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Ma Mathematics test KEY STAGE 3 TIER Paper 2 5–7 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 KS3_p2_57_275665.indd 1 Borderline check http://www.SATs-Papers.co.uk 15/11/06 8:58:44 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 2 2 http://www.SATs-Papers.co.uk 15/11/06 8:58:44 pm Frog spawn 1. The graph shows the date each year that frogs’ eggs were ﬁrst seen. 28th Feb 21st Feb 14th Feb Date eggs first seen 7th Feb 31st Jan 24th Jan 87 88 89 90 91 92 93 94 95 96 97 98 99 Year (a) On what date in 1997 were frogs’ eggs ﬁrst seen? 1 mark (b) At the beginning of each year, the warmer the weather, the earlier frogs’ eggs are ﬁrst seen. What can you say about the weather at the beginning of 1991? 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 3 3 Source: British Wildlife, August 2000 http://www.SATs-Papers.co.uk 15/11/06 8:58:44 pm Simplifying 2. (a) Here is an expression. 2a + 3 + 2a Which expression below shows it written as simply as possible? Put a ring round the correct one. 7a 7+a 4a + 3 2a + 5 4( a + 3) 1 mark (b) Here is a different expression. 3b + 4 + 5b – 1 Write this expression as simply as possible. 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 4 4 http://www.SATs-Papers.co.uk 15/11/06 8:58:45 pm Containers, Triangles 3. Here are two containers and the amounts they hold. B A Not drawn accurately 750 millilitres 0.5 litre Which container holds the greater amount? A B How much more does it hold? Give your answer in millilitres. millilitres 1 mark 4. (a) A triangle has three equal sides. Write the sizes of the angles in this triangle. ° , ° , ° 1 mark (b) A right-angled triangle has two equal sides. Write the sizes of the angles in this triangle. ° , ° , ° 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 5 5 http://www.SATs-Papers.co.uk 15/11/06 8:58:45 pm Spinners 5. The diagram shows ﬁve fair spinners with grey and white sectors. Each spinner is divided into equal sectors. A B C D E I am going to spin all the pointers. (a) For one of the spinners, the probability of spinning grey is 3 4 Which spinner is this? Write its letter. 1 mark (b) For two of the spinners, the probability of spinning grey is more than 60% but less than 70% Which two spinners are these? Write their letters. and 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 6 6 http://www.SATs-Papers.co.uk 15/11/06 8:58:45 pm Faces 6. (a) Look at the drawing of a prism on the grid. Isometric grid How many faces does the prism have? 1 mark (b) Use the grid below to draw a solid with 6 faces. Isometric grid KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 7 7 1 mark http://www.SATs-Papers.co.uk 15/11/06 8:58:45 pm Fir trees 7. The graph shows the average heights of ﬁr trees of different ages. 2.5 2 1.5 Height (metres) 1 0.5 0 2 3 4 Age (years) 5 6 The table shows the cost of ﬁr trees of different heights. 120cm to 159cm 160cm to 199cm 200cm to 239 cm £20.00 £25.00 £30.00 Cost (a) 1 years old. 2 How much is it likely to cost? One of these ﬁr trees is 5 £ 1 mark (b) One of these ﬁr trees costs £25.00 How old is the tree likely to be? Between and years old 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 8 8 http://www.SATs-Papers.co.uk 15/11/06 8:58:46 pm Rectangles and squares 8. Here is a rectangle. 8cm Not drawn accurately 2cm (a) A square has the same area as this rectangle. What is the side length of this square? cm 1 mark (b) A different square has the same perimeter as this rectangle. What is the side length of this square? cm 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 9 9 http://www.SATs-Papers.co.uk 15/11/06 8:58:46 pm Lemonade 9. Kate buys 24 cans of lemonade. She buys the cans in packs of 4 Each pack costs £ 1.20 Pack of 4 Cost £1.20 Steve buys 24 cans of lemonade. He buys the cans in packs of 6 Each pack costs £1.60 Pack of 6 Cost £1.60 Kate pays more for her 24 cans than Steve pays for his 24 cans. How much more? p 2 marks KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 10 10 http://www.SATs-Papers.co.uk 15/11/06 8:58:46 pm Three angles, Solving 10. Three shapes ﬁt together at point B. 93° A 24° Not drawn accurately 61° B C Will ABC make a straight line? Yes No Explain your answer. 1 mark 11. Solve these equations. 32x + 53 = 501 x = 1 mark 375 = 37 + 26y y = 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 11 11 http://www.SATs-Papers.co.uk 15/11/06 8:58:47 pm Newspaper 12. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 12 12 http://www.SATs-Papers.co.uk 15/11/06 8:58:47 pm Completing rules 13. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 13 13 http://www.SATs-Papers.co.uk 15/11/06 8:58:47 pm Parallelogram 14. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 14 14 http://www.SATs-Papers.co.uk 15/11/06 8:58:47 pm Relationships, Pi 15. Write the missing numbers. 6x + 2 so = 6x + 1 = 10 1 mark 1 – 2y so = 10 ( 1 – 2y )2 = 1 mark 16. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 15 3 16 9 1 7 15 2 355 113 1 mark http://www.SATs-Papers.co.uk 15/11/06 8:58:47 pm Enlarging 17. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 16 16 http://www.SATs-Papers.co.uk 15/11/06 8:58:48 pm Values 18. (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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 17 17 http://www.SATs-Papers.co.uk 15/11/06 8:58:48 pm Travelling by car 19. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 18 18 http://www.SATs-Papers.co.uk 15/11/06 8:58:48 pm Brackets 20. (a) Jenny wants to multiply out the brackets in the expression 3( 2a + 1 ) 3( 2a + 1 ) She writes: = 6a + 1 Show why Jenny is wrong. 1 mark (b) Sandeep wants to multiply out the brackets in the expression ( k + 4 )( k + 7) He writes: ( k + 4 )( k + 7) = k 2 + 28 Show why Sandeep is wrong. 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 19 19 http://www.SATs-Papers.co.uk 15/11/06 8:58:49 pm Vowels 21. 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 A E I O U Probability 0.08 0.13 0.07 0.08 0.03 What is the probability that it will not choose a vowel? 2 marks KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 20 20 http://www.SATs-Papers.co.uk 15/11/06 8:58:49 pm Beams 22. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 21 21 http://www.SATs-Papers.co.uk 15/11/06 8:58:49 pm Car park 23. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 22 22 http://www.SATs-Papers.co.uk 15/11/06 8:58:49 pm Volume of prisms 24. (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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 23 23 http://www.SATs-Papers.co.uk 15/11/06 8:58:49 pm Straight lines 25. 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 (b) The equation of another straight line is y = 5x + 20 Write the missing number. The straight line y = 5x + 20 passes through ( 0, ) 1 mark (c) A straight line is parallel to the line with equation y = 5x + 20 It passes through the point ( 0, 10 ) What is the equation of this straight line? 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 24 24 http://www.SATs-Papers.co.uk 15/11/06 8:58:50 pm Two semicircles 26. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 25 25 http://www.SATs-Papers.co.uk 15/11/06 8:58:50 pm Which pupil? 27. 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 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 26 26 http://www.SATs-Papers.co.uk 15/11/06 8:58:50 pm Pythagoras 28. The triangle in this question is not drawn accurately. Use Pythagoras’ theorem to explain why triangle A must be right-angled. 10cm A 6cm 8cm 1 mark KS3/07/Ma/Tier 5–7/P2 Sourced from SATs-Papers.co.uk KS3_p2_57_275665.indd 27 27 http://www.SATs-Papers.co.uk 15/11/06 8:58:50 pm END OF TEST Sourced from and Curriculum © Qualifications SATs-Papers.co.uk Authority 2007 KS3_p2_57_275665.indd 28 QCA/06/2784 (Pupil pack) http://www.SATs-Papers.co.uk 275665 QCA/06/2778 (Mark scheme pack) 15/11/06 8:58:50 pm