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Ma KEY STAGE 3 Mathematics test Paper 1 TIER Calculator not allowed 4–6 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, ruler, mirror 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/04/1197 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 4–6/P1 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Coins 1. There are seven different ways to make 8p with coins. Complete the table to show the seven ways to make 8p. Two have been done for you. Number of 5p coins Number of 2p coins Number of 1p coins 0 0 8 0 1 6 3 marks KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Matchboxes 2. The diagram shows a matchbox. Its length is 5.3cm. Its width is 3.6cm. Its height is 1.5cm. Not drawn accurately (a) I join two matchboxes in different ways. Fill in the missing values. 1 mark 1 mark 1 mark KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk (b) I start joining matchboxes like this: How many matchboxes will be in the pile when its height is 12 cm? 1 mark KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Folding shapes 3. When you fold a square along a diagonal, you see a triangle. (a) What do you see when you fold a rectangle along a diagonal? Ring the correct answer below. 1 mark KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk (b) Two different shapes are folded along a line of symmetry. For each shape, the dashed line is the fold line. For each shape, draw what the shape looked like before it was folded. 1 mark 1 mark Isometric grid KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Television, Measuring 4. I buy a widescreen television costing £1290 I pay £ 900 now, then I pay the rest of the money in 3 equal payments. How much is each payment? Show your working. £ 2 marks 5. Steve needs to put 1 litre of water in a bucket. He has a 500ml jug. Explain how he can measure 1 litre of water. 1 mark KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk Grid shapes 6. The diagram shows some shapes on a 10 by 6 square grid. (a) Which two shapes have the same area as shape A? 1 mark (b) Which two shapes have the same perimeter as shape A? 1 mark (c) How many of shape C would you need to cover a 10 by 6 square grid? 1 mark KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Club 7. The bar charts show how many pupils went to a maths club. KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Is each statement below true or false, or is there not enough information to tell? Tick ( ) the correct box. (a) In each of these weeks, the day with the most pupils was Monday. True False Not enough information Explain your answer. 1 mark (b) In each of these weeks, the same number of pupils went to the club on Friday. True False Not enough information Explain your answer. 1 mark (c) In each of these weeks, the same pupils went to the club on Friday. True False Not enough information Explain your answer. 1 mark KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Points of intersection 8. 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) Now draw three straight lines that have three points of intersection. 1 mark (c) 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 4–6/P1 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Daylight hours 9. 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 4–6/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Plasters 10. 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 4–6/P1 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk Calculators 11. 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 4–6/P1 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Delivery charges 12. A company sells books using the internet. The graph shows their delivery charges. KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 16 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 4–6/P1 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Magic square 13. 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 4–6/P1 Sourced from SATs-Papers.co.uk 18 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 4–6/P1 Sourced from SATs-Papers.co.uk b = c = 19 http://www.SATs-Papers.co.uk 2 marks Fractions 14. Look at this diagram. The diagram can help you work out some fraction calculations. Calculate 1 + 12 + 1 4 = 1 3 Sourced from SATs-Papers.co.uk = 1 3 KS3/04/Ma/Tier 4–6/P1 1 4 – 1 6 = 1 mark 1 mark 1 mark 20 http://www.SATs-Papers.co.uk Functions 15. (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 4–6/P1 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Cuboids 16. 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 4–6/P1 Sourced from SATs-Papers.co.uk 22 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 4–6/P1 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Shading 17. 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 4–6/P1 Sourced from SATs-Papers.co.uk 24 http://www.SATs-Papers.co.uk Sums and products, Thinking fractions 18. 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 19. –5 1 mark Calculate 5 t 3 6 5 Show your working. Write your answer as a fraction in its simplest form. 2 marks KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Rearrange 20. Rearrange the equations. b + 4 = a b = 4d = c d = 1 mark 1 mark m – 3 = 4k m = 1 mark KS3/04/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 26 http://www.SATs-Papers.co.uk END OF TEST KS3/04/Ma/Tier 4–6/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 259571