S A M s 2 GCSE Mathematics - Ysgol Uwchradd Caergybiysgoluwchraddcaergybi.cymru/cym/downloads/new-maths...Specimen Assessment Materials 2 GCSE Mathematics – Numeracy 2017. Question

Specimen Assessment Materials 2 GCSE Mathematics – Numeracy 2017

Question papers

Unit 1: Non-calculator, Foundation tier Unit 1: Non-calculator, Intermediate tier Unit 1: Non-calculator, Higher tier Unit 2: Calculator-allowed, Foundation tier Unit 2: Calculator-allowed, Intermediate tier Unit 2: Calculator-allowed, Higher tier

Mark schemes

Unit 1: Non-calculator, Foundation tier Unit 1: Non-calculator, Intermediate tier Unit 1: Non-calculator, Higher tier Unit 2: Calculator-allowed, Foundation tier Unit 2: Calculator-allowed, Intermediate tier Unit 2: Calculator-allowed, Higher tier

Assessment grids

Candidate Name Centre Number

Candidate Number

0

GCSE

MATHEMATICS - NUMERACY UNIT 1: NON - CALCULATOR FOUNDATION TIER

2nd SPECIMEN PAPER SUMMER 2017

1 HOUR 30 MINUTES

ADDITIONAL MATERIALS The use of a calculator is not permitted in this examination. A ruler, protractor and a pair of compasses may be required.

INSTRUCTIONS TO CANDIDATES Write your name, centre number and candidate number in the spaces at the top of this page.

Answer all the questions in the spaces provided in this booklet.

Take π as 3∙14.

INFORMATION FOR CANDIDATES

You should give details of your method of solution when appropriate.

Unless stated, diagrams are not drawn to scale.

Scale drawing solutions will not be acceptable where you are asked to calculate.

The number of marks is given in brackets at the end of each question or part-question.

The assessment will take into account the quality of your linguistic and mathematical organisation, communication and accuracy in writing in question 7.

For Examiner’s use only

Question Maximum

Mark Mark

Awarded

1. 4

2. 3

3. 2

4. 3

5. 5

6. 5

7. 6

8. 4

9. 5

10. 5

11. 4

12. 5

13. 5

14. 3

15. 4

16. 2

TOTAL 65

Formula list

Area of a trapezium = 1

( )2

a b h

1. Every week, Sarah does her family shopping on the Internet.

She has to be careful to order things in the correct quantities.

The following table shows the items and quantities that Sarah has ordered.

Place a ‘X’ by the items that do not appear to have a sensible quantity and a ‘’ by those that do.

Two have been completed for you. [4]

Item Quantity X or

Orange juice 2 litres

Mushrooms 50 kilograms

A bag of sugar 1 kilogram

Tomato sauce 350 litres

Potatoes 5 grams X

Chocolate bar 100 grams

Bottle of vinegar 250 millilitres

Butter 500 grams

Milk 4 litres

Washing-up liquid 500 litres

2. The diagram shows the ground layout of the Liberty Stadium.

During a recent game, the number of spectators in the

West Stand was 7345 East Stand was 6339 South Stand was 4991.

The North Stand is kept for away team spectators. All 1093 away supporters were in the North Stand.

Showing all your working, calculate the total attendance at the game, giving your answer correct to the nearest 100.

[3]

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3. Jay and Alex design a game for their school fete. They each have a copy of a fair spinner as

shown below.

The game is based on the probability of obtaining certain numbers on the spinner, when the

spinner is spun once.

(a) Jay decides that she wants to place numbers on her spinner that would give an even chance of

getting a number greater than 4.

Place 4 numbers on Jay’s spinner to show this.

[1]

Jay’s Spinner

(b) Alex decides that he wants to place numbers on his spinner that would make it certain that you

would get a number less than 3.

Place 4 numbers on Alex’s spinner to show this.

[1]

Alex’s Spinner

•

•

•

4. A jewellery shop wishes to create boxes to use for packaging gifts.

(a) Which one of the following patterns cannot be used to form a box in the shape of a cube? Circle your answer.

[1]

(b) The net of a gift box is shown below.

What is the name of the 3D shape made from this net? Circle your answer.

[1]

Cuboid Triangular prism Cylinder Sphere Cone

(c) The shape of another gift box is a triangular based pyramid (tetrahedron). Which of the following diagrams shows the top view of this gift box? Circle your answer.

[1]

A B C D

5. The table below shows the scores in the final of the Langford Bay Golf Championship.The player with the lowest score wins the championship.

(a) Complete the table below to show the names and scores of the players in order from 1st place to 7th place.

[3]

Position Name Score

1st

2nd L. Hakami -3

3rd

4th

5th J. Evans 1

6th P.J. Ames 5

7th

(b) What was the difference between the scores of the players in 2nd and 6th places? Circle your answer.

[1]

2 -4 8 7 -2

(c) How much less would H. Smith need to score in order to win the championship? [1]

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

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Name Score

A. Jenkins - 2

H. Smith 8

J. Evans 1

L. Hakami -3

F. Loxley -7

P.J. Ames 5

G. Francis -1

6. Gethin wants to organise a mountain walk in the Brecon Beacons with his 3 friends Chloe, Robertand Martyn during 2015.

He has the following information:

He (Gethin) can only go on a Sunday;

Chloe cannot go during the last 4 months of the year;

Martyn works on the first 3 Sundays of each month;

Robert cannot go during the school holidays;

All his friends agree that the months of November, December and January are unsuitable forthe walk.

The calendar shown on the opposite page is for 2015. The school holidays are represented by

What would be the latest date that they could all go for the mountain walk? You may use the calendar provided to show your working.

[5]

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JANUARY 2015 FEBRUARY 2015 MARCH 2015 APRIL 2015

S M T W T F S S M T W T F S S M T W T F S S M T W T F S

1 2 3 1 2 3 4

4 5 6 7 8 9 10 1 2 3 4 5 6 7 1 2 3 4 5 6 7 5 6 7 8 9 10 11

11 12 13 14 15 16 17 8 9 10 11 12 13 14 8 9 10 11 12 13 14 12 13 14 15 16 17 18

18 19 20 21 22 23 24 15 16 17 18 19 20 21 15 16 17 18 19 20 21 19 20 21 22 23 24 25

25 26 27 28 29 30 31 22 23 24 25 26 27 28 22 23 24 25 26 27 28 26 27 28 29 30

29 30 31

MAY 2015 JUNE 2015 JULY 2015 AUGUST 2015


1 2 1 2 3 4 5 6 1 2 3 4 1

3 4 5 6 7 8 9 7 8 9 10 11 12 13 5 6 7 8 9 10 11 2 3 4 5 6 7 8

10 11 12 13 14 15 16 14 15 16 17 18 19 20 12 13 14 15 16 17 18 9 10 11 12 13 14 15

17 18 19 20 21 22 23 21 22 23 24 25 26 27 19 20 21 22 23 24 25 16 17 18 19 20 21 22

24 25 26 27 28 29 30 28 29 30 26 27 28 29 30 31 23 24 25 26 27 28 29

31 30 31

SEPTEMBER 2015 OCTOBER 2015 NOVEMBER 2015 DECEMBER 2015


1 2 3 4 5 1 2 3 1 2 3 4 5

6 7 8 9 10 11 12 4 5 6 7 8 9 10 1 2 3 4 5 6 7 6 7 8 9 10 11 12

13 14 15 16 17 18 19 11 12 13 14 15 16 17 8 9 10 11 12 13 14 13 14 15 16 17 18 19

20 21 22 23 24 25 26 18 19 20 21 22 23 24 15 16 17 18 19 20 21 20 21 22 23 24 25 26

27 28 29 30 25 26 27 28 29 30 31 22 23 24 25 26 27 28 27 28 29 30 31

29 30

7. You will be assessed on the quality of your organisation, communication andaccuracy in writing in this question.

The Jones family invited their friends, the Williams and the Phillips families to stay at the Marine Bay Camping and Caravan Park, West Wales.

The Jones family have a caravan and stayed for 3 nights. The Williams family have a motor-home and only stayed for one night. The Phillips family stayed in a tent.

The total fee for the 3 pitches was £99.

For how many nights did the Phillips family stay? You must show all your working.

[4 + OCW 2]

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Marine Bay

West Wales

Camping & Caravan Park

Pitch fees per night.

Tent = £12

Caravan = £16

Motor-home = £15

8. The electricity meter readings at the beginning and at the end of a 3-month period were:

Reading at the end of the period 6 5 1 9 7

Reading at the beginning of the period 6 4 9 4 7

The cost of the electricity used was 30p per unit and there was a standing charge of £25.34 for the 3-month period.

Complete the following table to find the total cost. [4]

Reading at the end of the period

Reading at the beginning of the period

Number of units used

Cost of the units, in £

Standing charge for the 3 months

Total cost

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9.

Ten people work at Dragon Fitness. One of these people earns £1000 per week. All the other 9 people earn the same weekly wage. The mean wage for all of these 10 people is £280 per week.

(a) Complete the table below to show the different types of average weekly wage for these 10 people.

[4] …………………………………………………………………………………..………………………………

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Mean Median Mode

£280

(b) Complete the following sentence and give a reason for your choice of mode, median or mean.

[1]

‘The average wage of people working at Dragon Fitness is most typically £………’

Reason…………………………………………………………………………………………………………

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

10. Carys is planning a visit to Blaenau Ffestiniog tomorrow. Carys lives in Rhyl and plans to travel by train.

She will need to travel by train from Rhyl to Llandudno Junction, then change train to travel on to Blaenau Ffestiniog.

Carys has collected the timetables she needs to plan her day out.

Going to Blaenau Ffestiniog:

Departs From To Arrives Duration

07:08 Rhyl Llandudno Junction 07:28 20m







07:39 Llandudno Junction Blaenau Ffestiniog 08:42 1h 03m



16:33 Llandudno Junction Blaenau Ffestiniog 17:35 1h 02 m

Returning from Blaenau Ffestiniog:


14:57 Blaenau Ffestiniog Llandudno Junction 15:57 1h 00m

17:37 Blaenau Ffestiniog Llandudno Junction 18:35 58m



16:18 Llandudno Junction Rhyl 16:34 16m








(a) If Carys leaves Rhyl after 9 a.m., what is the earliest possible time at which she could arrive in Blaenau Ffestiniog? Circle your answer.

[1]

10:28 11:30 13:30 14:32 14:57

(b) Carys plans to be at the railway station in Blaenau Ffestiniog by 5 p.m. to begin her return journey home. How much time, in hours and minutes, will it take to travel back (from the time she leaves Blaenau Ffestiniog to the time she arrives back at Rhyl station)?

[4] ……………………………………………………………………………………………………………………

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11. Gwesty Traeth is a guest house and has six bedrooms.

Two of the rooms are described as Double (they have a double bed). Two of the rooms are described as Twin (they have two single beds). Two of the rooms are described as Single (they have one single bed).

The diagram below shows a plan of these rooms.

w

The people listed below have contacted Gwesty Traeth requesting rooms for dates in July 2016.

Sasha and Mia want to share a twin room for the 6th and 7th.

Mr & Mrs Jones want a double room for the 5th.

Flavia wants a single room for the 5th and 6th.

Mr & Mrs Evans want a double room for themselves and a twin room for their sons, Morysand Ifan, to share for the three nights 5th, 6th and 7th.

Their daughter Heledd will join them on the 6th and 7th, and she requires a single room.

Mr & Mrs Igorson want a double room for the 6th and 7th.

Use the table below to show who is given which room for each of the dates from the 5th July until the 7th July. No-one should have to change rooms during their stay.

[4]

Room 1 Room 2 Room 3 Room 4 Room 5 Room 6

5th July

6th July

7th July

12. Thomas buys a number of items from a market stall with two £20 notes and one £10 note.

These are the items Thomas buys:

7 cereal bars at 99p each 5 pairs of socks at £3.95 each 3 sweaters at £7.49 each

Thomas waits for the owner of the market stall to list all the items he has selected.

The owner then uses a calculator to add these costs individually and gives Thomas 75p change.

(a) Without the use of a calculator, how could Thomas check the calculation by using an efficient method? You must show all your working.

[4] ……………………………………………………………………………………………………………………

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(b) Did Thomas receive the correct change? If not, state the correct amount. [1]

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

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

13. Billy and Shaun both completed a survey.They collected leaves from a number of trees and decided to measure them.

They agreed on the following decisions

The length of the leaf does not include the stem

The width of the leaf is measured at the widest section of the leaf

(a) Why have they both agreed on these decisions about measuring the leaves? [1]

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

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

(b) Billy measured the length and width of each leaf he had collected. Shaun did the same with his leaves. They displayed the lengths and widths of their own leaves on separate scatter diagrams. Billy’s scatter diagram is shown below and Shaun’s scatter diagram is shown opposite.

(i) Who found the longest leaf? ……………….

Write down the length of this leaf. .................. cm [1]

(ii) Only one of the two boys collected all his leaves from the same tree. Who was this, Billy or Shaun? Give a reason for your answer.

[1] …………………………………………………………………………………..………………………………

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(iii) Draw, by eye, a line of best fit on Shaun’s scatter diagram. [1]

(iv) Shaun realises he has one more leaf that he has not included on his scatter diagram. The leaf is damaged in such a way that Shaun cannot measure its width. The length of the leaf is 8·5 cm. Write down a reasonable estimate for the width of this leaf.

Width ………. cm [1]

14.

Ingredients to make 4 pancakes

55 g plain flour

1 egg

100 ml milk

37·5 ml water

25 g butter

Useful information: metric and imperial units

4 ounces is approximately 110 g

Using the recipe shown above, calculate the quantity of plain flour needed to make 48 pancakes. Give your answer in ounces.

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15. In a supermarket, the same brand of shampoo is sold in two different-sized bottles.

Large bottle 800 ml for £1.28 Small bottle 300 ml for 45p

Which bottle of shampoo offers the better value for money? You must show your working and give a reason for your choice.

[4] ……………………………………………………………………………………………………………………

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16. The three Welsh castles, shown below, are all within walking distance of each other.

White Castle Skenfrith Castle Grosmont Castle

These castles are shown on the map below. The black lines represent the footpaths between the castles.

Complete the following statements.

The bearing of Skenfrith Castle from White Castle is .................... °

The bearing of White Castle from Grosmont Castle is .................... ° [2]

END OF PAPER

N


Candidate Number

0

GCSE

MATHEMATICS - NUMERACY UNIT 1: NON - CALCULATOR INTERMEDIATE TIER


1 HOUR 45 MINUTES

ADDITIONAL MATERIALS The use of a calculator is not permitted in this examination. A ruler, protractor and a pair of compasses may be required.



Take π as 3∙14.






The assessment will take into account the quality of your linguistic and mathematical organisation, communication and accuracy in writing in question 2(c)(i).


Question Maximum

Mark Mark

Awarded

1. 5

2. 9

3. 4

4. 5

5. 5

6. 6

7. 4

8. 9

9. 2

10. 4

11. 7

12. 8

13. 4

14. 8

TOTAL 80

Formula list


( )2

a b h

Volume of a prism = area of cross section length

1.

Ten people work at Dragon Fitness. One of these people earns £1000 per week. All the other 9 people earn the same weekly wage. The mean wage for all of these 10 people is £280 per week.

(a) Complete the table below to show the different types of average weekly wage for these 10 people.

[4] …………………………………………………………………………………………………

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…………………………………………………………………………………………………

…………………………………………………………………………………………………

Mean Median Mode

£280

(b) Complete the following sentence and give a reason for your choice of mode, median or mean.

[1]

‘The average wage of people working at Dragon Fitness is most typically £………’

Reason…………………………………………………………………………………………

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

2. Carys is planning a visit to Blaenau Ffestiniog tomorrow.Carys lives in Rhyl and plans to travel by train.

She will need to travel by train from Rhyl to Llandudno Junction, then change train to travel on to Blaenau Ffestiniog.

Carys has collected the timetables she needs to plan her day out.

Going to Blaenau Ffestiniog:













Returning from Blaenau Ffestiniog:


14:57 Blaenau Ffestiniog Llandudno Junction 15:57 1h 00m












(a) If Carys leaves Rhyl after 9 a.m., what is the earliest possible time at which she could arrive in Blaenau Ffestiniog? Circle your answer.

[1]

10:28 11:30 13:30 14:32 14:57

(b) Carys decides to leave Rhyl after 9 a.m. She would like to spend the least time possible changing trains on her way to Blaenau Ffestiniog, so she selects the most suitable train.

How long will she have to wait for her connecting train to Blaenau Ffestiniog at Llandudno Junction station? Circle your answer. [1]

12 minutes 16 minutes 19 minutes 45 minutes 1h 2 minutes

(c)(i) You will be assessed on the quality of your organisation, communication and accuracy in writing in this part of the question.

Carys plans to be at the railway station in Blaenau Ffestiniog by 5 p.m. to begin her return journey home. How much time, in hours and minutes, will it take to travel back (from the time she leaves Blaenau Ffestiniog to the time she arrives back at Rhyl station)?

[4 + OCW 2]

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(ii) Delays on the Blaenau Ffestiniog to Llandudno Junction railway line are expected tomorrow. A delay may cause Carys to miss her connecting train on the way home. If this happens, at what time will Carys arrive back at Rhyl station? You may assume that Carys misses only one train. Circle your answer.

18:35 21:21 18:55 19:12 19:42

Explain how you decided on your answer. [1]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

3. Gwesty Traeth is a guest house and has six bedrooms.

Two of the rooms are described as Double (they have a double bed). Two of the rooms are described as Twin (they have two single beds). Two of the rooms are described as Single (they have one single bed).

The diagram below shows a plan of these rooms.

w

The people listed below have contacted Gwesty Traeth requesting rooms for dates in July 2016.

Sasha and Mia want to share a twin room for the 6th and 7th.

Mr & Mrs Jones want a double room for the 5th.

Flavia wants a single room for the 5th and 6th.

Mr & Mrs Evans want a double room for themselves and a twin room for theirsons, Morys and Ifan, to share for the three nights 5th, 6th and 7th.

Their daughter Heledd will join them on the 6th and 7th, and she requires asingle room.

Mr & Mrs Igorson want a double room for the 6th and 7th.

Use the table below to show who is given which room for each of the dates from the 5th July until the 7th July. No-one should have to change rooms during their stay.

[4]

Room 1 Room 2 Room 3 Room 4 Room 5 Room 6

5th July

6th July

7th July

4. Thomas buys a number of items from a market stall with two £20 notes andone £10 note.

These are the items Thomas buys:

7 cereal bars at 99p each 5 pairs of socks at £3.95 each 3 sweaters at £7.49 each

Thomas waits for the owner of the market stall to list all the items he has selected.

The owner then uses a calculator to add these costs individually and gives Thomas 75p change.

(a) Without the use of a calculator, how could Thomas check the calculation by using an efficient method? You must show all your working.

[4] …………………………………………………………………………………………………

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(b) Did Thomas receive the correct change? If not, state the correct amount. [1]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

5. Billy and Shaun both completed a survey. They collected leaves from a number of trees and decided to measure them.

They agreed on the following decisions

The length of the leaf does not include the stem

The width of the leaf is measured at the widest section of the leaf

(a) Why have they both agreed on these decisions about measuring the leaves? [1]

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

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

(b) Billy measured the length and width of each leaf he had collected. Shaun did the same with his leaves. They displayed the lengths and widths of their own leaves on separate scatter diagrams. Billy’s scatter diagram is shown below and Shaun’s scatter diagram is shown opposite.

(i) Who found the longest leaf? ……………….

Write down the length of this leaf. .................. cm [1]

(ii) Only one of the two boys collected all his leaves from the same tree. Who was this, Billy or Shaun? Give a reason for your answer.

[1] ……………………………………………………………………………………………....

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

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

(iii) Draw, by eye, a line of best fit on Shaun’s scatter diagram. [1]

(iv) Shaun realises he has one more leaf that he has not included on his scatter diagram. The leaf is damaged in such a way that Shaun cannot measure its width. The length of the leaf is 8·5 cm. Write down a reasonable estimate for the width of this leaf.

Width ………. cm [1]

6.


55 g plain flour

1 egg

100 ml milk

37·5 ml water

25 g butter


4 ounces is approximately 110 g 25 ml of milk or water is approximately 1 fluid ounce

(a) Using the recipe shown above, calculate the quantity of plain flour needed to make 48 pancakes. Give your answer in ounces.

[3] …………………………………………………………………………………………………

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(b) Owen works in a school kitchen. He uses the recipe information for pancakes shown above. He has measured out the plain flour, milk and butter and placed them with the eggs in a large bowl. Owen measures out 150 fluid ounces of water to add to his other pancake ingredients in the bowl. How many pancakes is Owen making?

[3] …………………………………………………………………………………………………

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7. In a supermarket, the same brand of shampoo is sold in two different-sizedbottles.

Large bottle 800 ml for £1.28 Small bottle 300 ml for 45p

Which bottle of shampoo offers the better value for money? You must show your working and give a reason for your choice.

[4] …………………………………………………………………………………………………

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8. Derek works for a company which designs and fits kitchen cupboards.Kitchen cupboards and worktops are usually measured in mm.

(a)(i) A worktop is 4500 mm long. How much is this in metres?

[1] ………………………………………………………………………………………………

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(ii) A rectangular worktop needs to be covered in a special varnish. The worktop measures 3000 mm long by 700 mm wide. Calculate the area of the top surface of the worktop in m2.

[2]

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(b) A kitchen cupboard is in the shape of a cuboid. Its capacity is 420 000 cm3. Internally, the cupboard measures 60 cm wide and 70 cm deep. Calculate the internal height of the cupboard in cm.

[2]

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(c) A kitchen worktop measures 301 cm, correct to the nearest 1 cm.

Derek needs to fit two of these worktops together along a wall measuring 605 cm, correct to the nearest 5 cm. Unfortunately, he finds that the worktops do not fit.

Explain why this might have happened, and state the greatest possible difference between the lengths of the wall and the two worktops.

[4]

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9.(a) Lucy has been given pie charts showing the number of computers sold by 2 different companies.

RG computers LF computers

Lucy says

Explain how this could be true. [1]

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

(b) Lucy sees a headline.

Sales of desktop computers are steadily falling.

A graph was printed under this headline. Which of the following graphs was it most likely to have been? Circle your answer. [1]

‘More men buy RG computers than LF computers.’

10. Coffee is often sold in a carton.The height of one coffee carton is 13·4 cm.

Diagram not drawn to scale

A stack of 4 empty coffee cartons is shown below.


(a) What is the total height of a stack of 21 coffee cartons? Circle your answer. [1]

32 cm 33·34 cm 33·6 cm 45·4 cm 47 cm

(b) The height of a stack of x coffee cartons is 61·4 cm.

By forming an equation, or otherwise, calculate the number of coffee cartons in the stack.

[3]

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11. The three Welsh castles, shown below, are all within walking distance of eachother.



N

(a) By road, White Castle is 11 km from Skenfrith Castle. Complete the sentence below.

The map scale is approximately 1 cm to represent …………. km. [3]

…………………………………………………………………………………………………

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…………………………………………………………………………………………………

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(b) Complete the following statements.

The bearing of Skenfrith Castle from White Castle is .................... °

The bearing of White Castle from Grosmont Castle is .................... ° [2]

(c) Treasure has been buried at a position X. X is the position that meets both the following criteria:

X is equidistant from Grosmont Castle and Skenfrith Castle.

X is equidistant from White Castle Castle and Skenfrith Castle.

Find the treasure by marking X on the map. [2]

12. Yolanda and Emyr set up a gardening business together.They decide to calculate the charge for the time that they spend on a gardeningjob using the following method.

Gardening by Yolanda and Emyr

START with a standard charge of £15

ADD a fee of £10 for every complete hour worked

ADD an additional fee of 20p for every additional minute worked

MULTIPLY the total charge so far by 2

EQUALS the final charge

(a) Calculate the charge for a gardening job that takes 2 hours.

[2]

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

(b) (i) The fourth bullet point in calculating the charge reads:

MULTIPLY the total charge so far by 2.

Why do you think this is included in Emyr and Yolanda’s method for calculating a charge for gardening?

[1] …………………………………………………………………………………………..………

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

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

(ii) Write a formula for working out the final charge, £T, for gardening that takes h

hours and m minutes.

[3]

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

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

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

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

(c) Yolanda notices that there is a problem with the method for calculating the charge. They spent 2 hours on gardening for Mr Rees, and 1 hour 55 minutes gardening for Ms Elmander.

Mr Rees paid less than Ms Elmander.Explain why this happens.

[2]

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

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

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

13. The information shown below was found in a holiday brochure for a small island.

The information shows monthly data about the rainfall in centimetres.

(a) Looking at the rainfall, which month had the most changeable weather? You must give a reason for your answer.

[1] …………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) Circle either TRUE or FALSE for each of the following statements. [2]

If you don’t want much rain, the time to visit the island is in June.

TRUE FALSE

The greatest difference in rainfall is between the months of February and March

TRUE FALSE

The interquartile range for May is approximately equal to the interquartile range for June.

TRUE FALSE

The range of rainfall in February was approximately 15 cm. TRUE FALSE

During June, there were more days with greater than 7·5 cm of rainfall than there were days with less than 7·5 cm of rainfall.

TRUE FALSE

(c) In July 2014, the interquartile range for the rainfall was 10 cm and the range was 40 cm. Is it possible to say whether July has more or less rainfall than June? You must give a reason for your answer.

[1] …………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

14. Two different European Political Parties are proposing changing the rules forincome tax payments for the tax year April 2018 to April 2019.

Income Tax proposed by the Yellow Party

April 2018 to April 2019

taxable income = gross income – personal allowance

personal allowance is €5000

basic rate of tax 10% on the first €10 000 of taxable income

middle rate of tax 25% is payable on all taxable income over €10 000and up to €30 000

higher rate tax 50% is payable on all taxable income over €30 000

Income Tax proposed by the Orange Party



personal allowance is €10 000


higher rate tax 40% is payable on all other taxable income

(a) During the tax year 2018 to 2019, Janina’s gross income is likely to be €55 000.

Which party’s tax proposal would result in Janina paying the least tax, and by how much?

You must show all your working [7]

…………………………………………………………………………………………

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…………………………………………………………………………………………

(b) Samuli plays rugby for an international team. He is likely to earn €200 000 during the tax year 2018 to 2019. Without any calculations, explain why Samuli might favour the Orange Party’s proposal for income tax.

[1]

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END OF PAPER


Candidate Number

0

GCSE

MATHEMATICS - NUMERACY UNIT 1: NON - CALCULATOR HIGHER TIER


1 HOUR 45 MINUTES

ADDITIONAL MATERIALS The use of a calculator is not permitted in this examination.. A ruler, protractor and a pair of compasses may be required.



Take π as 3∙14.








Question Maximum

Mark Mark

Awarded

1. 5

2. 8

3. 1

4. 4

5. 5

6. 8

7. 4

8. 8

9. 6

10. 6

11. 6

12. 4

13. 11

14. 4

TOTAL 80



55 g plain flour

1 egg

100 ml milk

37·5 ml water

25 g butter


25 ml of milk or water is approximately 1 fluid ounce

Owen works in a school kitchen. He uses the recipe information for pancakes shown above. He has measured out the plain flour, milk and butter and placed them with the eggs in a large bowl. Owen measures out 150 fluid ounces of water to add to his other pancake ingredients in the bowl. How many pancakes is Owen making?

[3 + OCW 2]

…………………………………………………………………………………………………

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2. Derek works for a company which designs and fits kitchen cupboards.Kitchen cupboards and worktops are usually measured in mm.

(a) A rectangular worktop needs to be covered in a special varnish. The worktop measures 3000 mm long by 700 mm wide. Calculate the area of the top surface of the worktop in m2.

[2]

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

(b) A kitchen cupboard is in the shape of a cuboid. Its capacity is 420 000 cm3. Internally, the cupboard measures 60 cm wide and 70 cm deep. Calculate the internal height of the cupboard in cm.

[2]

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………………………………………………………………………………………………

………………………………………………………………………………………………

(c) A kitchen worktop measures 301 cm, correct to the nearest 1 cm.

Derek needs to fit two of these worktops together along a wall measuring 605 cm, correct to the nearest 5 cm. Unfortunately, he finds that the worktops do not fit.

Explain why this might have happened, and state the greatest possible difference between the lengths of the wall and the two worktops.

[4]

………………………………………………………………………………………………

………………………………………………………………………………………………

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………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

3. Lucy has been given pie charts showing the number of computers sold by 2different companies.

RG computers LF computers

Lucy says

Explain how this could be true. [1]

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

‘More men buy RG computers than LF computers.’

4. Coffee is often sold in a carton.The height of one coffee carton is 13·4 cm.


A stack of 4 empty coffee cartons is shown below.


(a) What is the total height of a stack of 21 coffee cartons? Circle your answer. [1]

32 cm 33·34 cm 33·6 cm 45·4 cm 47 cm

(b) The height of a stack of x coffee cartons is 61·4 cm.

By forming an equation, or otherwise, calculate the number of coffee cartons in the stack.

[3]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

5. The three Welsh castles, shown below, are all within walking distance of eachother.



N

(a) By road, White Castle is 11 km from Skenfrith Castle. Complete the sentence below.

The map scale is approximately 1 cm to represent …………. km. [3]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) Treasure has been buried at a position X. X is the position that meets both the following criteria:

X is equidistant from Grosmont Castle and Skenfrith Castle.

X is equidistant from White Castle Castle and Skenfrith Castle.

Find the treasure by marking X on the map. [2]

6. Yolanda and Emyr set up a gardening business together.They decide to calculate the charge for the time that they spend on a gardeningjob using the following method.

Gardening by Yolanda and Emyr

START with a standard charge of £15

ADD a fee of £10 for every complete hour worked

ADD an additional fee of 20p for every additional minute worked

MULTIPLY the total charge so far by 2

EQUALS the final charge

(a) Calculate the charge for a gardening job that takes 2 hours.

[2]

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

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

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

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

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

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

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

(b)(i) The fourth bullet point in calculating the charge reads:

MULTIPLY the total charge so far by 2.

Why do you think this is included in Emyr and Yolanda’s method for calculating a charge for gardening?

[1] …………………………………………………………………………………………..………

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

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

(ii) Write a formula for working out the total charge, £T, for gardening that takes h

hours and m minutes.

[3]

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

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

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

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

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

(c) Yolanda notices that there is a problem with the method for calculating the charge. They spent 2 hours gardening for Mr Rees, and they spent 1 hour 55 minutes gardening for Ms Elmander.

Mr Rees paid less than Ms Elmander. Explain why this happens.

[2]

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

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

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

7. The information shown below was found in a holiday brochure for a small island.

The information shows monthly data about the rainfall in centimetres.

(a) Looking at the rainfall, which month had the most changeable weather? You must give a reason for your answer.

[1] …………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) Circle either TRUE or FALSE for each of the following statements. [2]

If you don’t want much rain, the time to visit the island is in June.

TRUE FALSE

The greatest difference in rainfall is between the months of February and March

TRUE FALSE

The interquartile range for May is approximately equal to the interquartile range for June.

TRUE FALSE

The range of rainfall in February was approximately 15 cm. TRUE FALSE

During June, there were more days with greater than 7·5 cm of rainfall than there were days with less than 7·5 cm of rainfall.

TRUE FALSE

(c) In July 2014, the interquartile range for the rainfall was 10 cm and the range was 40 cm. Is it possible to say whether July has more or less rainfall than June? You must give a reason for your answer.

[1] …………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

8. Two different European Political Parties are proposing changing the rules forincome tax payments for the tax year April 2018 to April 2019.

Income Tax proposed by the Yellow Party



personal allowance is €5000


middle rate of tax 25% is payable on all taxable income over €10 000and up to €30 000

higher rate tax 50% is payable on all taxable income over €30 000

Income Tax proposed by the Orange Party



personal allowance is €10 000


higher rate tax 40% is payable on all other taxable income

(a) During the tax year 2018 to 2019, Janina’s gross income is likely to be €55 000.

Which party’s tax proposal would result in Janina paying the least tax, and by how much?

You must show all your working [7]

…………………………………………………………………………………………

…………………………………………………………………………………………

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…………………………………………………………………………………………

(b) Samuli plays rugby for an international team. He is likely to earn €200 000 during the tax year 2018 to 2019. Without any calculations, explain why Samuli might favour the Orange Party’s proposal for income tax.

[1]

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

9. A team of examiners has 64 000 examination papers to mark. It takes each examiner 1 hour to mark approximately 10 papers.

(a) The chief examiner says that a team of 50 examiners could mark all 64 000

papers in 8 days. What assumption has the chief examiner made? You must show all your calculations to support your answer.

[4]

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

(b) Why is the chief examiner’s assumption unrealistic? What effect will this have on the number of days the marking will take?

[2]

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

10. Greta has 50 empty jelly moulds which she plans to fill with layers of red and green jelly. Each jelly mould is shaped as an inverted hollow cone of height 15 cm and volume 540 cm3. Greta begins by making 1 litre of red jelly. She then pours an equal amount into each of the 50 jelly moulds. Calculate the height of the red jelly in each jelly mould. You must show all your working.

[6]

Diagram not drawn to scale …………………………………………………………………………………………

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15 cm

11. (a) At the National Eisteddfod in August each year, a concert is performed on the opening night. Of those performing this year:

39 are primary school children,

73 are secondary school children,

128 are adults.

In order to gather opinions from the performers about the backstage facilities, the organisers decide to question a stratified sample of 40 people.

Find how many secondary school children should be selected. You must show all your working.

[3] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... .......................................................................................................................................

Number of secondary school children ........................................................

(b) Rhodri calculates that 7 primary school children should be selected. Rhodri selects the first 7 primary school children to get off the bus that brings them to the concert.

Explain why this does not represent a random sample of the primary school children.

[1]

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

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

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

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

(c) Of the 128 adult performers, 52 are male and 76 are female. Gwen decides to interview a stratified sample of 16 adults and has exactly 16 copies of the questionnaire ready for them.

Using these numbers, she calculates that she should interview 7 male performers and 10 female performers, making a total of 17 adults.

Explain how this has happened. [2]

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

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

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

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

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

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

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

12. Anwen is designing an indoor play centre.

The cuboid ABCDEFGH represents a diagram of the room to be used for the play centre.


Anwen measures the vertical height of the room to be 5 m. She measures the distance along the floor from E to F to be 9 m. The distance from E to G is 12 m.

Anwen is thinking of purchasing a long straight slide for the play centre. The total length of the slide, including space to get on and off, is 12·5 m.

Would it be possible to fit the slide into the room? You must show all your working.

[4]

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

A

E

D

C B H

G F

13. The histogram illustrates the floor areas of the offices available to let by OfficeSpace Wales letting agency.

(a) Calculate the number of offices available that have a floor area greater than 75 m2.

[3]

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050 100 150 200

Floor area (m2) 0

2

4

6

8

Frequency density

(b) Office Space Wales charges a £200 arrangement fee when any of the offices with a floor area of up to 100 m2 are let. Assuming that all of the offices under 100 m2 are let, how much will Office Space Wales receive in arrangement fees for these offices?

[3]

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(c) Circle either TRUE or FALSE for each of the following statements. [2]

There are definitely no offices available with less than 10 m2 of space.

TRUE FALSE

The modal class of office space is between 125 m2 and 150 m2. TRUE FALSE

The number of offices over 100 m2 is double the number under 100 m2.

TRUE FALSE

There is enough information in the histogram to allow us to calculate an exact value for the mean office space.

TRUE FALSE

The number of offices under 50 m2 is definitely the same as the number over 175 m2.

TRUE FALSE

(d) It is reported that the median size of office space available to let is 80 m2. Is this true for the offices that are available to let by Office Space Wales? You must give a reason for your answer.

[2] .......................................................................................................................................

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

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

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

14. Dafydd is an engineer working at the Welsh Science Research Centre.

During an experiment, Dafydd knows that a certain chemical particle loses half of

its mass every second.

The initial mass of the particle is 80 grams.

(a) The mass of the particle after 8 seconds is

0·15625 g 0·3125 g 0·625 g 5 g 10 g

[1]

(b) Dafydd needs to write down a formula for finding the final mass, f grams, of the particle after t seconds. What formula should he write?

[3] .......................................................................................................................................

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

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

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

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

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

(c) Comment on the mass of the particle after a long time, such as a whole day, has passed.

[1] .......................................................................................................................................

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

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END OF PAPER


Candidate Number

0

GCSE

MATHEMATICS - NUMERACY UNIT 2: CALCULATOR - ALLOWED FOUNDATION TIER


1 HOUR 30 MINUTES

ADDITIONAL MATERIALS A calculator will be required for this paper. A ruler, protractor and a pair of compasses may be required.



Take π as 3∙14 or use the π button on your calculator.








Question Maximum

Mark Mark

Awarded

1. 9

2. 43. 84. 4

5. 4

6. 5

7. 2

8. 4

9. 9

10. 6

11. 412. 8

TOTAL 65

Formula list


( )2

a b h

1. Alys carried out a survey of 30 people to find out which vegetable, from a choice ofcabbage, peas, broccoli and sprouts, they liked the most. Her results are as follows.

Cabbage Cabbage Peas Peas Sprouts Sprouts

Peas Cabbage Peas Sprouts Peas Peas

Broccoli Sprouts Cabbage Sprouts Peas Peas

Peas Peas Peas Cabbage Sprouts Cabbage

Cabbage Peas Cabbage Broccoli Broccoli Peas

(a) Use the data to draw a vertical line graph on the squared paper below. [6]

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(b) Why would Alys collect her data in a frequency table using a tallying method? [1]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(c) Alys wanted to compare the popularity of different vegetables. What is the modal vegetable? Put a tick next to your answer.

[1]

Cabbage

Peas

There is no modal vegetable

Broccoli

Sprouts

(d) Alys chose one person at random from the people that she had surveyed. What is the probability that the person chosen said that broccoli was the vegetable that they liked the most?

[1] …………………………………………………………………………………………………

…………………………………………………………………………………………………

2. Amelia is organising her 16th birthday party and decides to make the invitations for the party herself.

Each invitation is a rectangle measuring 6 cm by 8 cm.

She makes the invitations from coloured card measuring 18 cm by 16 cm.

(a) What is the maximum number of invitations that Amelia can cut from one piece of coloured card?

[2]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

Maximum number of invitations is …………………………….

(b) Amelia wishes to invite 120 people to her birthday party. What is the least number of pieces of coloured card, measuring 18cm by 16cm, that Amelia needs to buy?

[2] …………………………………………………………………………………………………

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Ashley usually works 32 hours a week at £6.50 per hour.

She pays one tenth of her earnings in tax and national insurance. She gives £50 of her weekly earnings to her family for her room and food. She spends £60 a week on socialising, clothing and other things. She saves the rest of her earnings.

Ashley wants to book a week’s holiday in Portugal costing £419. How many weeks will it take her to save for her holiday? You must show all your working.

[6 + OCW 2]

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4.

A local fitness centre wishes to build an outdoor 5-a-side football pitch of length 45 metres and width 25 metres.

The cost of building the outdoor 5-a-side football pitch is £85 per square metre.

Calculate the total cost of building the outdoor 5-a-side football pitch.

You must show your working. [4]

…………………………………………………………………………………………………

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45 metres

25 metres

5.

A chef needs to cook a 4 kilogramturkey. The following rule is used to calculate the cooking time:

“Cook for 40 minutes per kilogram

and then add an extra 25 minutes.”

The chef wants the turkey to be ready at 1:30pm. What is the latest time that the chef should begin cooking the turkey?

[4] …………………………………………………………………………………………………

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6. Teabags are on offer.

Offer A Offer B

Which is the better buy? Show all your calculations.

[5]

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7. A pair of trainers is sold in a box.

The number of pairs of trainers sold each month from January to April is shown in the pictogram.

The symbol represents 100 pairs of trainers

January

February

March

April

(a) What is the approximate range of the numbers of pairs of trainers sold each month? Circle your answer.

[1]

100 150 200 250 300

(b) The total number of trainers sold from January to April is 1300. What is the mean of the number of pairs of trainers sold each month? Circle your answer.

[1]

250 300 325 380 400

8. Bikes are built around a frame.

The diagram below is a scale drawing of a bike frame. It is drawn to a scale of 1: 8.

(a) Write down an approximate length of the cross bar AB. Give you answer in metres.

[2]

…………………………………………………………………………………………..

…………………………………………………………………………………………..

…………………………………………………………………………………………..

(b) Is AE parallel to BD? Use angle facts to explain your answer.

[2]

…………………………………………………………………………………………..

…………………………………………………………………………………………..

…………………………………………………………………………………………..

9. Boat owners are charged to keep their boats in a harbour.

Charges for a North Wales harbour are given in the table below.

Period Price per metre (£ per metre)

exclusive of VAT

Notes

Annual 320 Minimum length of boat 9 m

Six monthly 180 Minimum length of boat 7 m

Monthly 40 No minimum length

Notes

VAT is charged at a rate of 20%.

All charges are per metre; any part metre is charged as acomplete metre.

Combinations of the periods are allowed.For example, for exactly 7 months, pay for 6 months then payfor an extra month, or pay monthly for each of the 7 months.

(a) Including VAT, how much would the monthly charge be for a 10 m boat? Circle your answer.

[1]

£40 £48 £400 £480 £4800

(b) Excluding VAT, how much would the six monthly charge be for an 8·2 m boat?

[1]

£180 £1440 £1620 £1944 £1728

(c)(i) Lars owns a 9·3 m boat. He wants to keep his boat in the harbour for 11 months. Which option should he choose?

You should consider all possibilities, including VAT. Show all your working.

[6]

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(ii) What is the greatest saving that Lars could make by selecting your option? [1]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

Greatest possible saving is £ ……………

10. A container is used to collect the liquid produced by a factory.As soon as the container is full, it starts to empty the liquid into a tanker.As soon as the container is empty, it starts to fill again.

The graph shows the process of the container being filled and emptied into thetanker.

(a) What is the volume of the liquid in the container 2 hours into the process?

…………… m3 [1]

(b) How long does it take to half fill the container? Give your answer in minutes.

[2]

…………………………………………………………………………………………………

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(c) The container is empty at 8:36 a.m. At what other times is the container empty between 9 a.m. and 9 p.m.?

[2] …………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

Volume of liquid in the container (m3)

Time (hours)

(d) Put a tick in the box next to the correct statement. [1]

The container fills at a constant rate from when it is empty to when it is full.

The container fills at a constant rate to start with, then slows down.

After starting to fill, the rate at which the container fills up increases.

The container starts to fill quickly, then slows down to a constant rate.

It is not possible to tell whether or not the rate at which the tank fills up remains the same.

11. Newspapers often give temperatures in both degrees Fahrenheit (°F) and

degrees Celsius (°C).

In the formula below, c represents a temperature in Celsius and f represents a

temperature in Fahrenheit.

9c + 160 = 5f

(a) Complete the following statement.

10°C is the same as …….. °F. [2]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) Make c the subject of the formula.

9c + 160 = 5f

[2] …………………………………………………………………………………………………

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12. A construction company is working on plans to lay a new gas pipeline.The gas pipeline is to run from Abermor to Brentor to Cantefore then continue on to another town.

(a) The above diagram shows the section of gas pipeline from Abermor to Cantefore.

(i) The bearing of Brentor from Cantefore is

073° 107° 163° 253° 287°

(ii) Write down the bearing of Abermor from Brentor. [3]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) As the gas pipeline continues towards the next town, it has to make a 30° turn so that it follows the road, as shown in the sketch.

Using a pair of compasses and a ruler, construct a line that shows the direction of the gas pipeline as it follows the road after the 30° turn. You must show all of your construction lines and arcs.

[3]

END OF PAPER


Candidate Number

0

GCSE

MATHEMATICS - NUMERACY UNIT 2: CALCULATOR - ALLOWED INTERMEDIATE TIER


1 HOUR 45 MINUTES










The assessment will take into account the quality of your linguistic and mathematical organisation, communication and accuracy in writing in question 4(c)(i).


Question Maximum

Mark Mark

Awarded

1. 5

2. 2

3. 4

4. 11

5. 6

6. 3

7. 7

8. 5

9. 8

10. 3

11. 7

12. 8

13. 6

14. 5

TOTAL 80

Formula list


( )2

a b h

Volume of a prism = area of cross section length

1. Teabags are on offer.

Offer A Offer B

Which is the better buy? Show all your calculations.

[5]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

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…………………………………………………………………………………………………

…………………………………………………………………………………………………

2. A pair of trainers is sold in a box.

The number of pairs of trainers sold each month from January to April is shown in the pictogram.

The symbol represents 100 pairs of trainers

January

February

March

April

(a) What is the approximate range of the numbers of pairs of trainers sold each month? Circle your answer.

[1]

100 150 200 250 300

(b) The total number of trainers sold from January to April is 1300. What is the mean of the number of pairs of trainers sold each month? Circle your answer.

[1]

250 300 325 380 400

3. Bikes are built around a frame.

The diagram below is a scale drawing of a bike frame. It is drawn to a scale of 1: 8.

(a) Write down an approximate length of the cross bar AB. Give you answer in metres.

[2]

…………………………………………………………………………………………..

…………………………………………………………………………………………..

…………………………………………………………………………………………..

(b) Is AE parallel to BD? Use angle facts to explain your answer.

[2]

…………………………………………………………………………………………..

…………………………………………………………………………………………..

…………………………………………………………………………………………..

4. Boat owners are charged to keep their boats in a harbour.

Charges for a North Wales harbour are given in the table below.

Period Price per metre (£ per metre)

exclusive of VAT

Notes

Annual 320 Minimum length of boat 9 m

Six monthly 180 Minimum length of boat 7 m

Monthly 40 No minimum length

Notes

VAT is charged at a rate of 20%.

All charges are per metre; any part metre is charged as acomplete metre.

Combinations of the periods are allowed.For example, for exactly 7 months, pay for 6 months then payfor an extra month, or pay monthly for each of the 7 months.

(a) Including VAT, how much would the monthly charge be for a 10 m boat? Circle your answer.

[1]

£40 £48 £400 £480 £4800

(b) Excluding VAT, how much would the six monthly charge be for an 8·2 m boat?

[1]

£180 £1440 £1620 £1944 £1728

(c) (i) You will be assessed on the quality of your organisation, communication and accuracy in writing in this part of the question.

Lars owns a 9·3 m boat. He wants to keep his boat in the harbour for 11 months. Which option should he choose?

You should consider all possibilities, including VAT. Show all your working.

[6 + OCW 2]

…………………………………………………………………………………………………

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(ii) What is the greatest saving that Lars could make by selecting your option? [1]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

Greatest possible saving is £ ……………

5. A container is used to collect the liquid produced by a factory.As soon as the container is full, it starts to empty the liquid into a tanker.As soon as the container is empty, it starts to fill again.

The graph shows the process of the container being filled and emptied into thetanker.

(a) What is the volume of the liquid in the container 2 hours into the process?

…………… m3 [1]

(b) How long does it take to half fill the container? Give your answer in minutes.

[2]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(c) The container is empty at 8:36 a.m. At what other times is the container empty between 9 a.m. and 9 p.m.?

[2] …………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

Volume of liquid in the container (m3)

Time (hours)

(d) Put a tick in the box next to the correct statement. [1]

The container fills at a constant rate from when it is empty to when it is full.

The container fills at a constant rate to start with, then slows down.

After starting to fill, the rate at which the container fills up increases.

The container starts to fill quickly, then slows down to a constant rate.

It is not possible to tell whether or not the rate at which the tank fills up remains the same.

6. Newspapers often give temperatures in both degrees Fahrenheit (°F) and degrees

Celsius (°C).

In the formula below, c represents a temperature in Celsius and f represents a

temperature in Fahrenheit.

9c + 160 = 5f

(a) Complete the following statement.

10°C is the same as …….. °F. [2]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) Make c the subject of the formula.

9c + 160 = 5f

[2] …………………………………………………………………………………………………

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…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

7. A construction company is working on plans to lay a new gas pipeline.The gas pipeline is to run from Abermor to Brentor to Cantefore then continue on to another town.

(a) The above diagram shows the section of gas pipeline from Abermor to Cantefore.

(i) The bearing of Cantefore from Brentor is

073° 107° 163° 253° 287°

(ii) Write down the bearing of Abermor from Brentor. [3]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) As the gas pipeline continues towards the next town, it has to make a 30° turn so that it follows the road, as shown in the sketch.

Using a pair of compasses and a ruler, construct a line that shows the direction of the gas pipeline as it follows the road after the 30° turn. You must show all of your construction lines and arcs.

[3]

8.

A ribbon is tied around all the faces of a box, as shown in the picture. The ribbon is placed across each face of the box and meets all the edges of the box at right angles. A bow is tied on top of the box.

(a) A box has length 8·5 cm, width 4·6 cm and height 2·2 cm. The bow is made using 18 cm of ribbon. Calculate the total length of ribbon required.

[3] …………………………………………………………………………………………………

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…………………………………………………………………………………………………

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

(b) A different box is to be decorated with ribbon in the same way.

The box has length l cm, width w cm and height h cm.

The bow is made using 18 cm of ribbon. Write down an expression for the total length of ribbon needed to decorate this box.

[2] …………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

9. Lech went on holiday from his home in Wales to Poland.Before going, he went into his local money exchange shop to buy some Polishzloty.

Lech only had £250 to spend on buying zloty.He wanted to buy as many zloty as possible.Unfortunately, the money exchange shop only had 50 zloty notes.The exchange rate to buy zloty was £1 = 4.37 zloty.

(a) How much did Lech pay for the zloty? [5]

…………………………………………………………………………………………………

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…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) While in Poland, Lech spent 340.40 zloty. On returning to Wales from his holiday, Lech changed his zloty back to pounds. Unfortunately, the money exchange shop would only buy back a whole number of zloty. The exchange rate used for changing zloty back to pounds was £1 = 4.43 zloty. Calculate how much Lech received back from the money exchange shop. Give your answer correct to the nearest penny.

[3]

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…………………………………………………………………………………………………

10. Sabrina sees the following advertisement.

Money Today

Borrow today – why wait until payday?

Costs 1% per day compound interest

Sabrina knows that she will be paid in 2 weeks’ time. She decides to borrow £400 for a period of 2 weeks.

How much will Sabrina have to pay back after 2 weeks? Show all your working.

[3]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

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…………………………………………………………………………………………………

11.(a) The North Hoyle Offshore Wind Farm is located approximately 7·5 km off the coast of North Wales.

When this wind farm opened, it was working at 35% of its full capacity, and it produced enough annual electricity for 50 000 homes. For how many homes would the wind farm have been able to produce electricity each year if it had worked at full capacity?

[2]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) There are many offshore wind farms off the coast of Wales, Scotland and England.

The full power of the individual wind turbines is different in the various wind farms.

The table shows information for 4 wind farms.

Wind farm Full power of each turbine in Mega Watts (MW)

Number of wind turbines

North Hoyle 2·0 30

Lynn and Inner Dowsing 3·5 54

Rhyl Flats 3·6 25

Robin Rigg 3·0 60

If each of these 4 wind farms worked at 45% of full power, what would be the mean power of a single wind turbine? Give your answer correct to 2 decimal places. You must show all your working.

[5]

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12. In Aberfar, a group of local people took part in a challenge to learn how to tie aCeltic knot.

The frequency diagram shows the times taken by the local people to tie a Celtic knot for the first time.

(a) Complete the cumulative frequency table for the times taken by the local people to tie a Celtic knot for the first time.

[2]

Time, t in minutes t ≤ 2·5 t ≤ 5 t ≤ 7·5 t ≤ 10 t ≤ 12·5 t ≤ 15 t ≤ 17·5

Cumulative frequency

(b) The graph paper opposite shows a cumulative frequency diagram of the times taken by 140 visitors to Wales to tie a Celtic knot for the first time.

On the same graph, draw a cumulative frequency diagram for the times taken by the local people to tie a Celtic knot for the first time.

[2]

(c) The visitors had been set a target that 100 of the group would finish within 17 minutes.By how many minutes did they miss or beat their target?

[2] …………………………………………………………………………………………………

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

Did they miss the target or beat the target? …………………..

By how many minutes? …………………

(d) Circle either TRUE or FALSE for each of the following statements. [2]

The tenth percentile reading for the local people is between 5 minutes and 7 minutes.

TRUE FALSE

40% of the visitors took less than 12 minutes. TRUE FALSE

The estimated median time taken by the visitors is 13·75 minutes.

TRUE FALSE

The difference between the estimated median times of the two groups of people is about 3 minutes.

TRUE FALSE

If there had been only 120 visitors, they would certainly all have finished within 18 minutes.

TRUE FALSE

13. Luis has a large dog which lives in a kennel.In order to design a similar kennel for a smaller dog, Luis wants to calculate theangle of elevation of the roof of his dog’s kennel.He has noticed that the front of his dog’s kennel is symmetrical.

He has measured a number of lengths and recorded them on a diagram of thekennel, as shown below.


Luis has marked the angle of elevation with an x on the diagram.

(a) Calculate the size of angle x to an appropriate degree of accuracy.

[5] …………………………………………………………………………………………..

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(b) Explain why, in practice, this angle may not be as accurate as you have

calculated. [1]

…………………………………………………………………………………………..

…………………………………………………………………………………………..

…………………………………………………………………………………………..

14. The length of the flag shown is twice its width.

Diagram not drawn to scale The diagonal of the flag measures 2·5 metres. Calculate the width of the flag.

[5] …………………………………………………………………………………………..

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Width of the flag is ……………….

END OF PAPER

,


Candidate Number

0

GCSE

MATHEMATICS - NUMERACY UNIT 2: CALCULATOR - ALLOWED HIGHER TIER


1 HOUR 45 MINUTES










The assessment will take into account the quality of your linguistic and mathematical organisation, communication and accuracy in writing in question 2(a).


Question Maximum

Mark Mark

Awarded

1. 2

2. 10

3. 3

4. 7

5. 8

6. 6

7. 5

8. 4

9. 5

10. 8

11. 5

12. 7

13. 5

14 5

TOTAL 80

1.

A ribbon is tied around all the faces of a box, as shown in the picture. The ribbon is placed across each face of the box and meets all the edges of the box at right angles. A bow is tied on top of the box. The bow is made using 18 cm of ribbon.

The box has length l cm, width w cm and height h cm.

Write down an expression for the total length of ribbon needed to decorate this box. [2]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

2. Lech went on holiday from his home in Wales to Poland.Before going, he went into his local money exchange shop to buy some Polishzloty.

Lech only had £250 to spend on buying zloty.He wanted to buy as many zloty as possible.Unfortunately, the money exchange shop only had 50 zloty notes.The exchange rate to buy zloty was £1 = 4.37 zloty.

(a) You will be assessed on the quality of your organisation, communication and accuracy in writing in this part of the question.

How much did Lech pay for the zloty? [5 + OCW 2]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) While in Poland, Lech spent 340.40 zloty. On returning to Wales from his holiday, Lech changed his zloty back to pounds. Unfortunately, the money exchange shop would only buy back a whole number of zloty. The exchange rate used for changing zloty back to pounds was £1 = 4.43 zloty. Calculate how much Lech received back from the money exchange shop. Give your answer correct to the nearest penny.

[3] …………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

3. Sabrina sees the following advertisement.

Money Today

Borrow today – why wait until payday?

Costs 1% per day compound interest

Sabrina knows that she will be paid in 2 weeks’ time. She decides to borrow £400 for a period of 2 weeks.

How much will Sabrina have to pay back after 2 weeks? Show all your working.

[3]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

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…………………………………………………………………………………………………

…………………………………………………………………………………………………

4. (a) The North Hoyle Offshore Wind Farm is located approximately 7·5 km off thecoast of North Wales.

When this wind farm opened, it was working at 35% of its full capacity, and it produced enough annual electricity for 50 000 homes. For how many homes would the wind farm have been able to produce electricity each year if it had worked at full capacity?

[2]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(b) There are many offshore wind farms off the coast of Wales, Scotland and England.

The full power of the individual wind turbines is different in the various wind farms.

The table shows information for 4 wind farms.

Wind farm Full power of each turbine in Mega Watts (MW)

Number of wind turbines

North Hoyle 2·0 30

Lynn and Inner Dowsing 3·5 54

Rhyl Flats 3·6 25

Robin Rigg 3·0 60

If each of these 4 wind farms worked at 45% of full power, what would be the mean power of a single wind turbine? Give your answer correct to 2 decimal places. You must show all your working.

[5]

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5. In Aberfar, a group of local people took part in a challenge to learn how to tie aCeltic knot.

The frequency diagram shows the times taken by the local people to tie a Celtic knot for the first time.

(a) Complete the cumulative frequency table for the times taken by the local people to tie a Celtic knot for the first time.

[2]

Time, t in minutes t ≤ 2·5 t ≤ 5 t ≤ 7·5 t ≤ 10 t ≤ 12·5 t ≤ 15 t ≤ 17·5

Cumulative frequency

(b) The graph paper opposite shows a cumulative frequency diagram of the times taken by 140 visitors to Wales to tie a Celtic knot for the first time.

On the same graph, draw a cumulative frequency diagram for the times taken by the local people to tie a Celtic knot for the first time.

[2]

(c) The visitors had been set a target that 100 of the group would finish within 17 minutes.By how many minutes did they miss or beat their target?

[2] …………………………………………………………………………………………………

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

Did they miss the target or beat the target? …………………..

By how many minutes? …………………

(d) Circle either TRUE or FALSE for each of the following statements. [2]

The tenth percentile reading for the local people is between 5 minutes and 7 minutes.

TRUE FALSE

40% of the visitors took less than 12 minutes. TRUE FALSE

The estimated median time taken by the visitors is 13·75 minutes.

TRUE FALSE

The difference between the estimated median times of the two groups of people is about 3 minutes.

TRUE FALSE

If there had been only 120 visitors, they would certainly all have finished within 18 minutes.

TRUE FALSE

6. Luis has a large dog which lives in a kennel. In order to design a similar kennel for a smaller dog, Luis wants to calculate the angle of elevation of the roof of his dog’s kennel.

He has noticed that the front of his dog’s kennel is symmetrical.

He has measured a number of lengths and recorded them on a diagram of the kennel, as shown below.


Luis has marked the angle of elevation with an x on the diagram.

(a) Calculate the size of angle x to an appropriate degree of accuracy.

[5] …………………………………………………………………………………………..

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(b) Explain why, in practice, this angle may not be as accurate as you have

calculated.

[1]

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7. The length of the flag shown is twice its width.


The diagonal of the flag measures 2·5 metres. Calculate the width of the flag.

[5]

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Width of the flag is ……………….

8. On holiday, Ffion sees a necklace priced at 168 euros in a shop.

The shopkeeper tells her there is an error in the marked price. The rate of value

added tax (VAT) included in the price has been calculated as 15%, but it should be

20%.

As Ffion is disappointed, the shopkeeper offers her an additional reduction of 12%

after the VAT is corrected.

If she accepts the shopkeeper’s offer, how much does Ffion eventually pay for the

necklace?

[4] .......................................................................................................................................

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9. An engineer needs to check the density of steel produced by the factory where heworks. He collects a sample of 1000 ball bearings, each with a radius of 0·8 cm. The total mass of the ball bearings is 16·935 kg.

Calculate the density of the steel. Give your answer in kg / m3.

[5] .......................................................................................................................................

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10. Ceri is a jewellery designer and is making a brooch.

The brooch is in the shape of a sector of a circle of radius 2·8 cm, as shown in the

diagram.


(a) Ceri is planning to cover the brooch in gold leaf.

Ceri buys gold leaf in square sheets of side length 80 mm. The cost of one sheet of

gold leaf is £48.00.

Assuming that no gold leaf is wasted, find the cost of the gold leaf that is required to

cover the brooch.

[5]

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110°

(b) (i) The cost of the metal Ceri uses for the base of her first brooch should be £2.28.

She decides to produce a larger brooch in a similar shape, but with a base of the same thickness. The radius of the sector of the circle she uses this time is 4·2 cm.

The cost of the metal needed for the base of the second brooch should be

£3.19 £3.42 £4.47 £5.13 £9.58

[1]

(ii) Ceri finds that when she makes the base of a brooch, she wastes of the

metal that she buys. Including the waste, the actual cost of the metal for the base of the smaller brooch is

£0.57 £1.71 £2.85 £3.04 £9.12

[1]

11. Dragon Nation Bank is advertising a savings account.

Account Nominal interest rate AER Annual Equivalent Rate,

correct to 2 decimal places

Dragon Saver 7·6% p.a., paid quarterly .................... %

(a) Complete the AER entry in the table. [4]

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(b) Explain why AER is used by the bank. [1]

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12. A cylinder is made of bendable plastic.Part of a child’s toy is made by bending the cylinder to form a ring. The two circular ends of the cylinder are joined to form the ring.

The inner radius of the ring is 9 cm. The outer radius of the ring is 10 cm.


Calculate an approximate value for the volume of the ring. State and justify what assumptions you have made in your calculations and the impact they have had on your results.

[7] .......................................................................................................................................

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9 cm

13. Dewi was a cyclist.He travelled along a straight flat road to the bottom a hill and cycled up the hill. The gradient of the hill was constant at first, then decreased near the top, where Dewi stopped for a rest.

Dewi maintained the same level of effort throughout his journey.

(a) Which of the following velocity-time graphs represents Dewi’s journey? [1]

The graph which represents Dewi’s journey is graph ..........................

Time (s)

Velocity (m/s)

Time (s)

Velocity (m/s)

Time (s)

Velocity (m/s)

Time (s)

Velocity (m/s)

Time (s)

Velocity (m/s)A B

C

D E

(b) Later in the day, Dewi’s greatest velocity was 22 metres per second, measured to the nearest metre per second. In that location, the speed limit on the road was 80 kilometres per hour.

Is it possible that Dewi exceeded the speed limit? You must show all your working.

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14. A solid concrete base for a garden statue is to be made in the shape of afrustum of a pyramid. The frustum is formed by removing a small pyramid from a large pyramid, as shown in the diagram.

Calculate the volume of concrete required to make the base for the garden statue. Give your answer in litres.

[6]


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END OF PAPER

MATHEMATICS - NUMERACY

2nd

SAMs 2017Unit 1 (Non-calculator) Foundation Tier

Mark MARK SCHEME Comments (Page 1)

1.

Item Quantity X or

Orange juice 2 litres ()

Mushrooms 50 kilograms X

A bag of sugar 1 kilogram

Tomato sauce 350 litres X

Potatoes 5 grams (X)

Chocolate bar 100 grams

Bottle of vinegar 250 millilitres

Butter 500 grams

Milk 4 litres

Washing-up liquid 500 litres X

B4

4

Award B4 for all 8 correct responses Award B3 for 7 correct responses Award B2 for 6 correct responses Award B1 for 5 correct responses

2. 7345 + 6339 + 4991 + 1093= 19768

19800

M1 A1 B1

3

Attempt to add 3 or 4 numbers CAO FT their total

3.

(a) Two numbers less than or equal to 4 AND two numbers greater than 4. (b) Four numbers less than 3

B1

B1

2

For both parts accept use of appropriate decimal, fractional and/or negative values. e.g. 1, 2, 5, 6 OR 3, 4, 5, 6 OR 4, 4, 7, 7 etc e.g. 0, 0, 0, 0 OR 2, 1, 0, -1 etc

4. (a) Correct net circled or clearly indicated

(b) Triangular prism (c) A

B1

B1 B1

3

Accept answers either circled or clearly indicated.

5. (a)

Position Name Score

1st

F. Loxley -7

2nd

3rd

A. Jenkins -2

4th

G. Francis -1

5th

6th

7th

H. Smith 8

(b) 8 circled or clearly indicated (c) 16

B3

B1 B1

5

B2 for 3 correct B1 for 2 correct.

Accept 15 (for jointly winning) OR Accept 17, 18, 19. ……..

6.

Identifying/sight of when Chloe can(/cannot) go Identifying/sight of when Gethin can go

Identifying / sight of when Martyn can(/cannot) go

Identifying common dates – (25th

Jan), 22nd

March, 26th

April & 28th

JuneLatest date = 28

th June

B1 B1

B1

B1

B1

5

Look at calendar for indication throughout the question

e.g. Sept, Oct, Nov, Dec crossed out Look for focus on Sundays

(25th

Jan), (22nd

Feb), 22nd

(& 29th

)March, 26

th April, (24

th & 31

st May), 28

th

June, (26th July, 23

rd & 30

th Aug, 27

th

Sept, 25th

Oct, 22nd

& 29th

Nov & 27th

Dec) Sight of common dates triggers 1

st 4

marks

Award full marks for an unsupported correct answer


2nd


Mark MARK SCHEME Comments

(Page 2) 7. (Cost for the Jones and Williams families =)

3 × 16 + 1× 15 = (£)63 (Cost for the Phillips family =) (99 – 63) = 36 (Number of nights =) (36 ÷ 12 =) 3 nights

Organisation and communication Accuracy of writing

M1

A1 B1 B1

OC1 W1

6

FT ‘their 63’ if M1 awarded FT ‘their 36’. Not dependent on M1

8.

Reading at the end of the period 65197

Reading at the beginning of the period 64947

Number of units used 250

Cost of the units, in £ 75.00

Standing charge for the 3 months 25.34

Total cost 100.34

B1

B2

B1

4

FT their numbers of units in £. B1 for answer in pence.

FT their cost of units + 25.34. If any entry is blank, look in the work area.

9. (a) (Total wage for 10 people) 10 × 280 (Wage of each of the other 9 people =)

(2800 – 1000) ÷ 9 (£)200

Median AND modal wage (£)200

(b) Inserts £200 and gives a reason relating to ‘median’ or

‘mode’ including a related statement such as ‘the most common’ or ‘the middle value’

M1

m1 A1 B1

E1

5

(£2800)

FT ‘their 2800’

FT ‘their derived 200’

Needs sight of intention of reference to the median and / or mode

Only award if clearly linked to evidence of understanding of the average selected. Accept a reason justifying the selection of ‘mode or median’ or ‘not the mean’.

10.(a) 11:30

(b) 17:37 train selected at Blaenau Ffestiniog, (Arrives 18:35 Llandudno Junction,) and

Departs Llandudno Junction at 18:39

Arrives in Rhyl at 18:55

17:37 23 (minutes) + 55 (minutes) 18:55 or 78 (minutes)

1 hour 18 minutes

B1

M1

A1

M1

A1

5

Needs sight of 17:37 train and 18:39 train

May be implied

Or alternative method to find the time difference e.g. using the durations given in the timetables, 58 + 4 + 16 (= 78 mins) etc

11. Correct rooms allocated to(Sasha and Mia), (Mr & Mrs Jones), (Flavia), (Mr & Mrs Evans), (Morys & Ifan), (Heledd) and (Mr & Mrs Igorson).

B4

4

There are several acceptable combinations. B4 for all 7. B3 for 6. B2 for 5. B1 for 4.


2nd



12.

(a) 7 × 99p worked as 7×£1 – 7×1p 5 × £3.95 worked as 5×£4 – 5×5p 3×£7.50 – 3×1p or 3×£7 + 3×50p – 3×1p Total (£)49.15 or 4915p

(b) Wrong change, should be 85p

B1 B1 B1 B1

B1

5

Accept equivalent simple methods involving compensation from rounding with multiplication or any valid multiplication method throughout, but not repeated addition

Allow £49.15p. Answer in (a) or (b)

FT provided less than £50 and of equivalent difficulty.

13.(a) Reason e.g. ‘fair comparison’, ‘doing survey the same way’ (b) (i) Name: Shaun Length in range 10.3 to 10.5(cm) (ii) Shaun with a reason, e.g. ‘Shaun because (positive) correlation’, ‘Shaun because leaves are similar’, ‘Shaun as there is a connection between length and width’ (iii) Reasonable straight line of best fit

(iv) Width in the range 6.8 to 7.5 cm

B1

B1

B1

B1

B1

5

Points above and below following trend

OR correct reading from their line of best fit

14. Use of × 48 ÷ 4 or × 12 OR realising 55g is2oz (12 × 55) ÷ 110 × 4 OR 2 × 12 OR equivalent

24 (ounces)

B1

M1 A1

3

(2 oz for 4 pancakes, so 2 × 12)

15. Attempt at unit cost e.g. for 100ml or 1ml,OR 1(.)28 / 8(00) with 45 / 3(00) or similar, OR looking to equate volumes, OR looking to almost equate volumes no more

than 100ml difference, e.g. by looking at 3300ml

with 800ml, or 2800ml with 5300ml

Large bottle 16(p) per 100ml or 0.16(p) per 1ml Small bottle 15(p) per 100ml or 0.15(p) per 1ml

Better value statement, conclusion small bottle

S1

B1 B1

E1

4

e.g. Idea of doubling or halving to equate, each done more than once. Method that would lead to a correct equate or comparison, e.g. for 300ml, 1200ml, 2400ml, …

OR 2.4l costs (£)3.84 or 1.2l costs (£)1.92 OR 2.4l costs (£)3.60 or 1.2l costs (£)1.80

E mark is dependent on conditions: EITHER Award provided B1 and B1 awarded, OR Award as FT from their logical conclusion provided at least B1 awarded, ignoring further incorrect processing within a final statement, OR Award provided S1 awarded for conclusion from comparison with correct calculations and correct difference in price for stated extra volume, e.g. ‘(900ml in) 3 small bottles (is £1.35) which is better value because you get 100ml more (than a large bottle) for 7p more’

16. 065 °197 °

B1 B1

2

Allow a tolerance of ±2°.


2nd

SAMs 2017Unit 1 (Non-calculator) Intermediate Tier


1. (a) (Total wage for 10 people) 10 × 280 (Wage of each of the other 9 people =)

(2800 – 1000) ÷ 9 (£)200

Median AND modal wage (£)200

(b) Inserts £200 and gives a reason relating to

‘median’ or ‘mode’ including a related statement such as ‘the most common’ or ‘the middle value’

M1

m1 A1 B1

E1

5

(£2800)

FT ‘their 2800’

FT ‘their derived 200’

Needs sight of intention of reference to the median and / or mode

Only award if clearly linked to evidence of understanding of the average selected. Accept a reason justifying the selection of ‘mode or median’ or ‘not the mean’.

2.(a) 11:30 (b) 12 minutes (c)(i) 17:37 train selected at Blaenau Ffestiniog, (Arrives 18:35 Llandudno Junction,) and

Departs Llandudno Junction at 18:39

Arrives in Rhyl at 18:55

17:37 23 (minutes) + 55 (minutes) 18:55 or 78 (minutes)

1 hour 18 minutes


(ii) 19:12 AND reason e.g. catches the next train (at Llandudno Junction at 18:53)

B1 B1 M1

A1

M1

A1

OC1 W1

E1

9

Needs sight of 17:37 train and 18:39 train

May be implied

Or alternative method to find the time difference e.g. using the durations given in the timetables, 58 + 4 + 16 (= 78 mins) etc

3. Correct rooms allocated to(Sasha and Mia), (Mr & Mrs Jones), (Flavia), (Mr & Mrs Evans), (Morys & Ifan), (Heledd) and (Mr & Mrs Igorson).

B4

4

There are several acceptable combinations. B4 for all 7. B3 for 6. B2 for 5. B1 for 4.

4.

(a) 7 × 99p worked as 7×£1 – 7×1p 5 × £3.95 worked as 5×£4 – 5×5p 3×£7.50 – 3×1p or 3×£7 + 3×50p – 3×1p Total (£)49.15 or 4915p

(b) Wrong change, should be 85p

B1 B1 B1 B1

B1

5

Accept equivalent simple methods involving compensation from rounding with multiplication or any valid multiplication method throughout, but not repeated addition

Allow £49.15p. Answer in (a) or (b)

FT provided less than £50 and of equivalent difficulty.


2nd



5.(a) Reason e.g. ‘fair comparison’, ‘doing survey the same way’ (b) (i) Name: Shaun Length in range 10.3 to 10.5(cm) (ii) Shaun with a reason, e.g. ‘Shaun because (positive) correlation’, ‘Shaun because leaves are similar’, ‘Shaun as there is a connection between length and width’ (iii) Reasonable straight line of best fit

(iv) Width in the range 6.8 to 7.5 cm

B1

B1

B1

B1

B1

5

Points above and below following trend

OR correct reading from their line of best fit

6.(a) Use of × 48 ÷ 4 or × 12 OR realising 55g is 2oz (12 × 55) ÷ 110 × 4 OR 2 × 12 OR equivalent

24 (ounces)

(b) 150 fl oz = 150 × 25 (ml) (=3750 ml) 1 pancake 37.5 / 4 (= 9.375) ml water, or notices 3750 is 100 × ‘amount given in recipe’ (3750 / 9.375 OR 100 × 4 =)

400 (pancakes)

B1

M1 A1

M1 M1

A1

6

(2 oz for 4 pancakes, so 2 × 12)

OR 3750 ÷ 37.5 = 100

7. Attempt at unit cost e.g. for 100ml or 1ml,OR 1(.)28 / 8(00) with 45 / 3(00) or similar, OR looking to equate volumes, OR looking to almost equate volumes no more

than 100ml difference, e.g. by looking at 3300ml

with 800ml, or 2800ml with 5300ml.

Large bottle 16(p) per 100ml or 0.16(p) per 1ml. Small bottle 15(p) per 100ml or 0.15(p) per 1ml.

Better value statement, conclusion small bottle.

S1

B1 B1

E1

4

e.g. Idea of doubling or halving to equate, each done more than once. Method that would lead to a correct equate or comparison, e.g. for 300ml, 1200ml, 2400ml, …

OR 2.4l costs (£)3.84 or 1.2l costs (£)1.92 OR 2.4l costs (£)3.60 or 1.2l costs (£)1.80

E mark is dependent on conditions: EITHER Award provided B1 and B1 awarded, OR Award as FT from their logical conclusion provided at least B1 awarded, ignoring further incorrect processing within a final statement, OR Award provided S1 awarded for conclusion from comparison with correct calculations and correct difference in price for stated extra volume, e.g. ‘(900ml in) 3 small bottles (is £1.35) which is better value because you get 100ml more (than a large bottle) for 7p more’


2nd



8.(a)(i) 4.5(00 m)

(ii) 3000 700 with an attempt to change units

2.1 (m2)

(b) 60 70 .... = 420 000 100 (cm)

(c) Sight of maximum length of worktop(s) 301.5(cm) or 603 (cm)

Sight of minimum length of wall 602.5(cm) Problem caused by 603(cm) worktop along wall (only) 602.5(cm) long Difference in measurement is 0.5 cm

B1

M1

A1

M1 A1

B1

B1 E1

B1

9

Attempt to change units needs evidence of ÷10

n where n≥3

Or equivalent method

.

9.(a) Shows understanding that the pie charts don’t show how many computers were sold

(b) Top right graph

E1

B1

2

10.(a) 45.4 cm

(b) (x – 1) 1.6 + 13.4 = 61.4

OR x = 61.4 – 13.4 + 1

1.6

31 (cartons)

B1

M2

A1

4

Accept equation where x is the number of

stacked cups (excluding the bottom one), provided 1 is added at the end.

M1 for 1.6 x + 13.4 = 61.4 (omitting +1),

or x = (61.4 – 13.4) / 1.6, or

M1 for an equation that would be correct apart from missing brackets, or M1 for correct equation expressed in words. Accept missing brackets if implied by a correct response.

If no marks allow SC1 for 31 (cartons).

Alternative method (using answer to (a)):

(x – 21) 1.6 = 61.4 – 45.4 = 16 M1

x – 21 = 10 M1

x = 31 A1

11.(a) Measuring a distance slightly greater than the direct distance between White Castle and Skenfrith Castle. Approximate answer for 11 ÷ ‘their measured distance’.

Reasonable answer from appropriate calculation

(b) 065 ° 197 °

(c) One of the appropriate perpendicular bisectors ±2° shown X indicated, with both correct perpendicular bisectors ±2°

M1

M1

A1

B1 B1

M1

A1

7

FT their measured distance in cm.

FT from M0, M1

Allow a tolerance of ±2°.


2nd



12.(a) [15 + 10 × 2 + 15 × 0.20 ] × 2

(£)76

(b)(i) e.g. x 2 to account for 2 people working

(ii) Sight of 10 × h OR (0).2 × m OR m / 5

T = 2(15 + 10 h + 0.2m) or equivalent

(c) Explanation, e.g. ‘60×20p is more than the cost per hour’, or ‘£12 paying for an hour charged by the minute, but £10 for the hour’, ‘55×20p (=£11) is more than the cost per hour’, or ‘between 51 and 60 minutes cost more than an hour’, or similar

M1

A1

E1

B1

B2

E2

8

Intention to × 2, however brackets may be missing

Or equivalent in pence throughout

B1 for (T =) 15 + 10 × h + (0).2 × m (× 2),

i.e. missing brackets or partially in brackets OR (15 + 10 × h + (0).2 × m) × 2 with any

2 of the 3 terms within the brackets correct

E1 for an attempt to calculate the charge for 1 hour 55 minutes

13.(a) April Reason, e.g. greatest range, or greatest interquartile range

(b) TRUE FALSE

TRUE TRUE

FALSE

(c) States or implies ‘not possible to tell’ with a reason, e.g. ‘ can’t tell as it doesn’t give any information about how much rain fell’, or ‘just the difference between maximum and minimum not how much rain fell’, or ‘don’t know as the difference between UQ & LQ doesn’t give the actual amount of rain, just a range for the middle 50%’

E1

B2

B1

4

B1 for any 4 correct


2nd



14.(a) Yellow Party Taxable income (55000 – 5000=) (€)50000 AND (10% tax to be paid on (€)10000 =) (€)1000

(25% tax to be paid on (€)20000=) (€)5000 AND (50% tax to be paid on (€)20000=) (€)10000

Yellow Party Tax to pay (€)16000

Orange Party Taxable income (55000 – 10000=) (€)45000 AND (20% tax to be paid on (€)20000 =) (€)4000

(40% tax to be paid on (€)25000=) (€)10000

Orange Party Tax to pay (€)14000

Orange Party (€)2000 (less to pay)

(b) Reason, e.g. ‘most of his earnings taxed at 40% rather than at 50%’

B1

B1

B1

B1

B1

B1

B1

E1

8

FT 50% of (‘their 50000’ – 30000)

CAO

FT 40% of (‘their 45000’ – 20000)

CAO

FT their subtraction provided at least B2 awarded in each tax calculation.

The reason must focus on the 40% and 50% comparison. Do not accept ‘pays less tax’ without an explanation.


2nd

SAMs 2017Unit 1 (Non-calculator) Higher Tier


1. 150 fl oz = 150 × 25 (ml) (=3750 ml) 1 pancake 37.5 / 4 (= 9.375) ml water, or notices 3750 is 100 × ‘amount given in recipe’ (3750 / 9.375 OR 100 × 4 =)

400 (pancakes)


M1 M1

A1

OC1 W1

5

OR 3750 ÷ 37.5 = 100

2.

(a) 3000 700 with an attempt to change units

2.1 (m2)

(b) 60 70 .... = 420 000 100 (cm)

(c) Sight of maximum length of worktop(s) 301.5(cm) or 603 (cm)

Sight of minimum length of wall 602.5(cm) Problem caused by 603(cm) worktop along wall (only) 602.5(cm) long Difference in measurement is 0.5 cm

M1

A1

M1 A1

B1

B1 E1

B1 8

Attempt to change units needs evidence of ÷10

n where n≥3

Or equivalent method

3. Shows understanding that the pie chartsdon’t show how many computers were sold.

E1

1

4.(a) 45.4 cm

(b) (x – 1) 1.6 + 13.4 = 61.4

OR x = 61.4 – 13.4 + 1

1.6

31 (cartons)

B1

M2

A1

4

Accept equation where x is the number of

stacked cups (excluding the bottom one), provided 1 is added at the end.

M1 for 1.6 x + 13.4 = 61.4 (omitting +1),

or x = (61.4 – 13.4) / 1.6, or

M1 for equation that would be correct apart from missing brackets, or M1 for correct equation expressed in words. Accept missing brackets if implied by a correct response.

If no marks allow SC1 for 31 (cartons).

Alternative method (using answer to (a)):

(x – 21) 1.6 = 61.4 – 45.4 = 16 M1

x – 21 = 10 M1

x = 31 A1


2nd



5. (a) Measuring a distance slightly greater thanthe direct distance between White Castle and Skenfrith Castle Approximate answer for 11 ÷ ‘their measured distance’

Reasonable answer from appropriate calculation

(b) One of the appropriate perpendicular bisectors ±2° shown X indicated, with both correct perpendicular bisectors ±2°

M1

M1

A1

M1

A1

5

FT their measured distance in cm

FT from M0, M1

6. (a) [15 + 10 × 2 + 15 × 0.20 ] × 2

(£)76

(b)(i) e.g. x 2 to account for 2 people working

(ii) Sight of 10 × h OR (0).2 × m OR m / 5

T = 2(15 + 10 h + 0.2m) or equivalent

(c) Explanation, e.g. ‘60×20p is more than the cost per hour’, or ‘£12 paying for an hour charged by the minute, but £10 for the hour’, ‘55×20p (=£11) is more than the cost per hour’, or ‘between 51 and 60 minutes cost more than an hour’, or similar.

M1

A1

E1

B1

B2

E2

8

Intention to × 2, however brackets may be missing

Or equivalent in pence throughout

B1 for (T =) 15 + 10 × h + (0).2 × m (×2),

i.e. missing brackets or partially in brackets

OR (15 + 10 × h + (0).2 × m) × 2 with any

2 of the 3 terms within the brackets correct

E1 for an attempt to calculate the charge for 1 hour 55 minutes.

7. .(a) AprilReason, e.g. greatest range, or greatest interquartile range

(b) TRUE FALSE

TRUE TRUE

FALSE

(c) States or implies ‘not possible to tell’ with a reason, e.g. ‘can’t tell as it doesn’t give any information about how much rain fell’, or ‘just the difference between maximum and minimum not how much rain fell’, or ‘don’t know as the difference between UQ & LQ doesn’t give the actual amount of rain, just a range for the middle 50%’.

E1

B2

B1

4

B1 for any 4 correct.


2nd



8. (a) Yellow PartyTaxable income (55000 – 5000=) (€)50000 AND (10% tax to be paid on (€)10000 =) (€)1000

(25% tax to be paid on (€)20000=) (€)5000 AND (50% tax to be paid on (€)20000=) (€)10000

Yellow Party Tax to pay (€)16000

Orange Party Taxable income (55000 – 10000=) (€)45000 AND (20% tax to be paid on (€)20000 =) (€)4000

(40% tax to be paid on (€)25000=) (€)10000

Orange Party Tax to pay (€)14000

Orange Party (€)2000 (less to pay)

(b) Reason, e.g. ‘most of his earnings taxed at 40% rather than at 50%’

B1

B1

B1

B1

B1

B1

B1

E1

8

FT 50% of (‘their 50000’ – 30000)

CAO

FT 40% of (‘their 45000’ – 20000)

CAO

FT their subtraction provided at least B2 awarded in each tax calculation.

The reason must focus on the 40% and 50% comparison. Do not accept ‘pays less tax’ without an explanation.

9. (a) 64 000 ÷ 10 ÷ 50

÷ 8

= 16 (hours per examiner per day)

Correct interpretation of the answer e.g. assumption that each examiner works for a total of 16 hours per day.

(b) Reason e.g. it is unlikely that all examiners will work for as long as 16 hours in one day OR it is unlikely that the examiners will be able to work at the same rate for 16 hours AND effect e.g. 8 days is too short a time to complete the marking.

M2

A1

E1

E2

6

M1 for dividing 64 000 by two of 10, 50 or 8. Accept alternative method involving multiplication e.g.

50 × 10 = 500

64 000 / 500 (= 128) 128 / 8 (M1 for 2 of the 3 steps)

CAO

FT ‘their 16’ if appropriate. E1 for reason only.


2nd



10. Amount of jelly per mould = 1000 / 50= 20 (cm

3)

Volume scale factor = 540 / 20 = 27

Length scale factor = 3

Height of water = 15 / 3 = 5 (cm)

M1 A1

M1 A1 M1

A1

6

FT ‘their 20 cm3’.

FT cube root of ‘their 27’ provided M1 awarded.

Alternative for final 4 marks: M2 for h

3=15

3 × 20 / 540.

M1 for (h/15)3= 20 / 540 or equivalent.

m1 for h = √153 × 20

540

3 . A1 for 5(cm).

11. (a)(Number of secondary school children =) 73 / (39 + 73 + 128)

73 / 240 × 40 ( = 2920 / 240 or 73 / 6 or 12(.1666...) or 12 (1/6))

= 12

(b) Valid reason e.g. ‘all the children are not equally likely to be selected’ or ‘the children selected are likely to be in a friendship group’.

(c) 6.5 (male performers) OR 9.5 (female performers)

Explanation that both numbers have been rounded up.

M1 m1

A1

E1

B1

E1

6

Intention to find proportion of 40

Must be given as a whole number.

Showing understanding of the definition of a random sample.

12. Identifying a suitable right-angled trianglee.g. AEG

AG2 = 5

2 + 12

2

AG = 13 (m)

Conclusion e.g. ‘Yes, because 12·5 m < 13 m’

S1

M1 A1 B1

4


2nd



13. (a) Method of finding 1 correct area.2 correct areas AND intention to add all areas.

525

(b) 1×75 + 4×25 (= 175)

× 200

(£) 35 000

(c) FALSE TRUE

FALSE FALSE

FALSE

(d) No, stated or implied with a reason, e.g. ‘skew to offices greater than 80m

2’, ‘the median

(300th

value) lies within the 100-125 interval’, ‘No,the majority are greater than 80m

2 (or 100m

2)’

M1 M1

A1

M1

m1

A1

B2

E2

10

Areas are 4×25 + 6×25 + 7×25 + 2×50 = 100 + 150 + 175 + 100

CAO For an answer of 600 by considering full area, award M1, SC1

If no marks, then SC1 for ‘their 175’ × 200 correctly evaluated.

B1 for any 4 correct

E1 for an answer that implies no with a statement implying that the median is greater than 80m

2 but without giving a

reason why , OR E1 for NO with an incorrect median stated in the range 100<median<125 without further statement. Do not accept reference to mode.

14. (a) 0·3125 g

(b) f = 80 / 2t or f = 80 × 0·5

t.

(c) Valid explanation e.g. ‘tends to zero’ or ‘becomes negligibly small’.

B1

B3

E1

5

B2 for expression 80 / 2t or 80 × 0·5

t

OR B1 for evidence of 80 repeatedly

being divided by 2 or multiplied by 0·5 i.e. more than once, or sight of 2

t or 0·5

t.


2nd

SAMs 2017 Unit 2 (Calculator allowed) Foundation Tier


1. (a) Cabbage 8, Peas 13, Sprouts 6, Broccoli 3

Both axes labelled, e.g. frequency or number of people along one axis and Cabbage, Peas, Sprouts, Broccoli along the other axis (or on the bars), anywhere within the base (inc) of the corres. bar AND uniform scale for the frequency axis starting at 0.

Four bars at correct heights (bars must be of equal width). Can be in any order.

(b) Suitable reason given linked to organising and/or collecting her data in a methodical way.

(c) Peas

(d) 3/30 or equivalent

B2

B2

B2

E1

B1

B1 9

May be inferred from their bar chart. B1 for any two/three correct frequencies. If frequencies score 0, then give B1 for all 4 correct tallies.

B1 if no scale but allow one square to represent 1 OR B1 if not labelled as ‘frequency’ or similar. If frequency scale starts with 1 at the top of the first square the starting at 0 will be implied for this axis. Condone frequency values alongside square instead of at the top of the squares.

FT their frequencies throughout. FT their scale. B1 for any 2 or 3 correct bars on FT.

ISW

2. (a) 6 rectangles, measuring 6cm by 8cm,correctly drawn or stated.

(b) 120 ÷ 6 20 (pieces of card)

B2

M1 A1

4

Award B1 for 2, 3, 4 or 5 rectangles correctly drawn.

FT their number of rectangles.

3. (earnings) (32 × 6.50=) (£)208(Tax &NI )(1/10 of 208=) (£)20.8(0) (Total outgoings) (20.8(0) + 50 + 60=) (£)130.8(0) (Has left) (208 – 130.8(0)=) (£)77.2(0) (Number of weeks) (419 ÷ 77.2(0)= 5.427...) 6


B1 B1 B1 B1 B2

OC1 W1

8

CAO FT ‘their 208’ FT ‘their 20.8(0)’ FT ‘their 130.8(0)’ B1 for 5(.427) weeks. FT ‘their 77.2(0)’ for equivalent difficulty

Alternative method Earnings = 208 B1 Tax = 20.80 B1 (208 – 20.80 = )187.20 B1 Has left 77.20 B1 FT ‘their 187.20’ – 50 – 60Number of weeks = 6 weeks B2 FT their 77.2(0) B1 for 5(.427) weeks

4. (a) (area =) 45 × 251125(m

2)

(Cost =) 1125 × (£)85 (£) 95625

M1 A1 M1 A1

4

FT ‘their area’

If no marks awarded, award SC2 for sight of (£)11900

OR award SC1 for 85 correctly

5. 4 ½ × 40 = 180(Cooking time =) 180 mins (or 3 hrs) + 25 mins

= 205 mins or 3 hours 25 mins (Chef begins cooking at) 10.05 (am)

B1 M1 A1 B1 4

FT ‘their 180’

FT their cooking time


2nd



6. Use of 30 teabags (for £1.80)Method to compare, e.g. multiples of 30 & 40: 30, 60, 90, 120 & 40, 80, 120

4 × 1.8(0) and 3 × 2.60

(£)7.2(0) and (£)7.8(0) or equivalent

Offer A (20 teabags + 50% free) is better value

B1 M1

m1

A1

E1

5

OR equivalent, e.g. 1 or 10 teabags considered for both bags of 30 & 40 OR 1(.)80 ÷ 3(0) and 2(.)60 ÷ 4(0) with consistent place value to compare OR 60(p for 10) and 65(p for 10) with consistent place value to compare OR 60(p for 10) and (£) 2(.)60 – (£)1(.)80 = 80p for extra 10 OR 2.40 for 40 OR 1.80 ÷ 30 × 40 OR 1.80 ÷ 3 × 4 OR 60(p) for 10 and 80(p) for extra 10.

Depends on M1, m1 awarded with appropriate FT Accept answers suggesting ‘depends if you need 40 teabags exactly’ etc. provided M1, m1, A1 previously awarded.

SC1 for an answer based on comparison of 20 teabags for £1.80 with 40 teabags for £2.60, appropriate working with conclusion of 40 teabags

7.(a) 150 (b) 325

B1 B1

2

8.(a) 7cm (± 0.2cm) × 8 (÷ 100)

0.56 (m)

(b) Measuring 2 appropriate angles (±2°) to check interior (allied), or appropriate corresponding or alternate angles

Conclusion based on the angles measured and accurate knowledge of parallel line angle facts.

M1

A1

B1

E1

4

Award M1 only for answers 56cm or 56m or 56 or similar from ± 0.2cm tolerance

The size of angles may not actually be recorded, e.g. on diagram equal angles marked x and y.

Accept references to the angles which are equal or sum to 180° Do not accept ‘travelling in the same direction so won’t meet’


2nd



9.(a) £480 (b) £1620

(c)(i) Paying for 10m

11×1mth (11×10×40×1.2 =) (£)5280 AND

12mth charge (320×10×1.2 =) (£)3840

6mth + 5×1mth 180×10 + 5×40×10 (×1.2) (£)4560

Conclusion to pay annual charge based on the calculation of all 3 possibilities

(ii) Greatest saving (£5280 - £3840 =) (£)1440

B1 B1

B1

B2

M1 A1

E1

B1

9

If not awarded, FT use of 9m throughout

B1 for either correct, or if neither correct award for excluding VAT charges of (£)4400 and (£)3200 respectively

Accept excluding VAT (£3800)

FT appropriate conclusion depending on the sight of any two of the 3 correct charges given including VAT

If misread not using ‘per metre’ consistently, hence MR-1, then B0, then FT throughout

FT their least of 3 possibilities subtracted correctly from their greatest of 3 possibilities

10.(a) 5·5 (metres)

(b) Intention to read horizontal scale for depth of 3m filling

36 (minutes)

(c) 13(:)36 or 1 36 pm AND 18(:)36 or 6 36 pm

(d) 4th

statement identified

B1

M1

A1

B2

B1

6

Accept answers in the range 5.4 to 5.6 inclusive Accept sight of 0.6 (hours)

B1 for either correct, or B1 if both given with incorrect time notation or B1 for two times given that are 5 hours apart e.g. 14:36 and 19:36, i.e. FT 'their first time' + 5 hours for second B1. B0 if more than one statement identified.

11.(a) 9 × 10 + 160 = 250 or equivalent 50(°F)

(b) 9c =5f – 160 c = 5f – 160 or c = 5(f – 32)

9 9

M1 A1

B1 B1

4

FT until 2nd

error

12. (a)(i) 253(°)

(ii) 360 – 42 = 318(°)

(b) 60° with construction arcs

(30° by) bisecting ‘their angle’, with arcs shown Correct 30° from appropriate construction with line shown at the right hand end of the given line

B1

M1 A1

M1

M1 A1

6

SC1 for answers of 073(°) and 138(°) in (i) and (ii)

Accept anywhere on the line Allow sight of construction arcs for 60°

Line (road) may not be shown Depends on both M marks


2nd

SAMs 2017Unit 2 (Calculator allowed) Intermediate Tier


1. Use of 30 teabags (for £1.80)Method to compare, e.g. multiples of 30 & 40: 30, 60, 90, 120 & 40, 80, 120

4 × 1.8(0) and 3 × 2.60

(£)7.2(0) and (£)7.8(0) or equivalent

Offer A (20 teabags + 50% free) is better value

B1 M1

m1

A1

E1

5

OR equivalent, e.g. 1 or 10 teabags considered for both bags of 30 & 40 OR 1(.)80 ÷ 3(0) and 2(.)60 ÷ 4(0) with consistent place value to compare OR 60(p for 10) and 65(p for 10) with consistent place value to compare OR 60(p for 10) and (£) 2(.)60 – (£)1(.)80 = 80p for extra 10 OR 2.40 for 40 OR 1.80 ÷ 30 × 40 OR 1.80 ÷ 3 × 4 OR 60(p) for 10 and 80(p) for extra 10.

Depends on M1, m1 awarded with appropriate FT Accept answers suggesting ‘depends if you need 40 teabags exactly’ etc. provided M1, m1, A1 previously awarded.

SC1 for an answer based on comparison of 20 teabags for £1.80 with 40 teabags for £2.60, appropriate working with conclusion of 40 teabags

2.(a) 150 (b) 325

B1 B1

2

3.(a) 7cm (± 0.2cm) × 8 (÷ 100)

0.56 (m)

(b) Measuring 2 appropriate angles (±2°) to check interior (allied), or appropriate corresponding or alternate angles

Conclusion based on the angles measured and accurate knowledge of parallel line angle facts.

M1

A1

B1

E1

4

Award M1 only for answers 56cm or 56m or 56 or similar from ± 0.2cm tolerance

The size of angles may not actually be recorded, e.g. on diagram equal angles marked x and y.

Accept references to the angles which are equal or sum to 180° Do not accept ‘travelling in the same direction so won’t meet’


2nd



4.(a) £480 (b) £1620

(c)(i) Paying for 10m

11×1mth (11×10×40×1.2 =) (£)5280 AND

12mth charge (320×10×1.2 =) (£)3840

6mth + 5×1mth 180×10 + 5×40×10 (×1.2) (£)4560

Conclusion to pay annual charge based on the calculation of all 3 possibilities


(ii) Greatest saving (£5280 - £3840 =) (£)1440

B1 B1

B1

B2

M1 A1

E1

OC1 W1

B1

11

If not awarded, FT use of 9m throughout

B1 for either correct, or if neither correct award for excluding VAT charges of (£)4400 and (£)3200 respectively

Accept excluding VAT (£3800)

FT appropriate conclusion depending on the sight of any two of the 3 correct charges given including VAT

If misread not using ‘per metre’ consistently, hence MR-1, then B0, then FT throughout

FT their least of 3 possibilities subtracted correctly from their greatest of 3 possibilities

5.(a) 5·5 (metres)

(b) Intention to read horizontal scale for depth of 3m filling

36 (minutes)

(c) 13(:)36 or 1 36 pm AND 18(:)36 or 6 36 pm

(d) 4th

statement identified

B1

M1

A1

B2

B1

6

Accept answers in the range 5.4 to 5.6 inclusive Accept sight of 0.6 (hours)

B1 for either correct, or B1 if both given with incorrect time notation or B1 for two times given that are 5 hours apart e.g. 14:36 and 19:36, i.e. FT 'their first time' + 5 hours for second B1. B0 if more than one statement identified.

6.(a) 9 × 10 + 160 = 250 or equivalent 50(°F)

(b) 9c = 5f – 160 c = 5f – 160 or c = 5(f – 32)

9 9

M1 A1

B1 B1

4

FT until 2nd

error

7. (a)(i) 253(°)

(ii) 360 – 42 = 318(°)

(b) 60° with construction arcs

(30° by) bisecting ‘their angle’, with arcs shown Correct 30° from appropriate construction with line shown at the right hand end of the given line

B1

M1 A1

M1

M1 A1

6

SC1 for answers of 073(°) and 138(°) in (i) and (ii)

Accept anywhere on the line Allow sight of construction arcs for 60°

Line (road) may not be shown Depends on both M marks


2nd



8.(a) 2(8.5 + 4.6) + 42.2 ( + 18) and no others

= 53 (cm)

(b) 2l + 2w + 4h + 18 (cm) or equivalent

(and no extras)

M2

A1

B2

5

Or equivalent. Attempt to consider all 6 faces or all 8

lengths (+ 18) M1 for omitting one dimension OR for adding all three dimensions with at least one multiplied by 2 or 4.

CAO. An answer of 35 implies M2A0.

B1 for 1 error or 1 slip in notation.

Treat an answer of l + w + 4 h + 18 as 1

error (omitting bottom), hence award B1. If B2 penalise extra incorrect working -1

9.(a) 250 4.37 = 1092.5(0)

(Buys )1050 (zloty)

1050 4.37 = (£)240.27(46)

(b) (1050 – 340.40 =) 709.6(0)

709 4.43

(£) 160.05

M1 A1 A1

M1 A1

B1 M1

A1

8

FT provided M1 awarded

FT ‘their 1050 zloty’ provided rounded to the nearest 50. Must be in zloty not £s.

FT ‘their (a)’ provided >340.40 FT rounding down their 709.60 to whole number Accept (£)160.04 but not (£)160.045 An answer of (£)160.18 (omitting to round down) should be awarded B1 then SC1 in (b). An answer of (£)160.27 (rounding up instead of down) should be awarded SC1, with B1 if 709.6(0) seen.

10. 400 × 1.0114

or equivalent full method

(£)459.79

M2

A1

3

M1 for correctly multiplying by 1.01 n

where n is a positive integer. Award M2A0 for (£)459.789(685...)

11.(a) 50 000 ÷ 0.35 =

142857

(b) (Total power in MW is) 2.0×30 + 3.5×54 + 3.6×25 + 3.0×60 (Total number of turbines 30+54+25+60 = 169) (Mean full power of a turbine is)

519 ÷ 169 3.07(1…. MW)

(At 45% power) 0.45 × 3.07(….) or equivalent

1.38 (MW)

M1 A1

M1

m1 A1

m1

A1

7

(Σfx = 60+189+90+180 = 519)

FT ‘their Σfx’ ÷ ‘their 517’ CAO. Do not accept 3.1 or 3 (MW)

FT ‘their 3.07(…)’ provided M1, m1 previously awarded Their answer must be given correct to 2 decimal places, i.e. award M1A0 for 1.381(95...) or 1.3815 or 1.382.

Alternative: (45% power) 0.45×2, 0.45×3.5, 0.45×3.6, 0.45×3 M1 0.9×30 + 1.575×54 + 1.62×25 + 1.35×60

m1 233.55 (MW) CAO A1

÷169 m1 1.38 (MW) A1


2nd



12. (a) 0, 5, 25, 49, 83, 113, 120

(b) 3 unique vertical plots correct at upper bounds All plots correct and joined, including to 0 at t=2.5

(d) TRUE FALSE

TRUE

TRUE

FALSE

(c) Use of 15 minutes

Conclusion: Target beaten by 2 minutes

B2

M1 A1

B2

M1

A1

8

B1 for any three correct values, OR FT from 1 error for finding 3 further cumulative values accurately

Only FT their cumulative table to (c) Accuracy of plotting: time on the grid line, cumulative frequency within the appropriate square with 1

st & last plots on

the grid lines

B1 for any 4 correct FT their cumulative frequency diagram CAO CAO FT their cumulative frequency diagram CAO

13.(a) Form and use a right-angled triangle with base 55cm and height 50 cm. Tan x = 50/55

42(°) or 42.3(°)

(a) Reason, e.g. ‘original measurements may not have been accurate’, or ‘doesn’t consider the thickness of the wood’, …

S1

M1 A3

E1

6

Or alternative FULL method. A2 for 42.27….(°) A1 for tan

-1 0.909… or tan

-1 (50/55)

14. Attempt to use Pythagoras’ Theorem, e.g.length

2 + width

2 = 2.5

2

Use of length = 2 × width (2 × width)

2 + width

2 = 2.5

2 or equivalent

width2 = 1.25 or width = √1.25

Width 1.1(2 metres) or 1.118(03… metres)

M1

M1 m1 m1 A1

5

OR equivalent. If units are given they must be correct.

Alternative: Attempt to use Pythagoras’ Theorem, e.g. length

2 + width

2 = 2.5

2 M1

Use of length = 2 × width M1 Trial of a pair of values(< 2.5), one double

the other in Pythagoras’ Theorem m1

Trial of a pair of values(< 2.5), one double the other in Pythagoras’ Theorem

with improvement, closer to 2.5m m1

Width 1.1 metres or equivalent A1

MATHEMATICS - NUMERACY 2

nd SAMs 2017

Unit 2 (Calculator allowed) Higher Tier


1.

2l + 2w + 4h + 18 (cm) or equivalent (and

no extras)

B2

2

B1 for 1 error or 1 slip in notation.

Treat an answer of l + w + 4 h + 18 as 1

error (omitting bottom), hence award B1. If B2 penalise extra incorrect working -1.

2.(a) 250 4.37 = 1092.5(0)

(Buys )1050 (zloty)

1050 4.37 = (£)240.27(46)


(b) (1050 – 340.40 =) 709.6(0)

709 4.43

(£) 160.05

M1 A1 A1

M1 A1

OC1 W1

B1 M1

A1

10

FT provided M1 awarded

FT ‘their 1050 zloty’ provided rounded to the nearest 50. Must be in zloty not £s.

FT ‘their (a)’ provided >340.40 FT rounding down their 709.60 to whole number Accept (£)160.04 but not (£)160.045 An answer of (£)160.18 (omitting to round down) should be awarded B1 then SC1 in (b). An answer of (£)160.27 (rounding up instead of down) should be awarded SC1, with B1 if 709.6(0) seen.

3. 400 × 1.0114

or equivalent full method

(£)459.79

M2

A1

3

M1 for correctly multiplying by 1.01 n

where n is a positive integer. Award M2A0 for (£)459.789(685...)

4. (a) 50 000 ÷ 0.35 =

142857

(b) (Total power in MW is) 2.0×30 + 3.5×54 + 3.6×25 + 3.0×60 (Total number of turbines 30+54+25+60 = 169) (Mean full power of a turbine is)

519 ÷ 169 3.07(1…. MW)

(At 45% power) 0.45 × 3.07(….) or equivalent

1.38 (MW)

M1 A1

M1

m1 A1

m1

A1

7

(Σfx = 60+189+90+180 = 519)

FT ‘their Σfx’ ÷ ‘their 517’ CAO. Do not accept 3.1 or 3 (MW)

FT ‘their 3.07(…)’ provided M1, m1 previously awarded Their answer must be given correct to 2 decimal places, i.e. award M1A0 for 1.381(95...) or 1.3815 or 1.382.

Alternative: (45% power) 0.45×2, 0.45×3.5, 0.45×3.6, 0.45×3 M1 0.9×30 + 1.575×54 + 1.62×25 + 1.35×60

m1 233.55 (MW) CAO A1

÷169 m1 1.38 (MW) A1

MATHEMATICS - NUMERACY 2

nd SAMs 2017

Unit 2 (Calculator allowed) Higher Tier


5. (a) 0, 5, 25, 49, 83, 113, 120

(b) 3 unique vertical plots correct at upper bounds All plots correct and joined, including to 0 at t=2.5

(d) TRUE

FALSE

TRUE

TRUE FALSE

(c) Use of 15 minutes.

Conclusion: Target beaten by 2 minutes.

B2

M1 A1

B2

A1

8

B1 for any three correct values, OR FT from 1 error for finding 3 further cumulative values accurately.

Only FT their cumulative table to (c) Accuracy of plotting: time on the grid line, cumulative frequency within the appropriate square with 1

st & last plots on

the grid lines.

B1 for any 4 correct. FT their cumulative frequency diagram. CAO CAO FT their cumulative frequency diagram. CAO

6. (a) Form and use a right-angled triangle withbase 55 cm and height 50 cm. Tan x = 50/55

42(°) or 42.3(°)

(b) Reason, e.g. ‘original measurements may not have been accurate’, or ‘doesn’t consider the thickness of the wood’, …

S1

M1 A3

E1

6

Or alternative FULL method. A2 for 42.27….(°) A1 for tan

-1 0.909… or tan

-1 (50/55)

7. Attempt to use Pythagoras’ Theorem, e.g.length

2 + width

2 = 2.5

2

Use of length = 2 × width (2 × width)

2 + width

2 = 2.5

2 or equivalent

width2 = 1.25 or width = √1.25

Width 1.1(2 metres) or 1.118(03… metres)

M1

M1 m1 m1 A1

5

OR equivalent. If units are given they must be correct.

Alternative: Attempt to use Pythagoras’ Theorem, e.g. length

2 + width

2 = 2.5

2 M1

Use of length = 2 × width M1 Trial of a pair of values (< 2.5), one

double the other in Pythagoras’ Theorem m1

Trial of a pair of values (< 2.5), one double the other in Pythagoras’ Theorem

with improvement, closer to 2.5m m1

Width 1.1 metres or equivalent . A1

8. ((€)168) ÷ 1.15

× 1.2(0)

× 0.88

= 154.27 (euros)

M1 M1 M1 A1

4

Or equivalent e.g. × 120 / 115

CAO

M1


2nd

SAMs 2017 Unit 2 (Calculator allowed) Higher Tier


9. Volume = 4/3 × π × 0.83 (× 1000)

[OR 4/3 × π × 0.0083 (× 1000)]

= 2144(.6605...) cm3

[OR 0.002144(6605...) m3].

Use of conversion 1 m3 = 1 000 000 cm

3.

Use of mass / volume e.g. 16.935 ÷ 0.002144

7896 (kg / m3)

M1

A1

B1

M1

A1

5

Accept incorrect place value for digit 8 for M1.

Accept answers in range 2143 to 2146 Or 2048 π / 3

FT ‘their derived volume’ from dimensionally correct use of formula.

Accept answers in the range 7893 to 7901.

10. (Area of brooch =)110 / 360 × π × 2.8

2 OR 110 / 360 × π × 28

2

= 7.52(5...) (cm2) or 752.58(5...) (mm

2)

or equivalent e.g. 539π / 225 (cm

2) or 2156 π / 9 (mm

2)

(Cost of gold leaf per unit =) (£)48 ÷ (8 × 8) (per cm

2) or (£)48 ÷ (80 × 80) (per

mm2)

= (£)0.75 (per cm2) or (£)0.0075 (per mm

2)

or equivalent in pence

(Cost of gold leaf for brooch = 7.52(5...) × 0.75 or 752(.585...) × 0.0075)

= (£)5.64 which is rounded UP to give (£)5.65

(b) (i) £5.13

(ii) £3.04 9.

M1

A1

M1

A1

A1

B1

B1

7

Accept answers in range 7.52 to 7.53

(cm2)

Accept (£)5.64 (rounded down) or (£)5.65

(directly from rounded area)

10. 11. (a)Use of i = 0·076 AND n = 4

(1 + 0·076 / 4)4 – 1

AER 7·82(%)

(b) Explanation, based on need for fair comparison of interest rates.

B1 M1 A2

E1

5

Check table.

Correct substitution in the formula. A1 for 0·078(19...) or incorrect rounding or truncation of the AER percentage.

Accept ‘percentage of interest paid annually’. Must mention ‘year’ or ‘annual’.


2nd

SAMs 2017 Unit 2 (Calculator allowed) Higher Tier


11. 12. Radius of the cylinder = 0.5 cm12. OR diameter = 1 cm 13.

Idea that height of cylinder is approximately the circumference of the ring.

Circumference of ring = 2 × π × value between 9

and 10 inclusive

Volume = π × 0.52 × circumference of ring

Volume in the range 44.3 to 49.4 (cm3)

inclusive.

Statement about assumption, e.g. volume of

cylinder used to calculate volume of toy, use of mid-value for radius of ring.

Justification, e.g. used smaller radius so actual

volume will be greater, or used larger radius so actual volume will be less, or used 9.5 cm as height of cylinder is clearly between 9 cm and 10 cm.

B1

S1

M1

M1

A1

E1

E1

7

May be shown on the diagram

May be internal, external or somewhere in between. Accept sight of 9 × π or 10 × π for S1.

13. (a) D

(b) 22.5 × 60 × 60

÷ 1000 ‘Yes’ AND 81 (km / h)

B1

B1 M1 M1 A1

5

FT ‘their 22.5’

CAO

14. (Ratio of lengths 45 : 60 = ) 3 : 4

(Height of small pyramid =) 90 (cm)

(Volume of frustum =)

× 602 × 120 – × 45

2 × 90

= 83·25 (litres)

B1

B1

M2

A2

6

M1 for one correct product attempted for a volume (or sight of 144 000 or 60 750)

A1 for 83 250 (cm3)

FT their answer in cm3 for conversion to

litres for final A1.

Alternative solution: Ratio of lengths = 3 : 4 B1 Ratio of volumes = 27 : 64 B1 Volume of large pyramid = 144 000 cm

3 B1

Volume of frustum = 64 – 27 × 144 000 M1 64

83·25 (litres) A2 Award A1 for 83 250 (cm

3)

FT their answer in cm3 for conversion to

litres for final A1.

GCSE Mathematics - Numeracy

Foundation Unit 1

Qu. TopicMax

markAO1 AO2 AO3

Common

(Interm)OCW

1 Sarah's shopping 4 4

2 Liberty stadium rounding 3 3

3 Jay and Alex fair spinner 2 2

4 Jewellery boxes 3 3

5 Golf Negative numbers 5 1 4

6 Mountain walk 5 5

7 Marine Bay Caravan park 6 6

8 Electricity bill 4 4

9 Dragon fitness centre wages average 5 4 1 5(Q1)

10 Rhyl to Blaenau Ffestiniog 5 5 5(Q2)

11 Gwesty Traeth accommodation 4 4 4(Q3)

12 Market stall addition method reflection 5 1 4 5(Q4)

13 Leaf comparison scatter diagram 5 2 1 2 5(Q5)

14 Pancake recipe with change of units 3 3 3(Q6)

15 Best buy shampoo 4 4 4(Q7)

16 Three castles 2 2 2(Q11)

Totals 65 12 35 18 33

AOs


Intermediate Unit 1

Qu. TopicMax

markAO1 AO2 AO3

Common

(Found)

Common

(Higher)OCW

1 Dragon fitness centre wages average 5 4 1 5(Q9)

2 Rhyl to Blaenau Ffestiniog 9 9 5(Q10)

3 Gwesty Traeth accommodation 4 4 4(Q11)

4 Market stall addition method reflection 5 1 4 5(Q12)

5 Leaf comparison scatter diagram 5 2 1 2 5(Q13)

6 Pancake recipe with change of units 6 6 3(Q14) 3(Q1)

7 Best buy shampoo 4 4 4(Q15)

8 Kitchen cupboards 9 5 4 8(Q2)

9 Computer misleading piecharts and headline graph 2 1 1 1(Q3)

10 Stacking coffee cartons equation 4 4 4(Q4)

11 Three castles 7 4 3 2(Q16) 5(Q5)

12 Yolanda and Emyr gardening business 8 2 4 2 8(Q6)

13 Box and whisker rainfall graph 4 2 2 4(Q7)

14 European Tax political party proposals 8 7 1 8(Q8)

Totals 80 13 46 21 33 41

AOs


Higher Unit 1

Qu. TopicMax

mark

N

u

m

AO1 AO2 AO3Common

(Interm)OCW

1 Pancake recipe with change of units 5 5 3(Q6)

2 Kitchen cupboards 8 4 4 8(Q8)

3 Computer misleading piecharts 1 1 1(Q9)

4 Stacking coffee cartons equation 4 4 4(Q10)

5 Three castles 5 2 3 5(Q11)

6 Yolanda and Emyr gardening business 8 2 4 2 8(Q12)

7 Box and whisker rainfall graph 4 3 1 4(Q13)

8 European Tax political party proposals 8 7 1 8(Q14)

9 Marking exam papers (proportions) 6 6

10 Jelly moulds (similar cone volumes) 6 6

11 Eisteddfod performers 6 1 3 2

12 Slide (3D Pythagoras) 4 4

13 Office Space Wales (histogram) 10 3 5 2

14 Particle mass formula 5 4 1

Totals 80 16 40 24 41

AOs


Foundation Unit 2

Qu. TopicMax

markAO1 AO2 AO3

Common

(Interm)OCW

1 Alys's survey on vegetables 9 8 1

2 Amelia's 16th birthday party invitations 4 4

3 Ashley's holiday savings 8 8

4 Local fitness centre football pitch 4 4

5 Cooking a turkey 4 4

6 Teabag best value multiples with 50% extra free 5 5 5(Q1)

7 Pictogram trainers mean and range 2 2 2(Q2)

8 Bike frame parallel 4 2 2 4(Q3)

9 Harbour boat charges 9 9 9(Q4)

10 Filling and emptying a tank 6 5 1 6(Q5)

11 Celsius to Fahrenheit rearrange formula 4 4 4(Q6)

12 Laying a gas pipe 6 6 6(Q7)

Totals 65 16 33 16 36

AOs


Intermediate Unit 2

Qu. TopicMax

markAO1 AO2 AO3

Common

(Found)

Common

(Higher)OCW

1 Teabag best value multiples with 50% extra free 5 5 5(Q6)

2 Pictogram trainers mean and range 2 2 2(Q7)

3 Bike frame parallel 4 2 2 4(Q8)

4 Harbour boat charges 11 11 9(Q9)

5 Filling and emptying a tank 6 5 1 6(Q10)

6 Celsius to Fahrenheit rearrange formula 4 4 4(Q11)

7 Laying a gas pipe 6 6 6(Q12)

8 Package with a ribbon 5 5 2(Q1)

9 Holiday to Poland (zloty) 8 8 8(Q2)

10 Pay Day loan 3 3 3(Q3)

11 Off shore wind farm 7 2 5 7(Q4)

12 Celtic knot frequency cumulative frequency 8 4 2 2 8(Q5)

13 Dog kennel angle of elevation 6 5 1 6(Q6)

14 Width of a flag Pythagoras' Theorem 5 5 5(Q7)

Totals 80 19 45 16 36 39

AOs


Higher Unit 2

Qu. TopicMax

mark

N

u

m

AO1 AO2 AO3Common

(Interm)OCW

1 Package with a ribbon 2 2 2(Q8)

2 Holiday to Poland (zloty) 10 10 8(Q9)

3 Pay Day loan 3 3 3(Q10)

4 Off shore wind farm 7 2 5 7(Q11)

5 Celtic knot frequency cumulative frequency 8 4 2 2 8(Q12)

6 Dog kennel angle of elevation 6 5 1 6(Q13)

7 Width of a flag Pythagoras' Theorem 5 5 5(Q14)

8 Necklace VAT error 4 4

9 Density of steel (volume of a sphere) 5 5

10 Gold leaf for brooch 7 7

11 Dragon Nation Bank AER 5 4 1

12 Child's toy 7 7

13 Dewi's bicycle journey 5 5

14 Concrete base for garden statue 6 6 .

Totals 80 17 42 21 39

AOs

Documents

S A M s 2 GCSE Mathematics - Ysgol Uwchradd Caergybiysgoluwchraddcaergybi.cymru/cym/downloads/new-maths...Specimen Assessment Materials 2 GCSE Mathematics – Numeracy 2017. Question