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Ma KEY STAGE 3 Mathematics test Paper 1 Calculator not allowed TIER 6–8 2003 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 must not use a calculator for any question in this test. ■ You will need: pen, pencil, rubber and a ruler. ■ 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/03/970 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 Area = 1 (a + b)h 2 Prism Volume = area of cross-section t length KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Solving 1. Solve these equations. Show your working. 3 t + 4 = t + 13 t= 2 marks 2 (3n + 7) = 8 n= 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Shapes 2. The drawing shows how shapes A and B fit together to make a right-angled triangle. Work out the size of each of the angles in shape B. Write them in the correct place in shape B below. Not drawn accurately 3 marks KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk Mixed numbers 3. (a) Add 6 6 and 10 5 1 mark Now use an arrow ( ) to show the result on the number line. 1 mark 1 3 (b) How many sixths are there in 3 ? 1 mark (c) Work out 3 1 3 ÷ 5 6 Show your working. 2 marks KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Areas algebraically 4. (a) The diagram shows a rectangle. Its dimensions are 3a by 5b Write simplified expressions for the area and the perimeter of this rectangle. Area: 1 mark Perimeter: 1 mark (b) A different rectangle has area 12 a 2 and perimeter 14 a What are the dimensions of this rectangle? Dimensions: by 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Arranging 5. Here are six number cards. (a) Arrange these six cards to make the calculations below. The first one is done for you. 1 mark 1 mark (b) Now arrange the six cards to make a difference of 115 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Lines on a square 6. The diagram shows a square drawn on a square grid. (a) The points A, B, C and D are at the vertices of the square. Match the correct line to each equation. One is done for you. 2 marks KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk The mid-points of each side, E, F G and H, join to make a different square. , (b) Write the equation of the straight line through E and H. 1 mark (c) Is y = – x the equation of the straight line through E and G? Tick ( ) Yes or No. Yes No Explain how you know. 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Scatter graphs 7. The scatter graph shows information about trees called poplars. (a) What does the scatter graph show about the relationship between the diameter of the tree trunk and the height of the tree? 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk (b) The height of a different tree is 3m. The diameter of its trunk is 5cm. Use the graph to explain why this tree is not likely to be a poplar. 1 mark (c) Another tree is a poplar. The diameter of its trunk is 3.2 cm. Estimate the height of this tree. m 1 mark (d) Below are some statements about drawing lines of best fit on scatter graphs. For each statement, tick ( ) to show whether the statement is True or False. Lines of best fit must always ... go through the origin. True False have a positive gradient. True False join the smallest and the largest values. True False pass through every point on the graph. True False 2 marks KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Winning ticket 8. A headteacher wants to choose a pupil from year 7, 8 or 9 to appear on television. The headteacher gives each pupil one ticket. Then she will select the winning ticket at random. The table shows information about the tickets used. Colour of the ticket Numbers used Year 7 red 1 to 80 Year 8 blue 1 to 75 Year 9 yellow 1 to 90 (a) What is the probability that the winning ticket will be blue? 1 mark (b) What is the probability that the winning ticket will show number 39? 1 mark (c) The headteacher selects the winning ticket at random. She says: ‘The winning ticket number is 39’. What is the probability that this winning ticket is blue? 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Journeys 9. The diagram shows the distance between my home, H, and two towns, A and B. It also shows information about journey times. (a) What is the average speed of the journey from my home to town A? 1 mark (b) What is the average speed of the journey from my home to town B? 1 mark (c) I drive from town A to my home and then to town B. The journey time is 30 minutes. What is my average speed? Show your working. 2 marks KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Different ways 10. (a) Pupils started to solve the equation 6 x + 8 = 4 x + 11 in different ways. For each statement below, tick ( ) True or False. 3 marks (b) A different pupil used trial and improvement to solve the equation 6x + 8 = 4 x + 11 Explain why trial and improvement is not a good method to use. 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Locus of points 11. The diagram below shows two points A and B that are 6cm apart. Around each point are six circles of radius 1cm, 2cm, 3cm, 4cm, 5cm and 6cm. Each circle has either A or B as its centre. (a) On the diagram, mark with a cross any points that are 4cm away from A and 4cm away from B. 1 mark (b) Now draw the locus of all points that are the same distance from A as they are from B. 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Evens or odds 12. For each part of the question, tick ( ) the statement that is true. When x is even, ( x – 2 ) 2 is even (a) When x is even, ( x – 2 ) 2 is odd Show how you know it is true for all even values of x 1 mark (b) When x is even, ( x – 1 )( x + 1 ) is even When x is even, ( x – 1 )( x + 1 ) is odd Show how you know it is true for all even values of x 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Straight line 13. Look at the graph. (a) The gradient of the line through R and Q is 0.5 Show how you can work this out from the graph. 1 mark (b) What is the equation of the straight line through R and Q? 2 marks (c) Write the equation of a line that is parallel to the straight line through R and Q. 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Theme park 14. Tom did a survey of the age distribution of people at a theme park. He asked 160 people. The cumulative frequency graph shows his results. 160 140 120 100 Cumulative frequency 80 60 40 20 0 0 10 20 30 40 50 60 70 80 Age (years) KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk (a) Use the graph to estimate the median age of people at the theme park. median = years 1 mark (b) Use the graph to estimate the interquartile range of the age of people at the theme park. Show your method on the graph. interquartile range = years 2 marks (c) Tom did a similar survey at a flower show. Results: The median age was 47 years. The interquartile range was 29 years. Compare the age distribution of the people at the flower show with that of the people at the theme park. 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Inequality 15. (a) Solve these inequalities. Show your working. 2(2y + 7) < 2 3 2 marks 4(7 – 2y ) >1 12 2 marks (b) Kate is solving the inequality y 2 < 9 She says: ‘ y 2 < 9 whenever y is less than 3’ Kate is not correct. Explain why. 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Angle proof 16. The diagram shows 3 points, A, B and C, on a circle, centre O. AC is a diameter of the circle. (a) Angle BAO is x ° and angle BCO is y ° Explain why angle ABO must be x ° and angle CBO must be y ° 1 mark (b) Use algebra to show that angle ABC must be 90 ° 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Computer game 17. A girl plays the same computer game lots of times. The computer scores each game using 1 for win, 0 for lose. After each game, the computer calculates her overall mean score. The graph shows the results for the first 20 games. (a) For each of the first 3 games, write W if she won or L if she lost. first game second game third game 1 mark (b) What percentage of the 20 games did the girl win? % 1 mark KS3/03/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk The graph below shows the girl’s results for the first 100 games. (c) She is going to play the game again. Estimate the probability that she will win. 1 mark (d) Suppose for the 101st to 120th games, the girl were to lose each game. What would the graph look like up to the 120th game? Show your answer on the graph below. 1 mark KS3/03/Ma/Tier 6–8/P1 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 2003 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk 254653
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