out this distance in kilometres.

Answer km [2]

2 Jack’s bus was late three times out of fifty.

Write 350

as a decimal.

Answer [1]

3 13

of all babies born in Northern Ireland last year can expect to live to

90 years of age.

Last year, 24 393 babies were born in Northern Ireland.

How many are expected to live to 90 years of age?

Answer [2]

4 Tom buys three shirts.

Each shirt costs £5 correct to the nearest pound (£).

What is the most that Tom could have paid in total for his three shirts?

Answer £ [2]

Examiner Only

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96

5 There are 60 pupils in Year 8.

A pupil is chosen at random.

What is the probability that a boy is chosen?

Tick a box and give a reason for your answer.

exactly 0.5 about 0.5 cannot say

Reason

[2]

6 (a) The probability that a bus is on time is 0.7

Mark with an X on the scale, the probability that the bus is not on time.

0 1 [1]

(b) A fair dice is thrown once.

Explain why the probability of getting a prime number is greater than the probability of getting a factor of 5

[3]

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97

7 A builder estimates that it will cost £30 000 to build a school extension.

£1 = 1.44 euro

How much is the estimate in euro?

Answer € [1]

8 The cost to floor a kitchen is 110 of the cost to floor a house.

Which of these is the correct formula where K is the cost to floor the kitchen and H is the cost to floor the house?

A K = 10H

B K = H10

C H = K

10 D K =

10H

Answer Formula [1]

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Marks Re-mark

98

9 There are 200 tickets on sale for a concert.

75% of the tickets need to be sold to avoid making a loss.

145 tickets are sold.

Will there be a loss?

Show your working.

Answer because [2]


C = 2.50 + 1.25M

£2.50 is the initial charge, M = number of miles. Julie has £10 and Kate has £20 Kate says she can travel exactly twice the number of miles that Julie can by

taxi.

Is Kate correct?


Examiner Only

Marks Re-mark

99

[3]

11 A fair 4-sided spinner is spun twice.

1

4

2

3

The product of the two numbers on each spin is recorded in the table below.

(a) Complete the table below to show the possible outcomes.

Number on first spin

Number on second spin

1 2 3 4

1 1

2 4

3 9

4 16

[2]

(b) Work out the probability that the product is a square number.

Answer [1]

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100

12 There are 30 passengers in a train carriage.

The probability that a passenger in the train carriage is male is 25

At the next station 5 people get off and no-one gets on.

The probability that a passenger in the train carriage is male is still 25

How many females are still on the train?

Answer [3]

13 Pete and Bob pay for a boat in the ratio 2:3

The boat costs £8000

How much does Bob pay?

Answer £ [2]

Examiner Only

Marks Re-mark

101

14 A band is hired at a wedding from 8 pm to 11.30 pm.

The band plays from 8 pm until 9:15 pm and from 10:15 pm until 11:30 pm.

What is the ratio of the amount of time the band plays to the amount of time when the band does not play?

Answer [4]

15 The cost of a ticket for a disco is worked out using this formula.

C = F + B + HN + D where

C = cost of ticket (£) F = total cost of food (£) B = cost of band (£) H = hall hire charge (£) N = number expected to attend D = donation to charity (£)

Given that F = £155, B = £240, H = £85, N = 120 and D = £1,

work out the cost of a ticket for the disco.

Answer £ [2]

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Marks Re-mark

102

16 Mark writes out the first five terms of the sequence with one nth term rule

5n – 3

as 2, 7, 12, 18, 22

Is he correct?


Answer because [2]

17 Make n the subject of the formula y + 8 = n – 4

Answer n = [2]

Examiner Only

Marks Re-mark

103

18 Over a period of 8 hours, the temperature of a room follows the relationship

T = h2 – 6h + 15

T is the temperature in degrees Celsius, h hours after the experiment started.

(a) Complete the table below:

h 0 1 2 3 4 5 6 7

T 15 10 6 7 15 22

[1]

(b) Plot the points and draw the graph on the grid below:

0

10

5

15

25

20

30

h (hours)

2 4 6 8 10

T (c

elsi

us)

1 3 5 7 9 11 120

[2]

(c) Use your graph to find the times when the temperature in the room was 12 degrees Celsius.

Answer , [1]

Examiner Only

Marks Re-mark

104

19 From a lighthouse, L, a ship can be seen 30 km away on a bearing of 030° From L, an oil rig can be seen 43 km away on a bearing of 120° Calculate the direct distance between the ship and the oil rig. A solution by scale drawing will not be accepted.

Answer km [5]

Examiner Only

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105

20 John and Jake roll a dice which is biased.

They both roll the dice a number of times.

The table below shows the results of their trials.

Number of trials Number of sixes Relative frequency

John 60 13

Jake 150 44

(a) Calculate the relative frequencies, to 2 decimal places, for each boy and complete the table. [2]

(b) Which boy’s trials give a more reliable estimate of the likelihood of rolling a six on this dice?


Answer [1]


106

Centre Number

Candidate Number


For Examiner’s

use only

Question

Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

TotalMarks

TIME2 hours.

INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided. Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all twenty-five questions.


Mathematics

[CODE]

SPECIMEN PAPER

M3

Calculator Paper

Higher Tier

107

108

Examiner Only

Marks Re-mark

109



A family spends £53 on tickets. They buy at least one of each type of ticket. How many of each ticket do they buy?

Answer Adult

Answer Child


Examiner Only

Marks Re-mark

110

2 The diagram shows two identical squares.

Find the size of the angle x.

x

70°


Answer x = [4]


All four digits are different. The first digit is an even prime. The second and third digits have a sum of 8 and a product of 15. The fourth digit is double the third digit. What is Farrah’s passcode?

Answer [3]

Examiner Only

Marks Re-mark

111


Answer [2]


Answer [1]

5 Shelly’s oil tank is two-fifths full. Three hundred and fifteen litres are added to the tank. The tank is now three-quarters full. Show clearly that the tank has a capacity of 900 litres.

[4]

Examiner Only

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112



Jay’s share is 14

Gino pays £36 000


Answer £ [4]

7 In Northern Ireland, a survey of 15 000 first class letters showed that 13 905 were delivered on time.

What percentage of first class letters were delivered on time?

Answer % [3]

Examiner Only

Marks Re-mark

113

8 (a) Ali has x cards. Belinda has twice as many cards as Ali. Charlie has 5 more cards than Ali. They have a total of 33 cards. Show that

4x + 5 = 33

[2]

(b) Hence, find the number of cards which Ali has.

Answer cards [2]

9

24° 3x°

56°4x°

To calculate the value of x, Julie uses the equation

24 + 4x + 56 + 3x = 180

(a) Explain why Julie’s equation is incorrect.

[1]

Examiner Only

Marks Re-mark

114

(b) Calculate the correct value for x.

Answer x = [4]


6 cm 4 cm

6 cm 6 cm

6 cm L cm


Answer L = cm [3]

Examiner Only

Marks Re-mark

115


The two-way table below shows the results.

Pass Fail

Male 12 10

Female 20



Fail

Fail

Pass

Pass

50

Female

Male

[2]

12 Neil is taking 8 examinations in the summer.

His parents promise him £20 if his mean mark for the eight examinations is more than 60

After seven examinations his mean mark is 58

What is the lowest mark he can score in the final examination if he is to receive his £20?

Answer [4]

Examiner Only

Marks Re-mark

116

13 Margaret bought 36 memory sticks at £4.20 each.

She sold 28 of them for £4.50 each and the other 8 for £3 each.

Did she make a profit or a loss, and by how much?

Answer by £ [3]



27 33 29 24 34

22 26 28 22 31

19 38 36 18 30

23 35 27 21 37

24 26 25 28 21

(a) Use the information above to complete the grouped frequency table below.


15–19

20–24

25–29

30–34

35–39

[2]

Examiner Only

Marks Re-mark

117

(b) (i) Use the table in part (a) to calculate an estimate of the mean time.

Answer min [4]

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

[1]

15


B

A C

D

ABCD is a kite. The length of AB is 2 cm less than the length of AD. The perimeter of the kite is 30 cm. Let the length of AD = x

Work out the length of AB.

Answer AB = cm [4]

Examiner Only

Marks Re-mark

118

16 The diagram below shows a rectangle ABCD.

Calculate the length of the diagonal AC of the rectangle ABCD.

Answer [3]

10

8

6

4

2

0

–2

5 10

y

x

D

BA

C

1

3

5

7

9

1 2 3 4 6 7 8 9–1

#

42 in $

Examiner Only

Marks Re-mark

119

17 In the centre of a town there are three shops. The Post Office, the Greengrocers and the Butchers.

In a survey on shopping habits, 100 people were asked which shops they had used in the past week.

31 had been to the Post Office; 54 had been to the Greengrocers; and 36 had been to the Butchers.

Of these, 8 had been in the Post Office and Greengrocers only; 12 had been in the Butchers and Greengrocers only; 3 had been to all the shops; and 15 had been to the Butchers only.

(a) Complete the Venn diagram to represent the number of people in each shop. [3]

Post Office Greengrocer

Butcher

(b) Hence, calculate how many people did not use any of the shops in the past week.

Answer [2]

Examiner Only

Marks Re-mark

120

18 John states “If you add two consecutive numbers, you always get an odd answer but if you multiply two consecutive numbers you always get an even answer”.

Is John correct?

Show working to justify your answer.

[4]

19 (a) A number has 23 32 5 7 as the product of its prime factors.

What is the number?

Answer [1]

(b) Carlo says that another number has 22 5 9 as its product of prime factors.

Explain why he is wrong and write down what the correct product is.

[2]

Examiner Only

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121

20

3x – 1

x + 3

4

The perimeter of the rectangle is equal to the perimeter of the square. All the lengths are measured in cm.

Calculate x.

Answer x = [4]

Examiner Only

Marks Re-mark

122


0

20

10

30

50

70

90

100

40

60

80

Number of days, d

21 3 5 74 6 8

Cos

t, C

(£)


Answer [2]


[1]

d

c

Examiner Only

Marks Re-mark

123

(c) Rachel owns a car rental company.

She charges £40 to rent a car plus £5 for each day the car is rented.


(d) A man wants to rent a car for 5 days.

Should he use Roy’s Rentals or Rachel’s Rental?


[1]

22 Solve

x2 – 5x + 4 = 0

Answer x = [3]

23 A force of 120 N is applied to a circular area with radius 96 cm. Work out the pressure in N/m2

Round your answer to 3 significant figures.

Answer N/m2 [4]

Examiner Only

Marks Re-mark

124

24 Solve the equation

2x – 15

+ 4x + 510

= 52

Answer x = [4]

Examiner Only

Marks Re-mark

125

25 The diagram shows a tent.

4.8 m

2.2 m

3.2 m

The base of the tent is a circle of diameter 4.8 m. The walls are vertical and are 2.2 m high. The roof of the tent is a cone with perpendicular height 3.2 m. The material to make the tent costs £7.95 per square metre.

Calculate the total cost of the material needed to make the walls and roof of the tent.

Answer £ [7]


126

Centre Number

Candidate Number



Question Number

Marks

1

2

3

4

5

6

7

8

9

10

11

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13

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16

TotalMarks


INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided. Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all sixteen questions.


Mathematics

[CODE]

SPECIMEN PAPER

M7.1


Higher Tier

127

128

Examiner Only

Marks Re-mark

129

1 Sean is making plans to build a shed with a rectangular floor.

The floor has length 4 m and width 3 m. He thinks the area of the floor is too small. He wants to have exactly double the floor area. He writes down 3 ideas:

Idea 1 Add 2 m to the length and add 2 m to the width. Idea 2 Double the length and double the width. Idea 3 Double the length only.

Which idea will work? Explain your answer.

Answer Idea because

[4]

2 Given 25 = 1 + 22 + 3n

Find the value of n.

Answer n = [4]

Examiner Only

Marks Re-mark

130

3 Pablo is an artist. He paints on canvas. He uses different sizes of canvas but they all have their width and height in

the ratio 4:3

(a) Which of the following canvas sizes could he use?

32 cm by 24 cm 60 cm by 45 cm

100 cm by 70 cm 120 cm by 90 cm

Circle the correct answer(s). [3]

(b) Write down another canvas size that he could use that is not given in the list above.

Answer [1]4 Estimate 3855

37.5

Answer [2]

5 Mary ran 50 km last week.

She ran 30 miles this week. She says she ran at least 100 km over the 2 weeks. Is she right? Explain your answer.

Answer because [3]

Examiner Only

Marks Re-mark

131


The table shows the probability of some of these word lengths.


1 – 2 0.1

3 – 4 0.25

5 – 6 0.45

7 – 8 0.15

9 or more

The first chapter contains 7500 words.

How many words of 9 or more letters would you expect in the first chapter?

Answer words [4]

7 The lengths of the sides of two squares are integers when measured in cm.

The difference between the areas of the two squares is 28 cm2

Find the difference between the lengths of the sides of the two squares.

Answer cm [4]

Examiner Only

Marks Re-mark

132

8 A book costs £3 and a pen costs £2

Write a formula for the total cost, C, in £, for x books and y pens.

Answer C = [3]

9 (a) Draw the image of shape A after a reflection in the line y = 2. [2]

(b) How many lines of symmetry has shape A?

Answer [1]

10987654321–1–2–3–4–5–6–7–8–9–10

1

2

3

4

5

–6

6

–5

7

–4

8

–3

9

–2

10

–1

y

x

A

Examiner Only

Marks Re-mark

133

10 (a) Write the binary number 1101 as a decimal number.

Answer [1]

(b) Write the decimal number 31 as a binary number.

Answer [1]

11 Which of the following is the calculation to increase 2000 by 5%? 2000 1.5 2000 0.5

2000 1.05 2000 0.05

Circle the correct answer. [1]

12 Tiles measure 50 cm by 30 cm.



Answer £ [4]

Examiner Only

Marks Re-mark

134

13 There are 20 boys and 12 girls in a chess club.

Three fifths of the boys have been members for over 2 years. Two thirds of the girls have been members for over 2 years.

What is the probability that a child taken at random from the chess club has been a member for over 2 years?

Answer [3]

14 Joe was changing the subject of the formula

A = 3b√c to c

Joe has written A = 3b√c

Line 1 A2 = 3b2

c

Line 2 A2c = 3b2

Line 3 c = 3b2

A2

(a) Identify the line where Joe made a mistake.

Answer Line [1]

(b) Write down the correct answer:

Answer c = [1]

Examiner Only

Marks Re-mark

135

15 y = kx2 , k > 0

Which graph shows this?

Answer [1]

y

y

A

C

B

D

y

y

x

x

x

x

Examiner Only

Marks Re-mark

136

16 Jill buys the tea and coffee for everyone in the office at break time.

On Monday she bought 3 teas and 5 coffees. The bill on Monday was £10.50

On Tuesday she bought 4 teas and 4 coffees. The bill on Tuesday was £10

On Wednesday she bought 2 teas and 6 coffees. What was the total bill on Wednesday?

A solution by trial and improvement will not be accepted.

Answer £ [6]


137

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138

Centre Number

Candidate Number



Question Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

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TotalMarks


INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided. Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all fourteen questions.


Mathematics

[CODE]

SPECIMEN PAPER

M7.2

Calculator paper

Higher Tier

139

140 [Turn over

Examiner Only

Marks Re-mark

141

1 A fair 4-sided spinner is spun twice.

1

4

2

3

The product of the two numbers on each spin is recorded in the table below.

(a) Complete the table below to show the possible outcomes.



1 2 3 4

1 1

2 4

3 9

4 16

[2]

(b) Work out the probability that the product is a square number.

Answer [1]

Examiner Only

Marks Re-mark

142

2 Karen buys 1.6 kg of apples on Monday. She pays £2.80 Karen buys 2 kg of apples in the same shop on Tuesday. How much in total does Karen pay for apples on Monday and Tuesday?

Answer [4]

3 There are 30 passengers in a train carriage.

The probability that a passenger in the train carriage is male is 25

At the next station a number of female passengers get off and no-one gets on.

The probability that a passenger now in the train carriage is male is 12

How many female passengers got off the train?

Answer [3]

Examiner Only

Marks Re-mark

143


C = 2.50 + 1.25 × M

£2.50 is the initial charge, M = number of miles. Julie has £10 and Kate has £20. Kate says she can travel exactly twice the number of miles that Julie can by

taxi.

Is Kate correct?


[3]

5 Matthew changes £500 into euro. The exchange rate is £1 = 1.23 euro. Matthew spends 480 euro on his holiday. He changes the remainder of his

euro into pounds (£) when he gets home. The exchange rate is now £1 = 1.18 euro. How much, in pounds, does he get?

Answer [4]

Examiner Only

Marks Re-mark

144

6 Make n the subject of the formula

y + 8 = n – 4

Answer n = [2]

7 Diane is making shortbread biscuits.

She has: 900 g of flour 454 g of butter 250 g of caster sugar

Here is a list of ingredients needed to make 15 shortbread biscuits: 175 g flour 110 g butter 50 g caster sugar

Diane wants to make as many biscuits as she can using her ingredients. Calculate how many biscuits she can make.

Answer [3]

Examiner Only

Marks Re-mark

145

8 (a) A rectangular swimming pool measures 35 m by 15 m.

Use a scale of 1 cm to represent 5 m and make an accurate drawing of the swimming pool.

[2]

(b) Using your scale drawing find the actual length of the diagonal which goes from one corner to another.

Answer [2]

9 Mark writes out the terms of the sequence with n th term rule 3n + 5 Sean writes out the terms of the sequence with n th term rule 5n – 3 Which term number has the same value for both sequences?

Answer [4]

Examiner Only

Marks Re-mark

146

10 John and Jake think a dice is biased.

They both roll the dice a number of times. The table below shows the results of their trials.


John 60 13

Jake 150 44


(b) Explain why Jake’s relative frequency gives a more reliable estimate of the likelihood of rolling a six.

Answer [1]

Examiner Only

Marks Re-mark

147

11 Over a period of 8 hours, the temperature of a room follows the relationship

T = h2 – 6h + 15

T is the temperature in degrees Celsius, h hours after the experiment started.

(a) Complete the table below:

h 0 1 2 3 4 5 6 7 8

T 15 10 6 7 15 22 31

[1]

(b) Plot your points on the graph below:

0

10

5

15

25

20

30

h (hours)

2 4 6 8 10

T (c

elsi

us)

1 3 5 7 9 11 120

[2]


Answer [1]

Examiner Only

Marks Re-mark

148

12 P Q

S T

36 cm

12.5 cm 12.5 cm

20 cm

Diagram notdrawn accuratelyR

PQR and STR are similar triangles.

(a) Calculate the length of QR.

Answer cm [2]

20 cm

12.5 cm

R

S Tt

(b) Calculate the size of angle t

Answer t = [3]

12.5 cm

Examiner Only

Marks Re-mark

149

13 A menu in a restaurant prices the meals as follows:

2 courses: £16

3 courses: £21

The menu offers 5 starters, 8 mains and 4 desserts. John wants a 2 course meal which includes a main. How many choices does John have?

Answer [3]

14 Find the value of the positive number x if the ratio 10 : x is the same as the ratio (x +2) : 12


Answer x = [5]


150

Centre Number

Candidate Number



Question Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

TotalMarks

TIME2 hours.

INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided.Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all twenty-one questions.


Mathematics

[CODE]

SPECIMEN PAPER

M4

Calculator Paper

Higher Tier

151

152

Examiner Only

Marks Re-mark

153

1 (a) A number has 23 × 32 × 5 × 7 as the product of its prime factors.

What is the number?

Answer [1]

(b) Carlo says that another number has 22 × 5 × 9 as its product of prime factors.

Explain why he is wrong and write down what the correct product is.

[2]

2 10.8 cm

18 cm

9 cm

Diagram not drawn accurately

Find the area of the trapezium.

Answer cm2 [5]

Examiner Only

Marks Re-mark

154

3 The percentage marks in a class test were recorded in the following table.

Marks (%) Frequency

55–59 1

60–64 1

65–69 2

70–74 5

75–79 9

80–84 5

85–89 2

Calculate an estimate for the mean mark.

Answer % [4]

Examiner Only

Marks Re-mark

155

4

3x – 1

x + 3

4

The perimeter of the rectangle is equal to the perimeter of the square. All the lengths are measured in cm.

Calculate x

Answer x = [4]

Examiner Only

Marks Re-mark

156

5 Linda has £500 to invest. She can choose from two accounts, A and B.

Account A Account B

Simple interest:

5% per year

Compound interest:

3% in the first year4% in the second yearand5% in the third year

Calculate which account would give Linda the most money if she invests her money for 3 years.

Show all your working clearly.

Answer [5]

Examiner Only

Marks Re-mark

157



Answer [2]


[1]

0

20

10

30

50

70

90

100

40

60

80

Number of days, d

21 3 5 74 6 8

Cos

t, C

(£)

Examiner Only

Marks Re-mark

158

(c) Rachel owns a car rental company. She charges £40 to rent a car plus £5 for each day the car is rented.


(d) A man wants to rent a car for 5 days.

Should he use Roy’s Rentals or Rachel’s Rental? Give a reason for your answer.

[1]

Examiner Only

Marks Re-mark

159

7 A

B

CD

56 ft

50 ft


Mast

Building

A building is 56 feet high. A vertical mast, AB, is situated at the top edge of the building. The angle of elevation of the top of the mast A, measured from a point D

50 feet horizontally from the base of the building, is 58°

Calculate the height, AB, of the mast.

A solution by scale drawing will not be accepted.

Answer ft [5]

Examiner Only

Marks Re-mark

160

8 (a) Expand and simplify (3w – 7)(5w – 8)

Answer [2]

(b) Factorize x2 – 16

Answer [1]

(c) Factorize 6x2 + 18xy

Answer [2]

Examiner Only

Marks Re-mark

161

9 A hotel advertises a 22% reduction in price if booked online. Ruth books a hotel online and pays £195

How much did Ruth save by booking the hotel online?

Answer £ [3]

162

10 This is a cumulative frequency curve for the marks in a Science test.

(a) Use the curve to estimate

(i) the median mark,

Answer [1]

(ii) the interquartile range,

Answer [2]

(iii) the number of candidates who passed when the pass mark was 45 marks.

Answer [2]

Examiner Only

Marks Re-mark

0

20

40

60

80

100

120

140

30 40 50 60 70 80 90

Cum

ulat

ive

freq

uenc

y

Mark (less than)

Examiner Only

Marks Re-mark

163

This is a cumulative frequency curve for the marks in a Mathematics test.

Mark (less than)

(b) (i) Sketch on the same diagram the shape of the cumulative frequency curve for a harder test when all the pupils scored a lower mark. [2]

(ii) Will the harder test have a higher or lower median mark?

Answer [1]

Cum

ulat

ive

freq

uenc

y

Examiner Only

Marks Re-mark

164

11 Solve the equation

2x – 15

+ 4x + 510

= 52

Answer x = [4]

Examiner Only

Marks Re-mark

165

12 The diagram shows a tent.

4.8 m

2.2 m

3.2 m

The base of the tent is a circle of diameter 4.8 m. The walls are vertical and are 2.2 m high. The roof of the tent is a cone with perpendicular height 3.2 m. The material to make the tent costs £7.95 per square metre.

Calculate the total cost of the material needed to make the walls and roof of the tent.

Answer £ [7]

Examiner Only

Marks Re-mark

166

13 A force of 120 N is applied to a circular area with radius 96 cm. Work out the pressure in N/m2

Round your answer to 3 significant figures.

Answer N/m2 [4]

14 258 pupils chose a subject from an option block which they would study in year 11.

The table below shows the information about these pupils.

Subjects to be studied

Geography History Spanish

Male 45 52 26

Female 25 48 62

A sample, stratified by the subject studied and by gender, of 50 of the 258 pupils is taken.

(a) Calculate an estimate of the number of female pupils in the sample.

Answer [2]

(b) Calculate an estimate of the number of male pupils studying Spanish in the sample.

Answer [2]

Examiner Only

Marks Re-mark

167

15 Solve 8y – 3y2 = 2, correct to 2 decimal places.

Answer y = [3]

16 John drove on a stretch of road with an average speed limit of 50 miles per hour.

He drove a distance of 6.3 miles (correct to the nearest 0.1 mile) in a time of 8.0 minutes (correct to 2 significant figures).

Could John have broken the average speed limit? Justify your answer.

Answer [5]

Examiner Only

Marks Re-mark

168

17 Jan uses this data about the heights of plants, h (cm), to draw the histogram below.

Height, h (cm) 0 < h ≤ 10 10 < h ≤ 20 20 < h ≤ 30 30 < h ≤ 45 45 < h ≤ 50

Frequency 7 8 3 6 5

Write down three different mistakes that she has made.

Mistake 1

Mistake 2

Mistake 3 [3]

Heights of plants

Frequency

Height, h (cm)

Examiner Only

Marks Re-mark

169

18 The triangle below is right angled.

3x + 3

x + 25x – 2

All the lengths are given in cm.

Calculate the value of x.


Answer x = [6]

Examiner Only

Marks Re-mark

170

19

SR

P

Q

T V

74°37°


TV is a tangent to the circle at P. SR = RQ Angle QPV = 37° and angle SPQ = 74°

Show that SP is parallel to RQ. You must give reasons to justify any angles that you calculate.

Answer [4]

Examiner Only

Marks Re-mark

171

20 OABC is a kite. O is the origin. A is (0, 3), B is (3, 3) and C is (k, – 4)

Work out the value of k

You must show all your working.

Answer k = [5]

Examiner Only

Marks Re-mark

172

21 Find three consecutive positive odd integers such that 5 times the square of the middle integer exceeds the product of the other two by 488

Candidates should use an algebraic method.


Answer [7]


173

BLANK PAGE

174

Centre Number

Candidate Number


For Examiner’s

use only

Question

Number

Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

TotalMarks


INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided. Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all fourteen questions.


Mathematics

[CODE]

SPECIMEN PAPER

M8.1


Higher Tier

175

176r

Examiner Only

Marks Re-mark

177

1 John has a fair 6-sided dice.

He throws it twice.

What is the probability that he throws a ‘3’ both times?

Answer [2]

2 (a) Write the binary number

1101

as a decimal number.

Answer [1]

(b) Write the decimal number 31 as a binary number.

Answer [1]

3 Which of the following is the calculation to increase 2000 by 5%? 2000 1.5 2000 0.5

2000 1.05 2000 0.05

Circle the correct answer. [1] 4 Tiles measure 50 cm by 30 cm.



Answer £ [4]

Examiner Only

Marks Re-mark

178

5 There are 20 boys and 12 girls in a chess club.

Three fifths of the boys have been members for over 2 years. Two thirds of the girls have been members for over 2 years.

What is the probability that a child chosen at random from the chess club has been a member for over 2 years?

Answer [3]

6 Joe was changing the subject of the formula

A = 3b√c to c

Joe has written A = 3b√c

Line 1 A2 = 3b2

c

Line 2 A2c = 3b2

Line 3 c = 3b2

A2

(a) Identify the line where Joe made a mistake.

Answer line [1]

(b) Write down the correct answer:

Answer c = [1]

Examiner Only

Marks Re-mark

179

7 y is directly proportional to x2

Which graph shows this?

Answer [1]

y

y

A

C

B

D

y

y

x

x

x

x

Examiner Only

Marks Re-mark

180

8 Jill buys the tea and coffee for everyone in the office at break time.

On Monday she bought 3 teas and 5 coffees. The bill on Monday was £10.50

On Tuesday she bought 4 teas and 4 coffees. The bill on Tuesday was £10

On Wednesday she bought 2 teas and 6 coffees. What was the total bill on Wednesday?


Answer £ [6]

9 (a) A bag contains triangles and quadrilaterals in the ratio of the number of sides of each shape.

Explain why the least number of shapes that could be in the bag is 7

[1]

Examiner Only

Marks Re-mark

181

(b) A shape is taken at random from the bag and replaced. Another shape is then taken from the bag.

Work out the probability that the two shapes taken from the bag are the same.

Answer [3]

10 Change the recurring decimal 0.727272........ into a fraction in its simplest form.

Answer [2]

11 Evaluate each of the following.

(a) 823

Answer [1]

(b) 90.5 27 13

÷ 36–0.5

Answer [3]

Examiner Only

Marks Re-mark

182

12 A circle has centre (0,0) and radius 5

(a) Show that the point P (3, –4) lies on the circle.

[2]

(b) Find the coordinates of the point where the tangent to the circle at point P meets the x axis.

Answer [6]

13 A cylinder has a radius of (5 – √2) cm and a height of 3√2 cm.

Show that the volume of the cylinder can be written as (81√2 – 60) π cm3

[4]

Examiner Only

Marks Re-mark

183

14 A line has equation y = 2x 3

A curve has equation y2 = 8x 33

The line and the curve meet at the points A and B.

Calculate the length of AB, leaving your answer in the form p√q where p and q are integers.

Answer [7]


184

Centre Number

Candidate Number



Question Number

Marks

1

2

3

4

5

6

7

8

9

10

11

TotalMarks


INSTRUCTIONS TO CANDIDATESWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer the questions in the spaces provided. Complete in blue or black ink only. Do not write with a gel pen.All working should be clearly shown since marks may be awarded for partially correct solutions.Where rounding is necessary give answers correct to 2 decimal places unless stated otherwise.Answer all eleven questions.


Mathematics

[CODE]

SPECIMEN PAPER

M8.2

Calculator Paper

Higher Tier

185

186

Examiner Only

Marks Re-mark

187

1 John and Jake roll a dice which is biased.

They both roll the dice a number of times.

The table below shows the results of their trials.


John 60 13

Jake 150 44


(b) Which boy’s trials give a more reliable estimate of the likelihood of rolling a six on this dice?


Answer ______________ because _________________________ [1]

Examiner Only

Marks Re-mark

188

2 At a football match the ratio of male to female spectators was 11:3 The attendance was 50 092

(a) How many male spectators were there?

Answer [2]

(b) How many female spectators were there?

Answer [1]

3 27 cm

19 cm


Six congruent rectangles fit together as shown.

Find the total area that they cover.

Answer [5]

Examiner Only

Marks Re-mark

189

4 A train leaves at 1435 and arrives at the next station at 1620 on the same day.

It covers a distance of 210 miles.

Work out the average speed of the train in km/hr.

Answer km/hr [5]

Examiner Only

Marks Re-mark

190

5

0

y

x–1 1 2 3 4 5 6 7 8–2–3–4–5–6–7–8

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

B

A

(a) Describe fully the single transformation which will take triangle B to triangle A.

Answer [3]

Examiner Only

Marks Re-mark

191

(b) In the diagram rectangle C has been enlarged by a scale factor of 4 to give rectangle D.

How many times bigger is the area of rectangle D than the area of rectangle C?

C

D

Answer times bigger [2]

6 A menu in a restaurant prices the meals as follows:

2 courses £16

3 courses £21

The menu offers 5 starters, 8 mains and 4 desserts. John wants a 2 course meal which includes a main.

How many choices does John have?

Answer [3]

Examiner Only

Marks Re-mark

192

7

0

y

x–1 1 2 3 4 5 6 7–2–3–4–5–6–7

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

A

Shape A is transformed to give shape C.

It undergoes 2 successive transformations:

1. A rotation of 180° about (0,1) to give image B

followed by

2. A reflection in the x-axis to give image C.

Describe fully the single transformation which will map C onto A.

Answer [4]

Examiner Only

Marks Re-mark

193

8 (a) On the grid below, show by shading and the letter R, the region represented by the inequalities.

x + y 6 x 2 2y x

0

1

2

3

4

5

6

1 2 3 4 5 60

y

x

[3]

(b) Find the maximum value of 2x + 3y in the region R, where x and y are integers.

Answer [2]

Examiner Only

Marks Re-mark

194

9 Over a period of 8 hours, the temperature of a room is given by

T = h2 – 6h + 15

where T is the temperature in degrees Celsius, h hours after the experiment started.

(a) Complete the table below.

h 0 1 2 3 4 5 6 7

T 15 10 6 7 15 22

[1]

(b) Plot the points and draw the graph on the grid below.

0

10

5

15

25

20

30

h (hours)

2 4 6 8 10

T (c

elsi

us)

1 3 5 7 9 11 120

[2]


Answer , [1]

Examiner Only

Marks Re-mark

195

(d) Use your graph to calculate the gradient of the curve when h = 6

Answer [2]

(e) What is the meaning of the value you found in (d)?

Answer [1]

10

B

A

D

E

C

10 cm

15 cm

40°

80°


In the diagram above, CE = 15 cm and BC = 10 cm

Calculate the length of AB.

Answer cm [4]

Examiner Only

Marks Re-mark

196

11 There are two blue beads and x red beads in a box.

The probability that two beads, taken at random from the box, are both

red is 1522

Find x

A solution by trial and error will not be accepted.

Answer [6]


197

BLANK PAGE

198

MARK SCHEMES

199

200


GENERAL MARKING INSTRUCTIONS

Mathematics

201

202

General Marking Instructions

Introduction

The mark scheme normally provides the most popular solution to each question. Other solutions given by candidates are evaluated and credit given as appropriate; these alternative methods are not usually illustrated in the published mark scheme.

The solution to a question gains marks for correct method and marks for accurate working based on this method. The marks awarded for each question are shown in the right hand column and they are prefixed by the letters M, A and MA as appropriate. The key to the mark scheme is given below:

M indicates marks for correct method.A indicates marks for accurate working, whether in calculation, reading from tables, graphs or answers. Accuracy marks may depend on preceding M (method) marks, hence M0 A1 cannot be awarded, i.e. where the method is not correct no marks can be given.MA indicates marks for combined method and accurate working.

A later part of a question may require a candidate to use an answer obtained from an earlier part of the same question. A candidate who gets the wrong answer to the earlier part and goes on to the later part is naturally unaware that the wrong data is being used and is actually undertaking the solution of a parallel problem from the point at which the error occurred. If a candidate continues to apply correct method, then the candidate’s individual working must be followed through from the error. If no further errors are made, then the candidate is penalised only for the initial error. Solutions containing two or more working or transcription errors are treated in the same way. This process is usually referred to as “follow-through marking” and allows a candidate to gain credit for that part of a solution which follows a working or transcription error.

It should be noted that where an error trivialises a question, or changes the nature of the skills being tested, then as a general rule, it would be the case that not more than half the marks for that question or part of that question would be awarded; in some cases the error may be such that no marks would be awarded.

Positive marking

It is our intention to reward candidates for any demonstration of relevant knowledge, skills or understanding. For this reason we adopt a policy of following through their answers, that is, having penalised a candidate for an error, we mark the succeeding parts of the question using the candidate’s value or answers and award marks accordingly.

Some common examples of this occur in the following cases:

(a) a numerical error in one entry in a table of values might lead to several answers being incorrect, but these might not be essentially separate errors;(b) readings taken from a candidate’s inaccurate graphs may not agree with the answers expected but might be consistent with the graphs drawn.

When the candidate misreads a question in such a way as to make the question easier, only a proportion of the marks will be available (based on the professional judgement of the examiner).

203

General Marking Advice

(i) If the correct answer is seen in the body of the script and the answer given in the answer line is clearly a transcription error, full marks should be awarded.(ii) If the answer is missing, but the correct answer is seen in the body of the script, full marks should be awarded.(iii) If the correct answer is seen in working but a completely different answer is seen in the answer space, then some marks will be awarded depending on the severity of the error.(iv) Work crossed out but not replaced should be marked.(v) In general, if two or more methods are offered, mark only the method that leads to the answer on the answer line. If two (or more) answers are offered (with no solution offered on the answer line), mark the poorest answer.(vi) For methods not provided for in the mark scheme, give as far as possible equivalent marks for equivalent work.(vii) Where a follow through mark is indicated on the mark scheme for a particular part question, the marker must ensure that you refer back to the answer of the previous part of the question.(viii) Unless the question asks for an answer to a specific degree of accuracy, always mark at the greatest number of significant figures seen, e.g. the answer in the mark scheme is 4.65 and the candidate then correctly rounds to 4.7 or 5 on the answer line. Allow full marks for 4.65 seen in the working.(ix) Anything in the mark scheme which is in brackets (...) is not required for the mark to be earned, but if present it must be correct.(x) For any question, the range of answers given in the mark scheme is inclusive.

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1 (a) £180 MA1

(b) 20 MA1

(c) 1307 A1

(d) 9300 MA1

2 (a) 42 A1

(b) (i) £108.47 A1

(ii) 10% of £108.47 = £10.847 MA1 £10.85 A1 £119.32 MA1

3 1.2 m × 0.6 m × 0.355 m 3 correct – 2 marks 2 correct – 1 mark

4 1 hour 15 minutes MA1

5 400 + 300 + 200 + 500 + 100 = 1500 M1A1

6 (a) Week 4 A1

(b) 50 – 20 = 30 M1A1

(c) (30 + 50 + 25 + 15) = 120 M1A1

120 4 = 30 MA1

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7 1016 A1

58 A1

8 isosceles A1

9 (a) 32 M1A1

(b) E A1

10 0.5, 0.625, 0.75, 0.25 MA1 Recipe D, Recipe A, Recipe B, Recipe C A1

11 (a) 24 A1

(b) 3 A1

(c) 3 circle A1

(d) e.g. more compact diagram, one circle can easily be split into 4 etc. A1

12 (a) 5.29 A1

(b) Factors of 10 are 1, 2, 5, 10 Factors of 15 are 1, 3, 5, 15 A1 HCF = 5 A1

(c) Explanation based on 42 = 16, 52 = 25 and ….. 23 is between 16 and 25 MA2

13 £2, 20p, 20p, 20p, 20p, 5p A1 £2, 50p, 10p, 10p, 10p, 5p A1 £2, 50p, 20p, 5p, 5p, 5p A1

14 16 + 6 + 9 = 31 (cost for one of each ticket) MA1 53 – 31 = 22 (money left after buying one of each ticket) MA1

16 + 6 = 22 (only arrangement possible) Answer: 2 adult, 2 child, 1 senior citizen A1

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1

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15 35% + 25% = 60% M1 Gino pays 40% MA1

£36 000 = 40% MA1 100% = £90 000 MA1

16 (a) x = 4 A1 (b) y = 20 A1

17 6 × 19 × 26 = 2964 M1A1

cm3 A1

18 (a) Household A1

(b) The area for clothes is twice the size of the area for food. A1

19 (a) £7 A1

(b) Data ordered 3,4,5,6,7,7,9 MA1 6 A1

20 13 of £54 = £18 MA1

Jeans cost 54 – 18 = £36 MA1 20% of £28 = £5.60 MA1 Shirt cost 28 – 5.60 = £22.40 MA1 £36 + £22.40 = £58.40 MA1

21 6% of £3000 = £180 MA1 8% of £3000 = £240 MA1 240 – 180 = £60 MA1

22 180 – 70 – 70 = 40 M1A1 360 – 90 – 90 – 40 = 140 M1A1

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23 First digit = 2 A1 3 and 5 identified MA1 Passcode = 2536 MA1

24 (a) 14a + 21 + 12a – 6 A1 26a + 15 A1

(b) 5(4d – 7) A1

25 Cube: 6 × 6 × 6 = 216 cm3 MA1 Cuboid: 6 × 4 × L = 216 L = 216 ÷ 24 M1 L = 9 A1

26 (a) 8 A1

(b)

Fail

Fail

Pass

Pass

50

Female

Male

22

28

12

10

20

8

A2

27 (a) Radius = 4.5 A1 π × 4.52 = 63.617... M1A1 64 A1

(b) π × 9 = 28.274...... M1A1 28.3 A1

28 1100 = 45N + 200 M1 900 = 45N MA1

90045 = N M1

N = 20 MA1

3

3

3

3

7

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29 (a) Time taken (min) Tally (if required) Frequency

15–19 2

20–24 7

25–29 8

30–34 4

35–39 4

MA2

(b) (i) Accept pie chart or bar chart or grouped frequency diagram A1

(ii) Visual representations of data Pie chart: comment on sectors, proportion of categories OR Bar chart: comment on heights of bars A1

30 Let AD = x

AB = x – 2 M1 x + x – 2 + x + x – 2 = 30 MA1 4x – 4 = 30 4x = 34 MA1 x = 8.5 AB = 6.5 A1

Total

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1 710

A1

2 15 – 8.5 = 6.5 M1A1

3 £1.50 ÷ 6 = 25p or £0.25 M1A1

4 No, 12 × 12 = 144, so !120 should be less than 12 or 11 × 11 = 121 so !120 should be less than 11 A1A1

5 P = 2l + 2b P = l + l + b + b (Tick both) A1A1

6 (a) 0941 A1

(b) 12 + 7 = 19 minutes M1A1

7 (a) 34

A1

(b) 1500 ÷ 3 = 500 A1

(c) 95 A1

8 310

A1

9 14:25 A1

10 No as there should be about 40 sixes A1A1

11 2 × 5 – 10 + 4 × 12 = 2 M1A1

12 13 × 4 × 2 = 104 M1A1 Yes, the chest can hold 104 cubes A1

13 105 × 2 = 210 miles MA1 210 ÷ 35 = 6 gallons (or 210 ÷ 6 = 35) M1A1 So Elsie is correct

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2

2

2

2

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14 6 ÷ 3 = 2 M1A1

15 9 × 2 = 18 M1A1

16 5 miles = 8 km A1 30 miles = 48 km A1 50 + 48 = 98; 98 < 100; no A1

17 (a) 32 × 24; 60 × 45; 120 × 90 A1A1A1 (b) any not listed in correct ratio MA1

18 (a) 1 A1

(b) correct position A1

(c) correct reflection M1A1

19 1 – (0.1 + 0.25 + 0.45 + 0.15) M1 0.05 A1 0.05 × 7500 M1 = 375 A1

20 p = 36° 36 × 2 = 72° MA1 180 – 72 = 108° MA1 Sum = 108 × 5 = 540° M1A1 (or 3 × 180 = 540°)

Total

2

2

3

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4

4

4

50

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216 [Turn over

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1 5 A1

2 8 + 8.50 = 16.50 126.60 – 16.50 = 110.10 M1A1

3 52 litres = 52 × 11 = 572 miles M1A1

4 (a) Shape 4 drawn correctly A1

(b) 14, 17 filled in A1

(c) Goes up by 3 each time A1

5 (a) Square number as it only occurs 4 times M1A1

(b) (i) evens A1

(ii) impossible A1

6 75 × 3 = 2.25 5 – 2.25 = 2.75 M1A1

7 24 393 ÷ 3 = 8131 M1A1

8 (a) 1 500 000 A1

(b) Value between 33⅓% and 40% exclusive A1

9 8 × 30 + 20 × 30 = £840 (or 30 × 30 = £900) M1A1

10 5.49 A1 3 × 5.49 = 16.47 MA1

11 Cannot say, as we are not told how many boys and girls there are A1MA1

12 5 × 3 = £15 But 5 × £3.25 will be more M1A1

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50

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13 (a) 0.3 indicated A1 (b) p (prime) = 36 {2, 3, 5} A1 P (factor of 5) = 26 {1, 5} A1

36 > 26 A1

14 (a) 37.5 cm (or 0.375 m) need units MA1

(b) space is 1 m × 1.5 m, display unit is 0.9 m × 1.7 m no M1A1

15 Julie: = 6 miles MA1 Kate: = 14 miles MA1 No; 14 > (2 6) MA1

16 6 × 20p = £1.20 M1A1 4 × 32p = £1.28 M1A1 No, NIBS cheaper

17 No as terms should be 2, 7 12, 17, 22 M1A1

18 (a) Values plotted A1 Line drawn, all correct A1

(b) Line drawn at 100 gallons (about 450/460 litres) M1A1

19 500 × 1.23 = 615 euro MA1 615 – 480 = 135 euro MA1 135/1.18 = £114(.41) M1A1

Total

7.501.2517.501.25

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1 40 × 20 × 0.75 M1 = 600 A1

2 (a) 7510

= 7.50 M1A1

(b) (i) More people available on Saturdays as not working A1

(ii) (12.50 - 7.50) × 10 = 50 MA1 3 (a) Order data MA1

12

(295 + 315) MA1

= 305 A1

(b) 360 – 275 = 85 M1A1 4 62.5 A1

5 (a) 3.5 × 6 × 2 = 42 M1A1 3 + 42 × 0.25 = 13.50 M1A1

(b) 8 – 3 = 5 MA1

50.25

= 20 MA1

205

= 4 MA1

6 (a) = A1

(b) < A1

(c) > A1

(d) < A1

7 £2, 20p, 20p, 20p, 20p, 5p A1 £2, 50p, 10p, 10p, 10p, 5p A1 £2, 50p, 20p, 5p, 5p, 5p A1

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9 35% + 25% = 60% M1 Gino pays 40% MA1

£36 000 = 40% MA1 100% = 90 000 MA1

10 (a) q = 4 A1

(b) r = 20 A1

11 (a) kite MA2

(b) Any 2 of Rectangle, Parallelogram, Rhombus A1, A1

12 180 – 70 – 70 = 40 M1A1 360 – 90 – 90 – 40 = 140 M1A1

13 First digit = 2 A1 3 and 5 identified A1 Passcode = 2536 A1

14 (a) 14a + 21 + 12a – 6 A1 26a + 15 A1

(b) 5(4d – 7) A1

15 Cube: 6 × 6 × 6 = 216 cm3 MA1 Cuboid: 6 × 4 × L = 216 L = 216 ÷ 24 M1 L = 9 cm A1

3

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16 (a) 8 A1

(b)

Fail

Fail

Pass

Pass50

Female

Male22

28

12

10

20

8

A2

17 (a) The angles in a quadrilateral add up to 360 degrees A1

(b) 4x + 56 + 3x + 24 = 360 M1 7x + 80 = 360 A1 7x = 360 – 80 A1 7x = 280 x = 40 A1

18 π × 82 M1 = 201 A1

19 13

of £8.40 = £2.80 MA1

£5.60 × 10 = £56 MA1 18% of £16 = £2.88 MA1 £13.12 × 6 = £78.72 MA1 £160 – £56 – £78.72 = £25.28 MA1

20 1500 × 3100 = 45 so rates = £1500 + £45 = £1545 M1A1

1545 ÷ 12 = 128.75 A1

21 Let AD = x AB = x – 2 MA1 x + x – 2 + x + x – 2 = 30 MA1 4x – 4 = 30 4x = 34 MA1 x = 8.5 AB = 6.5 A1

22 Use of Pythagoras AC2 = 62 + 82 M1A1 AC = √100 = 10 A1 14 – 10 = 4 MA1

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222

23 (a) Middle section = 3 A1 Centre sections = 6, 8, 12 MA1 Outer sections = 14, 31, 15 MA1

(b) 100 – (3 + 6 + 12 + 31 + 8 + 14 + 15) = M1 11 A1

24 (a) Time taken (min) Tally (if required) Frequency

15 – 19 2

20 – 24 7

25 – 29 8

30 – 34 4

35 – 39 4 MA2

(b) (i) [(17 × 2) + (22 × 7) + (27 × 8) + (32 × 4) + (37 × 4)] M1A1

= 68025

= 27.2 (27) M1A1

(ii) The mid values are used rather than the original data A1

25 2 (3x – 1) + 8 = 4(x + 3) M1 6x – 2 + 8 = 4x + 12 A1 6x – 4x = 12 + 2 – 8 A1 2x = 6 x = 3 A1

26 (a) 70 – 205 – 0

= 10 M1A1

(b) Hire cost per day A1

(c) 40 on vertical axis, correct slope A1 A1

(d) If renting for less than 4 days, use Roy’s Rentals, for more than 4 days, use Rachel’s company A1

Total

5

7

4

6

100

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1 No as there should be about 40 sixes A1A1

2 13 × 4 × 2 = 104 M1A1 Yes the chest can hold 104 cubes A1

3 (a) Triangle or triangular numbers A1

(b) 66 A1

4 2 × 5 – 10 + 4 × 12

= 2 M1A1

5 (a) Estimate √400 = 20 M1A1

(b) Greater than A1

6 (a) One or none A1

(b) One A1

(c) Correct reflection M1A1

7 (a) Lines from (1000, 0) to (1040, 40), A1 (1040, 40) to (1100, 40) and A1 (1100, 40) to (1200, 85) A1

(b) Correct reading from graph (62 or 63 miles) MA1

8 37.5% A1

9 Area = 12 so we need 24m2 MA1 Idea 1: 6 × 5 = 30; no MA1 Idea 2: 8 × 6 = 48; no MA1 Idea 3: 8 × 3 = 24; yes, idea 3 works MA1

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10 (a) 3 cm by 2 cm, 30 m by 20 m (or reverse) M1A1

(b) 8 cm by 6 cm, 80 m by 60 m MA1MA1 4800 m2 (A1 units) M1A1

(c) Area = 2 × 30 × 20 = 1200 MA1 1200 : 4800 = 1:4 M1A1

11 12 spaces drawn in box M1A1

12 1 – (0.1 + 0.25 + 0.45 + 0.15) M1 0.05 A1 0.05 × 7500 M1 = 375 A1

13 3000 ml A1 3000 ÷ 25 = 120 ml M1A1

14 23 + 22 + 20 = 13 A1

15 = (9) M1A1

= (10) A1

90 tiles × 2 = 180

[or = 14 and = 6 giving 84 × 2 = 168] MA1

16 75 + 180 = 255° M1A1

Total

9

2

4

3

1

27230

41850

41830

27250 4

2

50

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1 1.609 × 1.5 M1 2.41 km (2.4135) A1

2 0.06 A1

3 24 393 ÷ 3 = 8131 M1A1

4 £5.49 A1 3 × £5.49 = £16.47 MA1

5 Cannot say; A1 Not told how many boys and girls there are A1

6 (a) 0.3 indicated A1

(b) P(prime) = {2, 3, 5} A1 P(factor of 5) = {1,5} A1

> A1

7 30 000 × 1.44 = 43200 A1

8 B ( K = ) A1 9 75% of 200 = 150 MA1 Yes A1

10 Julie: = 6 miles MA1 Kate: = 14 miles MA1 No; 14 > (2 6) MA1

2

1

2

2

2

36 2

636

26 4

1

H10 1

2

7.501.2517.501.25

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11 (a) Number on first spin


1 2 3 4

1 1 2 3 4

2 2 4 6 8

3 3 6 9 12

4 4 8 12 16

2 marks (A2); allow 1 mark for 8 correct

(b) 616 MA1

12 of 30 = 12 males, 18 females M1A1

of 25 = 10 males, 25 − 10 = 15 females MA1

13 8000 ÷ 5 × 3 M1 4800 A1

14 Band plays for 2 × 1 hour 15 minutes M1A1 2.5 : 1 MA1 5 : 2 A1

15 (155 + 240 + 85) ÷ 120 then + 1 5 M1A1

16 No as terms should be 2, 7, 12, 17, 22 M1A1

17 y + 8 + 4 = n MA1 n = y + 12 A1

38 3

2525 3

2

4

2

2

2

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18 (a) 7, 10 A1

(b) Correct plots and curve M1A1

(c) Correct readings (2 correct) approx 0.55 and 5.45 A1

19

M1A1

302 + 432 = x2 MA1 2749 = x2 MA1 x = 52.43 km A1

20 (a) John: 0.22 MA1 Jake: 0.29 MA1

(b) Jake’s as there are more trials A1

Total

4

30°

43

L

S

O

5

3

50

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2 180 – 70 – 70 = 40 M1A1 360 – 90 – 90 – 40 = 140 M1A1

3 First digit = 2 A1 3 and 5 identified MA1 Passcode = 2536 MA1 4 (a) 14a + 21 + 12a – 6 A1 26a + 15 A1

(b) 5(4d – 7) A1

5 34

– 25

= 1520

− 820

= 720

(or 35%) M1A1

720

= 315 litres; 120

= 45 litres (or 5%) MA1

20 × 45 = 900 litres MA1

6 35% + 25% = 60% M1 Gino pays 40% MA1

£36 000 = 40% MA1 100% = £90 000 MA1

7 M1A1

= 92.7 A1

8 (a) x + 2x + (x + 5) = 33 MA1 4x + 5 = 33 A1

(b) 4x = 33 – 5 = 28 MA1 x = 7 Ali has 7 cards A1

1390515000

× 100

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235

5

3

3

4

3

9 (a) The angles in a quadrilateral add up to 360 degrees A1

(b) 4x + 56 + 3x + 24 = 360 M1 7x + 80 = 360 A1 7x = 360 – 80 A1 7x = 280 x = 40 A1

10 Cube: 6 × 6 × 6 = 216 cm3 MA1 Cuboid: 6 × 4 × L = 216 L = 216 ÷ 24 M1 L = 9 A1

11 (a) 8 A1

(b)

Fail

Fail

Pass

Pass

50

Female

Male

22

28

12

10

20

8

A2

12 Total for seven examinations 7 × 58 = 406 MA1 Total for all eight exams must be more than 8 × 60 = 480 MA1 480 − 406 = 74 A1 Lowest mark = 75 MA1

13 36 × £4.20 = £151.20 MA1 28 × £4.50 = £126 8 × £3 = £24 MA1 Total = £126 + £24 = £150 Loss of £1.20 MA1

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14 (a)


15 – 19 2

20 – 24 7

25 – 29 8

30 – 34 4

35 – 39 4 MA2

(b) (i) [(17 × 2) + (22 × 7) + (27 × 8) + (32 × 4) + (37 × 4)] M1A1

= 68025

= 27.2 (27) M1A1

(ii) The mid values are used rather than the original data A1

15 Let AD = x AB = x – 2 MA1 x + x – 2 + x + x – 2 = 30 MA1 4x – 4 = 30 MA1 4x = 34 x = 8.5 AB = 6.5 A1

16 Use of Pythagoras AC2 = 62 + 82 M1A1 AC = √100 = 10 A1

17 (a) Middle section = 3 A1 Centre sections = 6, 8, 12 MA1 Outer sections = 14, 31, 15 MA1

(b) 100 – (3 + 6 + 12 + 31 + 8 + 14 + 15) = 11 M1 11 A1

18 Shows consecutive numbers even + odd = odd, E + O = O, 2n + (2n + 1) = 4n + 1 A2 Shows consecutive numbers even × odd = even, E × 0 = E, 2n(2n + 1) = 4n2 + 2n = E A2

19 (a) 8 × 9 × 5 × 7 = 2520 MA1 (b) 9 is not a prime number A1 22 × 32 × 5 A1

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20 2 (3x – 1) + 8 = 4(x + 3) M1 6x – 2 + 8 = 4x + 12 A1 6x – 4x = 12 + 2 – 8 A1 2x = 6 x = 3 A1

21 (a) 70 – 205 – 0

= 10 M1A1


(c) 40 on vertical axis, correct slope A1 A1

(d) Rachel’s Rental. If renting for less than 4 days, use Roy’s Rentals, for more than 4 days, use Rachel’s Rentals. A1

22 (x – 1)(x – 4) = 0 MA2 x = 1, x = 4 A1

23 Area = πr2 = π × 0.962 = 2.89529179 M1A1

Pressure = 120 ÷ 2.89529179 = 41.4 (5) M1A1

24 2(2x – 1) + 1(4x + 5) = 25 MA1 4x – 2 + 4x + 5 = 25 MA1 8x = 22 MA1

x = 228

MA1

25 CSA of cylinder = 2 πrh 2 × π × 2.4 × 2.2 M1 33.175 (21 842) A1

l 2 = 2.42 + 3.22 MA1 l 2 = 16 l = 4 A1

CSA of cone = πrl = π × 2.4 × 4 MA1 = 30.159 (28 947) A1 Total area = 63.33 (450 789) Cost = 7.95 × 63.33 (450 789) = 503.51 MA1

Total 100

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1 Area = 12 so will need 24m2 MA1 Idea 1: 6 × 5 = 30; no MA1 Idea 2: 8 × 6 = 48; no MA1 Idea 3: 8 × 3 = 24; yes, idea 3 works MA1

2 2 × 2 × 2 × 2 × 2 = 32 MA1 32 = 1 + 4 + 3n MA1 3n = 27 MA1 n = 3 A1

3 (a) 32:24 = 4:3, 60:45 = 4:3, 100:70 = 10:7, 120:90 = 4:3 MA2 32 cm by 24 cm, 60 cm by 45 cm and 120 cm by 90 cm A1 (b) any sensible size in ratio 4:3 A1 4 √100 = 10 M1A1 5 30 × 1.6 = 48 MA2 48 + 50 = 98 km, no she ran less than 100 km A1

6 1 – (0.1 + 0.25 + 0.45 + 0.15) = 0.05 M1A1 0.05 × 7500 = 375 M1A1

7 1, 4, 9, 16, 25, 36, 49, 64, M1 Square numbers with difference of 28 = 64 and 36 A1 Lengths of sides = 8 and 6 MA1 Difference in sides = 8 – 6 = 2 MA1

8 C = 3x + 2y A3

9 (a) Correct reflection A2 (b) One A1

10 (a) 1 + 4 + 8 = 13 MA1 (b) 11111 MA1

11 2000 × 1.05 MA1

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12 Tiles needed = 9 M1A1

= 10 A1

9 × 10 = 90 tiles × 2 = 180 MA1

(or = 14 and = 6 giving 6 × 14 = 84, 84 × 2 = 168)

13 boys = 12 MA1 girls = 8 MA1

2032

= 58 )( MA1

14 (a) Line 1 A1

(b) c = 9b2

A2 A1

15 C A1

16 3t + 5c = 1050 4t + 4c = 1000 MA2

12t + 20c = 4200 12t + 12c = 3000

8c = 1200, c = 150 (£1.50) MA2

600 + 4t = 1000 4t = 400, t = 100 (£1.00) A1

2t + 6c = 2 × 1 + 6 × 1.5 = 11 A1

Total

41830

27250

4

3

2

1

6

41850

27230

50

242

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244 [Turn over

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1 (a)



1 2 3 4

1 1 2 3 4

2 2 4 6 8

3 3 6 9 12

4 4 8 12 16MA2

(b) 616 A1

2 2.80 ÷ 1.6 = 1.75 M1A1 2 × 1.75 = 3.50 MA1 2.80 + 3.50 = 6.30 MA1

3 25

of 30 = 12 males, 18 females M1A1

There are now 12 females so 6 got off MA1

4 10 = 2.50 + 1.25M ; M = 6 MA1 20 = 2.50 + 1.25M; M = 14 MA1

No she can travel more than twice as far, 14 is more than 2 × 6 = 12 A1 5 500 × 1.23 = 615 euro M1A1 615 – 480 = 135 euro 135 ÷ 1.18 = 114.41 M1A1

6 n = y + 8 + 4 A1 n = y + 12 A1

38

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4

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7 454 ÷ 110 = 4.13 MA1 4 × 15 = 60 biscuits MA2 Alternative, accept 61 with method

8 (a) Rectangle 7 cm by 3 cm MA2

(b) 7.6 cm A1 7.6 × 5 = 38 MA1

9 5n – 3 = 3n + 5 MA1 5n – 3n = 5 + 3 MA1 2n =8 MA1 n = 4 A1

ALTERNATIVE 8, 11, 14, 17, 20…. 2, 7, 12, 17, 22…. 17 is the same 4th term

10 (a) John: 0.22 MA1 Jake: 0.29 MA1

(b) It is based on more trials. MA1

11 (a) 7,10 A1 (b) Points plotted A1 Smooth curve A1

(c) Answer from pupil’s graph A1

12 (a) 36 ÷ 20 = 1.8 MA1 12.5 × 1.8 = 22.5 cm MA1

(b) cos t = 1012.5

M1A1

t = 36.87 A1

13 Starter and main 5 × 8 = 40 A1 Main and dessert 8 × 4 = 32 A1 Total number 40 + 32 = 72 A1

246

5

50

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14 10x

= x + 212

M2

x (x + 2) = 120 x2 + 2x – 120 = 0 A1 (x + 12)(x – 10) = 0 A1 x = –12 or 10

So x = 10 A1

Total

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247

1 (a) 8 × 9 × 5 × 7 = 2520 MA1 (b) 9 is not a prime number A1 22 × 32 × 5 A1

2 18 – 10.8 = 7.2 MA1 h2 + 7.22 = 92 MA1 h2 = 29.16 h = 5.4 A1

area = 12

× (10.8 + 18) × 5.4 MA1 = 77.76 A1

3 Mid pt x fx 57 57 62 62 67 134 72 360 77 693 82 410 87 174 M1A1

189025

MA1

75.6 A1 4 2 (3x – 1) + 8 = 4 (x + 3) M1 6x – 2 + 8 = 4x + 12 A1 6x – 4x = 12 + 2 – 8 A1 2x = 6 x = 3 A1 5 £25 £25 × 3 = £75 MA1 £515 MA1 £535.60 MA1 £562.38 MA1

Account A A1

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248

6 (a) 70 – 205 – 0

= 10 M1A1


(c) 40 on vertical axis, correct slope A1A1

(d) Rachel’s Rental. If renting for less than 4 days, use Roy’s Rentals, for more than 4

days,use Rachel’s company A1

7 Find height AC tan 58 = x/50 M1A1 x = 80.016... A1 Mast = x – 56 M1 Mast = 24.02 A1

8 (a) 15w2 – 24w – 35w + 56 15w2 – 59w + 56 M1A1

(b) (x – 4) (x + 4) MA1

(c) 6x (x + 3y) A1A1

9 195 = 78% MA1

19578

× 22 = 55 M1A1

10 (a) (i) (Reading from 70) 51 MA1

(ii) (Readings from 35, 105) 46, 58 MA1 (Subtracts answers) 12 A1 (iii) (Reading up from 45) 28 M1 140 – 28 = 112 candidates (or 98) A1

(b) (i) Sketch of curve to the left of original M1A1

(ii) Lower A1

11 2(2x – 1) + 1(4x + 5) = 25 MA1 4x – 2 + 4x + 5 = 25 MA1 8x = 22 MA1

x = 228

oe MA1

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12 CSA of cylinder = 2 πrh 2 × π × 2.4 × 2.2 M1 33.175 (21 842) A1

l2 = 2.42 + 3.22 MA1 l2 = 16 l = 4 A1

CSA of cone = πrl = π × 2.4 × 4 MA1 = 30.159 (28 947) A1

Total area = 63.33 (450 789) Cost = 7.95 × 63.33 (450 789) = 503.51 MA1

13 Area = πr2 = π × 0.962 = 2.89529179 M1A1

Pressure = 120 ÷ 2.89529179 = 41.4 (5) M1A1

14 (a) × 50 = 26.162... M1

26 females A1

(b) 26258

× 50 = 5.038... M1

5 males A1

15 y = −(−8) ± √{ (−8)2 − 4(3)(2)}2 × 3 MA1

y = 8 ± √406 A1

y = 2.39 or 0.28 A1

16 6.25 ≤ distance < 6.35 miles MA1 7.95 ≤ time taken < 8.05 minutes MA1 Max average speed 6.35

7.95 × 60 = 47.9 mph M1A1

No – John’s maximum average speed was below 50 mph A1

7

4

4

3

5

25 + 48 + 62258

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250

17 Vertical axis should read ‘frequency density’ A1 Height of last bar is incorrect (should be 1) A1 Scale on vertical axis A1 (A1 for each of 3 correct)

18 (5x – 2)2 = (x + 2)2 + (3x + 3)2 MA1

25x2 – 20x + 4 = x2 + 4x + 4 + 9x2 + 18x + 9 A2 15x2 – 42x – 9 = 0 (5x2 – 14x – 3 =0) A1 (5x + 1)(x – 3) = 0 A1 x = – 1/5 or x = 3

Only feasible solution x = 3 A1

19 Angle PSQ = 37° alternate segment theorem MA1 Angle SRQ = 106° opposite angles in a cyclic quadrilateral MA1 Angle SQR = 37° isosceles triangle MA1

SP is parallel to RQ as alternate angles PSQ and SQR are equal MA1

20 Method 1

Grad of OB = 3 – 03 – 0

= 1 MA2

Grad of AC = –1 MA1

– 4 – 3k – 0

= –1 MA1

k = 7 A1or Method 2 Grad of OB = 1 MA2 Grad of AC = –1 MA1

Equation of AC is y = – x + 3 MA1 Therefore – 4 = – k + 3 k = 7 A1or Method 3 Mid point of OB is M (1.5, 1.5) MA2 Gradient of AM = Gradient of MC MA2

3 – 1.50 – 1.5

= 1.5 – -41.5 – k

–1 = 5.51.5 – k

k – 1.5 = 5.5 k = 7 A1

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21 x, x + 2, x + 4 MA1 5(x + 2)2 = x(x + 4) + 488 MA1 5(x2 + 4x + 4) = x2 + 4x + 488 A1 5x2 + 20x + 20 = x2 + 4x + 488 4x2 + 16x – 468 = 0 A1 x2 + 4x – 117 = 0 A1 (x + 13) (x – 9) = 0 x = –13, x = 9 x ≠ –13 so x = 9, 11, 13 selected A2

Total

7

100

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253

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254 [Turn over

1 16 ×

16 M1

136 A1

2 1 + 4 + 8 = 13 MA1 11111 MA1

3 2000 × 1.05 MA1

4 Tiles needed 41850 = 9 MA1

27230 = 10 MA1

9 × 10 = 90 A1

Cost 90 × 2 = 180 A1

[or 41830

= 14 and 27250 = 6 giving 14 × 6 = 84

84 × 2 = 168]

5 boys = 12 MA1 girls = 8 MA1

2032 (=

58 ) MA1

6 (a) Line 1 A1

(b) c = 9b2

A2 A1

7 C A1

8 3t + 5c = 1050 MA2 4t + 4c = 1000

12t + 20c = 4200 12t + 12c = 3000

8c = 1200, c = 150 (£1.50) MA2

600 + 4t = 1000 4t = 400, t = 100 (£1.00) A1

2t + 6c = 2 × 1 + 6 × 1.5 = 11 A1

2

2

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255

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9 (a) Total number of shapes in the bag must be divisible by (3 + 4) = 7 A1

(b) (37 ×

37 ) + (

47 ×

47 ) =

2549 M2, A1

10 n = 0.727272........ M1 100n = 72.7272.......

99n = 72

n = 7299 =

811 A1

11 (a) 4 A1

(b) 3 + 3 ÷ 16 A2

21 A1

12 (a) x2 + y2 = 25 A1

32 + (–4)2 = 25 MA1

(b) Gradient of radius = –43 MA1

Gradient of tangent = 34 MA1

y = 34 x + c MA1

–4 = 34 (3) + c M1

–4 – 94 = c

c = – 254

y = 34 x –

254 MA1

y = 0, x = 253 or 25

3 , 0 MA1

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256 [Turn over

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7

50

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13 (5 – √2)2 = 25 – 10√2 + 2 = 27 – 10√2 A2

3√2 (27 – 10√2) = 81 √2 – 60 A1

πr2h = π (81 √2 – 60 ) = (81 √2 – 60) π A1

14 (2x + 3)2 = 8x + 33 MA1

4x2 + 12x + 9 = 8x + 33

4x2 + 4x – 24 = 0 MA1

x2 + x – 6 = 0

(x + 3)(x – 2) = 0 MA1

x = –3 or x = 2 A1

(–3, –3) (2, 7) A1

Distance AB = √{ (–3 –2)2 + (–3 –7)2 } MA1

= √(25 + 100) = √ 125 = √25 √5 = 5 √5 A1

Total

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257

258 [Turn over

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1 (a) John: 0.22 MA1 Jake: 0.29 MA1

(b) Jake’s as it is based on more trials MA1

2 (a) 50 092 ÷ 14 = 3578 MA1 11 3578 = 39 358 MA1 (b) 10 734 MA1

3 Dimensions of rectangle 8 cm by 3 cm MA2 Area = 6 × 24 MA1 = 144 cm2 (units) A1A1 4 Time = 1 hr 45 mins MA1 Distance = 210 × 1.6 = 336 km MA2 Speed = 336 ÷ 1.75 = 192 km/hr MA2

5 (a) Enlargement A1

Scale factor 12

A1

Centre (1 , 2) A1

(b) 42 = 16 bigger M1A1

6 Starter and main 5 × 8 = 40 A1 Main and dessert 8 × 4 = 32 A1 Total number 40 + 32 = 72 A1

7 Object A rotated correctly MA1 Object B reflected correctly MA1

Translation (52) MA2

8 (a) 3 correct lines and shading A3

(b) (2, 4) gives 16 as the maximum M1A1

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9 (a) 7, 10 A1

(b) Points plotted A1 Smooth curve A1

(c) Answer from pupil’s graph A1

(d) Gradient from pupil’s graph M1A1

(e) Rate at which the temperature is increasing A1

10

A

B

C40°

60°

80°

MA1

10sin 40

= ABsin 60

M1A1

AB = 10sin 60sin 40

AB = 13.47 A1

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260 [Turn over

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50

AVAILABLE MARKS11 Total beads = (x + 2) A1

xx + 2

× x – 1x + 1

= 1522 M1A1

7x2 – 67x – 30 = 0 MA1

67 ± 7314

or (7x + 3) (x – 10) = 0 M1

x = 10 A1

Total

© CCEA 2017

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