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Ma KEY STAGE 3 Mathematics test Paper 2 Calculator allowed TIER 4–6 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. ■ Some formulae you might need are on page 2. ■ 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/03/967 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. Formulae You might need to use these formulae Trapezium Area = 1 (a + b)h 2 Prism Volume = area of cross-section t length KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Kings and queens 1. 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 4–6/P2 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk School uniform 2. 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 4–6/P2 Sourced from SATs-Papers.co.uk 4 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 4–6/P2 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Admission 3. 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 4–6/P2 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Cubes in bags 4. 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 4–6/P2 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Temperature 5. (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 4–6/P2 Sourced from SATs-Papers.co.uk 8 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 4–6/P2 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Drawing 6. 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 4–6/P2 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk (c) Draw a triangle that has an area of 6cm2 1 mark KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Ages 7. (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 4–6/P2 Sourced from SATs-Papers.co.uk 12 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 4–6/P2 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Grid percentages 8. 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 4–6/P2 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Data collection 9. 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 4–6/P2 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Coins 10. (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 4–6/P2 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Explaining why 11. 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 KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 1 mark 1 mark 17 http://www.SATs-Papers.co.uk Water 12. (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 4–6/P2 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Ratio of ages 13. Paul is 14 years old. His sister is exactly 6 years younger, so this year she is 8 years old. This year, the ratio of Paul’s age to his sister’s age is 14 : 8 14 : 8 written as simply as possible is 7 : 4 (a) When Paul is 21, what will be the ratio of Paul’s age to his sister’s age? Write the ratio as simply as possible. : 1 mark (b) When his sister is 36, what will be the ratio of Paul’s age to his sister’s age? Write the ratio as simply as possible. : 1 mark (c) Could the ratio of their ages ever be 7 : 7? Tick ( ) Yes or No. Yes No Explain how you know. 1 mark KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Sizing 14. The information in the box describes three different squares, A, B and C. The area of square A is 36cm2 The side length of square B is 36 cm The perimeter of square C is 36cm Put squares A, B and C in order of size, starting with the smallest. You must show calculations to explain how you work out your answer. smallest KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 2 marks largest 20 http://www.SATs-Papers.co.uk Nets 15. The squared paper shows the nets of cuboid A and cuboid B. (a) Do the cuboids have the same surface area? Show calculations to explain how you know. 1 mark (b) Do the cuboids have the same volume? Show calculations to explain how you know. 2 marks KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Beaches 16. Two beaches are very similar. A survey compared the number of animals found in one square metre on each beach. One beach had not been cleaned. The other beach had been cleaned. (a) The data for the beach that had not been cleaned represent 1620 animals. Complete the table to show how many of each animal were found. 2 marks KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk (b) The data for the beach that had been cleaned represent 15 animals. Complete the table to show how many of each animal were found on the cleaned beach. 2 marks (c) Cleaning the beach changes the numbers of animals and the proportions of animals. Write a sentence to describe both these changes. 1 mark KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Equations 17. Find the values of t and r 2 t = 3 6 t= 1 mark 2 5 = r 3 r= KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 24 1 mark http://www.SATs-Papers.co.uk Star design 18. This pattern has rotation symmetry of order 6 What is the size of angle w ? Show your working. Not drawn accurately ° 2 marks KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Ks and ms 19. On the square grids below you can join dots with two different length lines. Length m is greater than length k Draw a shape with each perimeter shown below. The first one is done for you. Perimeter 4k + 3 m Perimeter 4k + m 1 mark Perimeter 2 ( 2 k + m ) 1 mark KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 26 http://www.SATs-Papers.co.uk END OF TEST KS3/03/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 27 http://www.SATs-Papers.co.uk 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 254649