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Mathematics test Ma KEY STAGE 3 Paper 1 Calculator not allowed TIER 4–6 2001 Please read this page, but do not open the booklet until your teacher tells you to start. Write your name and the name of your school in the spaces below. If you have been given a pupil number, write that also. First name Last name School Pupil number Remember I The test is 1 hour long. I You must not use a calculator for any question in this test. I You will need: pen, pencil, rubber, ruler, tracing paper and mirror (optional). I Some formulae you might need are on page 3. I This test starts with easier questions. I Try to answer all the questions. I Write all your answers and working on the test paper – do not use any rough paper. I Check your work carefully. I Ask your teacher if you are not sure what to do. For marker’s use only QCA/01/665 Sourced from SATs-Papers.co.uk Total marks http://www.SATs-Papers.co.uk BLANK PAGE KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 4–6 /P1 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 b Area e (a p b) t h 2 height (h) a Prism length Volume e area of cross-section t length KS3/01/Ma/Tierfrom SATs-Papers.co.uk Sourced 4–6 /P1 3 http://www.SATs-Papers.co.uk Computation, What’s the Point? Work out ○ ○ ○ ○ ○ ○ ○ ○ 1 mark ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ e ○ 154 e ○ 723 m 2. 1487 ○ 238 p ○ 1. 1 mark Look at the diagram. (a) The point K is halfway between points B and C What are the coordinates of point K? ○ ○ ) ○ , ○ ( 1 mark (b) Shape ABCD is a rectangle. What are the coordinates of point D? ○ ○ ) ○ , ○ ( 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 4 http://www.SATs-Papers.co.uk Temperature 3. The arrow by this thermometer O shows a temperature of 20 C O C O 20 C O (a) In New York the temperature was –2 C O In Atlanta the temperature was 7 C warmer. What was the temperature in Atlanta? ○ ○ C ○ ○ O ○ ○ ○ ○ ○ ○ ○ 1 mark O (b) In Amsterdam the temperature was 3 C O In Helsinki the temperature was – 8 C How many degrees warmer was it in Amsterdam than in Helsinki? ○ ○ C ○ ○ O ○ ○ ○ ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 5 http://www.SATs-Papers.co.uk Twenty-seven 4. (a) Fill in the missing numbers. e 27 ○ 1 mark ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ of 27 ○ a quarter e ○ of ○ 50% 1 mark ○ (b) Write numbers in each space below to make the calculation correct. ○ ○ 27 ○ ○ ○ ○ ○ ○ ○ 6 e ○ ○ ○ ○ ○ ○ ○ ○ ○ KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk ÷ 1 mark http://www.SATs-Papers.co.uk Clocks 5. My clock shows: The hours and the minutes are both multiples of 3 multiple of 3 multiple of 3 (a) Write a different time when the hours and the minutes are both multiples of 3 ○ ○ ○ ○ (b) 1 mark multiple of 3 multiple of 3 Later, my clock shows: How many minutes will it be before the hours and the minutes are both multiples of 6? ○ ○ ○ minutes ○ ○ ○ ○ ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 7 http://www.SATs-Papers.co.uk Folding and Cutting 6. (a) I start with a rectangle of paper. I fold it in half, then I cut out three shapes. Then I unfold my paper. Circle the diagram below that shows what my paper looks like now. ○ ○ ○ ○ 1 mark (b) I start again with a different rectangle of paper. I fold it in half, then in half again, then I cut out two shapes. Then I unfold my paper. Circle the diagram below that shows what my paper looks like now. ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 8 http://www.SATs-Papers.co.uk (c) I start with a square of paper. I fold it in half, then in half again, then I cut out one shape. Then I unfold my paper. Circle the diagram below that shows what my paper looks like now. ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 9 http://www.SATs-Papers.co.uk Motorway 7. The diagram shows how many miles there are between junctions on a motorway. junction 6 junction 5 junction 4 22 miles 3 miles 15 miles junction 3 junction 2 6 miles 4 ? miles ○ ○ ○ ○ ○ ○ ○ to ○ 2 ○ (a) How many miles is it from ○ junction 1 7 miles ○ 1 mark 1 ? ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ (b) Which junction is 31 miles from ○ 1 mark (c) Mr Patel uses the motorway. He drives from 2 to 3 and back again from 3 to 2 He does this every day for five days. How many miles does he drive on the motorway altogether? ○ ○ ○ ○ miles ○ ○ ○ ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 10 http://www.SATs-Papers.co.uk Using Brackets 8. (a) Write the answers. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 4 p (2 t 3) e ○ (4 p 2) t 3 e 1 mark (b) Work out the answer to (2 p 4) t (6 p 3 p 1) ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark Put brackets in the calculation to make the answer 50 ○ ○ 4 p 5 p 1 t 5 ○ (c) ○ 1 mark (d) Now put brackets in the calculation to make the answer 34 ○ ○ ○ 4 p 5 p 1 t 5 ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 11 http://www.SATs-Papers.co.uk Box 9. The diagram shows a box. Complete the net for the box. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 3 marks KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 12 http://www.SATs-Papers.co.uk Fractions 10. (a) Look at these fractions. 1 2 1 3 5 6 Mark each fraction on the number line. The first one is done for you. ○ ○ ○ ○ 1 mark (b) Fill in the missing numbers in the boxes. 2 e 12 6 1 12 e 2 6 ○ ○ ○ ○ 24 ○ ○ e ○ 1 ○ 2 marks KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 13 http://www.SATs-Papers.co.uk Crisps 11. Mark and Kate each buy a family pack of crisps. Each family pack contains ten bags of crisps. The table shows how many bags of each flavour are in each family pack. flavour number of bags plain 5 vinegar 2 chicken 2 cheese 1 (a) Mark is going to take a bag of crisps at random from his family pack. Complete these sentences. 1 ○ ○ ○ 1 mark ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ The probability that the flavour will be cheese is is 2 ○ The probability that the flavour will be ○ 1 mark (b) Kate ate two bags of plain crisps from her family pack of 10 bags. Now she is going to take a bag at random from the bags that are left. What is the probability that the flavour will be cheese? ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 14 http://www.SATs-Papers.co.uk (c) A shop sells 12 bags of crisps in a large pack. I am going to take a bag at random from the large pack. The table below shows the probability of getting each flavour. Use the probabilities to work out how many bags of each flavour are in this large pack. 7 12 1 4 1 6 0 ○ 15 ○ KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk ○ cheese ○ chicken ○ vinegar ○ plain number of bags ○ probability ○ flavour 2 marks http://www.SATs-Papers.co.uk Sunshine 12. The diagrams show the number of hours of sunshine in two different months. Number of hours of sunshine in month A 20 15 Number of days 10 5 less than 4 4 to 8 more than 8 Hours of sunshine Number of hours of sunshine in month B Key: number of days with less than 4 hours number of days with 4 to 8 hours number of days with more than 8 hours KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 16 http://www.SATs-Papers.co.uk (a) How many days are there in month A? Tick () the correct box. not possible to tell ○ 31 ○ 30 ○ 29 ○ 28 1 mark (b) How many days are there in month B? Tick () the correct box. not possible to tell ○ 31 ○ 30 ○ 29 ○ 28 1 mark (c) Which month had more hours of sunshine? Tick () the correct box. month A month B Explain how you know. ○ ○ ○ KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 17 http://www.SATs-Papers.co.uk ○ 1 mark Shapes 13. (a) What fraction of this shape is shaded? Write your fraction as simply as possible. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark (b) What percentage of this shape is shaded? ○ ○ ○ % ○ ○ ○ ○ ○ ○ ○ 1 mark (c) Which shape has the greater percentage shaded? Tick () the correct box. Shape A Shape B Shape A Both the same Explain how you know. Shape B ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 18 http://www.SATs-Papers.co.uk Trip 14. (a) A football club is planning a trip. The club hires 234 coaches. Each coach holds 52 passengers. How many passengers is that altogether? Show your working. ○ ○ ○ ○ ○ ○ ○ passengers ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 2 marks (b) The club wants to put one first aid kit into each of the 234 coaches. These first aid kits are sold in boxes of 18 How many boxes does the club need? boxes ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 19 http://www.SATs-Papers.co.uk BLANK PAGE KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 20 http://www.SATs-Papers.co.uk Glasses 15. There are 60 pupils in a school. 6 of these pupils wear glasses. (a) The pie chart is not drawn accurately. What should the angles be? Show your working. ○ ○ ○ ○ ○ O ○ ○ ○ ○ ○ ○ ○ ○ ○ and ○ O ○ ○ ○ ○ ○ ○ ○ 2 marks (b) Exactly half of the 60 pupils in the school are boys. From this information, what percentage of boys in this school wear glasses? Tick () the correct box below. 10% 50% not possible to tell ○ 20% ○ 6% ○ 5% ○ 1 mark KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 21 http://www.SATs-Papers.co.uk Bags 16. Ali, Barry and Cindy each have a bag of counters. They do not know how many counters are in each bag. They know that Barry has two more counters than Ali. Cindy has four times as many counters as Ali. (a) Ali calls the number of counters in her bag a Write expressions using a to show the number of counters in Barry’s bag and in Cindy’s bag. Ali’s bag Barry’s bag Cindy’s bag a ○ ○ ○ ○ 1 mark (b) Barry calls the number of counters in his bag b Write expressions using b to show the number of counters in Ali’s bag and in Cindy’s bag. Cindy’s bag ○ ○ ○ ○ b ○ Barry’s bag ○ Ali’s bag ○ ○ 2 marks KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 22 http://www.SATs-Papers.co.uk (c) Cindy calls the number of counters in her bag c Ali’s bag Barry’s bag Cindy’s bag c Which of the expressions below shows the number of counters in Barry’s bag? Circle the correct one. cp2 cm2 4 4 23 http://www.SATs-Papers.co.uk ○ KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 4 p2 ○ m 2 4 c ○ c 4c m 2 1 mark ○ 4c p 2 Finding Angles 17. The diagram shows two isosceles triangles inside a parallelogram. Not drawn accurately (a) On the diagram, mark another angle that is 75 O ○ ○ ○ ○ Label it 75 O 1 mark (b) Calculate the size of the angle marked k Show your working. ○ ○ ○ ○ ○ ○ O ○ ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 24 http://www.SATs-Papers.co.uk Statistics, Lambs 18. Here are three number cards. ? The numbers are hidden. ? ? The mode of the three numbers is 5 The mean of the three numbers is 8 What are the three numbers? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ , ○ ○ ○ ○ ○ ○ ○ ○ , ○ ○ ○ ○ ○ ○ ○ 2 marks 19. On a farm 80 sheep gave birth. 30% of the sheep gave birth to two lambs. The rest of the sheep gave birth to just one lamb. In total, how many lambs were born? Show your working. ○ ○ ○ ○ ○ ○ ○ ○ lambs ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 25 http://www.SATs-Papers.co.uk Tiles 20. Two parts of this square design are shaded black. Two parts are shaded grey. Show that the ratio of black to grey is 5 : 3 ○ ○ ○ ○ ○ ○ ○ ○ 2 marks KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 26 http://www.SATs-Papers.co.uk Thinking Equations 21. (a) Solve this equation. 7 p 5 k e 8k p 1 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ k e 1 mark (b) Solve this equation. Show your working. 10 y p 23 e 4y p 26 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 27 ○ KS3/01/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk ○ y e 2 marks http://www.SATs-Papers.co.uk Sourced from SATs-Papers.co.uk © Qualiﬁcations and Curriculum Authority 2001 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA 00-6651/4 http://www.SATs-Papers.co.uk