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Ma KEY STAGE 3 TIERS 4–6 2006 Mathematics test Paper 2 Calculator allowed 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, tracing paper and mirror (optional) 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 Total marks Borderline check QCA/06/1927 270033_KS3_MaP2_T4-6.indd 1 Sourced from SATs-Papers.co.uk 14/12/05 10:45:34 pm 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 b Area = 1 (a + b)h 2 height (h) a Prism length area of cross-section Volume = area of cross-section × length KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 2 Sourced from SATs-Papers.co.uk 2 14/12/05 10:45:35 pm http://www.SATs-Papers.co.uk Mirror lines 1. The square grid shows a rectangle reﬂected in two mirror lines. mirror line mirror line On the square grid below, show the triangle reﬂected in the two mirror lines. mirror line 2 marks mirror line KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 3 Sourced from SATs-Papers.co.uk 3 14/12/05 10:45:36 pm http://www.SATs-Papers.co.uk Using rules 2. (a) These rules show how to get from one number to the next in these sequences. Use the rules to write the next two numbers in each sequence. Rule: Add 8 4 12 1 mark Rule: Multiply by 3 4 12 1 mark Rule: Divide by 4 then add 11 4 12 1 mark (b) A sequence of numbers starts like this: 30 22 18 Could the rule be Subtract 8? Yes No Explain your answer. 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 4 Sourced from SATs-Papers.co.uk 4 14/12/05 10:45:36 pm http://www.SATs-Papers.co.uk Cough mixture 3. A bottle contains 250ml of cough mixture. Adult - take 10 ml four times a day Child - take 5ml four times a day One adult and one child need to take cough mixture 4 times a day every day for 5 days. Will there be enough cough mixture in the bottle? Explain your answer. 2 marks KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 5 Sourced from SATs-Papers.co.uk 5 14/12/05 10:45:37 pm http://www.SATs-Papers.co.uk Working with areas 4. The grids in this question are centimetre square grids. For each shape on the left, draw a rectangle that has the same area. The ﬁrst one is done for you. Shape Rectangle 1 mark 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 6 Sourced from SATs-Papers.co.uk 6 14/12/05 10:45:38 pm http://www.SATs-Papers.co.uk Pregnancy 5. The table shows the average length of pregnancy for different mammals. Mammal Average length of pregnancy Dolphin 276 days Horse 337 days Seal 350 days Whale 365 days Camel 406 days Elephant 640 days Use the information in the table to answer these questions. (a) Which mammal has an average length of pregnancy of 1 year? 1 mark (b) Which mammal has an average length of pregnancy of 50 weeks? 1 mark (c) A human has an average length of pregnancy of about 9 months. Which other mammal also has an average length of pregnancy of about 9 months? 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 7 Sourced from SATs-Papers.co.uk 7 14/12/05 10:45:38 pm http://www.SATs-Papers.co.uk Missing numbers 6. Write the missing numbers in the boxes. 4 × + 20 = 180 1 mark 4 × 20 + = 180 1 mark 4 × – 20 = 180 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 8 Sourced from SATs-Papers.co.uk 8 14/12/05 10:45:38 pm http://www.SATs-Papers.co.uk Hexagons 7. I use two congruent trapeziums to make the shapes below. Tick ( ) all the shapes that are hexagons. 2 marks KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 9 Sourced from SATs-Papers.co.uk 9 14/12/05 10:45:39 pm http://www.SATs-Papers.co.uk Sponsored swim 8. The pupils in a class had a sponsored swim. They collected £429.24 (a) How much is £429.24 to the nearest hundred pounds? £ 1 mark (b) How much is £429.24 to the nearest ten pounds? £ 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 10 Sourced from SATs-Papers.co.uk 10 14/12/05 10:45:39 pm http://www.SATs-Papers.co.uk Cat food 9. I buy 12 packets of cat food in a box. The table shows the different varieties in the box. Variety Cod 3 Salmon 3 Trout 3 Tuna (a) Number of packets 3 I am going to take out a packet at random from the box. What is the probability that it will be cod? 1 mark (b) My cat eats all the packets of cod. I am going to take out a packet at random from the ones left in the box. What is the probability that it will be salmon? 1 mark (c) A different type of cat food has 10 packets in a box. The probability that the variety is chicken is 0.7 What is the probability that the variety is not chicken? 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 11 Sourced from SATs-Papers.co.uk 11 14/12/05 10:45:40 pm http://www.SATs-Papers.co.uk Wine gums 10. Wine gums are sweets that are made in different colours. Pupils tested whether people can taste the difference between black wine gums and other wine gums. The percentage bar charts show three pupils’ results. Key: Cannot taste the difference Can taste the difference Ravi’s results Sita’s results Tina’s results 100% 100% 100% 80% 80% 80% 60% 60% 60% 40% 40% 40% 20% 20% 20% 0% 0% 0% Ravi asked 50 people KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 12 Sourced from SATs-Papers.co.uk Sita asked 100 people Tina asked 200 people 12 14/12/05 10:45:40 pm http://www.SATs-Papers.co.uk Values (a) Complete the table. Number of people who were tested Ravi 100 Tina Number of people who cannot taste the difference 50 Sita Number of people who can taste the difference 200 3 marks (b) Explain why Tina’s results are likely to be more reliable than Ravi’s or Sita’s. 1 mark 11. Look at the three expressions below. 8+k k2 3k When k = 10, what is the value of each expression? 8+k= k2 = 3k = 2 marks KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 13 Sourced from SATs-Papers.co.uk 13 14/12/05 10:45:40 pm http://www.SATs-Papers.co.uk Thinking triangularly 12. Some statements in the table are true. Some are false. Beside each statement, write true or false. For true statements you must draw an example. The ﬁrst one is done for you. Statement Write true or false. If true, draw an example. Some triangles have one right angle and true two acute angles. Some triangles have three right angles. Some triangles have three acute angles. Some triangles have one obtuse angle and two acute angles. Some triangles have two obtuse angles and one acute angle. 3 marks KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 14 Sourced from SATs-Papers.co.uk 14 14/12/05 10:45:41 pm http://www.SATs-Papers.co.uk Toilet rolls 13. A shop sells toilet rolls. You can buy them in packs of 9 or packs of 6 90 ls 9 50 . £3 ls l ro 6 Pack of 9 toilet rolls £3.90 . £2 l ro Pack of 6 toilet rolls £2.50 Which pack gives you better value for money? You must show your working. 3 marks KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 15 Sourced from SATs-Papers.co.uk 15 14/12/05 10:45:41 pm http://www.SATs-Papers.co.uk Woodpeckers 14. Three different types of woodpecker live in Britain. The pictogram shows information about the numbers of each type. Type A Type B Type C great spotted woodpecker lesser spotted woodpecker green woodpecker represents 10 000 woodpeckers Key: (a) Complete the table below to show the percentages of each type of woodpecker. Type A Type B % Type C % % 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 16 Sourced from SATs-Papers.co.uk 16 14/12/05 10:45:42 pm http://www.SATs-Papers.co.uk Changing 120 (b) The ratio of type A : type B woodpeckers is 6 : 1 What is the ratio of type B : type C woodpeckers? : 15. 1 mark Write the missing numbers in the boxes. 120mm is the same as cm 1 mark 120cm is the same as m 1 mark 120m is the same as km 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 17 Sourced from SATs-Papers.co.uk 17 14/12/05 10:45:42 pm http://www.SATs-Papers.co.uk Four angles 16. Look at the diagram, made from four straight lines. The lines marked with arrows are parallel. Not drawn accurately b a 70° c 60° d Work out the sizes of the angles marked with letters. a= 270033_KS3_MaP2_T4-6.indd 18 Sourced from SATs-Papers.co.uk b= ° c= KS3/06/Ma/Tier 4–6/P2 ° ° d= ° 3 marks 18 14/12/05 10:45:43 pm http://www.SATs-Papers.co.uk Balancing 17. Look at this equation. 3a + 20 = 4a + k (a) If a = 15, ﬁnd the value of k k= 1 mark (b) If a = –15, ﬁnd the value of k k= 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 19 Sourced from SATs-Papers.co.uk 19 14/12/05 10:45:43 pm http://www.SATs-Papers.co.uk Five cubes 18. Each shape below is made from ﬁve cubes that are joined together. Complete the missing diagrams below. Shape drawn on an isometric grid View from above of the shape drawn on a square grid 1 mark 2 marks KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 20 Sourced from SATs-Papers.co.uk 20 14/12/05 10:45:43 pm http://www.SATs-Papers.co.uk nth term 19. Look at these pairs of number sequences. The second sequence is formed from the ﬁrst sequence by adding a number or multiplying by a number. Work out the missing n th terms. 5, 9, 13, 17, … n th term is 6, (a) 10, 14, 18, … 4n + 1 n th term is 1 mark 12, 18, 24, 30, … n th term is 6, (b) … n th term is 9, 12, 15, 2, 7, 12, 17, … n th term is 4, (c) 6n + 6 14, 24, 34, … 1 mark 5n – 3 n th term is 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 21 Sourced from SATs-Papers.co.uk 21 14/12/05 10:45:44 pm http://www.SATs-Papers.co.uk Enlargement 20. Look at the square grids. Each diagram shows an enlargement of scale factor 2 The centre of this enlargement is marked with a cross. Where is the centre of enlargement in these diagrams? Mark each one with a cross. 1 mark 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 22 Sourced from SATs-Papers.co.uk 22 14/12/05 10:45:45 pm http://www.SATs-Papers.co.uk Error 21. Kate asked people if they read a daily newspaper. Then she wrote this table to show her results. No 80 people = 40% Yes 126 people = 60% The values in the table cannot all be correct. The error could be in the number of people. Complete each table to show what the correct numbers could be. No 80 people = 40% Yes people = 60% 1 mark No people = 40% 1 mark Yes KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 23 Sourced from SATs-Papers.co.uk 126 people = 60% 23 14/12/05 10:45:45 pm http://www.SATs-Papers.co.uk Tomatoes 22. The graph shows information about the diameters and heights of a sample of three types of tomato. height, h The dotted lines on the graph can be used to decide which type of tomato each point is likely to represent. diameter, d type A 12 type B 11 10 type C 9 8 7 Height 6 (cm) 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Diameter (cm) (a) The diameter of a tomato of type C is 11cm. What would you expect its height to be? cm 1 mark KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 24 Sourced from SATs-Papers.co.uk 24 14/12/05 10:45:46 pm http://www.SATs-Papers.co.uk Expressions (b) The diameter of a different tomato is 3.2cm. Its height is 5.8cm. Which of the three types of tomato is it most likely to be? A B C Explain your answer. 1 mark (c) Which type of tomato is most nearly spherical in shape? A B C Explain your answer. 1 mark 23. Multiply out this expression. Write your answer as simply as possible. 5( x + 2 ) + 3( 7 + x ) 2 marks KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 25 Sourced from SATs-Papers.co.uk 25 14/12/05 10:45:46 pm http://www.SATs-Papers.co.uk END OF TEST KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 26 Sourced from SATs-Papers.co.uk 26 14/12/05 10:45:47 pm http://www.SATs-Papers.co.uk END OF TEST KS3/06/Ma/Tier 4–6/P2 270033_KS3_MaP2_T4-6.indd 27 Sourced from SATs-Papers.co.uk 27 14/12/05 10:45:47 pm http://www.SATs-Papers.co.uk © Qualiﬁcations and Curriculum Authority 2006 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA 270033_KS3_MaP2_T4-6.indd 28 Sourced from SATs-Papers.co.uk 270033 14/12/05 10:45:47 pm http://www.SATs-Papers.co.uk