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Ma KEY STAGE 3 Mathematics test Paper 2 Calculator allowed TIER 3–5 2003 Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your school in the spaces below. First name Last name School Remember ■ The test is 1 hour long. ■ You may use a calculator for any question in this test. ■ You will need: pen, pencil, rubber, ruler and a calculator. ■ This test starts with easier questions. ■ Try to answer all the questions. ■ Write all your answers and working on the test paper – do not use any rough paper. Marks may be awarded for working. ■ Check your work carefully. ■ Ask your teacher if you are not sure what to do. For marker’s use only QCA/03/965 Sourced from SATs-Papers.co.uk Total marks Borderline check http://www.SATs-Papers.co.uk Instructions Answers This means write down your answer or show your working and write down your answer. Calculators You may use a calculator to answer any question in this test. KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Hexagons 1. (a) Look at these shapes. Isometric grid Explain why the shapes are hexagons. 1 mark (b) Draw a regular hexagon on the grid below. Isometric grid KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk 1 mark Cities 2. Look at this diagram. It shows distances in miles between some cities. 72 80 134 90 172 212 91 121 143 120 Not drawn accurately (a) How far is it from Bristol to Manchester? miles 1 mark (b) Which two cities are 212 miles apart? and 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk (c) Kim lives in Birmingham. She wants to visit either York or London. Which of these cities is nearer to Birmingham? Tick ( ) your answer. York London How many miles nearer to Birmingham is it? miles 1 mark (d) Sanjay drives from London to Bristol, then he drives to Birmingham, and then he drives directly back to London. How many miles does he drive altogether? Show your working. miles 2 marks KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Number cards 3. (a) Look at these three number cards. 0 9 4 You can put them together to show different numbers. For example: 0 9 4 ninety-four Put the three cards together in a different way. Write in words what number the cards show. 0 1 mark Now put the three cards together in another different way. Write in words what number the cards show. 0 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk (b) Here are three different number cards. 5 8 3 What is the biggest number you can show with these cards? 1 mark What is the biggest even number you can show with these cards? 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Late 4. A school records how many pupils are late each day. The bar charts show the results for one week. KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk (a) Altogether, how many pupils were late on Monday? 1 mark (b) Altogether, how many lates were recorded for Y9 pupils? 1 mark (c) The school bus broke down on one of the days. Which day do you think that was? Explain why you chose that day. 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Slicing cubes 5. (a) I slice a cube in half like this: How many faces does each piece have? 1 mark (b) Then I slice another cube in half like this: How many faces does each piece have? 1 mark (c) I slice a different cube in half through its corners like this: How many faces does each piece have? 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Buying a bicycle 6. Alice and Ben each buy a bicycle but they pay in different ways. Ben pays more than Alice. How much more? Show your working. £ 2 marks KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk School uniform 7. Mark did a survey. He asked pupils in his school: ‘Do you like the colour of the school uniform?’ The table shows his results. Yes No Don’t know Year 7 35 17 2 Year 8 20 24 5 Year 9 19 17 6 (a) How many pupils from year 7 took part in the survey? 1 mark (b) Altogether, more pupils said ‘Yes’ than said ‘No’. How many more? 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk (c) Mark asked the same question to 40 pupils in year 11 25% said ‘Yes’. 50% said ‘No’. The rest said ‘Don’t know’. Complete the table to show how many pupils from year 11 gave each answer. Yes No Don’t know Year 11 2 marks (d) Anna does a different survey with pupils in year 9 She wants to know if more boys than girls have pets. She asks: ‘Do you have a pet?’ What labels should Anna use on her results table? Fill in the missing labels. 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Kings and queens 8. The chart shows information about seven kings and queens. It shows their ages when they died and how many years they ruled. Use the chart to answer these questions. (a) For how many years did Edward III rule? years 1 mark (b) Which king or queen died at the age of 69 and ruled for 44 years? 1 mark (c) Queen Victoria died at the age of 81 and ruled for 63 years. Put a cross on the chart to show this information. 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Admission 9. The table shows how much it costs to go to a cinema. Before 6pm After 6pm Adult £ 3.20 £ 4.90 Child (14 or under) £ 2.50 £ 3.50 Senior Citizen (60 or over) £ 2.95 £ 4.90 Mrs Jones (aged 35), her daughter (aged 12), her son (aged 10) and a friend (aged 65) want to go to the cinema. They are not sure whether to go before 6pm or after 6pm. How much will they save if they go before 6pm? Show your working. £ 3 marks KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Temperature 10. (a) The thermometer shows Alan’s temperature. Alan’s normal temperature is 37.0°C How many degrees higher than normal is Alan’s temperature? °C 1 mark (b) On Monday morning, Bina’s temperature was 39.2 °C By Tuesday morning, Bina’s temperature had fallen by 1.3°C What was Bina’s temperature on Tuesday morning? °C 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk (c) You can measure temperature in °C or in °F The diagram shows how to change °F to °C The highest temperature ever recorded in a human was 115.7 °F What is this temperature in °C? Show your working. °C 2 marks KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Drawing 11. In this question, all the grids are centimetre square grids. (a) Draw a rectangle that has an area of 12cm2 1 mark (b) Draw another rectangle that has an area of 12cm2 This rectangle must have a different perimeter from the rectangle in part (a). 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk (c) Draw a triangle that has an area of 6cm2 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Cubes in bags 12. I have two bags of cubes. Each bag contains more than 20 but fewer than 30 cubes. (a) I can share the cubes in bag A equally between 9 people. How many cubes are in bag A? 1 mark (b) I can share the cubes in bag B equally between 4 people. How many cubes could be in bag B? There are two answers. Write them both. or 2 marks KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Grid percentages 13. Each diagram below was drawn on a square grid. (a) Write what percentage of each diagram is shaded. The first one is done for you. 75 % % 1 mark % 1 mark (b) Explain how you know that 12 1 % of the diagram below is shaded. 2 1 mark 1 2 (c) Shade 37 % of the diagram below. 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Ages 14. (a) It is Tina’s birthday. We do not know how old Tina is. Call Tina’s age, in years, n The expressions below compare Tina’s age to some other people’s ages. Use words to compare their ages. The first one is done for you. Tina’s age n Ann is Ann’s age n+3 Tina’s age n 3 years older than Tina Barry is Barry’s age n–1 Tina’s age n Carol’s age 2n Carol is 2 marks (b) In one year’s time Tina’s age will be n + 1 Write simplified expressions to show the ages of the other people in one year’s time. Tina Ann Barry Carol Age now n n+3 n–1 2n Age in one year’s time n+1 2 marks KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk (c) When n = 30, find the value of 2 n + 1 1 mark When n = 30, find the value of 2( n + 1) 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Data collection 15. Some pupils plan a survey to find the most common types of tree in a wood. The pupils will only use one design. (a) Choose a design they should not use. Design Explain why it is not a good design to use. 1 mark (b) Choose the design that is the best. Design Explain why it is the best. 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 24 http://www.SATs-Papers.co.uk Coins 16. (a) Jo has these 4 coins. Jo is going to take one of these coins at random. Each coin is equally likely to be the one she takes. Show that the probability that it will be a 10p coin is 1 2 1 mark (b) Colin has 4 coins that total 33p. He is going to take one of his coins at random. What is the probability that it will be a 10p coin? You must show your working. 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Explaining why 17. Look at the diagram. Triangle ABD is the reflection of triangle ABC in the line AB. Not drawn accurately Fill in the gaps below to explain how to find angle x The length of AC is 12 cm. The length of AD is cm. The length of CD is cm. ACD is an equilateral triangle because 1 mark so angle y is ° because so angle x is ° because 1 mark 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 26 http://www.SATs-Papers.co.uk Water 18. (a) A glass holds 225ml. An adult needs about 1.8 litres of water each day to stay healthy. How many glasses is that? Show your working. 2 marks (b) An adult weighs 80kg. 60% of his total mass is water. What is the mass of this water? kg 1 mark KS3/03/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 27 http://www.SATs-Papers.co.uk END OF TEST Sourced from SATs-Papers.co.uk © Qualifications and Curriculum Authority 2003 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk 254647