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Ma Mathematics test KEY STAGE 3 TIER Paper 1 4–6 Calculator not allowed First name Last name 2007 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 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 1 TOTAL MARKS http://www.SATs-Papers.co.uk 15/11/06 8:41:58 pm 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 = 1 (a + b)h 2 height (h) a Prism length area of cross-section Volume = area of cross-section × length KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 2 2 http://www.SATs-Papers.co.uk 15/11/06 8:41:59 pm Populations 1. The table shows the approximate populations of ﬁve different places. Place London 7 000 000 Shefﬁeld 700 000 Harrogate 70 000 Ash Vale 7 000 Binbrook (a) Approximate population 700 Which of the places has a population of about seventy thousand? 1 mark (b) Use the table to complete these sentences. The population of Harrogate is about 10 times as big as the population of The population of is about 100 times as big as the population of Harrogate. The population of Shefﬁeld is about times as big as 2 marks the population of Ash Vale. KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 3 3 http://www.SATs-Papers.co.uk 15/11/06 8:41:59 pm Number grids 2. Here are the rules for a number grid. This number is the sum of the numbers in the middle row. 12 10 2 20 This number is the product of the numbers in the middle row. Use the rules to write the missing numbers in these number grids. 12 4 7 9 10 24 KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 4 4 3 marks http://www.SATs-Papers.co.uk 15/11/06 8:41:59 pm Babies 3. The lengths of babies are measured at different ages. The graph shows the longest and shortest a baby boy is likely to be. longest baby boy 80 76 72 shortest baby boy 68 Length (cm) 64 60 56 52 48 44 0 0 4 8 12 16 20 24 28 32 36 40 44 48 Age (weeks) (a) Write the missing numbers below. A baby boy is 8 weeks old. The longest he is likely to be is about cm. 1 mark The shortest he is likely to be is about cm. 1 mark (b) A 34 week old baby boy is 72cm long. Put a cross on the graph to show this information. 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 5 5 http://www.SATs-Papers.co.uk 15/11/06 8:42:00 pm Cards for fractions 4. Here are six number cards. 2 (a) 4 6 8 10 12 Choose two of these six cards to make a fraction that is equivalent to 1 3 1 mark (b) Choose two of these six cards to make a fraction that is greater than 1 but less than 1 2 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 6 6 http://www.SATs-Papers.co.uk 15/11/06 8:42:00 pm Pentagon perimeter 5. The shape below is a regular pentagon. All five sides are exactly the same length. Measure accurately one of the sides, then work out the perimeter of the pentagon. 1 mark 1 mark Perimeter = cm 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 7 7 http://www.SATs-Papers.co.uk 15/11/06 8:42:00 pm Multiple and factor 6. (a) A three-digit number is a multiple of 4 What could the number be? Give an example. Now give a different example. 1 mark (b) A two-digit number is a factor of 100 What could the number be? Give an example. 1 mark Now give a different example. 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 8 8 http://www.SATs-Papers.co.uk 15/11/06 8:42:00 pm Same number, Squares 7. (a) Write the answer to this calculation. 2.5 (b) + 2.5 + 2.5 = 1 mark Now write a number in each box to make this calculation correct. The three numbers must be the same. + 8. + = 4.5 1 mark Sam says: The only four-sided shape with four right angles is a square. Is Sam correct? Yes No Explain your answer. 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 9 9 http://www.SATs-Papers.co.uk 15/11/06 8:42:01 pm x=8 9. When x = 8, what is the value of 5 x ? (a) Tick ( ) the correct box below. 5 13 40 58 None of these 1 mark When x = 8, what is the value of 3 x – x ? (b) Tick ( ) the correct box below. 0 3 16 30 None of these 1 mark When x = 8, what is the value of x 2 ? (c) Tick ( ) the correct box below. 8 10 16 64 None of these 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 10 10 http://www.SATs-Papers.co.uk 15/11/06 8:42:01 pm Grid 10. Lisa uses a grid to multiply 23 by 15 × 20 3 10 200 30 5 100 15 200 + 100 + 30 + 15 = 345 Answer: 345 Now Lisa multiplies two different numbers. Complete the grid, then give the answer below. × 40 3 30 600 18 Answer: 3 marks KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 11 11 http://www.SATs-Papers.co.uk 15/11/06 8:42:01 pm Sweets 11. Fred has a bag of sweets. Contents 3 yellow sweets 5 green sweets 7 red sweets 4 purple sweets 1 black sweet He is going to take a sweet from the bag at random. (a) What is the probability that Fred will get a black sweet? 1 mark (b) Write the missing colour in the sentence below. The probability that Fred will get a KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 12 sweet is 12 1 4 1 mark http://www.SATs-Papers.co.uk 15/11/06 8:42:02 pm Completing calculations, Rectangles 12. Write a number in each box to make the calculations correct. + = –8 – = –8 1 mark 1 mark A rectangle has an area of 24cm2 13. How long could the sides of the rectangle be? Give three different examples. cm and cm cm and cm cm and cm 2 marks KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 13 13 http://www.SATs-Papers.co.uk 15/11/06 8:42:02 pm Percentages 14. (a) Write the missing numbers. 50% of 80 = 5% of 80 = 1% of 80 = 2 marks (b) Work out 56% of 80 You can use part (a) to help you. 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 14 14 http://www.SATs-Papers.co.uk 15/11/06 8:42:02 pm Positive and negative 15. Look at this equation. y = 2x + 10 When x = 4, what is the value of y ? (a) 1 mark When x = – 4, what is the value of y ? (b) 1 mark Which equation below gives the same value of y for both x = 4 and x = – 4? (c) Put a ring round the correct equation. y = 2x KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 15 y = x2 y = 2 + x 15 y = x 2 1 mark http://www.SATs-Papers.co.uk 15/11/06 8:42:03 pm Barrels 16. The diagram shows four different sized barrels. Barrel A Barrel B Barrel C Barrel D holds holds holds holds 54 gallons 36 gallons 18 gallons 9 gallons Write the missing fractions as simply as possible. The ﬁrst one is done for you. Barrel C holds 1 2 of the amount barrel B holds. Barrel D holds of the amount barrel B holds. Barrel C holds of the amount barrel A holds. Barrel B holds of the amount barrel A holds. 2 marks KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 16 16 http://www.SATs-Papers.co.uk 15/11/06 8:42:03 pm Speed 17. The line on the graph below represents a speed of 60km/hour. 60km/hour 60 50 40 Distance 30 (km) 20 10 0 0 10 20 30 40 50 60 Time (minutes) (a) Draw a line on the graph to represent a speed of 30km/hour. Label the line by writing 30km/hour. 1 mark (b) Now draw a line on the graph to represent a speed of 120km/hour. Label the line by writing 120km/hour. 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 17 17 http://www.SATs-Papers.co.uk 15/11/06 8:42:03 pm Grey and black designs 18. (a) In this design, the ratio of grey to black is 3 : 1 What percentage of the design is black? % 1 mark (b) In this design, 60% is grey and the rest is black. What is the ratio of grey to black? Write your ratio in its simplest form. : 2 marks KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 18 18 http://www.SATs-Papers.co.uk 15/11/06 8:42:04 pm Counter probabilities 19. In a bag there are only red, blue and green counters. (a) I am going to take a counter out of the bag at random. Complete the table below. Colour of counters Number of counters Red 6 Probability 1 5 Blue Green 6 2 marks (b) Before I take a counter out of the bag, I put one extra blue counter into the bag. What effect does this have on the probability that I will take a red counter? Tick ( ) the correct box. The probability has increased. The probability has decreased. The probability has stayed the same. It is impossible to tell. 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 19 19 http://www.SATs-Papers.co.uk 15/11/06 8:42:04 pm Three straight lines 20. The diagram shows three straight lines. 60° Not drawn accurately b c a 130° Work out the sizes of angles a, b and c Give reasons for your answers. a = ° because 1 mark b = ° because 1 mark c = ° because 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 20 20 http://www.SATs-Papers.co.uk 15/11/06 8:42:04 pm Ninths 21. (a) Some of the fractions below are smaller than 1 9 Tick ( ) them. 1 10 4 9 1 2 1 100 1 8 1 mark (b) To the nearest per cent, what is 1 as a percentage? 9 Tick ( ) the correct percentage. 0.9% 9% 10% 11% 19% 1 mark (c) Complete the sentence below by writing a fraction. 1 is half of 9 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 21 21 http://www.SATs-Papers.co.uk 15/11/06 8:42:05 pm Equation, Circle working 22. Solve this equation. 2 ( 2n + 5 ) = 12 n = 2 marks 23. Kevin is working out the area of a circle with radius 4 He writes: 4 Area = × 8 Explain why Kevin’s working is wrong. 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 22 22 http://www.SATs-Papers.co.uk 15/11/06 8:42:06 pm Thinking fractions, Cube 24. Write the missing numbers in these fraction sums. 1 + = 4 1 8 1 mark 1 8 + = 1 3 1 mark 25. Look at the cube. The area of a face of the cube is 9 x 2 Area = 9 x 2 Write an expression for the total surface area of the cube. Write your answer as simply as possible. 1 mark KS3/07/Ma/Tier 4–6/P1 Sourced from SATs-Papers.co.uk 275662_p1_46.indd 23 23 http://www.SATs-Papers.co.uk 15/11/06 8:42:06 pm END OF TEST Sourced from and Curriculum © Qualifications SATs-Papers.co.uk Authority 2007 275662_p1_46.indd 24 QCA/06/2781 (Pupil pack) http://www.SATs-Papers.co.uk 275662 QCA/06/2778 (Mark scheme pack) 15/11/06 8:42:07 pm