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Mathematics test Ma KEY STAGE 3 Paper 2 Calculator allowed TIER 6–8 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 and a scientific or graphic 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/02/841 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/Tierfrom SATs-Papers.co.uk Sourced 6–8/P2 2 http://www.SATs-Papers.co.uk Same volume 1. 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 6–8/P2 3 1 mark http://www.SATs-Papers.co.uk Angles again 2. 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 6–8/P2 4 ° 3 marks http://www.SATs-Papers.co.uk Photos 3. 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: How much cheaper KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8/P2 photos £ 5 http://www.SATs-Papers.co.uk 4 marks Equating 4. 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 6–8/P2 6 http://www.SATs-Papers.co.uk Same areas 5. 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 6–8/P2 7 http://www.SATs-Papers.co.uk Libraries 6. 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 6–8/P2 8 Data L.I.S.U./Loughborough University; Graphic T.E.S. http://www.SATs-Papers.co.uk Equations 7. (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 6–8/P2 9 http://www.SATs-Papers.co.uk Walk, Swimming clubs 8. 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. 9. (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 6–8/P2 10 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 6–8/P2 11 http://www.SATs-Papers.co.uk Arrow 10. (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 6–8/P2 12 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 6–8/P2 13 http://www.SATs-Papers.co.uk Questions 11. 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 6–8/P2 14 http://www.SATs-Papers.co.uk Circling 12. 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 6–8/P2 15 3 marks http://www.SATs-Papers.co.uk Blackbirds 13. The percentage charts show information about the wing length of adult blackbirds, measured to the nearest millimetre. (a) 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 6–8/P2 16 http://www.SATs-Papers.co.uk (b) Calculate an estimate of the mean wing length of the male blackbirds. You must show your working. mm KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8/P2 17 3 marks http://www.SATs-Papers.co.uk Percentage change 14. (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 6–8/P2 18 1 mark http://www.SATs-Papers.co.uk (c) A 10% increase followed by another 10% increase is not the same as a total increase of 20%. What is the total percentage increase? Show your working. % KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8/P2 19 http://www.SATs-Papers.co.uk 2 marks Star 15. The star nearest the Earth (other than the Sun) is Proxima Centauri. Proxima Centauri is 4.22 light-years away. (One light-year is 9.46 t 1012 kilometres.) Suppose a spaceship could travel at 40000 km per hour. (a) Write what the following calculations represent. The first one is done for you. 4.22 t 9.46 t 1012 Number of km from Earth to Proxima Centauri 4.22 t 9.46 t 1012 40000 1 mark 4.22 t 9.46 t 1012 40000 t 24 t 365.25 1 mark (b) Work out 4.22 t 9.46 t 1012 40000 t 24 t 365.25 Give your answer to the nearest thousand. 1 mark KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8/P2 20 http://www.SATs-Papers.co.uk Trigonometry 16. (a) Calculate the value of y Not drawn accurately Show your working. y= 2 marks (b) Calculate the value of angle m Not drawn accurately Show your working. m= KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8/P2 ° 2 marks 21 http://www.SATs-Papers.co.uk Satellite 17. A satellite passes over both the north and south poles, and it travels 800 km above the surface of the Earth. The satellite takes 100 minutes to complete one orbit. Assume the Earth is a sphere and that the diameter of the Earth is 12 800 km. Calculate the speed of the satellite, in kilometres per hour. Show your working. km/h KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8/P2 22 3 marks http://www.SATs-Papers.co.uk Simplify a2 – b2 18. (a) Show that simplifies to a + b a–b 1 mark (b) Simplify the expression a3 b2 a2 b2 1 mark a3 b2 – a2 b3 (c) Simplify the expression a2 b2 Show your working. 2 marks KS3/02/Ma/Tierfrom SATs-Papers.co.uk Sourced 6–8/P2 23 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 01-8633/9