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Ma KEY STAGE 3 Mathematics test Paper 1 Calculator not allowed TIER 3–5 2003 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, a pair of compasses, tracing paper and mirror (optional). ■ 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/03/964 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. KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 2 http://www.SATs-Papers.co.uk Pictogram 1. (a) Jeff asked 30 pupils if they travel to school by bus. 20 pupils said yes. 10 pupils said no. He started to draw a pictogram using the key represents 5 pupils. Complete the pictogram to show Jeff’s results. 1 mark (b) Sue asked 20 pupils which subject they like best. She drew this pictogram but forgot to write the key. How many pupils does represent? pupils 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 3 http://www.SATs-Papers.co.uk Missing numbers 2. Write in the boxes what the missing numbers could be. + + = 15 1 mark t = ÷ = 15 1 mark 15 1 mark t KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk + = 15 1 mark 4 http://www.SATs-Papers.co.uk Scales 3. (a) Look at this scale. What value is the arrow pointing to on the scale? 1 mark (b) Here is a different scale. Draw an arrow ( ) so that it shows the same value as the arrow in part (a). 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Prices 4. Look at these prices. Ruler 30p Pencil 15p Blue pen 35p Green pen 40p Eraser 20p (a) Use the prices to fill in the gaps below. The total cost of two rulers and one pencil. 1 mark The total cost of three blue pens. 1 mark The total cost of one blue pen and 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 6 http://www.SATs-Papers.co.uk (b) There are many different ways to make the total cost 60p. Use the prices to fill in the gaps below. One way is done for you. two rulers The total cost of The total cost of 1 mark The total cost of 1 mark The total cost of 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Clock 5. (a) My wall clock shows this time: Which two of the digital clocks below could be showing the same time as my wall clock? Tick ( ) the correct two. 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk (b) Early in the morning my wall clock shows this time: morning My digital clock shows the same time as my wall clock. Write what time my digital clock is showing. 1 mark (c) In the afternoon my wall clock shows this time: afternoon My digital clock is a 24 hour clock. Now what time is my digital clock showing? 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Calculations 6. (a) What number should you add to 28 to make 100? 1 mark (b) What number should you subtract from 100 to make 78? 1 mark (c) Work out 48 + 49 = 1 mark 78 ÷ 3 = 1 mark 1048 + 208 = 1 mark 4828 – 480 = 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Chains 7. (a) The number chain below is part of a doubling number chain. Fill in the two missing numbers. .................... .................... 1 mark (b) The number chain below is part of a halving number chain. Fill in the two missing numbers. .................... .................... 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Puzzling out 8. A teacher has five number cards. She says: ‘I am going to take a card at random. Each card shows a different positive whole number. It is certain that the card will show a number less than 10 It is impossible that the card will show an even number.’ What numbers are on the cards? 2 marks KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Wind chill 9. When the wind blows it feels colder. The stronger the wind, the colder it feels. Fill in the gaps in the table. The first row is done for you. Wind strength Temperature out of the wind (°C) How much colder it feels in the wind (°C) Moderate breeze –5 7 degrees colder Fresh breeze –8 Temperature it feels in the wind (°C) 11 degrees colder –2 1 mark Strong breeze Gale –4 degrees colder – 20 1 mark 23 degrees colder – 45 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Throwing dice 10. Some pupils throw two fair six-sided dice. Each dice is numbered 1 to 6 One dice is blue. The other dice is red. Anna’s dice show blue 5, red 3 Her total score is 8 The cross on the grid shows her throw. (a) Carl’s total score is 6 What numbers could Carl’s dice show? Put crosses on the grid to show all the different pairs of numbers Carl’s dice could show. 2 marks KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk (b) The pupils play a game. Winning rule: Win a point if the number on the blue dice is the same as the number on the red dice. Put crosses on the grid to show all the different winning throws. 2 marks (c) The pupils play a different game. The grid shows all the different winning throws. Complete the sentence below to show the winning rule. Winning rule: Win a point if the number on the blue dice is 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 15 http://www.SATs-Papers.co.uk Perimeter and area 11. Look at the hexagon and the triangle. Isometric grid (a) Do the hexagon and triangle have the same area? Tick ( ) Yes or No. Yes No Explain your answer. 1 mark (b) Do the hexagon and triangle have the same perimeter? Tick ( ) Yes or No. Yes No Explain your answer. 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk Weighing 12. There are two small tins and one big tin on these scales. The two small tins each have the same mass. The mass of the big tin is 2.6kg. What is the mass of one small tin? Show your working. kg 2 marks KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk Patterns 13. I have a square grid and two rectangles. I make a pattern with the grid and the two rectangles: The pattern has no lines of symmetry. (a) Put both rectangles on the grid to make a pattern with two lines of symmetry. You must shade the rectangles. 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Patterns cont, Simplifying (b) Put both rectangles on the grid to make a pattern with only one line of symmetry. You must shade the rectangles. 1 mark (c) Put both rectangles on the grid to make a pattern with rotation symmetry of order 2 You must shade the rectangles. 1 mark 14. Simplify these expressions. 5k + 7 + 3k = 1 mark k+1+k+4= 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk Car parking 15. A car park shows this sign. Complete the table to show all the different ways of paying exactly 70p. Number of 10p coins Number of 20p coins Number of 50p coins 7 0 0 2 marks KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Thinking fractions 16. Fill in the missing numbers. 1 2 3 4 of 1 3 KS3/03/Ma/Tier 3–5/P1 of of Sourced from SATs-Papers.co.uk 20 100 60 1 4 = 21 of 2 3 = of 1 2 = of 1 mark 1 mark 1 mark http://www.SATs-Papers.co.uk Moving C 17. On this square grid, A and B must not move. When C is at ( 6, 6 ), triangle ABC is isosceles. (a) C moves so that triangle ABC is still isosceles. Where could C have moved to? Write the coordinates of its new position. ( , ) 1 mark (b) Then C moves so that triangle ABC is isosceles and right-angled. Where could C have moved to? Write the coordinates of its new position. ( , ) 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk Shoe sizes 18. (a) There are four people in Sita’s family. Their shoe sizes are 4, 5, 7 and 10 What is the median shoe size in Sita’s family? 1 mark (b) There are three people in John’s family. The range of their shoe sizes is 4 Two people in the family wear shoe size 6 John’s shoe size is not 6 and it is not 10 What is John’s shoe size? 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 23 http://www.SATs-Papers.co.uk Construction 19. Use compasses to construct a triangle that has sides 8cm, 6cm and 7cm. Leave in your construction lines. One side of the triangle is drawn for you. 2 marks KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 24 http://www.SATs-Papers.co.uk Travel to work 20. (a) I pay £16.20 to travel to work each week. I work for 45 weeks each year. How much do I pay to travel to work each year? Show your working. £ 2 marks (b) I could buy one season ticket that would let me travel for all 45 weeks. It would cost £630 How much is that per week? £ 1 mark KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Solving 21. Solve these equations. 8k – 1 = 15 k= 1 mark 2m + 5 = 10 m= KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 26 1 mark http://www.SATs-Papers.co.uk END OF TEST KS3/03/Ma/Tier 3–5/P1 Sourced from SATs-Papers.co.uk 27 http://www.SATs-Papers.co.uk Sourced from SATs-Papers.co.uk © Qualifications and Curriculum Authority 2003 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk 254646