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Ma Mathematics test KEY STAGE 3 TIER 4–6 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. 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 282670_p2_46.indd 1 TOTAL MARKS http://www.SATs-Papers.co.uk 30/11/07 20:46:10 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 KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 2 2 http://www.SATs-Papers.co.uk 30/11/07 20:46:10 Time machine 1. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 3 3 http://www.SATs-Papers.co.uk 30/11/07 20:46:11 Four cards 2. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 4 4 http://www.SATs-Papers.co.uk 30/11/07 20:46:11 Sleep 3. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 5 5 http://www.SATs-Papers.co.uk 30/11/07 20:46:11 Sorting shapes 4. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 6 6 http://www.SATs-Papers.co.uk 30/11/07 20:46:11 Shopping 5. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 7 7 http://www.SATs-Papers.co.uk 30/11/07 20:46:11 Speedometer 6. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 8 8 http://www.SATs-Papers.co.uk 30/11/07 20:46:12 Football survey 7. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 9 2 marks 9 http://www.SATs-Papers.co.uk 30/11/07 20:46:12 Jug 8. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 10 10 http://www.SATs-Papers.co.uk 30/11/07 20:46:12 Double shape 9. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 11 11 http://www.SATs-Papers.co.uk 30/11/07 20:46:12 Cube edges 10. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 12 12 http://www.SATs-Papers.co.uk 30/11/07 20:46:13 Track 11. (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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 13 13 http://www.SATs-Papers.co.uk 30/11/07 20:46:13 Matching expressions 12. 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 Divide a by 2 a a2 Multiply a by itself a 2 2 marks KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 14 14 http://www.SATs-Papers.co.uk 30/11/07 20:46:13 Area, Values 13. 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 14. (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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 15 15 http://www.SATs-Papers.co.uk 30/11/07 20:46:13 Symmetry patterns 15. (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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 16 16 http://www.SATs-Papers.co.uk 30/11/07 20:46:14 Goldbach 16. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 17 17 http://www.SATs-Papers.co.uk 30/11/07 20:46:14 Shop 17. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 18 18 http://www.SATs-Papers.co.uk 30/11/07 20:46:14 Using algebra How much was Kim’s pay for this week? £ 2 marks 18. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 19 19 http://www.SATs-Papers.co.uk 30/11/07 20:46:14 Side length 19. 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 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 20 20 http://www.SATs-Papers.co.uk 30/11/07 20:46:14 Value of x 20. (a) Look at the equation. 5x + 1 = 2x – 8 Complete the sentence below by ticking ( ) the correct box. The value of x is … … one particular number. … any number less than zero. … any number greater than zero. … any whole number. … any number at all. 1 mark (b) Now look at this equation. y = 3x – 2 Complete the sentence below by ticking ( ) the correct box. The value of x is … … one particular number. … any number less than zero. … any number greater than zero. … any whole number. … any number at all. 1 mark KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 21 21 http://www.SATs-Papers.co.uk 30/11/07 20:46:15 Darts, Conversions 21. Gita threw three darts. Use the information in the box to work out what numbers she threw. The lowest number was 10 The range was 10 The mean was 15 Gita’s numbers were , and 1 mark 22. A cookery book shows this conversion table. Mass in ounces Mass in grams 1 25 2 50 3 75 4 110 5 150 10 275 Use the table to explain how you can tell the conversions cannot all be exact. 1 mark KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 22 22 http://www.SATs-Papers.co.uk 30/11/07 20:46:15 Concorde, Counters in a bag 23. Concorde could travel 1 mile every 3 seconds. How many miles per hour (mph) is that? mph 2 marks 24. In a bag, there are only red, white and yellow counters. I am going to take a counter out of the bag at random. The probability that it will be red is more than 1 4 It is twice as likely to be white as red. Give an example of how many counters of each colour there could be. Write numbers in the sentence below. There could be red, white and yellow counters. 2 marks KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 23 23 http://www.SATs-Papers.co.uk 30/11/07 20:46:15 Perimeters 25. (a) The perimeter of a regular hexagon is 42 a + 18 Write an expression for the length of one of its sides. 1 mark (b) The perimeter of a different regular polygon is 75 b – 20 The length of one of its sides is 15 b – 4 How many sides does this regular polygon have? 1 mark (c) The perimeter of a square is 4 ( c – 9 ) Find the perimeter of the square when c = 15 1 mark KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 24 24 http://www.SATs-Papers.co.uk 30/11/07 20:46:15 Yoghurt, Lawn 26. A dessert has both fruit and yoghurt inside. Altogether, the mass of the fruit and yoghurt is 175g. The ratio of the mass of fruit to the mass of yoghurt is 2 : 5 What is the mass of the yoghurt? g 2 marks 27. The diagram shows a plan of Luke’s new lawn. The lawn is a circle with radius 3m. Work out the area of the lawn. 3m m2 2 marks KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 25 25 http://www.SATs-Papers.co.uk 30/11/07 20:46:15 Triangular numbers To ﬁnd the n th triangular number, you can use this rule. 28. n th triangular number = n ( n + 1 ) 2 Example: 3rd triangular number = 3 ( 3 + 1) 2 = 6 (a) Work out the 10th triangular number. 1 mark (b) Now work out the 100th triangular number. 1 mark KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 26 26 http://www.SATs-Papers.co.uk 30/11/07 20:46:16 Isosceles triangle 29. Look at triangle ABC. ABD is an isosceles triangle where AB = AD. A y x z Not drawn accurately 28° 74° B C D Work out the sizes of angles x, y and z Give reasons for your answers. x= y= z= ° ° ° because because because 2 marks KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 282670_p2_46.indd 27 27 http://www.SATs-Papers.co.uk PLEASE TURN OVER 30/11/07 20:46:16 Journeys 30. The graphs show information about the different journeys of four people. Ann Ben Distance from starting point 0 Distance from starting point 0 Time Dee Chris Distance from starting point Distance from starting point 0 Time Time 0 Time Write the correct names next to the journey descriptions in the table below. Name Journey description This person walked slowly and then ran at a constant speed. This person walked at a constant speed but turned back for a while before continuing. This person walked at a constant speed without stopping or turning back. This person walked at a constant speed but stopped for a while in the middle. 1 mark END OF TEST KS3/08/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk © Qualifications and Curriculum Authority 2008 282670_p2_46.indd 28 28 QCA/08/3290 (Pupil pack) http://www.SATs-Papers.co.uk QCA/08/3286 (Mark scheme pack) 282670 30/11/07 20:46:16