We have almost every SATs paper within our archives including KS1 *Money Problems* and many other KS1, KS2 and KS3 SATs papers and worksheets. SATs papers are fantastic practise tools, especially for literacy, problem solving and maths. Alternative sources for study include the Bitesize resources and Revisewise for more SATs practice, SATs revision and SATs preparation!

Ma KEY STAGE 3 Mathematics test Paper 2 TIER Calculator allowed 5–7 2005 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 may use a calculator for any question in this test. ■ You will need: pen, pencil, rubber, ruler, angle measurer or protractor and a scientific or graphic calculator. ■ 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 Sourced from SATs-Papers.co.uk Total marks use only QCA/05/1434 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 KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Algebra grids 1. Look at this algebra grid. Complete the algebra grids below, simplifying each expression. 1 mark 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk 1976 v 2002 2. Look at this information. In 1976, a man earned £ 16 each week. The pie chart shows how he spent his money. Other Clothes Entertainment Rent Food (a) How much did the man spend on food each week? £ 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk (b) Now look at this information. In 2002, a man earned £ 400 each week. The table shows how he spent his money. Rent £ 200 Food £ 100 Entertainment £ 50 Other £ 50 Complete the pie chart below to show how the man spent his money. Remember to label each sector of the pie chart. 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Pens 3. Two shops sell packs of pens. Supermarket Village shop Pack of 5 pens Pack of 6 pens £ 6.25 £ 7.20 I want to buy 30 pens. In which shop are the pens cheaper? You must show your working. Tick ( ) your answer. Supermarket Village shop 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Counters 4. (a) Aidan puts 2 white counters and 1 black counter in a bag. He is going to take one counter without looking. What is the probability that the counter will be black? 1 mark (b) Aidan puts the counter back in the bag and then puts more black counters in the bag. He is going to take one counter without looking. The probability that the counter will be black is now 2 3 How many more black counters did Aidan put in the bag? 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk From London 5. The scale drawing shows the positions of London and Paris. North London Paris (a) From London to Paris, the angle from north is angle a Measure accurately angle a a= ° 1 mark (b) On the scale drawing, 1cm represents 50 km. What is the distance, in km, from London to Paris? km 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk (c) A newspaper printed this information about London and Madrid. From London to Madrid, the angle from north is 195° clockwise. Madrid is 1300 km from London. Show this information on a scale drawing. Use the scale 1cm represents 200 km. The position of London is shown for you. North London 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk How many? 6. Work out the number of boys and girls in each class below. (a) In class 8M, there are 27 pupils. There are twice as many boys as girls. Number of boys Number of girls 1 mark (b) In class 8K, there are 28 pupils. There are two more boys than girls. Number of boys Number of girls 1 mark (c) In class 8T, there are 9 boys. The ratio of boys to girls is 1 : 2 Number of boys Number of girls 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Pentagon, Using a calculator 7. Here are three lines on a centimetre square grid. Draw two more lines on the grid to make a pentagon that has an area of 14 cm2 1 mark 8. Use your calculator to work out the answers. (48 + 57) t (61 – 19) = 1 mark 48 + 57 = 61 – 19 KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 1 mark 11 http://www.SATs-Papers.co.uk Tennis prizes 9. Each year, there is a tennis competition in Australia and another one in France. The table shows how much money was paid to the winner of the men’s competition in each country in 2002. Country Money Australia 1 000 000 Australian dollars (£ 1 = 2.70 Australian dollars) France 780 000 Euros (£ 1 = 1.54 Euros) Which country paid more money? You must show your working. Tick ( ) the country that paid more. Australia France 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Enlargement 10. Look at the rectangle drawn on a square grid. Draw an enlargement of this rectangle with scale factor 2 Use point A as the centre of enlargement. A 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Heron of Alexandria 11. About 2000 years ago, a Greek mathematician worked out this formula to find the area of any triangle. For a triangle with sides a, b and c Area = s ( s – a )( s – b )( s – c ) where s = a+b+c 2 A triangle has sides, in cm, of 3, 5 and 6 Use a = 3, b = 5 and c = 6 to work out the area of this triangle. cm2 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Hands 12. Here is some information about all the pupils in class 9A. girls boys right-handed 13 14 left-handed 1 2 A teacher is going to choose a pupil from 9A at random. (a) What is the probability that the pupil chosen will be a girl? 1 mark (b) What is the probability that the pupil chosen will be left-handed? 1 mark (c) The teacher chooses the pupil at random. She tells the class the pupil is left-handed. What is the probability that this left-handed pupil is a boy? 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Screens 13. The screens of widescreen and standard televisions look different. They have different proportions. Keri starts to draw scale drawings of the televisions. For each, the height is 4.5 cm. What should the width of each scale drawing be? The width of this scale drawing should be cm 1 mark The width of this scale drawing should be cm 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Spinning, Number 14. A spinner has the numbers 1 to 4 on it. The probability of spinning a number 4 is 0.1 The probability of spinning a number 1 is 0.6 The probability of spinning a number 2 is the same as the probability of spinning a number 3 Calculate the probability of spinning a number 3 2 marks 15. I think of a number. I multiply this number by 8, then subtract 66 The result is twice the number that I was thinking of. What is the number I was thinking of? 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk A level results 16. Here is some information about A levels in 2002. English Mathematics Number of students 72 000 54 000 Percentage gaining grade A 19 % 37% How many more students gained grade A in mathematics than in English? 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Solutions 17. (a) Look at this equation. 14 y – 51 = 187 + 4 y Is y = 17 the solution to the equation? Yes No Show how you know. 1 mark (b) Now look at this equation. 3y 2 = 2601 Is y = 17 a solution to the equation? Yes No Show how you know. 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Simplify 18. Write these expressions as simply as possible. 9 – 3k + 5k = 1 mark k 2 + 2k + 4k = 1 mark 3k t 2 k = 9k2 3k KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 1 mark = 1 mark 20 http://www.SATs-Papers.co.uk Watching 19. In one week Jamal watched television for 26 hours. In that week: He watched television for the same length of time on Monday, Tuesday, Wednesday and Thursday. On each of Friday, Saturday and Sunday, he watched television for twice as long as on Monday. How long did he spend watching television on Saturday? Write your answer in hours and minutes. hours minutes 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Milk 20. Here are four charts drawn by a computer. Charts to show the average amount of milk produced by different breeds of cow Chart 1 Chart 2 25 25 20 20 Litres 15 of milk 10 Litres 15 of milk 10 5 5 0 A D G H J Breed of cow 0 S A D G H J Breed of cow S Chart 4 Chart 3 25 20 A S Litres 15 of milk 10 G H 5 0 D J A D G H J Breed of cow S Key: A - Ayrshire D - Dexter KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk G - Guernsey H - Holstein J - Jersey S - Shorthorn 22 http://www.SATs-Papers.co.uk Only one of these charts is a good way of showing the data. For each of the other three charts, explain why the type of chart is not a good way of showing the data. Chart because 1 mark Chart because 1 mark Chart because 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Sequences, Bracket multiplication 21. (a) The nth term of a sequence is 3n + 4 What is the 8th term of this sequence? 1 mark (b) The nth term of a different sequence is n–2 n2 Write the first three terms of this sequence. 2 marks 22. Multiply out the brackets in these expressions. y (y – 6) = 1 mark (k + 2)(k + 3) = 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 24 http://www.SATs-Papers.co.uk Parallelogram 23. ABCD is a parallelogram. C B 60˚ 80˚ A D Not drawn accurately Work out the sizes of angles h and j Give reasons for your answers. h= ° because 1 mark j= ° because 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Rich and poor 24. A newspaper printed this information about the world’s population. If the world was a village of 100 people, 6 people would have 59% of the total wealth. The other 94 people would have the rest. On average, how many times as wealthy as one of the other 94 people would one of these 6 people be? 2 marks KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 26 As reported in the Metro newspaper, Feb 2001 http://www.SATs-Papers.co.uk Area 25. The diagram shows two circles and a square, ABCD. A and B are the centres of the circles. The radius of each circle is 5 cm. A B Not drawn accurately 5 cm 5 cm D C Calculate the area of the shaded part of the square. 2 marks 1 mark KS3/05/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk 27 http://www.SATs-Papers.co.uk END OF TEST © Qualifications and Curriculum Authority 2005 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA Sourced from SATs-Papers.co.uk 265283 http://www.SATs-Papers.co.uk