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Mathematics test Ma KEY STAGE 3 Paper 1 Calculator not allowed TIER 4–6 2005 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 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. For marker’s use only QCA/05/1431 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 KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Number lines 1. Write the missing numbers on the number lines. +3 –8 1 mark +6 +6 –3 2 marks KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Shapes 2. Look at the diagrams on the centimetre square grid. Work out the area that is shaded on each diagram. cm2 cm2 cm2 2 marks KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk Computation 3. (a) Add together 3.7 and 6.5 1 mark (b) Subtract 5.7 from 15.2 1 mark (c) Multiply 254 by 5 1 mark (d) Divide 342 by 6 1 mark KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Scales 4. (a) I weigh a melon. 0 0 200 400 600 800 1000 1200 1400 200 400 600 800 1600 1000 1200 grams 1400 1600 1800 1800 2000 2000 grams Then I weigh an apple and the melon. 0 0 200 400 600 800 1000 1200 1400 200 400 600 1600 800 1000 1200 grams 1400 1600 1800 1800 2000 2000 grams Write the missing numbers in the sentences below. The melon weighs grams. 1 mark The apple weighs grams. 1 mark (b) How many grams are in one kilogram? Put a ring round the correct number below. 1 10 100 1000 10 000 1 mark KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Range of ages 5. (a) There are two children in the Smith family. The range of their ages is exactly 7 years. What could the ages of the two children be? Give an example. and 1 mark (b) There are two children in the Patel family. They are twins of the same age. What is the range of their ages? years 1 mark KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Placing fractions 6. Here are four fractions. 3 4 1 8 1 3 3 5 Look at the number line below. Write each fraction in the correct box. 0 0.5 1 2 marks KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk Survey results 7. (a) Jackie asked 27 people: ‘Do you like school dinners?’ The bar chart shows her results for ‘Yes’ and ‘No’. Complete the bar chart to show her result for ‘Don’t know’. 14 12 10 Number of people 8 6 4 2 1 mark 0 Yes No Don't know (b) This pictogram also shows her results for ‘Yes’ and ‘No’. Complete the pictogram to show her result for ‘Don’t know’. Yes No Don’t know KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 1 mark 9 http://www.SATs-Papers.co.uk Percentages 8. (a) Complete the sentences. out of 10 is the same as 70% 10 out of 20 is the same as % 1 mark 1 mark (b) Complete the sentence. out of is the same as 5% 1 mark Now complete the sentence using different numbers. out of KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk is the same as 5% 10 http://www.SATs-Papers.co.uk 1 mark Rotating 9. The shapes below are drawn on square grids. The diagrams show a rectangle that is rotated, then rotated again. The centre of rotation is marked Rotate another 90°clockwise Rotate 90°clockwise Complete the diagrams below to show the triangle when it is rotated, then rotated again. The centre of rotation is marked Rotate another 90°clockwise Rotate 90°clockwise 2 marks KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk What is my number?, Completing 10. I am thinking of a number. My number multiplied by 15 is 315 My number multiplied by 17 is 357 What is my number? 2 marks 11. Complete the statements below. When x is 8 , 4x is 1 mark When x is , 4x is 48 1 mark When x is 8 , is 48 1 mark KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Mean and median 12. (a) Look at these three numbers. 9 11 10 Show that the mean of the three numbers is 10 1 mark Explain why the median of the three numbers is 10 1 mark (b) Four numbers have a mean of 10 and a median of 10, but none of the numbers is 10 What could the four numbers be? Give an example. 1 mark KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Angles 13. The diagram shows triangle PQR. R Not drawn accurately 30° b a c 40° P Q Work out the sizes of angles a, b and c 1 mark 1 mark a = KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk ° ° b = c = ° 14 http://www.SATs-Papers.co.uk 1 mark Equations, Long multiplication 14. Solve these equations. 3y + 1 = 16 y = 1 mark 18 = 4k + 6 k = 1 mark 15. Work out 374 t 23 2 marks KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Midpoint 16. (a) P is the midpoint of line AB. 120 A P B What are the coordinates of point P? 0 P is ( 120 , ) 1 mark (b) Q is the midpoint of line MN. The coordinates of Q are ( 30, 50 ) M Q ( 30, 50 ) N What are the coordinates of points M and N? 0 M is ( , ) 1 mark N is ( , ) 1 mark KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Square cut 17. The diagram shows a square. Two straight lines cut the square into four rectangles. The area of one of the rectangles is shown. 3cm 12cm2 2cm A Not drawn accurately Work out the area of the rectangle marked A. cm2 2 marks KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Making zero 18. (a) Look at this information. Two numbers multiply to make zero. One of the statements below is true. Tick ( ) the true statement. Both numbers must be zero. At least one number must be zero. Exactly one number must be zero. 1 mark Neither number can be zero. (b) Now look at this information. Two numbers add to make zero. If one number is zero, what is the other number? 1 mark If neither number is zero, give an example of what the numbers could be. and 1 mark KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Cuboid 19. I join six cubes face to face to make each 3-D shape below. Isometric grid Then I join the 3-D shapes to make a cuboid. Draw this cuboid on the grid below. 2 marks Isometric grid KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Dividing fractions, Solving an equation 20. How many eighths are there in one quarter? Now work out 1 3 ÷ 4 8 3 marks 21. Solve this equation. 75 + 2t = 100 – 2t t= 2 marks KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Angle p 22. This shape has been made from two congruent isosceles triangles. 35˚ Not drawn accurately 35˚ What is the size of angle p? p= ° 2 marks KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Speed bumps 23. Bumps are built on a road to slow cars down. The stem-and-leaf diagrams show the speed of 15 cars before and after the bumps were built. Key: 2 Before 3 means 23 mph After 2 7 3 0 2 4 3 5 6 8 9 4 1 3 4 4 4 6 4 6 6 7 8 8 0 0 0 1 2 3 8 4 3 2 3 2 2 5 9 4 4 4 Use the diagrams to write the missing numbers in these sentences. Before the bumps: The maximum speed was mph, and cars went at more than 30 mph. After the bumps: The maximum speed was mph, and cars went at more than 30 mph. 2 marks KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Straight line graph 24. y The graph shows the straight line with equation y = 3x – 4 4 –4 0 4 x –4 (a) A point on the line y = 3x – 4 has an x -coordinate of 50 What is the y -coordinate of this point? 1 mark (b) A point on the line y = 3x – 4 has a y -coordinate of 50 What is the x -coordinate of this point? 1 mark KS3/05/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk END OF TEST © Qualifications and Curriculum Authority 2005 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 265280