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Ma Mathematics test KEY STAGE 3 TIER Paper 1 5–7 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, ruler and a pair of compasses. 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 KS3_p1_T5-7 275664.indd 1 TOTAL MARKS http://www.SATs-Papers.co.uk 15/11/06 10:14:00 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 2 2 http://www.SATs-Papers.co.uk 15/11/06 10:14:01 pm x=8 1. (a) When x = 8, what is the value of 5 x ? Tick ( ) the correct box below. 5 13 40 58 None of these 1 mark (b) When x = 8, what is the value of 3 x – x ? Tick ( ) the correct box below. 0 3 16 30 None of these 1 mark (c) When x = 8, what is the value of x 2 ? Tick ( ) the correct box below. 8 10 16 64 None of these 1 mark KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 3 3 http://www.SATs-Papers.co.uk 15/11/06 10:14:01 pm Grid 2. 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 4 4 http://www.SATs-Papers.co.uk 15/11/06 10:14:02 pm Sweets 3. 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 5 sweet is 1 4 1 mark 5 http://www.SATs-Papers.co.uk 15/11/06 10:14:02 pm Completing calculations, Rectangles 4. Write a number in each box to make the calculations correct. + –8 – 5. = = –8 1 mark 1 mark A rectangle has an area of 24cm2 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 6 6 http://www.SATs-Papers.co.uk 15/11/06 10:14:02 pm Percentages 6. (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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 7 7 http://www.SATs-Papers.co.uk 15/11/06 10:14:03 pm Positive and negative 7. Look at this equation. y = 2x + 10 (a) When x = 4, what is the value of y ? 1 mark (b) When x = – 4, what is the value of y ? 1 mark (c) Which equation below gives the same value of y for both x = 4 and x = – 4? Put a ring round the correct equation. y = 2x KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 8 y = x2 y = 2 + x y = x 2 1 mark 8 http://www.SATs-Papers.co.uk 15/11/06 10:14:03 pm Barrels 8. 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 9 9 http://www.SATs-Papers.co.uk 15/11/06 10:14:03 pm Speed 9. 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 10 10 http://www.SATs-Papers.co.uk 15/11/06 10:14:04 pm Grey and black designs 10. (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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 11 11 http://www.SATs-Papers.co.uk 15/11/06 10:14:04 pm Counter probabilities 11. 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 12 12 http://www.SATs-Papers.co.uk 15/11/06 10:14:05 pm Three straight lines 12. 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 13 13 http://www.SATs-Papers.co.uk 15/11/06 10:14:05 pm Ninths 13. (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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 14 14 http://www.SATs-Papers.co.uk 15/11/06 10:14:06 pm Equation, Circle working 14. Solve this equation. 2 ( 2n + 5 ) = 12 n = 2 marks 15. 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 15 15 http://www.SATs-Papers.co.uk 15/11/06 10:14:06 pm Thinking fractions, Cube 16. Write the missing numbers in these fraction sums. 1 + = 4 1 8 1 mark 1 8 + = 1 3 1 mark 17. 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 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 16 16 http://www.SATs-Papers.co.uk 15/11/06 10:14:07 pm Random numbers 18. Chris read the first 55 numbers from a book of random numbers. As he read each number he recorded it in the diagram below. 0 9 9 8 3 1 6 3 1 0 3 2 8 2 3 1 1 6 9 3 4 6 9 9 4 7 0 5 5 7 7 6 6 0 2 8 4 8 0 7 6 8 0 1 5 4 8 6 6 9 2 8 5 9 (a) 5 6 7 8 0 0 4 1 Key 1 3 3 represents 13 5 7 What was the largest number he recorded? 1 mark (b) Explain how Chris could change the diagram to make it easier for him to ﬁnd the median of his data set. 1 mark KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 17 17 http://www.SATs-Papers.co.uk 15/11/06 10:14:07 pm Geometric mean 19. Here is the rule to ﬁnd the geometric mean of two numbers. Multiply the two numbers together, then ﬁnd the square root of the result. Example: geometric mean of 4 and 9 = = 4×9 36 = 6 (a) For the two numbers 10 and x, the geometric mean is 30 What is the value of x? x= 1 mark (b) Reena says: ‘For the two numbers –2 and 8, it is impossible to ﬁnd the geometric mean.’ Is Reena correct? Yes No Explain your answer. 1 mark KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 18 18 http://www.SATs-Papers.co.uk 15/11/06 10:14:07 pm Sequences 20. (a) Draw lines to match each nth term rule to its number sequence. nth term Number sequence 4n 4, 7, 12, 19, … ( n + 1)2 4, 8, 12, 16, … n2 + 3 4, 9, 16, 25, … n( n + 3) 4, 10, 18, 28, … 2 marks (b) Write the first four terms of the number sequence using the nth term rule below. n3 + 3 , , , 2 marks KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 19 19 http://www.SATs-Papers.co.uk 15/11/06 10:14:08 pm Rhombus 21. The diagram shows a rhombus. The midpoints of two of its sides are joined with a straight line. p 110° Not drawn accurately What is the size of angle p ? p= KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 20 ° 2 marks 20 http://www.SATs-Papers.co.uk 15/11/06 10:14:08 pm Counters 22. A bag contains counters that are red, black, or green. 1 of the counters are red 3 1 of the counters are black 6 There are 15 green counters in the bag. How many black counters are in the bag? 2 marks KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 21 21 http://www.SATs-Papers.co.uk 15/11/06 10:14:09 pm Fence plan 23. Here is a plan of some land. There will be a fence that is always the same distance from tree A as from tree B, going all the way from one road to the other road. Use compasses and a straight edge to show accurately on the plan where the fence will go. You must leave in your construction lines. Road Tree A Tree B 2 marks Road KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 22 22 http://www.SATs-Papers.co.uk 15/11/06 10:14:09 pm Powers 24. Work out the values of m and n 58 × 54 = 5 m m = 1 mark 58 = 5n 54 n = KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 23 1 mark 23 http://www.SATs-Papers.co.uk 15/11/06 10:14:09 pm Dissection 25. A square of area 64cm2 is cut to make two rectangles, A and B. A B Not drawn accurately Area = 64cm2 The ratio of area A to area B is 3 : 1 Work out the dimensions of rectangles A and B. Rectangle A: cm by cm Rectangle B: cm by cm 2 marks KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 24 24 http://www.SATs-Papers.co.uk 15/11/06 10:14:09 pm Coins 26. A teacher has some coins in his pocket. He is going to take one of the coins at random. He says: There are more than four coins in my pocket. The total value of the coins is 25p. The probability that I will take a 1p coin is 1 4 List all the coins that must be in his pocket. 2 marks KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 25 25 http://www.SATs-Papers.co.uk 15/11/06 10:14:10 pm END OF TEST KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 26 26 http://www.SATs-Papers.co.uk 15/11/06 10:14:10 pm END OF TEST KS3/07/Ma/Tier 5–7/P1 Sourced from SATs-Papers.co.uk KS3_p1_T5-7 275664.indd 27 27 http://www.SATs-Papers.co.uk 15/11/06 10:14:10 pm © QualificationsSATs-Papers.co.uk Authority 2007 Sourced from and Curriculum KS3_p1_T5-7 275664.indd 28 QCA/06/2783 (Pupil pack) QCA/06/2778 (Mark scheme pack) http://www.SATs-Papers.co.uk 275664 15/11/06 10:14:10 pm