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Ma KEY STAGE 3 TIERS 6–8 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 Sourced from SATs-Papers.co.uk QCA/06/1931 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 6–8/P2 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Four angles 1. 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 6–8/P2 ° ° d= ° 3 marks 3 http://www.SATs-Papers.co.uk Balancing 2. 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 6–8/P2 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk Five cubes 3. 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 6–8/P2 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk nth term 4. 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 6–8/P2 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Enlargement 5. 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 6–8/P2 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Error 6. 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 6–8/P2 Sourced from SATs-Papers.co.uk 126 people = 60% 8 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 6–8/P2 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Tomatoes 7. 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 6–8/P2 Sourced from SATs-Papers.co.uk 10 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 6–8/P2 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Expressions 8. 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 6–8/P2 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Tracking elephants 9. 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 6–8/P2 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Algebra grids 10. 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 6–8/P2 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Four kites 11. 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 6–8/P2 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Volume of 100 12. 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 6–8/P2 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Bias 13. 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 6–8/P2 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Area A 14. 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 6–8/P2 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Field voles 15. 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 these questions. (a) Estimate the probability that a ﬁeld vole will live to be at least 20 weeks old. 1 mark (b) A ﬁeld vole is 40 weeks old. Estimate the probability that it will live to be at least 50 weeks old. 1 mark KS3/06/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Films 16. Films at the cinema and ﬁlms on television are shown at different speeds. Cinema Television 24 pictures per second 25 pictures per second At the cinema a ﬁlm lasts 175 minutes. How many minutes does the same ﬁlm last on television? minutes 2 marks KS3/06/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Equations of lines The graph shows the y straight line with equation y = x + 1 17. 6 This straight line passes through the point ( 0, 1 ) 4 2 0 0 (a) 2 4 6 x Write the equations of two different straight lines that also pass through the point ( 0, 1) 1 mark and 1 mark The straight line with equation x + y = 5 y is perpendicular to y = x + 1 (b) 6 4 2 0 0 2 4 6 x Write the equation of a different straight line that is also perpendicular to y = x + 1 1 mark KS3/06/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Households 18. A housing report gave this information. In the year 2001, the population of England was 49.87 million people. Most of these people lived in households. The total number of households was 20.97 million. The average (mean) household size was 2.34 people. In the year 2001, what percentage of people in England did not live in households? Give your answer to 1 decimal place. % 3 marks KS3/06/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Cuboid 19. Six cubes each have a surface area of 24cm2 They are joined together to make a cuboid. What could the surface area of this cuboid be? There are two different answers. Write them both. cm2 or cm2 2 marks KS3/06/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Five points 20. The diagram shows ﬁve points joined with four straight lines. BC and AD are parallel. BCE and ADE are isosceles triangles. A B E 4 cm 6cm C D Not drawn accurately The total length of the four straight lines is 40cm. What is the length of EA? cm 3 marks KS3/06/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 24 http://www.SATs-Papers.co.uk Three dice 21. I have three fair dice, each numbered 1 to 6 I am going to throw all three dice. What is the probability that all three dice will show the same number? 2 marks KS3/06/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Population of Wales 22. Since 1952 the total number of people living in Wales has increased by about one eighth. The total number of people living in Wales now is about 3 million. About how many people lived in Wales in 1952? million 2 marks KS3/06/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 26 http://www.SATs-Papers.co.uk Leaning tower of Pisa 23. Engineers have worked on the leaning tower of Pisa to make it safe. A website gave this information about the tower before the work. 5.2m The height of the tower is 56m. The angle of tilt is 5.5° 56m The tower leans 5.2m 5.5° from the perpendicular. Not drawn accurately Give calculations to show that the information cannot all be true. 2 marks KS3/06/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 27 http://www.SATs-Papers.co.uk END OF TEST © Qualiﬁcations and Curriculum Authority 2006 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA Sourced from SATs-Papers.co.uk 270037 http://www.SATs-Papers.co.uk