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Mathematics test Ma KEY STAGE 3 Paper 2 Calculator allowed TIER 5–7 2002 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 scientific or graphic calculator. I Some formulae you might need are on page 3. 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/02/839 Sourced from SATs-Papers.co.uk Total marks Borderline check http://www.SATs-Papers.co.uk BLANK PAGE KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 2 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 3 http://www.SATs-Papers.co.uk Yards 1. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 4 http://www.SATs-Papers.co.uk 2 marks Scales 2. A scale measures in grams and in ounces. Use the scale to answer this question. About how many ounces is 1 kilogram? Explain your answer. ounces KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 5 http://www.SATs-Papers.co.uk 2 marks Security lock 3. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 6 http://www.SATs-Papers.co.uk Screenwash 4. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 7 http://www.SATs-Papers.co.uk Net 5. (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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 8 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 9 http://www.SATs-Papers.co.uk Piles of cards 6. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 10 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 11 http://www.SATs-Papers.co.uk Cycling 7. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 12 http://www.SATs-Papers.co.uk Same volume 8. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 13 1 mark http://www.SATs-Papers.co.uk Angles again 9. The diagram shows a rectangle. Not drawn accurately Work out the size of angle a You must show your working. a = KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 14 ° 3 marks http://www.SATs-Papers.co.uk Photos 10. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 15 http://www.SATs-Papers.co.uk Equating 11. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 16 http://www.SATs-Papers.co.uk Same areas 12. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 17 http://www.SATs-Papers.co.uk Libraries 13. 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 18 Data L.I.S.U./Loughborough University; Graphic T.E.S. http://www.SATs-Papers.co.uk Equations 14. (a) 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 (b) Plot on the grid below at least 6 points whose x coordinate and y coordinate multiply together to make 12 Then draw the part of the curve xy = 12 that you would see on the grid below. 2 marks KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 19 http://www.SATs-Papers.co.uk Walk, Swimming clubs 15. 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. 16. (a) From 5th May 2000 to 5th May 2001 a swimming club had the same members. Complete the table to show information about the ages of these members. Ages of members Mean (5th May 2000) 24 years 3 months Range (5th May 2000) 4 years 8 months Mean (5th May 2001) Range (5th May 2001) KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 20 1 mark http://www.SATs-Papers.co.uk (b) The table below shows information about members of a different club. Ages of members Mean 17 years 5 months Range 2 years 0 months A new member, aged 18 years 5 months, is going to join the club. What will happen to the mean age of the members? Tick ( ) the correct statement below. It will increase by more than 1 year. It will increase by exactly 1 year. It will increase by less than 1 year. It will stay the same. 1 mark It is not possible to tell. What will happen to the range of ages of the members? It will increase by more than 1 year. It will increase by exactly 1 year. It will increase by less than 1 year. It will stay the same. 1 mark It is not possible to tell. KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 21 http://www.SATs-Papers.co.uk Arrow 17. (a) 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/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 22 http://www.SATs-Papers.co.uk (b) The sketch below shows two arrows. The bigger arrow is an enlargement of scale factor 1.5 of the smaller arrow. Write down the three missing values. 1 mark Not drawn accurately 1 mark 1 mark KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 23 http://www.SATs-Papers.co.uk Questions 18. A box contains cards with one question on each card. There are 4 categories of questions. Each category has some easy and some difficult questions. The table shows the probability of selecting a card at random from the box. Category Easy Difficult Music 0.2 0.15 Sport 0.2 0.1 History 0.1 0.05 Nature 0.15 0.05 (a) I am going to take one card at random from the box. What is the probability that it will be a history question? 1 mark an easy question? 1 mark (b) There are 40 cards in the box. How many of these are music questions? 1 mark KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 24 http://www.SATs-Papers.co.uk Circling 19. The diagram shows a square and a circle. The circle touches the edges of the square. What percentage of the diagram is shaded? Show your working. % KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 25 3 marks http://www.SATs-Papers.co.uk Blackbirds 20. The percentage charts show information about the wing length of adult blackbirds, measured to the nearest millimetre. Use the data to decide whether these statements are true or false, or whether there is not enough information to tell. The smallest male’s wing length is larger than the smallest female’s wing length. True False Not enough information Explain your answer. 1 mark The biggest male’s wing length is larger than the biggest female’s wing length. True False Not enough information Explain your answer. 1 mark KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 26 http://www.SATs-Papers.co.uk Percentage change 21. (a) One calculation below gives the answer to the question What is 70 increased by 9%? Tick ( ) the correct one. 70 t 0.9 70 t 1.9 70 t 0.09 70 t 1.09 1 mark Choose one of the other calculations. Write a question about percentages that this calculation represents. calculation chosen: question it represents: 1 mark Now do the same for one of the remaining two calculations. calculation chosen: question it represents: 1 mark (b) Fill in the missing decimal number. To decrease by 14%, multiply by KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 5–7/P2 27 1 mark http://www.SATs-Papers.co.uk END OF TEST Sourced from SATs-Papers.co.uk © Qualifications and Curriculum Authority 2002 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk 01-8633/7