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Ma Mathematics test KEY STAGE 3 TIER 3–5 Paper 2 Calculator allowed _______________________________________________ Last name _______________________________________________ School 2008 First name _______________________________________________ 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 (optional) 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 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 1 TOTAL MARKS http://www.SATs-Papers.co.uk 30/11/07 20:13:18 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. KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 2 2 http://www.SATs-Papers.co.uk 30/11/07 20:13:19 Rounding 1. (a) Draw lines to show all the numbers rounded to the nearest hundred. The ﬁrst one is done for you. Number Nearest hundred 912 800 990 955 900 849 1000 2 marks 881 (b) A number rounded to the nearest ten is 50 Give an example of what the number could be. 1 mark Give a different example of what the number could be. 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 3 3 http://www.SATs-Papers.co.uk 30/11/07 20:13:19 Cuboid 2. Look at this drawing of a cuboid. (a) How many rectangular faces does the cuboid have? 1 mark (b) The cuboid is cut in half through its corners. Here is the shape of one half. How many triangular faces does this shape have? 1 mark How many rectangular faces does this shape have? 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 4 4 http://www.SATs-Papers.co.uk 30/11/07 20:13:19 Placing 40 3. Here are three different number lines. Show the position of 40 by drawing an arrow ( ) on each one. The ﬁrst one is done for you. 40 0 100 1 mark 0 200 1 mark 0 KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 5 400 5 http://www.SATs-Papers.co.uk 30/11/07 20:13:20 Directions 4. Look at the map. C B A Here are the directions to get from house A to house B. Come out of house A and turn right. Then take the ﬁrst road on the left. Then house B is on the right. (a) Complete the directions to get back from house B to house A. Come out of house B and turn left Then take the ﬁrst road on the Then house A is on the 1 mark (b) Andrew wants to know how to get from house A to house C. Write directions for Andrew below. 2 marks KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 6 6 http://www.SATs-Papers.co.uk 30/11/07 20:13:20 Writing cheques 5. Write the missing numbers on these cheques. The ﬁrst one is done for you. Pay Date: 30.04.08 J. Baker £ 38 . 67 Thirty-eight pounds and sixty-seven pence H. Norris Pay Date: 30.04.08 T. Jones One hundred and two pounds and £ 1 mark seventy pence H. Norris Pay Date: 30.04.08 B. Torres One hundred and twenty pounds and £ 1 mark seven pence H. Norris KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 7 7 http://www.SATs-Papers.co.uk 30/11/07 20:13:20 Theme park 6. The table shows the opening times for a theme park. April 1st to October 31st Monday to Friday 11am to 7pm Closed Saturday and Sunday (a) November 1st to March 31st 10am to 8pm 11am to 4pm At what time does the theme park close on Saturdays in August? pm 1 mark (b) For how many months is the theme park open 7 days a week? months 1 mark (c) On a Saturday in January, Mina arrives at the theme park at 11am. She stays until closing time. How long does she stay at the theme park? hours 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 8 8 http://www.SATs-Papers.co.uk 30/11/07 20:13:20 Adding odd, Calculating 7. James says: Adding two odd numbers always gives an odd number answer. Give an example to show that James is wrong. 1 mark 8. (a) What number is 378 more than 1756? 1 mark (b) What number is 378 times as big as 1756? 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 9 9 http://www.SATs-Papers.co.uk 30/11/07 20:13:20 Time machine 9. Here is a question from a survey. In a time machine, would you like to go forwards or backwards in time? People said ‘Forwards’, ‘Backwards’ or ‘Don’t know’. Results: Forwards 46% Backwards 48% Don’t know ? The bar for ‘Don’t know’ has not been drawn. What percentage of people said ‘Don’t know’? % 2 marks KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 10 10 http://www.SATs-Papers.co.uk 30/11/07 20:13:21 Four cards 10. A pupil has these four number cards. 2 4 6 8 She is going to mix them up and take one card at random. Match each statement to the correct position on the probability scale. One is done for you. She will take a number in the 4 times table. Certain She will take an even number. She will take an odd number. Even chance She will take a number less than 7 She will take the number 2 Impossible 2 marks KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 11 11 http://www.SATs-Papers.co.uk 30/11/07 20:13:21 Sleep 11. Some people use this rule to work out how many hours’ sleep each night young children need. Subtract the child’s age in years from 30, then divide the result by 2 (a) Sanjay is 8 years old. Use the rule to work out how many hours’ sleep he needs. hours 1 mark (b) Lisa is 6 years old. She wakes up every morning at 7am. Use the rule to work out what time she needs to go to sleep. 2 marks KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 12 12 http://www.SATs-Papers.co.uk 30/11/07 20:13:21 Sorting shapes 12. Look at the shaded shapes drawn on an isometric grid. B A C D Write each of B, C and D in its correct place in the table below. No equal sides Has 3 sides Exactly 2 equal sides More than 2 equal sides A Has more than 3 sides 2 marks KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 13 13 http://www.SATs-Papers.co.uk 30/11/07 20:13:21 Shopping 13. Some people in a supermarket are shopping for food. (a) 100g of cheese costs 46p. Peter buys 250g of the cheese. How much does he pay? £ 1 mark (b) Tins of beans cost 36p each. What is the largest number of these tins John can buy with £2? 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 14 14 http://www.SATs-Papers.co.uk 30/11/07 20:13:21 Speedometer 14. The arrow on this dial shows a speed of 20mph. 40 60 20 80 mph 0 (a) 100 Draw an arrow on the dial below to show a speed of 65mph. 40 60 20 80 mph 1 mark 0 (b) 100 160km/h is about the same as 100mph. What speed in km/h is about the same as 25mph? km/h 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 15 15 http://www.SATs-Papers.co.uk 30/11/07 20:13:22 Football survey 15. Sam asked pupils in his class: Do you like American football? There were 30 pupils in his class. The same number of pupils said ‘Yes’ as said ‘No’. 12 pupils said ‘Don’t know’. Complete the key and the rows for Yes and No in Sam’s pictogram. Key: represents people Yes No Don’t know KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 16 2 marks 16 http://www.SATs-Papers.co.uk 30/11/07 20:13:22 Jug 16. A jug measures in litres and in millilitres. litres ml 1 1000 1 2 500 You can use the diagram to help you write the missing values below. The first one is done for you. 1 litre = 2 500 3 litre = 4 1 10 ml ml 1 mark litre = ml 1 mark litre = 200 ml 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 17 17 http://www.SATs-Papers.co.uk 30/11/07 20:13:22 Double shape 17. Look at the shaded shapes drawn on a square grid. A (a) B Nick says: The area of rectangle A is double the area of square B. Is he correct? Yes No Explain your answer. 1 mark (b) Alice says: The perimeter of rectangle A is double the perimeter of square B. Is she correct? Yes No Explain your answer. 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 18 18 http://www.SATs-Papers.co.uk 30/11/07 20:13:22 Cube edges 18. Look at the diagram of Megan’s cube. E F H G D C A B Megan puts her ﬁnger on point A. She can move her ﬁnger along 3 edges to get from point A to point H without taking it off the cube. Complete the table below to show all 6 ways she can do this. One way is done for you. Ways of moving from A to H A B C H 2 marks KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 19 19 http://www.SATs-Papers.co.uk 30/11/07 20:13:23 Track 19. (a) A straight piece of model car track is 20cm in length. 20cm How many of these straight pieces are needed to make a 1 metre track? 1 mark (b) A curved piece of track looks like this: 60° How many of these curved pieces are needed to make a complete circle of track? 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 20 20 http://www.SATs-Papers.co.uk 30/11/07 20:13:23 Matching expressions 20. Match each statement to the correct expression. The ﬁrst one is done for you. 2 Add 2 to a 2–a Subtract 2 from a a+2 2a Multiply a by 2 a–2 2 a Divide a by 2 a2 Multiply a by itself a 2 2 marks KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 21 21 http://www.SATs-Papers.co.uk 30/11/07 20:13:23 Area, Values 21. Look at the shapes drawn on the centimetre square grid. For each one, work out the area that is shaded. The ﬁrst one is done for you. Area = 12 cm2 Area = cm2 Area = cm2 1 mark 22. (a) Look at the equation. n + 3 = 12 Use it to work out the value of n–3 1 mark (b) Now look at this equation. n+3=7 Use it to work out the value of n–6 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 22 22 http://www.SATs-Papers.co.uk 30/11/07 20:13:23 Symmetry patterns 23. (a) Shade two more squares on the shape below so that it has rotation symmetry of order 4 1 mark (b) Now shade four more squares on the shape below so that it has rotation symmetry of order 2 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 23 23 http://www.SATs-Papers.co.uk 30/11/07 20:13:24 Shop 24. Kim works in a shop. The shaded squares on the diagram below show the hours she worked in one week. Monday Tuesday Wednesday Thursday Friday Saturday 9 10 11 12 1 2 am 3 4 5 6 7 8 pm The table shows her pay for each hour worked. Pay for each hour worked Monday to Friday, 9am to 5pm £6.35 Monday to Friday, after 5pm £7.50 Saturday £7.50 KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 24 24 http://www.SATs-Papers.co.uk 30/11/07 20:13:24 Using algebra How much was Kim’s pay for this week? £ 2 marks 25. Here is some information about three people. Jo is 2 years older than Harry. Kate is twice as old as Jo. Write an expression for each person’s age using n The ﬁrst one is given. n Harry’s age Jo’s age 1 mark Kate’s age 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 25 25 http://www.SATs-Papers.co.uk 30/11/07 20:13:24 Goldbach 26. A famous mathematician claimed that: Every even number greater than 4 can be written as the sum of a pair of prime numbers. For example: 8 can be written as the sum of 3 and 5, and 3 and 5 are both prime numbers. (a) Write a pair of prime numbers that sum to 16 and 1 mark Now write a different pair of prime numbers that sum to 16 and 1 mark (b) Now choose an even number that is greater than 16, then write a pair of prime numbers that sum to your even number. Complete the sentence below. The even number can be written as the sum of the prime numbers and 1 mark KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 26 26 http://www.SATs-Papers.co.uk 30/11/07 20:13:24 Side length 27. The diagrams show an equilateral triangle and a square. The shapes are not drawn accurately. 8.4cm The side length of the equilateral triangle is 8.4cm. The perimeter of the square is the same as the perimeter of the equilateral triangle. Work out the side length of the square. cm 2 marks KS3/08/Ma/Tier 3–5/P2 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 27 27 http://www.SATs-Papers.co.uk 30/11/07 20:13:24 END OF TEST © Qualifications and Curriculum Authority 2008 Sourced from SATs-Papers.co.uk 282668_p2_35.indd 28 QCA/08/3288 (Pupil pack) QCA/08/3286 (Mark scheme pack) http://www.SATs-Papers.co.uk 282668 30/11/07 20:13:25