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Ma KEY STAGE 3 Mathematics test Paper 1 TIER Calculator not allowed 5–7 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 ■ ■ You must not use a calculator for any question in this test. ■ You will need: pen, pencil, rubber, ruler, a pair of compasses 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. ■ QCA/05/1433 The test is 1 hour long. Ask your teacher if you are not sure what to do. For marker’s use only 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 5 –7/ P1 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Percentages 1. (a) Complete the sentence. out of 10 is the same as 70% 1 mark (b) Complete the sentence. out of is the same as 5% 1 mark Now complete the sentence using different numbers. out of is the same as 5% 1 mark KS3/05/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Rotating 2. 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 5 –7/ P1 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk What is my number?, Completing 3. 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 4. 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 5–7/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Mean and median 5. (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 5 –7/ P1 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Angles 6. 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 5–7/P1 Sourced from SATs-Papers.co.uk ° ° b = c = ° 7 http://www.SATs-Papers.co.uk 1 mark Equations, Long multiplication 7. Solve these equations. 3y + 1 = 16 y = 1 mark 18 = 4k + 6 k = 1 mark 8. Work out 374 t 23 2 marks KS3/05/Ma/Tier 5 –7/ P1 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk Midpoint 9. (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 5–7/P1 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Square cut 10. The diagram shows a square. Two straight lines cut the square into four rectangles. The area of one of the rectangles is shown. 3 cm 12cm2 2 cm A Not drawn accurately Work out the area of the rectangle marked A. cm2 2 marks KS3/05/Ma/Tier 5 –7/ P1 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Making zero 11. (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 5–7/P1 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Cuboid 12. 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 5 –7/ P1 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Dividing fractions, Solving an equation 13. How many eighths are there in one quarter? Now work out 1 3 ÷ 4 8 3 marks 14. Solve this equation. 75 + 2t = 100 – 2t t= 2 marks KS3/05/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Angle p 15. 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 5 –7/ P1 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Speed bumps 16. 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 (a) 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 (b) Show that the median speed fell by 10 mph. 1 mark KS3/05/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Straight line graph 17. The graph shows the straight line with equation y = 3x – 4 4 –4 0 4 –4 –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 (c) Is the point ( –10, –34 ) on the line y = 3x – 4? Yes No Show how you know. 1 mark KS3/05/Ma/Tier 5 –7/ P1 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk 64 18. Here is an equation. y x = 64 Give four different pairs of values that satisfy this equation. First pair x= y= Second pair x= y= Third pair x= y= Fourth pair x= y= 3 marks KS3/05/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Sixths 19. A teacher said to a pupil: To the nearest per cent, 1 is 17% 6 The pupil said: So, to the nearest per cent, 2 must be 34% 6 Show that the pupil is wrong. 1 mark KS3/05/Ma/Tier 5 –7/ P1 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Tyres 20. Car tyres are checked for safety by measuring the tread. The tread on a tyre and the distance travelled by that tyre were recorded for a sample of tyres. The scatter graph shows the results. 6 5 4 Tread (mm) 3 2 1 0 0 10 000 20 000 Distance (km) 30 000 40 000 Tyres with a tread of less than 1.6 mm are illegal. Suppose the government changes this rule to less than 2.5 mm. (a) How many of these tyres would now be illegal? 1 mark (b) About how many fewer kilometres would you expect a tyre to last before it was illegal? 1 mark KS3/05/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Which triangles? 21. (a) In which triangle below does a2 + b2 = c2 ? Tick ( ) the correct triangle. For the other triangle, write an equation linking a, b and c 1 mark (b) In which triangle below does a2 + b2 = c2 ? Tick ( ) the correct triangle. Not drawn accurately For the other triangle, explain why a2 + b 2 does not equal c2 1 mark KS3/05/Ma/Tier 5 –7/ P1 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Sweet peas 22. Meg and Ravi buy sweet pea seeds and grow them in identical conditions. Meg’s results: Number of packets Number of seeds in each packet 5 20 Number of seeds that germinate from each packet 18, 17, 17, 18, 19 Ravi’s results: Number of packets Number of seeds in each packet Total number of seeds that germinate 10 20 170 (a) Using Meg’s results and Ravi’s results, calculate two different estimates of the probability that a sweet pea seed will germinate. Using Meg’s results: 1 mark Using Ravi’s results: 1 mark (b) Whose results are likely to give the better estimate of the probability? Meg’s Ravi’s Explain why. 1 mark KS3/05/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk How many digits? 23. A three-digit number is multiplied by a two-digit number. How many digits could the answer have? Write the minimum number and the maximum number of digits that the answer could have. You must show your working. minimum number of digits maximum number of digits 2 marks KS3/05/Ma/Tier 5 –7/ P1 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Simultaneous 24. Solve these simultaneous equations using an algebraic method. 4 x + 3y = 21 2x + y = 8 You must show your working. x= y= 3 marks PLEASE TURN OVER KS3/05/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Angle bisector 25. In the diagram, lines AB and AC are straight lines. Using compasses and a straight edge, construct the angle bisector of angle BAC. You must leave in your construction lines. A C B 2 marks END OF TEST © Qualifications and Curriculum Authority 2005 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA KS3/05/Ma/Tier 5 –7/ P1 Sourced from SATs-Papers.co.uk 24 265282 http://www.SATs-Papers.co.uk