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Ma KEY STAGE 3 Mathematics test Paper 1 TIER Calculator not allowed 6–8 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 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/04/1201 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 KS3/04/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Functions 1. (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 6–8/P1 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Cuboids 2. 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 6–8/P1 Sourced from SATs-Papers.co.uk 4 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 6–8/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Shading 3. 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 6–8/P1 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk Sums and products 4. 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 6–8/P1 Sourced from SATs-Papers.co.uk –5 7 1 mark http://www.SATs-Papers.co.uk Thinking fractions 5. (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 6–8/P1 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk Rearrange 6. (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 6–8/P1 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Journey 7. 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 6–8/P1 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Factors again 8. (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 6–8/P1 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Rodents 9. 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 6–8/P1 Sourced from SATs-Papers.co.uk 12 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 10. 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 6–8/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Juice 11. 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 6–8/P1 Sourced from SATs-Papers.co.uk 14 1 1 2 litres http://www.SATs-Papers.co.uk 2 marks Triangles 12. 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 6–8/P1 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Births 13. The table shows data about births in the UK. Year Number of births 1910 1.05 t 106 1920 1.13 t 106 1930 7.69 t 105 1940 7.02 t 105 1950 8.18 t 105 1960 9.18 t 105 1970 9.04 t 105 1980 7.54 t 105 1990 7.99 t 105 (a) In which year was the number of births the highest? 1 mark (b) How many more births were there in 1990 than in 1980? Show your working and write your answer in standard form. 2 marks KS3/04/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Factors 14. (a) Look at these equations. 48 = 3 t 2 a 56 = 7 t 2 b What are the values of a and b? a = b = 1 mark (b) 48 t 56 = 3 t 7 t 2 c What is the value of c? c = 1 mark KS3/04/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Population 15. The chart shows the ages of the world’s population in 1998. It also shows a prediction of the ages of the world’s population in 2050. (a) Use the information in the chart to decide if the statement below is true or false or if there is not enough information to tell. The percentage of the population that is aged under 20 is expected to be about the same in 2050 as it was in 1998. True False Not enough information Explain your answer. 1 mark KS3/04/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk (b) Approximately, what is the expected percentage increase from 1998 to 2050 in the total world population? % 1 mark (c) Approximately, what is the expected percentage increase from 1998 to 2050 in the number of people who are aged 60 or over? % 1 mark (d) Using your answers to part (b) and part (c), write a sentence about the expected change in the ages of the world’s population from 1998 to 2050. 1 mark KS3/04/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Box plots 16. A pupil recorded the heights of all the girls in year 7 She summarised her results, then drew this box plot. The pupil compared the heights of year 7 boys with year 7 girls. the shortest boy was the same height as the shortest girl; the range of boys’ heights was greater than the range of girls’ heights; the inter-quartile range of boys’ heights was smaller than the inter-quartile range of girls’ heights. (a) Draw what the box plot for boys could look like. 2 marks KS3/04/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk There are 120 girls in year 9 The cumulative frequency diagram shows information about their heights. (b) Compare the heights of year 9 girls with year 7 girls. 3 marks KS3/04/Ma/Tier 6–8/P1 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Graphs 17. Match each graph to the correct equation. Graph Graph shows the equation y = 6x3 Graph shows the equation y = 6 – x Graph shows the equation y = x2 – 6 Graph KS3/04/Ma/Tier 6–8/P1 shows the equation y = 2x – 6 shows the equation y = Sourced from SATs-Papers.co.uk 22 1 6x http://www.SATs-Papers.co.uk 2 marks Proving 18. I start with any two consecutive integers. I square each of them, then I add the two squares together. Prove that the total must be an odd number. 3 marks KS3/04/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 2004 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk 259575
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