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Ma KEY STAGE 3 Mathematics test Paper 2 TIER Calculator allowed 6–8 2004 Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your school in the spaces below. First name Last name 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, a pair of compasses 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 QCA/04/1202 Sourced from SATs-Papers.co.uk Total marks Borderline check 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 may use a calculator to answer any question in this test. Formulae You might need to use these formulae Trapezium Area = 1 (a + b)h 2 Prism Volume = area of cross-section t length KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Same area, Holiday 1. The triangle and the rectangle below have the same area. Not drawn accurately Work out the value of w Show your working. w = 2. cm 2 marks In 2001 the average yearly wage was £21842 On average, people spent £1644 on their family holiday. What percentage of the average yearly wage is that? Show your working. % 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Straight lines 3. The graph shows a straight line. (a) Fill in the table for some of the points on the line. ( x, y ) ( , ) ( , ) ( , ) x+y 1 mark (b) Write an equation of the straight line. 1 mark (c) On the graph, draw the straight line that has the equation x + y = 6 1 mark KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk Quiz 4. There are 20 questions in a quiz. A correct answer scores 2 points. An incorrect answer loses 1 point. A question not answered scores 0 points. A negative total is possible. (a) What are the maximum and minimum points you could get on the quiz? maximum minimum 1 mark (b) A pupil answers 10 of the 20 questions. 8 are correct. How many points does he score? 1 mark (c) Complete the table to show 3 different ways to score 24 points. Number of answers that are correct Number of answers that are incorrect Number of questions that are not answered 12 0 8 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Cotton reel 5. (a) The cross-section of a cylindrical cotton reel is a circle. The diameter of this circle is 3cm. What is the circumference of this circle? cm 1 mark (b) 91 metres of cotton goes round the cotton reel. About how many times does the cotton go round the reel? Show your working, and give your answer to the nearest ten. 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Medicine 6. Doctors sometimes use this formula to calculate how much medicine to give a child. is the correct amount for a child, in ml = 12 + is the amount for an adult, in ml is the age of the child, in years (a) A child who is 4 years old needs some medicine. The amount for an adult is 20ml. Use the formula to work out the correct amount for this child. You must show your working. 2 marks (b) Another child needs some medicine. The amount for an adult is 30ml. The correct amount for this child is 15ml. How old is this child? Show your working. 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Recycling 7. (a) A teacher asked her pupils if they recycled newspapers and glass. The pie chart shows the results. 5 pupils answered ‘Neither’. How many pupils answered ‘Newspapers only’? Show your working. pupils 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk (b) The teacher asked a different class if they recycled newspapers and glass. There were 24 pupils in the class. 9 pupils answered ‘Newspapers only’. On a pie chart, what would the angle be for the sector ‘Newspapers only’? Show your working. ° 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Russian dolls 8. The heights of Russian dolls are in the ratio 4 : 6 : 7 (a) In a set of dolls, the height of the middle doll is 9cm. What are the heights of the other dolls? cm smallest 9 cm middle cm 1 mark tallest (b) In another set of dolls, the height of the tallest doll is 9cm. What are the heights of the other dolls? Show your working, and give your answers to 1 decimal place. cm smallest KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk cm middle 10 9 cm tallest http://www.SATs-Papers.co.uk 2 marks Sweets 9. Altogether, I have 10 bags of sweets. The mean number of sweets in the bags is 41 The table shows how many sweets there are in 9 of the bags. Number of sweets in a bag Frequency 39 3 40 2 41 1 42 1 43 0 44 2 Calculate how many sweets there are in the 10th bag. You must show your working. 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Pentagonal pyramid 10. The diagram shows the net for a right-pyramid with a regular pentagon as its base. The net is constructed using five straight lines. (a) Without measuring, explain why angle must be 108° 1 mark (b) Calculate the size of angle . You must show your working. ° 1 mark KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk (c) On these nets, the point marked P lies on the perpendicular bisector of a side of the pentagon. On side CD of the regular pentagon below, use compasses and a straight edge to construct the perpendicular bisector. You must leave in your construction lines. 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Running machine 11. Kali uses a running machine to keep fit. The simplified distance-time graph shows how she used the machine during one run. KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Use the graph to answer these questions. (a) Between 0930 and 0940, what was her speed in kilometres per hour? km/h 1 mark (b) Throughout the run, for how many minutes did she travel at this speed? minutes 1 mark (c) At 0940, she increased her speed. By how many kilometres per hour did she increase her speed? km/h 1 mark (d) On another day, Kali started running at 0935 She ran for 24 minutes at a constant speed of 10 kilometres per hour. Show this information on the graph opposite. Show any working in the space below. 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Squares 12. Some numbers are smaller than their squares. For example: 7 < 72 (a) Which numbers are equal to their squares? 2 marks (b) Some numbers are bigger than their squares. Describe this set of numbers. 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Triangle calculations 13. Is it possible to have triangles with the angles and lengths shown below? For each triangle, show calculations then tick ( ) Yes or No. 2 marks 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Algebraic expressions 14. Look at these expressions. 5 – 8 3 first expression (a) What value of + 5 second expression makes the two expressions equal? Show your working. = 2 marks (b) What value of makes the first expression twice as great as the second expression? Show your working. = 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk What fraction? 15. Each pattern below shows a square grid that is 2 squares high. Only one square at each end of the top row is shaded. All squares in the bottom row are shaded. Imagine one of these patterns that has n squares in the bottom row. Write an expression for the fraction of the pattern that is shaded. 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Eating, Equation solving 16. People were asked if they were considering changing what they eat. 29% of the people asked said yes. Of these, 23% said they were considering becoming vegetarian. What percentage of the people asked said they were considering becoming vegetarian? % 1 mark 17. Solve this equation. Show your working. 5(2 – 3) = 3 3 = 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk 3-D cut 18. The side length of a cube is 10cm. The cube is cut along a plane through three of the vertices to make a pyramid. Not drawn accurately A A B 10cm B C C Calculate the perimeter of the base, ABC, of the pyramid. Show your working. cm 2 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Tiles 19. A pupil has three tiles. One is a regular octagon, one is a regular hexagon, and one is a square. The side length of each tile is the same. The pupil says the hexagon will fit exactly like this. Not drawn accurately Show calculations to prove that the pupil is wrong. 3 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Dissection 20. The diagram shows a square inside a triangle. DEF is a straight line. Not drawn accurately The side length of square ABCE is 12cm. The length of DE is 15cm. Show that the length of EF is 20cm. 3 marks KS3/04/Ma/Tier 6–8/P2 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk END OF TEST Sourced from SATs-Papers.co.uk © Qualifications and Curriculum Authority 2004 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk 259576