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Ma Mathematics test KEY STAGE 3 TIER Paper 2 4–6 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, tracing paper and mirror (optional) and a 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 275663_p2_46.indd 1 Borderline check http://www.SATs-Papers.co.uk 15/11/06 10:20:41 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 2 2 http://www.SATs-Papers.co.uk 15/11/06 10:20:41 pm Coordinates 1. Look at the graph. y 8 7 A 6 5 4 3 C 2 B (2, 2) 1 0 0 (a) 1 2 3 4 5 6 7 8 x Write down the coordinates of points A and C. A is ( , ) 1 mark C is (b) ( , ) 1 mark Point D can be marked so that ABCD is a rectangle. Mark point D accurately on the graph. 1 mark KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 3 3 http://www.SATs-Papers.co.uk 15/11/06 10:20:42 pm Fitting tiles 2. (a) The diagram shows how two congruent ‘F-tiles’ fit together to make a rectangle. Show how the two congruent ‘F-tiles’ can fit together to make this shape. 1 mark (b) Two other tiles fit together to make a different shape. The two tiles are congruent but they are not ‘F-tiles’. What shape could the tiles be? Show them on the diagram. 1 mark What other shape could the tiles be? Show them on the diagram. 1 mark KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 4 4 http://www.SATs-Papers.co.uk 15/11/06 10:20:42 pm Names 3. These are the names of the twelve people who work for a company. Ali Kiki Suki Brian Claire Lucy Tom Claire (a) Claire James Ryan Tom What name is the mode? 1 mark (b) One person leaves the company. A different person joins the company. Now the name that is the mode is Tom. Write the missing names in the sentences below. The name of the person who leaves is The name of the person who joins is 1 mark KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 5 5 http://www.SATs-Papers.co.uk 15/11/06 10:20:43 pm Leaves 4. The scale drawing shows three leaves from different trees. The drawing on the right shows the leaves drawn on top of each other. Oak (a) Beech Willow Compare the areas of the leaves. Write the leaves in order, smallest area ﬁrst. 1 mark smallest area (b) largest area Now compare the perimeters of the leaves. Write the leaves in order, smallest perimeter ﬁrst. 1 mark smallest perimeter KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 6 largest perimeter 6 http://www.SATs-Papers.co.uk 15/11/06 10:20:43 pm Marbles 5. Here is information about some bags of marbles. Altogether, there are 10 bags. Each bag contains 12 marbles. Each marble weighs 7 grams. Use the information to match each question with the correct calculation. The first one is done for you. Question Calculation 10 How many bags are there altogether? 10 × 7 How many marbles are there altogether? 10 × 12 12 × 7 How much does each bag of marbles weigh? 10 × 12 × 7 How much do all 10 bags of marbles weigh altogether? KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 7 10 + 12 + 7 2 marks 7 http://www.SATs-Papers.co.uk 15/11/06 10:20:43 pm a and b 6. Look at this equation. 4 + a = b Write a pair of numbers for a and b to make the equation true. a= b= 1 mark Now write a different pair of numbers for a and b to make the equation true. a= b= 1 mark KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 8 8 http://www.SATs-Papers.co.uk 15/11/06 10:20:44 pm Turning, Party 7. Here is a shape. I turn the shape through 45° clockwise. Tick ( ) the diagram that shows the shape after the turn. 1 mark 8. Leena buys balloons, hats and masks for a party. Write the missing numbers in the table. Cost of each (£) Number bought Packets of balloons 4.95 5 Hats Total cost (£) 3.20 41.60 Masks 10 19.50 Total: 2 marks KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 9 9 http://www.SATs-Papers.co.uk 15/11/06 10:20:44 pm Survey 9. Carlos and Mary each did a survey. (a) Carlos asked people: ‘Have you ever been to North America?’ The percentage bar chart shows his results. No 0% 20% Yes 60% 40% 80% 100% 40 people said No. How many people said Yes? people 1 mark (b) Mary asked 10 people: Results: ‘Would you like to go to South America?’ 5 of the 10 people said ‘No’. 4 of the 10 people said ‘Don’t know’. 1 of the 10 people said ‘Yes’. Complete the percentage bar chart to show these results. 0% 20% KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 10 40% 60% 80% 100% 2 marks 10 http://www.SATs-Papers.co.uk 15/11/06 10:20:45 pm Frog spawn 10. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 11 11 Source: British Wildlife, August 2000 http://www.SATs-Papers.co.uk 15/11/06 10:20:45 pm Simplifying 11. (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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 12 12 http://www.SATs-Papers.co.uk 15/11/06 10:20:46 pm Containers, Triangles 12. 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 13. (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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 13 13 http://www.SATs-Papers.co.uk 15/11/06 10:20:46 pm Spinners 14. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 14 14 http://www.SATs-Papers.co.uk 15/11/06 10:20:46 pm Faces 15. (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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 15 1 mark 15 http://www.SATs-Papers.co.uk 15/11/06 10:20:47 pm Fir trees 16. 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 1 years old. 2 How much is it likely to cost? (a) 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 16 16 http://www.SATs-Papers.co.uk 15/11/06 10:20:47 pm Rectangles and squares 17. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 17 17 http://www.SATs-Papers.co.uk 15/11/06 10:20:48 pm Lemonade 18. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 18 18 http://www.SATs-Papers.co.uk 15/11/06 10:20:48 pm Three angles, Solving 19. 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 20. Solve these equations. 32x + 53 = 501 x = 1 mark 375 = 37 + 26y y = 1 mark KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 19 19 http://www.SATs-Papers.co.uk 15/11/06 10:20:49 pm Newspaper 21. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 20 20 http://www.SATs-Papers.co.uk 15/11/06 10:20:49 pm Completing rules 22. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 21 21 http://www.SATs-Papers.co.uk 15/11/06 10:20:50 pm Parallelogram 23. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 22 22 http://www.SATs-Papers.co.uk 15/11/06 10:20:50 pm Relationships, Pi 24. Write the missing numbers. 6x + 2 so = 6x + 1 = 10 1 mark 1 – 2y so = 10 ( 1 – 2y )2 = 1 mark 25. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 23 16 9 1 3 7 2 355 113 1 mark 23 http://www.SATs-Papers.co.uk 15/11/06 10:20:50 pm Enlarging 26. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 24 24 http://www.SATs-Papers.co.uk 15/11/06 10:20:51 pm Values 27. (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 KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 25 25 http://www.SATs-Papers.co.uk 15/11/06 10:20:52 pm Travelling by car 28. 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 4 3 2 KS3/07/Ma/Tier 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 26 26 http://www.SATs-Papers.co.uk 15/11/06 10:20:52 pm Brackets, Vowels Jenny wants to multiply out the brackets in the expression 3( 2a + 1 ) 29. 3( 2a + 1 ) She writes: = 6a + 1 Show why Jenny is wrong. 1 mark 30. 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 4–6/P2 Sourced from SATs-Papers.co.uk 275663_p2_46.indd 27 27 http://www.SATs-Papers.co.uk 15/11/06 10:20:52 pm END OF TEST © QualificationsSATs-Papers.co.uk Authority 2007 Sourced from and Curriculum 275663_p2_46.indd 28 QCA/06/2782 (Pupil pack) QCA/06/2778 (Mark scheme pack) http://www.SATs-Papers.co.uk275663 15/11/06 10:20:53 pm