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Mathematics test Ma KEY STAGE 3 Paper 1 Calculator not allowed TIER 5–7 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 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 3. ■ 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/04/1199 Sourced from SATs-Papers.co.uk Total marks http://www.SATs-Papers.co.uk BLANK PAGE KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 2 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 KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Points of intersection 1. The diagram shows two straight lines. Where the lines cross is called a point of intersection. (a) Draw three straight lines that have only one point of intersection. 1 mark (b) Three straight lines have exactly two points of intersection. Complete the sentence below. Two of the lines must be 1 mark KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk Daylight hours 2. The graph shows at what time the sun rises and sets in the American town of Anchorage. The day with the most hours of daylight is called the longest day. Fill in the gaps below, using the information from the graph. The longest day is in the month of On this day, there are about hours of daylight. The shortest day is in the month of On this day, there are about hours of daylight. 3 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Plasters 3. I buy a box of different size plasters. Assume each plaster is equally likely to be the top plaster inside the box. Altogether there are 35 plasters. I take the top plaster from inside the box. (a) What is the probability that the plaster is of size D? 1 mark (b) What is the probability that the plaster is of size A? 1 mark (c) What is the probability that the plaster is not of size A? 1 mark KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Calculators 4. You can buy a new calculator for £1.25 In 1979 the same type of calculator cost 22 times as much as it costs now. How much did the same type of calculator cost in 1979? Show your working. £ 2 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Delivery charges 5. A company sells books using the internet. The graph shows their delivery charges. KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk (a) Use the graph to fill in the values in this table. Number of books Delivery charge (£) 8 9 1 mark (b) For every extra book you buy, how much more must you pay for delivery? p 1 mark (c) A second company sells books using the internet. Its delivery charge is £1.00 per book. On the graph opposite, draw a line to show this information. 1 mark (d) Complete the sentence. Delivery is cheaper with the first company if you buy at least books. 1 mark KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Magic square 6. One way to make a magic square is to substitute numbers into this algebra grid. (a) Complete the magic square below using the values a = 10 b = 3 c = 5 2 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk (b) Here is the algebra grid again. I use different values for a, b and c to complete the magic square. What values for a, b and c did I use? a = KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk b = c = 11 http://www.SATs-Papers.co.uk 2 marks Fractions 7. Look at this diagram. The diagram can help you work out some fraction calculations. Calculate 1 + 12 = 1 3 + 1 4 = 1 3 KS3/04/Ma/Tier 5–7/P1 1 4 – 1 6 = Sourced from SATs-Papers.co.uk 1 mark 1 mark 1 mark 12 http://www.SATs-Papers.co.uk Functions 8. (a) A function maps the number n to the number n + 2 Complete the missing values. 1 mark (b) A different function maps the number n to the number 2n Complete the missing values. 1 mark (c) Many different functions can map the number 25 to the number 5 Complete the tables by writing two different functions. 2 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Cuboids 9. You can make only four different cuboids with 16 cubes. (a) Which of the cuboids A and D has the larger surface area? Tick ( ) the correct answer below. Cuboid A Cuboid D Both the same Explain how you know. 1 mark KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk (b) Which cuboid has the largest volume? Tick ( ) the correct answer below. Cuboid A Cuboid B Cuboid C Cuboid D 1 mark All the same (c) How many of cuboid D make a cube of dimensions 4 t 4 t 4? 1 mark (d) You can make only six different cuboids with 24 cubes. Complete the table to show the dimensions. Two have been done for you. 3 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Shading 10. The shapes below are drawn on square grids. (a) Is shape A an equilateral triangle? Tick ( ) Yes or No. Yes No Explain your answer. 1 mark (b) Is shape B a kite? Yes No Explain your answer. 1 mark (c) Is shape C a square? Yes No Explain your answer. 1 mark KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Sums and products 11. Write the missing numbers in the table. The first row is done for you. First number Second number Sum of first and second numbers Product of first and second numbers 3 6 9 18 5 –3 1 mark –8 KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk –5 17 1 mark http://www.SATs-Papers.co.uk Thinking fractions 12. (a) Calculate 5 t 3 6 5 Show your working. Write your answer as a fraction in its simplest form. 2 marks (b) Four-fifths of the members of a club are female. Three-quarters of these females are over 20 years old. What fraction of the members of the club are females over 20 years old? Show your working. 2 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Rearrange 13. (a) Rearrange the equations. b + 4 = a b = 4d = c d = 1 mark 1 mark m – 3 = 4k m = 1 mark (b) Rearrange the equation to make t the subject. Show your working. 5( 2 + t ) = w t = 2 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Journey 14. Two people, A and B, travel from X to Y along different routes. Their journeys take the same amount of time. B’s route A’s route B travels at an average speed of 40 km/h. What is A’s average speed? Show your working. km/h 2 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Factors again 15. (a) Ring the expression below that is the same as y 2 + 8y + 12 ( y + 3)( y + 4 ) ( y + 7)( y + 1) ( y + 2 )( y + 6 ) ( y + 1 )( y + 12 ) ( y + 3)( y + 5 ) 1 mark (b) Multiply out the expression ( y + 9 )( y + 2 ) Write your answer as simply as possible. 2 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Rodents 16. The scatter graph shows the average body length and average foot length of different species of rodents. (a) What does the scatter graph tell you about the type of correlation between the body length and foot length for these rodents? 1 mark (b) Draw a line of best fit on the scatter graph. 1 mark (c) If body length increased by 50mm, by approximately how many millimetres would you expect foot length to increase? Ring the correct value below. 2 7 15 50 275 1 mark KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Rodents cont, Two dice (d) An animal has a body length of 228mm, and foot length of 22mm. Is this animal likely to be one of these species of rodents? Tick ( ) Yes or No. Yes No Explain your answer. 1 mark 17. I have two fair 4-sided dice. One dice is numbered 2, 4, 6 and 8 The other is numbered 2, 3, 4 and 5 I throw both dice and add the scores. What is the probability that the total is even? You must show working to explain your answer. 2 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Juice 18. The table shows a recipe for a fruit drink. Type of juice Amount Orange 1 litre 2 Cranberry 1 litre 3 Grape 1 litre 6 Total I want to make 1 1 litre 1 litres of the same drink. 2 Complete the table below to show how much of each type of juice to use. Show your working. Type of juice Amount Orange litre Cranberry litre Grape litre Total KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 24 1 1 2 litres http://www.SATs-Papers.co.uk 2 marks Triangles 19. Think about triangles that have a perimeter of 15cm, two or more equal sides, and each side a whole number of centimetres. Prove that there are only four of these triangles. You do not need to construct the triangles. 3 marks KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk END OF TEST KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 26 http://www.SATs-Papers.co.uk BLANK PAGE KS3/04/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk 27 http://www.SATs-Papers.co.uk 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 259573