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Ma Mathematics test KEY STAGE 3 TIER Paper 2 6–8 Calculator allowed First name Last name 2007 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, an 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 use only TOTAL MARKS Sourced from SATs-Papers.co.uk 275667_p2_68.indd 1 Borderline check http://www.SATs-Papers.co.uk 15/11/06 9:38:42 pm 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 b Area = 1 (a + b)h 2 height (h) a Prism length area of cross-section Volume = area of cross-section × length KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 2 2 http://www.SATs-Papers.co.uk 15/11/06 9:38:43 pm Newspaper 1. In a survey, 60 people were asked: What kind of newspaper did you buy today? Here are the results. Type of newspaper Number of people Morning newspaper 35 Evening newspaper 10 No newspaper 15 Complete the pie chart to show this information. Morning newspaper 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 3 3 http://www.SATs-Papers.co.uk 15/11/06 9:38:43 pm Completing rules 2. Look at the information. x = 4 y = 13 Complete the rules below to show different ways to get y using x The first one is done for you. To get y, multiply x by 2 This can be written as y = 2x + 5 and add To get y, multiply x by 5 and add This can be written as y = 1 mark To get y, multiply x by and subtract This can be written as y = 1 mark To get y, divide x by and add This can be written as y = 1 mark KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 4 4 http://www.SATs-Papers.co.uk 15/11/06 9:38:43 pm Parallelogram 3. The diagram shows a shaded parallelogram drawn inside a rectangle. 3 cm 5cm Not drawn accurately 3cm 10cm What is the area of the shaded parallelogram? You must give the correct unit with your answer. 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 5 5 http://www.SATs-Papers.co.uk 15/11/06 9:38:44 pm Relationships, Pi 4. Write the missing numbers. 6x + 2 so = 6x + 1 = 10 1 mark 1 – 2y so = 10 ( 1 – 2y )2 = 1 mark 5. The value of correct to 7 decimal places is: 3.1415927 (a) Write the value of correct to 4 decimal places. 1 mark (b) Which value below is closest to the value of ? Put a ring round the correct one. 179 57 KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 6 16 9 1 3 7 2 355 113 1 mark 6 http://www.SATs-Papers.co.uk 15/11/06 9:38:44 pm Enlarging 6. Enlarge the shaded shape by a scale factor of 2, using P as the centre of enlargement. P 2 marks Isometric grid KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 7 7 http://www.SATs-Papers.co.uk 15/11/06 9:38:45 pm Values 7. (a) Here are two equations. k = a + b a + b + k = 30 What is the value of k ? k= (b) 1 mark Look at this information. 10 = c + d c is one more than d What is the value of c ? c= 1 mark (c) Now look at this information. 10 = e + f e is more than f What else can you say about the value of e ? 1 mark KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 8 8 http://www.SATs-Papers.co.uk 15/11/06 9:38:45 pm Travelling by car 8. A pupil investigated how the teachers at his school travel to work. The table shows the results. Number of teachers who travel by car 18 (a) Number of teachers who do not travel by car 7 What percentage of these teachers travel by car? % 1 mark (b) 18 teachers travel by car. Some of these teachers travel together. Write the missing frequency in the table below. Number of teachers in one car Number of cars 1 1 mark 2 3 (c) 4 2 What is the mean number of teachers in each car? 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 9 9 http://www.SATs-Papers.co.uk 15/11/06 9:38:46 pm Brackets 9. Jenny wants to multiply out the brackets in the expression 3( 2a + 1 ) (a) 3( 2a + 1 ) She writes: = 6a + 1 Show why Jenny is wrong. 1 mark Sandeep wants to multiply out the brackets in the expression ( k + 4 )( k + 7) (b) He writes: ( k + 4 )( k + 7) = k 2 + 28 Show why Sandeep is wrong. 1 mark KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 10 10 http://www.SATs-Papers.co.uk 15/11/06 9:38:46 pm Vowels 10. A computer is going to choose a letter at random from an English book. The table shows the probabilities of the computer choosing each vowel. Vowel E I O U Probability (a) A 0.08 0.13 0.07 0.08 0.03 What is the probability that it will not choose a vowel? 2 marks (b) The probability that the computer will choose the letter T is 0.09 The computer chooses a letter at random, and then another, and then another. What is the probability that these letters will be E, then A, then T? 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 11 11 http://www.SATs-Papers.co.uk 15/11/06 9:38:46 pm Beams 11. I am going to use a wooden beam to support a load. The cross-section of the beam is a rectangle. cross-section The formula below gives the greatest load, Mkg, that a beam of this length can support. M = 5d 2w where d is the depth of the beam in cm, w is the width of the beam in cm. I can place the cross-section of the beam in two different ways. d = 11 1st way d=8 2nd way w = 11 w=8 In which way will the beam be able to support the greater load? Calculate the difference. The way supports the greater load, with a difference of kg. 3 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 12 12 http://www.SATs-Papers.co.uk 15/11/06 9:38:47 pm Car park 12. One day, each driver entering a car park paid exactly £1.50 Car park Pay exactly £1.50 to enter Machine accepts only £1 coins and 50p coins Here is what was put into the machine that day. Number of £1 coins 136 Number of 50p coins 208 On that day, what percentage of drivers paid with three 50p coins? % 3 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 13 13 http://www.SATs-Papers.co.uk 15/11/06 9:38:47 pm Volume of prisms 13. (a) Look at the triangular prism. 6cm Not drawn accurately 10cm 4cm Work out the volume of the prism. cm3 1 mark (b) One face of another prism is made from 5 squares. Each square has side length 3cm. 3cm 10cm Not drawn accurately Work out the volume of the prism. cm3 1 mark KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 14 14 http://www.SATs-Papers.co.uk 15/11/06 9:38:47 pm Straight lines 14. The graph shows a straight line with gradient 1 y 10 0 –10 0 x 10 –10 (a) On the graph, draw a different straight line with gradient 1 1 mark The equation of another straight line is y = 5x + 20 (b) Write the missing number. The straight line y = 5x + 20 passes through ( 0, ) 1 mark A straight line is parallel to the line with equation y = 5x + 20 (c) It passes through the point ( 0, 10 ) What is the equation of this straight line? 1 mark KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 15 15 http://www.SATs-Papers.co.uk 15/11/06 9:38:48 pm Two semicircles 15. This shaded shape is made using two semicircles. One semicircle has a diameter of 20cm. The other has a diameter of 30cm. Not drawn accurately 20cm 30cm Calculate the perimeter of the shaded shape. cm 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 16 16 http://www.SATs-Papers.co.uk 15/11/06 9:38:48 pm Which pupil? 16. The table shows the number of boys and girls in two different classes. Class 9A Class 9B Boys 13 12 Girls 15 14 A teacher is going to choose a pupil at random from each of these classes. In which class is she more likely to choose a boy? You must show your working. Tick ( ) your answer. Class 9A Class 9B 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 17 17 http://www.SATs-Papers.co.uk 15/11/06 9:38:49 pm Pythagoras 17. The triangles in this question are not drawn accurately. (a) Use Pythagoras’ theorem to explain why triangle A must be right-angled. 10cm A 6cm 8cm 1 mark (b) Triangle A is enlarged to make triangle B. Use similar triangles to show that d = 9.2cm. 6.9 cm B d 1 mark KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 18 18 http://www.SATs-Papers.co.uk 15/11/06 9:38:49 pm (c) The diagram shows the Earth and two other planets. Planet P is 6.9 × 107 km from Earth. Planet P Planet Q is 9.2 × 107 km from Earth. 6.9 × 107 km Planet Q 9.2 × 107 km Earth How far is Planet P from Planet Q? Give your answer in standard form. 1 mark km 1 mark KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 19 19 http://www.SATs-Papers.co.uk 15/11/06 9:38:49 pm Expressions 18. Look at the equation in the box. x + ( x + 1) + (x + 2) = y Use it to help you write the missing expressions in terms of y The ﬁrst one is done for you. + ( x + 1) + (x + 2) = ( x + 5) + (x + 6) + (x + 7) = 2x 5 + 2( x + 1) + 2(x + 2) = + x y+5 (x + a) + (x + 1 + a) + (x + 2 + a) = 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 20 20 http://www.SATs-Papers.co.uk 15/11/06 9:38:50 pm Gorillas 19. Here is part of a newspaper report about wildlife in a country in Africa. The number of gorillas has fallen by 70% in the last ten years. Only about 5000 gorillas are left. About how many gorillas were there in this country ten years earlier? 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 21 21 As reported in the Metro Newspaper, March 2004 http://www.SATs-Papers.co.uk 15/11/06 9:38:50 pm Houses 20. On a street, there are 100 houses. 60 are terraced houses. 30 are semi-detached. The rest are detached. The table shows the mean number of bedrooms in each type of house. Type of house Mean number of bedrooms Terraced 2.5 Semi-detached 3.3 Detached 4.1 What is the mean number of bedrooms per house on this street? 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 22 22 http://www.SATs-Papers.co.uk 15/11/06 9:38:51 pm Subtracting and squaring 21. I am thinking of a number. When I subtract 25 from my number, then square the answer, I get the same result as when I square my number, then subtract 25 from the answer. What is my number? You must show an algebraic method. 2 marks KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 23 23 http://www.SATs-Papers.co.uk 15/11/06 9:38:51 pm Light years 22. (a) One light year is approximately 9 430 000 000 000 kilometres. Write this distance in standard form. km 1 mark (b) A star called Wolf 359 is approximately 7.8 light years from Earth. About how many kilometres is this? Write your answer in standard form. km 1 mark KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 24 24 http://www.SATs-Papers.co.uk 15/11/06 9:38:51 pm Octagon 23. I have a square piece of card. I cut a triangle from each corner so that the remaining card is in the shape of a regular octagon. Not drawn accurately y y The perimeter of the regular octagon is 32cm. Work out length y y= KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 25 cm 2 marks 25 http://www.SATs-Papers.co.uk 15/11/06 9:38:52 pm x, y, a and b 24. Look at the simultaneous equations. x + x + 2y = a y = b Write an expression for y in terms of a and b (a) y = 1 mark Now write an expression for x in terms of a and b (b) Write your expression as simply as possible. x = KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 26 2 marks 26 http://www.SATs-Papers.co.uk 15/11/06 9:38:52 pm END OF TEST KS3/07/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 275667_p2_68.indd 27 27 http://www.SATs-Papers.co.uk 15/11/06 9:38:52 pm © QualificationsSATs-Papers.co.uk Authority 2007 Sourced from and Curriculum 275667_p2_68.indd 28 QCA/06/2786 (Pupil pack) QCA/06/2778 (Mark scheme pack) http://www.SATs-Papers.co.uk 275667 15/11/06 9:38:52 pm