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Ma Mathematics test KEY STAGE 3 TIER 6–8 Paper 1 Calculator not allowed _______________________________________________ Last name _______________________________________________ School 2008 First name _______________________________________________ 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, ruler and a pair of compasses. 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 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 1 TOTAL MARKS http://www.SATs-Papers.co.uk 30/11/07 21:15:07 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 KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 2 2 http://www.SATs-Papers.co.uk 30/11/07 21:15:07 Expressions 1. Match each expression on the left with the equivalent expression on the right. The ﬁrst one is done for you. 3 3d + d 2d 3d 3d – d 4d 3d × d 2d 2 3d 2 3d ÷ d 2d 3 2 marks KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 3 3 http://www.SATs-Papers.co.uk 30/11/07 21:15:07 Views 2. Look at the two triangular prisms. Isometric grid They are joined to make the new shape below. TOP FRONT SIDE Isometric grid KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 4 4 http://www.SATs-Papers.co.uk 30/11/07 21:15:08 Multiple of 6 Complete the views of the new shape on the grid. The ﬁrst one is done for you. View from the TOP View from the FRONT View from the SIDE 2 marks Square grid 3. I am thinking of a number. My number is a multiple of 6 What three other numbers must my number be a multiple of? , and 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 5 5 http://www.SATs-Papers.co.uk 30/11/07 21:15:08 Test results 4. There are 25 pupils in a class. The table shows information about their test results in maths and English. English Level 5 Level 6 Level 7 Level 5 0 1 1 Level 6 2 7 0 Level 7 2 1 4 Level 8 0 1 6 maths (a) How many pupils had the same level in both maths and English? 1 mark (b) How many pupils had a higher level in maths than in English? 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 6 6 http://www.SATs-Papers.co.uk 30/11/07 21:15:08 Square tiles 5. The diagram shows a square with a perimeter of 12cm. Not drawn accurately Six of these squares ﬁt together to make a rectangle. Not drawn accurately What is the area of the rectangle? You must give the correct unit with your answer. 1 mark 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 7 7 http://www.SATs-Papers.co.uk 30/11/07 21:15:08 Walking to school 6. The table shows whether pupils in a class walk to school. Walk to school Do not walk to school Boys 8 Girls (a) 2 5 10 What percentage of the boys walk to school? % 1 mark (b) What percentage of the pupils in this class walk to school? % KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 8 2 marks 8 http://www.SATs-Papers.co.uk 30/11/07 21:15:08 100 metres 7. A pupil recorded the times of 23 people running the 100 metres. The stem-and-leaf diagram shows the results. Key: 13 14 1 3 4 14 7 7 8 9 15 0 1 1 3 4 15 5 7 8 8 9 16 (a) 6 2 2 4 4 13 6 represents 13.6 seconds 4 Two of the people ran the 100 metres in 14.7 seconds. How many of them ran the 100 metres faster than this? people 1 mark (b) What was the range of times? seconds 2 marks (c) What was the median time? seconds 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 9 9 http://www.SATs-Papers.co.uk 30/11/07 21:15:09 Sequences 8. (a) For each sequence below, tick ( ) the correct box to show if it is increasing, decreasing or neither. increasing 1 2 1 4 7 12 8 11 9 10 1 2 2 4 3 6 4 8 3 2 4 3 5 4 neither 1 5 6 13 (b) 1 3 decreasing 6 5 2 marks A different sequence has this expression for the nth term: 1 ( n + 1) 2 Work out the ﬁrst four terms in the sequence. 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 10 10 http://www.SATs-Papers.co.uk 30/11/07 21:15:09 Equation, Cancelling Find the value of x 9. 6 + 2x = x – 6 x = 10. 2 marks Work out 1 × 2 × 3 × 4 × 5 = 1 × 2 × 3 1 mark 2 (1 × 2 × 3 × 4 × 5) (1 × 2 × 3) 2 = 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 11 11 http://www.SATs-Papers.co.uk 30/11/07 21:15:09 Finding Atlanta 11. This map of part of America shows Chicago and New York. The scale is 1cm to 100 miles. Chicago New York Sea N Atlanta is further south than both Chicago and New York. It is 710 miles from Chicago and 850 miles from New York. Use accurate construction to show Atlanta on the map. You must leave in your construction lines. 2 marks KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 12 12 http://www.SATs-Papers.co.uk 30/11/07 21:15:09 Twice as far 12. Point A has coordinates ( 4, 3 ) and point B has coordinates ( 10, 3 ) They lie on a horizontal line. 6 4 A B 2 –2 0 2 4 6 8 10 12 14 16 Another point, P, lies on the same horizontal line. P is twice as far from A as it is from B. What could the coordinates of point P be? There are two possible answers. Give them both. ( KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 13 ) , or ( , ) 2 marks 13 http://www.SATs-Papers.co.uk 30/11/07 21:15:10 Functions In this question, consider only positive values of x 13. Look at this function. p = 3x As x increases, p increases. For each function below, tick ( ) the correct box. q=x–2 r= 1 x 2 s=2–x 1 t= x As x increases, q increases q decreases As x increases, r increases r decreases As x increases, s increases s decreases As x increases, t increases t decreases 2 marks KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 14 14 http://www.SATs-Papers.co.uk 30/11/07 21:15:10 Red and blue cubes 14. In a bag, there are red and blue cubes in the ratio 4 : 7 red : blue 4:7 I add 10 more red cubes to the bag. Now there are red and blue cubes in the ratio 6 : 7 red : blue 6:7 How many blue cubes are in the bag? 2 marks KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 15 15 http://www.SATs-Papers.co.uk 30/11/07 21:15:10 Straight lines 15. (a) A straight line goes through the points ( 0, 1 ), ( 2, 5 ) and ( 4, 9 ) The equation of the straight line is y = 2 x + 1 Is the point ( 7, 12 ) on this straight line? Yes No Explain your answer. 1 mark (b) A different straight line goes through the points ( 0, 1 ), ( 2, 7 ) and ( 4, 13 ) Write the equation of this straight line. 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 16 16 http://www.SATs-Papers.co.uk 30/11/07 21:15:10 Square root, Heads or tails 16. (a) Explain why 89 must be between 9 and 10 1 mark (b) 389 is also between two consecutive whole numbers. What are the two numbers? and 1 mark 17. Here are the rules of a game. Each person chooses heads or tails at random, then a coin is thrown. People who choose the side shown by the coin are left in the game. The rest are out of the game. If a group of 1000 people are going to play this game, how many people might you expect to be left in the game after 5 throws? people 2 marks KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 17 17 http://www.SATs-Papers.co.uk 30/11/07 21:15:10 Coordinate net 18. The diagram shows the net of a cube made of 6 squares. y Not drawn accurately K ( 20, 10 ) L x 0 M K is the point ( 20, 10 ) What are the coordinates of the points L and M? L is M is KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 18 ( , ( , ) ) 1 mark 1 mark 18 http://www.SATs-Papers.co.uk 30/11/07 21:15:11 Halving 19. (a) Ed writes: 1 of 10 3 = 5 3 2 Show why Ed is wrong. 1 mark (b) Sasha writes: 1 of 6 × 10 8 = 3 × 10 4 2 Show why Sasha is wrong. 1 mark (c) Work out 1 of 1.65 × 10 6 2 Give your answer in standard form. 2 marks KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 19 19 http://www.SATs-Papers.co.uk 30/11/07 21:15:11 Pay 20. Jane and Delia work together. Delia’s pay is exactly twice as much as Jane’s. They are each going to get a pay increase. (a) If they each get a pay increase of £2000, tick ( ) the true statement below. Delia’s pay will be more than twice as much as Jane’s. Delia’s pay will be exactly twice as much as Jane’s. Delia’s pay will be less than twice as much as Jane’s. There is not enough information to tell. (b) 1 mark If instead they each get a 5% pay increase, tick ( ) the true statement below. Delia’s pay will be more than twice as much as Jane’s. Delia’s pay will be exactly twice as much as Jane’s. Delia’s pay will be less than twice as much as Jane’s. There is not enough information to tell. 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 20 20 http://www.SATs-Papers.co.uk 30/11/07 21:15:11 Factorisation 21. Look at this factorisation. x 2 + 5x + 6 = ( x + 2 )( x + 3 ) Write numbers to make a correct factorisation below. x 2 + 7x + = (x + )( x + ) 1 mark Now write different numbers to make a correct factorisation. x 2 + 7x + = (x + )( x + ) 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 21 21 http://www.SATs-Papers.co.uk 30/11/07 21:15:11 Shape cards 22. Dario has ﬁve cards showing different shapes. He is going to mix them up, then take out one card at random. Then he is going to take out a second card without replacing the ﬁrst card. (a) What is the probability that he will take out the square ﬁrst and then the circle? 2 marks (b) What is the probability that he will take out the square and the circle, in either order? 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 22 22 http://www.SATs-Papers.co.uk 30/11/07 21:15:12 Lines 1 The graph shows the straight line with equation y = x + 1 2 23. y 6 5 1 2 y= x+1 4 3 2 1 0 0 –1 1 2 3 4 5 6 x –1 (a) For each point in the table, tick ( ) the correct box to show if it is above the line, on the line or below the line. The ﬁrst one is done for you. Point Above the line On the line Below the line (6, 3) (8, 5) (100, 60) (–4, –3) (b) 2 marks Write the equation of a different straight line that 1 is always below the line with equation y = x + 1 2 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 23 23 http://www.SATs-Papers.co.uk 30/11/07 21:15:12 Dimensions 24. Each expression below represents either a length, an area or a volume. a, b and c all represent lengths. For each expression, tick ( ) the correct one. The ﬁrst one is done for you. 2a + c length area volume area volume 3ab length 4a( b + c ) length area volume area volume a2b length KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 24 2 marks 24 http://www.SATs-Papers.co.uk 30/11/07 21:15:12 Speed 25. The cumulative frequency diagram shows the speeds of cars on a motorway on a Monday and a Thursday. 50 40 30 Key: Cumulative frequency Monday Thursday 20 10 0 0 30 35 40 45 50 55 60 65 70 75 80 85 Speed (mph) (a) The speed limit is 70mph. On Monday, about what proportion of these cars were going faster than the speed limit? 1 mark (b) On one of the days, it rained all day. Which day is this more likely to be? Monday Thursday Explain your answer. 1 mark KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 25 25 http://www.SATs-Papers.co.uk 30/11/07 21:15:12 Inequalities, Two more numbers Look at this information about a pair of numbers, k and n 26. k and < k2 > n n2 Give an example of what the numbers could be. k= n= 1 mark I think of two numbers, x and y 27. x – y is half of x + y Write x in terms of y x= 2 marks KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 26 26 http://www.SATs-Papers.co.uk 30/11/07 21:15:13 END OF TEST KS3/08/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 27 27 http://www.SATs-Papers.co.uk 30/11/07 21:15:13 END OF TEST © Qualifications and Curriculum Authority 2008 Sourced from SATs-Papers.co.uk 282673_p1_68.indd 28 QCA/08/3293 (Pupil pack) QCA/08/3286 (Mark scheme pack) http://www.SATs-Papers.co.uk 282673 30/11/07 21:15:13