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Ma KEY STAGE 3 TIER 4–6 2002 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. If you have been given a pupil number, write that also. First name Last name School Pupil number Remember I The test is 1 hour long. I You may use a calculator for any question in this test. I You will need: pen, pencil, rubber, ruler, an angle measurer or protractor, a pair of compasses and a calculator. I Some formulae you might need are on page 2. I This test starts with easier questions. I Try to answer all the questions. I Write all your answers and working on the test paper – do not use any rough paper. I Check your work carefully. I Ask your teacher if you are not sure what to do. For marker’s use only QCA/02/837 Sourced from SATs-Papers.co.uk 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 Area = 1 (a + b)h 2 Prism Volume = area of cross-section t length KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Place names 1. Some towns and villages have very long names. The table shows information about the ten longest place names in the UK. Number of letters Country 67 Wales 58 Wales 27 England 22 Wales 21 Wales 21 Wales 19 England 18 England 18 Scotland 17 Scotland (a) The longest place name in Wales has more letters than the longest place name in Scotland. How many more? 1 mark (b) 50% of the ten longest place names are in Wales. What percentage of the ten longest place names are in England? % KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 3 1 mark http://www.SATs-Papers.co.uk Dinner time 2. The diagram shows what pupils in years 7, 8 and 9 choose to do at dinner time. KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk (a) A pupil from each year group is chosen at random. Are they most likely to eat a packed lunch, or eat at home, or eat a school dinner? Tick ( ) the correct boxes. Eat a packed lunch Eat at home Eat a school dinner Pupil from year 7 Pupil from year 8 Pupil from year 9 2 marks (b) How many more pupils are there in year 8 than year 9? Show your working. 2 marks KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Which calculation? 3. Here is some information about a school. There are 3 classes in year 8. Each class has 27 pupils. There are 4 classes in year 9. Each class has 25 pupils. (a) Use the information to match each question with the correct calculation. The first one is done for you. Calculation Question 3+4 How many classes are there altogether in years 8 and 9? 3–4 4–3 There are more classes in year 9 than in year 8. How many more? (3 t 27) + (4 t 25) (3 + 27) + (4 + 25) How many pupils are there altogether in years 8 and 9? (3 t 27) – (4 t 25) There are more pupils in year 9 than in year 8. How many more? (4 + 25) – (3 + 27) 1 mark (4 t 25) – (3 t 27) 1 mark 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk (b) Use the information about the school to write what the missing question could be. Calculation Question 4 t 25 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Throwing coins 4. I throw a fair coin. For each statement below, put a tick ( ) to show if the statement is True or False. (a) On each throw, the probability of getting a head is True 1 2 False Explain your answer. 1 mark (b) On four throws, it is certain that I will get two heads and two tails. True False Explain your answer. 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk Folding 5. (a) I have a rectangle made out of paper. The rectangle measures 12cm by 8cm. I want to fold the rectangle in half to make a smaller rectangle. I can do this in two different ways. What size could the smaller rectangle be? Write both ways. first way: cm by cm second way: cm by cm 2 marks (b) I have a square made out of paper. The square measures 20cm by 20cm. I keep folding it in half until I have a rectangle that is 5cm by 10cm. How many times did I fold it? 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Yards 6. Some people use yards to measure length. The diagram shows one way to change yards to metres. (a) Change 100 yards to metres. metres 1 mark (b) Change 100 metres to yards. Show your working. yards KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 10 2 marks http://www.SATs-Papers.co.uk Scales 7. A scale measures in grams and in ounces. Use the scale to answer these questions. (a) About how many ounces is 400 grams? ounces 1 mark (b) About how many grams is 8 ounces? grams 1 mark (c) About how many ounces is 1 kilogram? Explain your answer. ounces KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 11 2 marks http://www.SATs-Papers.co.uk Security lock 8. A door has a security lock. To open the door you must press the correct buttons. The code for the door is one letter followed by a single digit number. For example: B6 (a) How many different codes are there altogether? Show your working. 2 marks (b) I know that the correct code begins with D I press D, then I guess the single digit number. What is the probability that I open the door? 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Screenwash 9. Screenwash is used to clean car windows. To use Screenwash you mix it with water. (a) In winter, how much water should I mix with 150 ml of Screenwash? ml 1 mark (b) In summer, how much Screenwash should I mix with 450 ml of water? ml 1 mark (c) Is this statement correct? 25% of winter mixture is Screenwash. Tick ( ) Yes or No. Yes No Explain your answer. 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Net 10. (a) I have a paper circle. Then I cut a sector from the circle. It makes this net. Which 3-D shape below could I make with my net? Tick ( ) your answer. 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk (b) Here is a sketch of my net. Not drawn accurately Make an accurate drawing of my net. 3 marks KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Piles of cards 11. A teacher has a large pile of cards. An expression for the total number of cards is 6n + 8 (a) The teacher puts the cards in two piles. The number of cards in the first pile is 2n + 3 Write an expression to show the number of cards in the second pile. 1 mark (b) The teacher puts all the cards together. Then he uses them to make two equal piles. Write an expression to show the number of cards in one of the piles. 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk (c) The teacher puts all the cards together again, then he uses them to make two piles. There are 23 cards in the first pile. How many cards are in the second pile? Show your working. 2 marks KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Cycling 12. Hannah went on a cycling holiday. The table shows how far she cycled each day. Monday Tuesday Wednesday Thursday 32.3 km 38.7 km 43.5 km 45.1 km Hannah says: ‘On average, I cycled over 40 km a day’. Show that Hannah is wrong. 2 marks KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Same volume 13. The drawing shows 2 cuboids that have the same volume. Not drawn accurately (a) What is the volume of cuboid A? Remember to state your units. 1 mark 1 mark (b) Work out the value of the length marked x cm KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 19 1 mark http://www.SATs-Papers.co.uk Angles again 14. The diagram shows a rectangle. Not drawn accurately Work out the size of angle a You must show your working. a = KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 20 ° 3 marks http://www.SATs-Papers.co.uk Photos 15. A company sells and processes films of two different sizes. The tables show how much the company charges. Film size: 24 photos Cost to buy each film Postage Film size: 36 photos Cost to buy each film £ 2.15 free £ 2.65 free Postage Cost to print each film £ 0.99 Cost to print each film £ 2.89 Postage for each film 60p Postage for each film 60p I want to take 360 photos. I need to buy the film, pay for the film to be printed, and pay for the postage. Is it cheaper to use all films of size 24 photos, or all films of size 36 photos? How much cheaper is it? Show your working. Use film size: photos How much cheaper £ 4 marks KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Equating 16. Look at the equations. 3a + 6b = 24 2c – d = 3 (a) Use the equations to work out the value of the expressions below. The first one is done for you. 8c – 4d = 12 a + 2b = 1 mark d – 2c = 1 mark (b) Use one or both of the equations to write an expression that has a value of 21 = 21 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Same areas 17. The shapes in this question are drawn on square grids. (a) Show that the triangle and the rectangle have the same area. 1 mark (b) On the grid below, draw a parallelogram that has the same area as the triangle. It must not have any right angles. 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Libraries 18. A newspaper wrote an article about public libraries in England and Wales. It published this diagram. Use the diagram to decide whether each statement below is true or false, or whether you cannot be certain. (a) The number of libraries open for more than 45 hours per week fell by more than half from 1988 to 1998. True False Cannot be certain Explain your answer. 1 mark (b) In 2004 there will be about 450 libraries open in England and Wales for more than 45 hours a week. True False Cannot be certain Explain your answer. 1 mark KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk Data L.I.S.U./Loughborough University; Graphic T.E.S. 24 http://www.SATs-Papers.co.uk Equations 19. Each point on the straight line x + y = 12 has an x coordinate and a y coordinate that add together to make 12 Draw the straight line x + y = 12 1 mark Please turn over KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Walk 20. I went for a walk. The distance–time graph shows information about my walk. Tick ( ) the statement below that describes my walk. I was walking faster and faster. I was walking slower and slower. I was walking north-east. I was walking at a steady speed. 1 mark I was walking uphill. KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 26 http://www.SATs-Papers.co.uk Arrow 21. The grid shows an arrow. On the grid, draw an enlargement of scale factor 2 of the arrow. Use point C as the centre of enlargement. 2 marks KS3/02/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 27 http://www.SATs-Papers.co.uk END OF TEST © Qualifications and Curriculum Authority 2002 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA Sourced from SATs-Papers.co.uk 01-8633/5 http://www.SATs-Papers.co.uk

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