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Ma KEY STAGE 3 TIERS 5–7 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/06/1928 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 1 http://www.SATs-Papers.co.uk 14/12/05 10:30:36 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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 2 2 http://www.SATs-Papers.co.uk 14/12/05 10:30:37 pm 28 times table 1. (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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 3 3 http://www.SATs-Papers.co.uk 14/12/05 10:30:37 pm Paper 2. (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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 4 4 http://www.SATs-Papers.co.uk 14/12/05 10:30:38 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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 5 5 http://www.SATs-Papers.co.uk 14/12/05 10:30:38 pm Matching expressions 3. 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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 6 6 http://www.SATs-Papers.co.uk 14/12/05 10:30:39 pm CD player 4. (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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 7 7 http://www.SATs-Papers.co.uk 14/12/05 10:30:39 pm Solving 5. Solve these equations. 2k + 3 = 11 k= 1 mark 2t + 3 = –11 t= 1 mark KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 8 8 http://www.SATs-Papers.co.uk 14/12/05 10:30:40 pm Odd or even? 6. (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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 9 9 http://www.SATs-Papers.co.uk 14/12/05 10:30:40 pm Hexagon patterns 7. 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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 10 10 http://www.SATs-Papers.co.uk 14/12/05 10:30:41 pm Dice 8. 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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 11 11 http://www.SATs-Papers.co.uk 14/12/05 10:30:41 pm Sizing 9. (a) Put these values in order of size with the smallest ﬁrst. 52 32 33 smallest (b) 24 largest 2 marks Look at this information. 55 is 3125 What is 57 ? 2 marks KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 12 12 http://www.SATs-Papers.co.uk 14/12/05 10:30:42 pm Operations, Finding y 10. Write the correct operations ( + or – or × or ÷ ) in these statements. a 0 a a = 1 a a = 2a a 11. a = a = a2 2 marks Solve this equation. 3y + 14 = 5y + 1 y= KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 13 2 marks 13 http://www.SATs-Papers.co.uk 14/12/05 10:30:42 pm Favourite sport 12. 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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 14 14 http://www.SATs-Papers.co.uk 14/12/05 10:30:42 pm Consideration 13. (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 (c) Is the statement below correct for all numbers? The square of a number is greater than the number itself. Yes No Explain how you know. 1 mark KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 15 15 http://www.SATs-Papers.co.uk 14/12/05 10:30:43 pm Test 14. 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 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 16 16 http://www.SATs-Papers.co.uk 14/12/05 10:30:43 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 (d) Another school has a different rule for pupils to win a prize. Rule: The coursework mark must be 25 or more, and the test mark must be 25 or more, and the total mark must be 65 or more. On the graph below, shade the region of total marks for which pupils would win a prize. 50 40 30 Test mark 20 10 2 marks 0 KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 17 0 10 20 30 40 Coursework mark 50 17 http://www.SATs-Papers.co.uk 14/12/05 10:30:44 pm Fractions 15. Work out 1 4 + 1 3 = 1 mark 1 mark 3 5 – 1 15 = 1 mark KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 18 18 http://www.SATs-Papers.co.uk 14/12/05 10:30:45 pm Triangle 16. Look at the triangle. Not drawn accurately a° 2b° b° a° Work out the value of a a= 3 marks KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 19 19 http://www.SATs-Papers.co.uk 14/12/05 10:30:45 pm Multiplication grids 17. Write the missing numbers in these multiplication grids. × 8 9 72 –6 × 30 0.2 3 1.2 6 3 marks KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 20 20 http://www.SATs-Papers.co.uk 14/12/05 10:30:45 pm Building 18. A teacher asked 21 pupils to estimate the height of a building in metres. The stem-and-leaf diagram shows all 21 results. 0 2 6 8 8 3 3 5 7 7 0 5 5 5 10 4 8 11 (a) 9 9 represents 6.5m 5 8 5 6 7 6 2 7 9 Show that the range of estimated heights was 5.2 m. 1 mark (b) What was the median estimated height? m 1 mark (c) The height of the building was 9.2 m. What percentage of the pupils over-estimated the height? % 1 mark KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 21 21 http://www.SATs-Papers.co.uk 14/12/05 10:30:46 pm Quiz 19. In a quiz game two people each answer 100 questions. They score one point for each correct answer. The quiz game has not yet ﬁnished. Each person has answered 90 questions. The table shows the results so far. Person A Person B 60% of the ﬁrst 90 50% of the ﬁrst 90 questions correct questions correct Can person B win the quiz game? Explain your answer. Tick ( ) your answer. B can win. B cannot win but can draw. 2 marks B cannot win or draw. KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 22 22 http://www.SATs-Papers.co.uk 14/12/05 10:30:46 pm x and y 20. Solve these simultaneous equations using an algebraic method. 3x + 7y = 18 x + 2y = 5 You must show your working. x= y= 3 marks KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 23 23 http://www.SATs-Papers.co.uk 14/12/05 10:30:47 pm Line of best ﬁt 21. A pupil investigated whether students who study more watch less television. The scatter graph shows his results. The line of best ﬁt is also shown. 40 30 Number of hours watching television in one week 20 10 0 0 10 20 30 40 Number of hours studying in one week (a) What type of correlation does the graph show? 1 mark (b) The pupil says the equation of the line of best ﬁt is y = x + 40 Explain how you can tell that this equation is wrong. 1 mark KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 24 24 http://www.SATs-Papers.co.uk 14/12/05 10:30:47 pm Thinking diagonally 22. The diagram shows a square with side length 5 cm. y cm 5cm Not drawn accurately 5cm The length of the diagonal is y cm. Show that the value of y is 50 1 mark KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 25 25 http://www.SATs-Papers.co.uk 14/12/05 10:30:47 pm END OF TEST KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 26 26 http://www.SATs-Papers.co.uk 14/12/05 10:30:48 pm END OF TEST KS3/06/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 27 27 http://www.SATs-Papers.co.uk 14/12/05 10:30:48 pm © Qualiﬁcations and Curriculum Authority 2006 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA Sourced from SATs-Papers.co.uk 270034_KS3_Ma_P1_57.indd 28 270034 http://www.SATs-Papers.co.uk 14/12/05 10:30:48 pm