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Ma KEY STAGE 3 TIERS 4–6 2006 Mathematics test Paper 1 Calculator not 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 must not use a calculator for any question in this test. ■ You will need: pen, pencil, rubber and a ruler. ■ 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 QCA/06/1926 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 1 http://www.SATs-Papers.co.uk 14/12/05 11:12:52 pm Instructions Answers This means write down your answer or show your working and write down your answer. Calculators You must not 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/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 2 2 http://www.SATs-Papers.co.uk 14/12/05 11:12:53 pm Spinners 1. On each spinner write ﬁve numbers to make the statements correct. It is certain that you will get a number less than 6 1 mark It is more likely that you will get an even number than an odd number. 1 mark It is impossible that you will get a multiple of 3 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 3 3 http://www.SATs-Papers.co.uk 14/12/05 11:12:53 pm Adding three 2. Add three to the number on each number line. The ﬁrst one is done for you. +3 50 47 +3 13 4 1 mark +3 –5 KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 4 1 mark 4 http://www.SATs-Papers.co.uk 14/12/05 11:12:53 pm Changing numbers 3. Work out the missing numbers. In each part, you can use the ﬁrst line to help you. (a) 16 × 16 15 = × 240 = 480 1 mark (b) 46 × 44 = 46 × 22 2024 = 1 mark (c) 600 ÷ 600 24 = ÷ 25 = 50 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 5 5 http://www.SATs-Papers.co.uk 14/12/05 11:12:54 pm Red Kites 4. Red Kites are large birds that were very rare in England. Scientists set free some Red Kites in 1989 and hoped they would build nests. The diagrams show how many nests the birds built from 1991 to 1996. Key: shows where the birds were set free. represents a nest without eggs. represents a nest with eggs. 1991 1992 1993 1994 1995 1996 KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 6 6 Source: British Wildlife, February 2002 http://www.SATs-Papers.co.uk 14/12/05 11:12:54 pm Use the diagrams to answer these questions. (a) Which was the ﬁrst year there were nests with eggs? 1 mark (b) In 1993, how many nests were there without eggs? 1 mark (c) In 1995, how many nests were more than 10 km from where the birds were set free? 1 mark (d) Explain what happened to the number of nests, over the years. 1 mark Now explain what happened to the distances of the nests from where the birds were set free, over the years. 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 7 7 http://www.SATs-Papers.co.uk 14/12/05 11:12:54 pm Place value 5. (a) Add together 1740 and 282 1 mark (b) Now add together 17.4 and 2.82 You can use part (a) to help you. 1 mark (c) 3.5 + 2.35 is bigger than 3.3 + 2.1 How much bigger? 2 marks KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 8 8 http://www.SATs-Papers.co.uk 14/12/05 11:12:55 pm Completing quadrilaterals 6. (a) The line on the square grid below is one side of a square. Draw 3 more lines to complete the square. 1 mark (b) The line on the square grid below is one side of a quadrilateral. The quadrilateral has only one pair of parallel sides. Draw 3 more lines to show what the quadrilateral could be. 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 9 9 http://www.SATs-Papers.co.uk 14/12/05 11:12:55 pm 28 times table 7. (a) Show that 9 × 28 is 252 1 mark (b) What is 27 × 28 ? You can use part (a) to help you. 2 marks KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 10 10 http://www.SATs-Papers.co.uk 14/12/05 11:12:56 pm Matching expressions 8. A ruler costs k pence. A pen costs m pence. Match each statement with the correct expression for the amount in pence. The ﬁrst one is done for you. Expression Statement 5k The total cost of 5 rulers 5m 5 – 5m The total cost of 5 rulers and 5 pens 500 – 5m 5k + m How much more 5 pens cost than 5 rulers 5(k + m) 5m – 5k The change from £5, in pence, when you buy 5 pens 1 mark 1 mark 5k – 5m 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 11 11 http://www.SATs-Papers.co.uk 14/12/05 11:12:56 pm Paper 9. (a) I have a square piece of paper. The diagram shows information about this square labelled A. 8cm A 8cm I fold square A in half to make rectangle B. B Then I fold rectangle B in half to make square C. C Complete the table below to show the area and perimeter of each shape. Area Perimeter Square A cm2 cm Rectangle B cm2 cm Square C cm2 cm 3 marks KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 12 12 http://www.SATs-Papers.co.uk 14/12/05 11:12:57 pm (b) I start again with square A. 8cm A 8cm Then I fold it in half to make triangle D. D What is the area of triangle D? cm2 1 mark (c) One of the statements below is true for the perimeter of triangle D. Tick ( ) the correct one. The perimeter is less than 24 cm. The perimeter is 24 cm. The perimeter is greater than 24 cm. Explain your answer. 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 13 13 http://www.SATs-Papers.co.uk 14/12/05 11:12:57 pm CD player 10. (a) Work out the missing values. 10% of 84 = 5% of 84 = 1 2 % of 2 84 = 2 marks (b) 1 The cost of a CD player is £84 plus 17 % tax. 2 What is the total cost of the CD player? You can use part (a) to help you. £ 2 marks KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 14 14 http://www.SATs-Papers.co.uk 14/12/05 11:12:58 pm Solving 11. Solve these equations. 2k + 3 = 11 k= 1 mark 2t + 3 = –11 t= 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 15 15 http://www.SATs-Papers.co.uk 14/12/05 11:12:58 pm Odd or even? 12. (a) I am thinking of a number. My number is a multiple of 4 Tick ( ) the true statement below. My number must be even My number must be odd My number could be odd or even Explain how you know. 1 mark (b) I am thinking of a different number. My number is a factor of 20 Tick ( ) the true statement below. My number must be even My number must be odd My number could be odd or even Explain how you know. 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 16 16 http://www.SATs-Papers.co.uk 14/12/05 11:12:58 pm Hexagon patterns 13. Look at this sequence of patterns made with hexagons. pattern number 2 pattern number 1 pattern number 3 To ﬁnd the number of hexagons in pattern number n you can use these rules: Number of grey hexagons = n+1 Number of white hexagons = 2n Altogether, what is the total number of hexagons in pattern number 20? 2 marks KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 17 17 http://www.SATs-Papers.co.uk 14/12/05 11:12:59 pm Dice 14. The diagrams show nets for dice. Each dice has six faces, numbered 1 to 6 Write the missing numbers so that the numbers on opposite faces add to 7 6 2 4 1 mark 4 1 5 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 18 18 http://www.SATs-Papers.co.uk 14/12/05 11:12:59 pm Sizing 15. (a) Put these values in order of size with the smallest ﬁrst. 2 5 3 2 3 3 smallest (b) 2 4 largest 2 marks Look at this information. 55 is 3125 What is 57 ? 2 marks KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 19 19 http://www.SATs-Papers.co.uk 14/12/05 11:13:00 pm Operations, Finding y 16. Write the correct operations ( + or – or × or ÷ ) in these statements. a 0 a a = 1 a a = 2a a 17. a = a = a2 2 marks Solve this equation. 3y + 14 = 5y + 1 y= KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 20 2 marks 20 http://www.SATs-Papers.co.uk 14/12/05 11:13:00 pm Favourite sport 18. Hanif asked ten people: ‘What is your favourite sport?’ Here are his results. football football hockey swimming hockey (a) cricket swimming football netball football Is it possible to work out the mean of these results? Yes No Explain how you know. 1 mark (b) Is it possible to work out the mode of these results? Yes No Explain how you know. 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 21 21 http://www.SATs-Papers.co.uk 14/12/05 11:13:01 pm Consideration 19. (a) Give an example to show the statement below is not correct. When you multiply a number by 2, the answer is always greater than 2 1 mark (b) Now give an example to show the statement below is not correct. When you subtract a number from 2, the answer is always less than 2 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 22 22 http://www.SATs-Papers.co.uk 14/12/05 11:13:01 pm Fractions 20. Work out 1 4 + 1 3 = 1 mark 1 mark 3 5 – 1 15 = 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 23 23 http://www.SATs-Papers.co.uk 14/12/05 11:13:01 pm Test 21. The scatter graph shows 15 pupils’ coursework and test marks. 50 K 40 N R 30 Test mark B E H C 20 F M J L A 10 0 0 10 D P G 20 30 40 Coursework mark 50 To ﬁnd a pupil’s total mark, you add the coursework mark to the test mark. (a) Which pupil had the highest total mark? 1 mark (b) Look at the statement below. Tick ( ) True or False. The range of coursework marks was greater than the range of test marks. True False Explain your answer. 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 24 24 http://www.SATs-Papers.co.uk 14/12/05 11:13:02 pm (c) Pupils with total marks in the shaded region on the graph win a prize. 50 40 30 Test mark 20 10 0 0 10 20 30 40 Coursework mark 50 What is the smallest total mark needed to win a prize? 1 mark KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 25 25 http://www.SATs-Papers.co.uk 14/12/05 11:13:02 pm END OF TEST KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 26 26 http://www.SATs-Papers.co.uk 14/12/05 11:13:03 pm END OF TEST KS3/06/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 27 27 http://www.SATs-Papers.co.uk 14/12/05 11:13:03 pm © Qualiﬁcations and Curriculum Authority 2006 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA Sourced from SATs-Papers.co.uk 270031_KS3_MaP1_T4-6.indd 28 270031 http://www.SATs-Papers.co.uk 14/12/05 11:13:03 pm