Functional Mathematics

Transcription

1 Surname Other names Functional Mathematics Level 2 Practice Paper For this paper you must have: a calculator mathematical instruments. Time allowed 1 hour 30 minutes Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Fill in the boxes at the top of this page. Answer all questions. You must answer the questions in the space provided. Do not write outside the box around each page or on blank pages. Do all rough work in this booklet. Cross through any work that you do not want to be marked. State the units of your answer where appropriate. Information The marks for questions are shown in brackets. The maximum mark for this paper is 60. You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer booklet. You are expected to use a calculator where appropriate. Evidence of checking is specifically assessed in questions 1b, 3c and 4b. These questions are indicated with a. Advice In all calculations, show clearly how you work out your answer. This paper is intended for practice only. Pearson Education does not guarantee that the style or content of this paper matches the public examination.

2 1 Skiing holiday You will need to use the Data Sheet for Skiing holiday to answer this question. Helen and Supraj are planning a skiing holiday. Helen sends Supraj an about their options. 1 (a) Supraj checks the exchange rates = 1.15 Work out the total cost of flights and transfers for each flight option. Give your answer in euros Question 1 continues on the next page (4 marks)

3 Helen and Supraj have a total budget for their holiday of They both need to hire boots and skis. Supraj wants to be able to access all the lifts in the valley, but Helen wants only to ski in the three main areas in Chamonix. They will book their holiday online to save money. They want to make sure they have at least 60 per day spending money between them. 1 (b) Plan Helen and Supraj s skiing holiday. You should choose one of the flight options from Helen s , and say which hotel they need to book and dates they need to book for. Calculate the total cost of the holiday you have planned and compare this cost to Helen and Supraj s budget.... (10 marks)

4 2 Choosing a flat-screen television You will need to use the Data Sheet for Flat-screen Televisions to answer this question. Harry wants to buy a flat-screen television for his living room. He has drawn a plan of his living room to help him choose which TV to buy. TV Chair Table Sofa The scale of the plan is 1 : 50. He wants to be able to watch the television from the sofa and from the chair. He has narrowed his selection to four choices. Television Screen size Optimum viewing angle Exfinity JJ32460B Mitsushito L32M Mitsushito PN40L Vuze LED37X (a) Which television is most suitable for Harry s living room? Show all of your working. You can draw on the plan of the living room to explain your choice. Remember 1 m = 3.3 feet. Question 2 continues on the next page (6 marks)

5 Harry orders a 32 television online. He measures the width of the screen when he receives it. He says, Oh no! I ordered a 32. They ve sent me the wrong one. 25 in 26 in 27 inch 28 in LED-TV Harry s television is a widescreen television. The ratio of the width of the screen to the height of the screen is 16 : 9. 2 (b) Make an accurate scale drawing of Harry s television screen. Use your drawing to explain why Harry s comment is wrong. (6 marks)

6 3 Fairtrade chocolate You will need to use the Data Sheet for Fairtrade chocolate to answer this question. This diagram shows where your money goes when you buy a certain brand of a non- Fairtrade chocolate bar. UK Government (VAT) 15% Shop where you bought the chocolate bar 22% Chocolate manufacturer 43% Other ingredients and costs 19% Farmers 1% (Source: Human Rights in the Curriculum, ISBN ) 3 (a) (i) Patrick says, If a bar of non-fairtrade chocolate costs him 65p, the farmer gets less than a penny. Show working to explain why Patrick is correct. (2 marks) 3 (a) (ii) Divide this bar in a similar way to show where your money goes when you buy a Fairtrade bar of chocolate. Question 3 continues on the next page (2 marks)

7 3 (a) (iii) Write down two differences between the Fairtrade bar of chocolate and the non- Fairtrade bar of chocolate. (2 marks) 3 (b) This table shows the total UK sales of Fairtrade chocolate from 2002 to Year Sales ( million) (Source: Human Rights in the Curriculum, ISBN ) Draw a suitable graph to represent this data. Question 3 continues on the next page (6 marks)

8 3 (c) Alix and Nisha are discussing this data. Alix says, In 2009, Cadbury agreed to make all of its chocolate bars Fairtrade. Nisha says, That caused the UK Fairtrade sales figures to increase by about 65%. Use evidence from the graph and the data to support Alix and Nisha s statements (4 marks)

9 4 Planting a window box You will need to use the Data Sheet for Planting a window box to answer this question. Safiya has bought an empty window box. 25 cm 35 cm 70 cm 4 (a) Safiya says, Two packets of fertilizer granules should be enough for this window box. Is Safiya correct? Show all your working (4 marks) Question 4 continues on the next page

10 Safiya wants to plant some herbs in her window box. The herbs that the garden centre sells are shown on the data sheet. Each herb comes in a cylinder of potting soil. This tells you how much space they need in the window box. 4 (b) Plan which herbs Safiya can plant in her window box. She should use as much of the space in the window box as possible, and plant at least three different varieties of herb. Work out the total price of the herbs and the potting materials. You can use this drawing to show how Safiya could arrange the herbs in her window box. 35 cm 70 cm Scale 1 : 10 Remember: Volume of a cylinder = π radius 2 height (14 marks)

11 Level 2 Functional Data Sheet Functional Skills Certificate MATHEMATICS Functional Mathematics Level 2 Data Book Instructions This copy of the Data Book is for use with the Practice Paper. Advice This book will not be collected in for marking. Ensure that all working that you wish to have marked is written in the space provided in the question/answer book. Pearson Education Limited 2010 Level 2 Functional Data Sheet

12 Level 2 Functional Data Sheet Data Sheet for Skiing Holiday This is an extract from a travel brochure. SKI-PARADISE HOLIDAYS CHAMONIX Set in the shadow of Mont Blanc, the town of Chamonix is a perfect skiing holiday destination, with more than 140 km of ski runs and a vibrant night-life. BOOK ONLINE TO RECEIVE A 10% DISCOUNT ON ALL PRICES Choose from one of our recommended hotels. All prices are given in euros. Hotel Price per person per night Monday Thursday Friday Sunday Special offers Chalet St Jean Free ski and boot hire Hotel Les Saisons Weekend special: Fri and Sat nights for 150 Auberge Fleur-de-lys You can hire skis and boots for low prices from the Chamonix ski-centre. Item Price for 1 week Price per day Skis Men s ski boots Women s ski boots 31 7 Many of the best skiing areas can only be accessed by cable car. To take full advantage of your skiing holiday in Chamonix we recommend buying a lift pass. You can choose between the Chamonix Le-Pass which will give you access to the three main skiing areas in Chamonix, or the Mont Blanc Unlimited pass which will give you unlimited skiing throughout the Chamonix Valley. Number of days skiing Chamonix Le Pass Mont Blanc Unlimited 1 day days days days days days days Pearson Education Limited 2010 Level 2 Functional Data Sheet

13 Level 2 Functional Data Sheet Data sheet for Choosing a Flat-screen Television Flat-screen televisions come in a variety of screen sizes. The most common sizes are 26, 32, 40 and 46. Television screen size is measured diagonally. 40 The size of the television you need depends on how far you plan to sit from the screen. Screen size (inches) Minimum viewing distance (feet) Maximum Viewing distance (feet) Flat-screen televisions don t display their best picture when viewed from an angle. Review websites often publish optimum viewing angles that tell you what angle you can view the screen from and still see the best picture. 30 This television has an optimum viewing angle of 30. Anyone sitting in the shaded area will see the best picture on the television. Pearson Education Limited 2010 Level 2 Functional Data Sheet

14 Level 2 Functional Data Sheet Data Sheet for Fairtrade Chocolate In the UK, we eat many products such as coffee and chocolate which are grown in developing countries. The farmers that produce the ingredients for these products are often paid very little. If you see the Fairtrade label on a product you know that the farmers producing the ingredients have been paid more for their work. The following shows you where the money goes when you buy a bar of Fairtrade chocolate. UK Government (VAT) 15% Shop where you bought chocolate bar 34% Chocolate manufacturer 10% Other ingredients and costs 37% Farmers 04% (Source: Human Rights in the Curriculum, ISBN ) Pearson Education Limited 2010 Level 2 Functional Data Sheet

15 Level 2 Functional Data Sheet Data Sheet for Planting a Window Box You can grow herbs, flowers or vegetables in a window box. When you are planting a window box you need: a layer of gravel at the bottom to prevent the soil from becoming waterlogged this should reach about 1 5 of the way up the window box mesh sheeting to keep the soil and gravel separate potting compost to fill up the rest of the window box. You must also add slow-release fertiliser granules. You can calculate the amount you need using the formula where F = 2V F is the mass of fertilizer granules needed in grams V is the volume of the window box in litres. These are the prices of the materials from a garden centre. Mesh sheeting (30 cm 30 cm) 0.45p Potting compost (8 litres) 4.50 Gravel (5 litres) 2.80 Fertilizer granules (100 g) 0.80p Example: 20 cm 25 cm 80 cm To fill this window box you would need: 16 cm 80 cm 25 cm = cm 3 Remember that 1 litre = 1000 cm 3 You would need 32 litres of potting compost or 4 bags. You would need to buy three sheets of mesh. You can cut the mesh to size. 1 5 of 20 cm = 4 cm, so the gravel should reach 4 cm up the window box. 4 cm 80 cm 25 cm = 8000 cm 3 You would need 8 litres of gravel or 2 bags. The total volume of the window box is 40 litres. F = 2V F = F = 180 You would need 180 g of fertilizer granules. Pearson Education Limited 2010 Level 2 Functional Data Sheet

16 Level 2 Functional Data Sheet These are the sizes and prices of the varieties of herbs available at the garden centre. Sage 12 cm Mint 12 cm 12 cm cm 1.50 Parsley 16 cm Thyme 16 cm 20 cm cm 2.95 Rosemary 20 cm 28 cm 4.95 Pearson Education Limited 2010 Level 2 Functional Data Sheet