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Ma KEY STAGE 3 Mathematics test Paper 1 Calculator not allowed TIER 5–7 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, ruler, a pair of compasses, tracing paper and mirror (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. For marker’s use only QCA/03/968 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 5–7/P1 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Car parking 1. A car park shows this sign. Complete the table to show all the different ways of paying exactly 70p. Number of 10p coins Number of 20p coins Number of 50p coins 7 0 0 2 marks KS3/03/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Patterns 2. I have a square grid and two rectangles. I make a pattern with the grid and the two rectangles: The pattern has no lines of symmetry. (a) Put both rectangles on the grid to make a pattern with only one line of symmetry. You must shade the rectangles. 1 mark KS3/03/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk Patterns cont, Simplifying (b) Put both rectangles on the grid to make a pattern with rotation symmetry of order 2 You must shade the rectangles. 1 mark 3. Simplify these expressions. 5k + 7 + 3k = 1 mark k+1+k+4= 1 mark KS3/03/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Thinking fractions 4. Fill in the missing numbers. 1 2 3 4 of 1 3 KS3/03/Ma/Tier 5–7/P1 of of Sourced from SATs-Papers.co.uk 20 100 60 1 4 = 6 of 2 3 = of 1 2 = of 1 mark 1 mark 1 mark http://www.SATs-Papers.co.uk Moving C 5. On this square grid, A and B must not move. When C is at ( 6, 6 ), triangle ABC is isosceles. (a) C moves so that triangle ABC is still isosceles. Where could C have moved to? Write the coordinates of its new position. ( , ) 1 mark (b) Then C moves so that triangle ABC is isosceles and right-angled. Where could C have moved to? Write the coordinates of its new position. ( , ) 1 mark KS3/03/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Shoe sizes 6. (a) There are four people in Sita’s family. Their shoe sizes are 4, 5, 7 and 10 What is the median shoe size in Sita’s family? 1 mark (b) There are three people in John’s family. The range of their shoe sizes is 4 Two people in the family wear shoe size 6 John’s shoe size is not 6 and it is not 10 What is John’s shoe size? 1 mark KS3/03/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk Construction 7. Use compasses to construct a triangle that has sides 8cm, 6cm and 7cm. Leave in your construction lines. One side of the triangle is drawn for you. 2 marks KS3/03/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Travel to work 8. (a) I pay £16.20 to travel to work each week. I work for 45 weeks each year. How much do I pay to travel to work each year? Show your working. £ 2 marks (b) I could buy one season ticket that would let me travel for all 45 weeks. It would cost £630 How much is that per week? £ 1 mark KS3/03/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Solving 9. Solve these equations. Show your working. 8 k – 1 = 15 k= 1 mark 2 m + 5 = 10 m= 1 mark 3 t + 4 = t + 13 t= 2 marks 2 (3 n + 7) = 8 n= 1 mark KS3/03/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Shapes 10. 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 5–7/P1 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Mixed numbers 11. (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 5–7/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Areas algebraically 12. (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 5–7/P1 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Arranging 13. 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 5–7/P1 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Lines on a square 14. 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 5–7/P1 Sourced from SATs-Papers.co.uk 16 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 5–7/P1 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Scatter graphs 15. 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 5–7/P1 Sourced from SATs-Papers.co.uk 18 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 5–7/P1 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Winning ticket 16. 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 5–7/P1 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Journeys 17. 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 5–7/P1 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Different ways 18. (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 5–7/P1 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Locus of points 19. 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 5–7/P1 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk PLEASE TURN OVER Evens or odds 20. 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 5–7/P1 Sourced from SATs-Papers.co.uk END OF TEST © Qualifications and Curriculum Authority 2003 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk 254650