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Ma Mathematics test KEY STAGE 3 TIER 4–6 Paper 1 Calculator not allowed First name Last name 2009 School 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 tracing paper (optional). 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. Sourced from SATs-Papers.co.uk TOTAL MARKS 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 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 KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Doctors 1. In a survey, people were asked: How good is your doctor? The pie chart shows the results. Key: Very good Satisfactory Poor Very poor Don’t know (a) About what percentage of the people said ‘Satisfactory’? % 1 mark (b) Altogether, about what percentage of the people said ‘Poor’ or ‘Very poor’? % 1 mark (c) Give one reason why a person may say ‘Don’t know’. 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Using tens 2. Fill in the boxes to complete each number chain. Use any of the following: + 10 – 10 × 10 450 ÷ 10 45 1 mark 450 35 1 mark 450 46 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk Card shape 3. Samir has a piece of card that is grey on one side and white on the other. He cuts out this shape from the card. He turns over the shape so that the white side is showing. Tick ( ) all the shapes below that show the white side of Samir’s shape. 2 marks KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Number lines 4. Write in the missing numbers. + + 1 mark –3 –1 7 +10 +7 1 mark 3 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Rhombus grid 5. Look at the shaded shapes. A B Isometric grid (a) The area of shape A is 3cm2 What is the area of shape B? cm2 1 mark (b) On the grid, draw a triangle that has an area of 6cm2 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Missing digits 6. Write the missing digits in each calculation below. The ﬁrst one is done for you. 1 3 = 5 7 3 = 5 1 × Sourced from SATs-Papers.co.uk × × KS3/09/Ma/Tier 4–6/P1 9 3 = 4 1 mark 1 mark 8 http://www.SATs-Papers.co.uk Clocks 7. (a) I started swimming at 9am. 12 9 3 6 When I ﬁnished swimming, the minute hand of the clock had turned 360° What time did I ﬁnish swimming? 1 mark (b) I started walking at 3pm. 12 9 3 6 When I ﬁnished walking, the hour hand of the clock had turned 90° What time did I ﬁnish walking? 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Sum of 80 8. Look at this set of four number cards. 20 20 20 20 The sum of these numbers is 80 Now look at the two sets of number cards below. Set A 17 18 Set B 19 20 21 22 23 24 Which set has a sum that is closer to 80? Set A Set B Explain your answer. 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Number chains 9. (a) A number chain starts 1 2 5 To find the next number you use the rule ×3 then –1 Write the next two numbers in the number chain. 1 2 5 1 mark (b) Here is a different number chain. 3 9 27 81 What could the rule be to find the next number? 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Making 1 10. (a) Join all the pairs of numbers that add together to equal 1 The first one is done for you. 0.1 0.99 0.11 0.9 0.01 0.999 0.91 0.89 0.001 0.09 2 marks (b) Now join all the pairs of numbers that multiply to equal 1 The first one is done for you. 1 2 0.5 4 0.25 1 0.1 20 0.05 10 KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk 2 marks T-shirts 11. Paul has 15 T-shirts. The information shows the colours of his T-shirts. 5 black 3 white 3 red 2 dark blue 1 light blue 1 yellow Paul is going to take one of his T-shirts at random. (a) What is the probability that the T-shirt will be red? 1 mark (b) What is the probability that the T-shirt will not be black? 1 mark (c) He takes one of his blue T-shirts at random. What is the probability that the T-shirt is light blue? 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Water 12. Zak has some water in a jug. litres 2 1 He pours this water into the jug below. Draw the correct level of the water on the jug. millilitres 1000 800 600 400 200 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Boxes 13. Lisa has some boxes that are all cubes of the same size. She uses four of the boxes to make a pile with a height of 72cm. She puts one more box on top of the pile. ? 72cm Work out the height of the pile of ﬁve boxes. cm 2 marks KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Percentages 14. (a) Work out 5% of 360 1 mark (b) Work out 15% of 360 You can use part (a) to help you. 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Number grids 15. In these number grids, two numbers are added to give the number below. Example: 13 12 13 + 12 = 25 25 Write numbers in the number grids below to make them correct. 22 35 17 1 mark 7 3 12 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Angles in a triangle 16. Look at the right-angled triangle ABC. A Not drawn accurately x B z 70° y C The square ﬁts exactly inside the triangle. Work out the sizes of angles x, y and z x= y= z= ° ° ° 3 marks KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Finding b, Matching 17. Look at these equations. 11 = 6 + a a + 7 = 10 + b Use both equations to work out the value of b b= 2 marks 18. Match each instruction on the left with an instruction on the right that has the same effect. The ﬁrst one is done for you. Subtract 0 1 2 Add 0 Add Add 2 Subtract Subtract 2 1 2 Add –2 Subtract –2 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Oak leaves 19. Pupils are investigating oak leaves. They want to collect a sample of oak leaves. Here is their plan for how to collect the sample. Plan Choose one oak tree. Take 10 leaves from the lowest branches of the tree. Give two reasons why this sample of leaves may not be representative of all oak leaves. First reason: 1 mark Second reason: 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Missing lengths 20. Look at the rectangle. Not drawn accurately y x 6.1cm 4cm The total area of the rectangle is 40cm 2 Work out lengths x and y x = KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk cm y = cm 2 marks 21 http://www.SATs-Papers.co.uk Counters 21. (a) Bags A and B contain some counters. 6y + 1 counters 4y + 7 counters Bag A Bag B The number of counters in each bag is the same. Work out the value of y 2 marks (b) Bag C contains more counters than bag D. 4k counters k + 12 counters Bag C Bag D What is the smallest possible value of k? 2 marks KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Prize money 22. Gary took part in a quiz show and won a million pounds. He spent £20 000 on a holiday. Then he spent half of the money left on a house. How much did Gary’s house cost? £ 2 marks KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Correlation 23. Look at these two scatter graphs. They are both drawn using the same scale. Graph A (a) Graph B Which scatter graph shows positive correlation? A B Explain your answer. 1 mark (b) Which scatter graph shows stronger correlation? A B Explain your answer. 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 24 http://www.SATs-Papers.co.uk Shape rules 24. Look at the sequence of shapes on a square grid. Shape number 1 Shape number 2 Shape number 3 Shape number 4 The table shows information about these shapes. Shape number Base Height Area N B H A 1 4 2 4 2 4 3 6 3 4 4 8 4 4 5 10 Rules connect N, B, H and A. Write one missing letter in each space below to complete the rule. H = + 1 A = × 2 + 2 2N = 2 marks KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Fortieths 25. Look at this information. 27 = 0.675 40 29 = 0.725 40 Use this information to write the missing decimals below. 31 = 40 23 = 40 KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 1 mark 1 mark 26 http://www.SATs-Papers.co.uk Expressions In this question, n stands for any whole number. 26. (a) For the expression 2n, tick ( ) the correct statement below. 2n must be odd. 2n must be even. 2n could be odd or even. Explain your answer. 1 mark (b) For the expression 3n, tick ( ) the correct statement below. 3n must be odd. 3n must be even. 3n could be odd or even. Explain your answer. 1 mark KS3/09/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 27 http://www.SATs-Papers.co.uk PLEASE TURN OVER Ratio, Powers 27. On this necklace the ratio of black beads to white beads is 1 : 3 How many more black beads do you need to add to make the ratio of black to white 3 : 1? black beads 1 mark 28. Show that the difference between 32 and 33 is 18 1 mark END OF TEST KS3/09/Ma/Tier 4–6/P1 ISBN No: 978-1-84721-702-8 Sourced from SATs-Papers.co.uk © Qualifications and Curriculum Authority 2009 28 QCA/09/3786 (Pupil http://www.SATs-Papers.co.uk pack) QCA/09/3783 (Mark scheme pack) 290009