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Ma KEY STAGE 3 TIERS 5–7 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, a pair of compasses and a scientific or graphic 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/06/1929 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 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 5–7/P2 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Cat food 1. 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 5–7/P2 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Wine gums 2. 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 5–7/P2 Sourced from SATs-Papers.co.uk Sita asked 100 people Tina asked 200 people 4 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 3. 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 5–7/P2 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Thinking triangularly 4. 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 5–7/P2 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Toilet rolls 5. 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 5–7/P2 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Woodpeckers 6. 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 5–7/P2 Sourced from SATs-Papers.co.uk 8 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? : 7. 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 5–7/P2 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Four angles 8. 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= Sourced from SATs-Papers.co.uk b= ° c= KS3/06/Ma/Tier 5–7/P2 ° ° d= ° 3 marks 10 http://www.SATs-Papers.co.uk Balancing 9. 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 5–7/P2 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Five cubes 10. 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 5–7/P2 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk nth term 11. 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 5–7/P2 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Enlargement 12. 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 5–7/P2 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Expressions 13. Multiply out these expressions. Write your answers as simply as possible. 5( x + 2 ) + 3( 7 + x ) 2 marks ( x + 2 )( x + 5 ) 2 marks KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Error 14. 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. (a) 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 5–7/P2 Sourced from SATs-Papers.co.uk 126 people = 60% 16 http://www.SATs-Papers.co.uk (b) The error could be in the percentages. Complete the table with the correct percentages. No 80 people = % Yes 126 people = % 2 marks KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Tomatoes 15. 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 5–7/P2 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk (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 (d) You can ﬁnd the approximate volume of a tomato by using this formula: V is the volume, 1 V= d 2h 6 d is the diameter, h is the height. The diameter and the height of a tomato are both 3.5cm. What is the approximate volume of this tomato? cm3 2 marks KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Tracking elephants 16. In a wildlife park in Africa, wardens want to know the position of an elephant in a certain area. They place one microphone at each corner of a 4km by 4km square. 1 Each microphone has a range of 3 km. 2 The elephant is out of range of microphones A and B. Where in the square could the elephant be? Show the region accurately on the diagram, and label the region R. A B Scale 2cm to 1km 2 marks KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Algebra grids 17. Here are the rules for an algebra grid. This value is the sum of the values 5x + 2 5x in the middle row. 2 10 x This value is the product of the values in the middle row. Use these rules to complete the algebra grids below. Write your expressions as simply as possible. 3x + 1 2x 4x x+1 5x 6 x2 3 marks KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Four kites 18. This shape is made of four congruent kites meeting at a point. k 40° Not drawn accurately Calculate the size of angle k k= ° 2 marks KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Volume of 100 19. Look at the diagram of a cuboid. Not drawn accurately x cm y cm x cm The volume of the cuboid is 100cm3 What could the values of x and y be? Give two possible pairs of values. x= y= 1 mark x= y= 1 mark KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Bias 20. A pupil wants to investigate a report that Belgian one euro coins are biased in favour of heads. Here is her plan for the investigation. I will spin 20 Belgian one euro coins to give one set of results. I will do this 10 times to give a total of 200 results to work out an estimated probability of spinning a head. If this probability is greater than 56% my conclusion will be that Belgian one euro coins are biased in favour of heads. The table shows the 10 sets of results. Number of each set of 20 coins that showed heads 10 13 11 11 12 12 11 9 10 11 Using the pupil’s plan, what should her conclusion be? You must show your working. 2 marks KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 24 http://www.SATs-Papers.co.uk Area A 21. The diagram shows a shaded rectangle. It is divided into four smaller rectangles, labelled A, B, C and D. 5cm A 3cm B C D 5cm 10 cm Not drawn accurately The ratio of area C to area B is 1 : 2 Calculate area A. cm2 2 marks KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Field voles 22. Field voles are small animals that do not live for very long. A scientist recorded data on 1000 of these voles that were born on the same day. The graph shows how many voles were still alive after a number of weeks. 1000 900 800 700 600 Number of voles still alive 500 400 300 200 100 0 0 10 20 30 40 50 60 Number of weeks 70 80 90 100 Use the graph to answer this question. Estimate the probability that a ﬁeld vole will live to be at least 20 weeks old. 1 mark KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 26 http://www.SATs-Papers.co.uk END OF TEST KS3/06/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 27 http://www.SATs-Papers.co.uk © Qualiﬁcations and Curriculum Authority 2006 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA Sourced from SATs-Papers.co.uk 270035 http://www.SATs-Papers.co.uk