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# 2005 mathematics paper b

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An interactive voting lesson designed for use with Qwizdom Classroom Response Systems

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### 2005 mathematics paper b

1. 1. 2005 MATHS PAPER B
2. 2. 2005 Mathematics Paper B Input your name and press send. Next Page
3. 3. 2005 Mathematics Paper B Q1 Next Page Write these prices in order from smallest to largest. A B C D E
4. 4. 2005 Mathematics Paper B Q2 Next Page <ul><ul><ul><li>64 </li></ul></ul></ul><ul><ul><ul><li>32 </li></ul></ul></ul><ul><ul><ul><li>16 </li></ul></ul></ul><ul><ul><ul><li>8 </li></ul></ul></ul><ul><ul><ul><li>4 </li></ul></ul></ul>Which three numbers will add up to 100?
5. 5. 2005 Mathematics Paper B Q3 Next Page Here is a shape. Which of the shapes below is the same as the one above. A B C D E Word file
6. 6. 2005 Mathematics Paper B Q4a Next Page These are the prices of coconuts and bananas. Josh buys one coconut and half a kilogram of bananas . How much does he spend altogether? {Answer using the decimal}.
7. 7. 2005 Mathematics Paper B Q4a Next Page These are the prices of coconuts and bananas. Josh buys one coconut and half a kilogram of bananas . How much does he spend altogether? <ul><li>(a) Award TWO marks for the correct answer of £1.38 </li></ul><ul><li>If the answer is incorrect, award ONE mark for evidence of appropriate method, eg </li></ul><ul><li>78 + ( ½ x 1.20) </li></ul><ul><ul><li>Accept for ONE mark £138p OR £138 as evidence of an appropriate method. </li></ul></ul><ul><ul><li>Answer need not be obtained for the award of ONE mark. </li></ul></ul>
8. 8. 2005 Mathematics Paper B Q4a Next Page Oranges cost 25p each. How many oranges can Josh buy for £1.50 ?
9. 9. 2005 Mathematics Paper B Q Next Page This grid is made of hexagons. Use the pen tool to draw the reflection of the shaded shape on the grid.
10. 10. 2005 Mathematics Paper B Q Next Page This grid is made of hexagons. Use the pen tool to draw the reflection of the shaded shape on the grid.
11. 11. 2005 Mathematics Paper B Q6a Next Page Each missing digit in these calculations is 2 , 5 or 7 Write in the missing digits. You may use each digit more than once. What is this digit?
12. 12. 2005 Mathematics Paper B Q6b Next Page Each missing digit in these calculations is 2 , 5 or 7 Write in the missing digits. You may use each digit more than once. What is this digit?
13. 13. 2005 Mathematics Paper B Q6c Next Page Each missing digit in these calculations is 2 , 5 or 7 Write in the missing digits. You may use each digit more than once. What is this digit?
14. 14. 2005 Mathematics Paper B Q6d Next Page Each missing digit in these calculations is 2 , 5 or 7 Write in the missing digits. You may use each digit more than once. What is this digit?
15. 15. 2005 Mathematics Paper B Q6e Next Page Each missing digit in these calculations is 2 , 5 or 7 Write in the missing digits. You may use each digit more than once. What is this digit?
16. 16. 2005 Mathematics Paper B Q6f Next Page Each missing digit in these calculations is 2 , 5 or 7 Write in the missing digits. You may use each digit more than once. What is this digit?
17. 17. 2005 Mathematics Paper B Q6g Next Page Each missing digit in these calculations is 2 , 5 or 7 Write in the missing digits. You may use each digit more than once. What is this digit? Xl FILE
18. 18. 2005 Mathematics Paper B Q7a Next Page This table shows information about four solid shapes. Complete the table. One has been done for you. What number should go here?   number of flat surfaces number of curved surfaces sphere 0 1 cone cuboid cylinder
19. 19. 2005 Mathematics Paper B Q7b Next Page This table shows information about four solid shapes. Complete the table. One has been done for you. What number should go here?   number of flat surfaces number of curved surfaces sphere 0 1 cone cuboid cylinder
20. 20. 2005 Mathematics Paper B Q7c Next Page This table shows information about four solid shapes. Complete the table. One has been done for you. What number should go here?   number of flat surfaces number of curved surfaces sphere 0 1 cone 1 1 cuboid cylinder
21. 21. 2005 Mathematics Paper B Q7d Next Page This table shows information about four solid shapes. Complete the table. One has been done for you. What number should go here?   number of flat surfaces number of curved surfaces sphere 0 1 cone 1 1 cuboid cylinder
22. 22. 2005 Mathematics Paper B Q7e Next Page This table shows information about four solid shapes. Complete the table. One has been done for you. What number should go here?   number of flat surfaces number of curved surfaces sphere 0 1 cone 1 1 cuboid 6 0 cylinder
23. 23. 2005 Mathematics Paper B Q7e Next Page Answers This table shows information about four solid shapes. Complete the table. One has been done for you. What number should go here?   number of flat surfaces number of curved surfaces sphere 0 1 cone cuboid cylinder
24. 24. 2005 Mathematics Paper B Q7 Next Page This table shows information about four solid shapes. Complete the table. One has been done for you. What number should go here?   number of flat surfaces number of curved surfaces sphere 0 1 cone 1 1 cuboid 6 0 cylinder 2 1
25. 25. 2005 Mathematics Paper B Q8a Next Page A shop sells different kinds of greeting cards. This pictogram shows how many they sold in a week. Estimate how many Birthday cards were sold.
26. 26. 2005 Mathematics Paper B Q8b Next Page Answer Key A shop sells different kinds of greeting cards. This pictogram shows how many they sold in a week. Estimate how many more Thank You cards than Get Well cards were sold.
27. 27. 2005 Mathematics Paper B Q8b A shop sells different kinds of greeting cards. This pictogram shows how many they sold in a week. Estimate how many more Thank You cards than Get Well cards were sold. Next Page Estimate how many Birthday cards were sold. (a) Answer in the range 340 to 360 inclusive. (b) Answer in the range 240 to 260 inclusive.
28. 28. 2005 Mathematics Paper B Q9a Next Page Here is part of a number line. What is the missing number?
29. 29. 2005 Mathematics Paper B Q9b Next Page Answers Here is part of a number line. What is the missing number?
30. 30. 2005 Mathematics Paper B Q9 Next Page Here is part of a number line. What is the missing number? First of all work out how much each “mark” is worth on the scale. The difference between 960 and 980 is 20 and there are… 4 steps in between so 20 divided by 4 = 5 Write in the values on each mark
31. 31. 2005 Mathematics Paper B Q9 Next Page Here is part of a number line. What is the missing number? First of all work out how much each “mark” is worth on the scale. The difference between 960 and 980 is 20 and there are… 4 steps in between so 20 divided by 4 = 5 Write in the values on each mark 960-5=955 980+5=985 985+5=990 990+5=995 995+5=1000 1000+5=1005 1005+5=1010
32. 32. 2005 Mathematics Paper B Q10 Next Page Answer key 1. Here is a spinner which is a regular octagon. Write 1, 2 or 3 in each section of the spinner so that 1 and 2 are equally likely to come up and 3 is the least likely to come up.
33. 33. 2005 Mathematics Paper B Q10 Next Page Answer key 1. Here is a spinner which is a regular octagon. Write 1, 2 or 3 in each section of the spinner so that 1 and 2 are equally likely to come up and 3 is the least likely to come up. <ul><li>Accept for TWO marks any arrangement using one of the following up to 2 sets of eight numbers: </li></ul><ul><li>1, 1, 1, 2, 2, 2, 3, 3 </li></ul><ul><li>OR </li></ul><ul><li>1, 1, 1, 1, 2, 2, 2, 2 </li></ul><ul><li>eg </li></ul><ul><ul><li>Numbers may be written in any order. </li></ul></ul><ul><li>If the answer is incorrect, award ONE mark for an arrangement such that: </li></ul><ul><li>· the number of 1s and 2s is equal </li></ul><ul><li>OR </li></ul><ul><li>· the number of 3s is less than the number of 2s AND the number of 3s is less than the number of 1s. </li></ul><ul><ul><li>Do not accept answers that leave sections blank or include numbers other than 1, 2 or 3. </li></ul></ul>
34. 34. 2005 Mathematics Paper B Q11 Next Page Answers Josh thinks of a number. He adds 4 He multiplies his result by 3 Then he takes away 9 His final answer is 90 What number did Josh start with?
35. 35. 2005 Mathematics Paper B Q11 Next Page Josh thinks of a number. He adds 4 He multiplies his result by 3 Then he takes away 9 His final answer is 90 What number did Josh start with? What is happening mathematically? Unknown number + 4 = Result1 x 3 = Result2 – 9 = 90 Working backwards: 90 + 9 = Result2 = 99 Result2 ÷ 3 = 99 ÷ 3 = Result1 = 33 Result1 – 4 = 33 – 4 = 29 XL file
36. 36. 2005 Mathematics Paper B Q12 Next Page Here is a 1cm square grid. Some of the grid is shaded. What is the area that is shaded in cm sq? Mark of with pen tool
37. 37. 2005 Mathematics Paper B Q13a Next Page Sapna and Robbie have some biscuits. Altogether they have 14 biscuits. Sapna has 2 more biscuits than Robbie. How many biscuits does Sapna have?
38. 38. 2005 Mathematics Paper B Q13b Next Page Sapna and Robbie have some biscuits. Altogether they have 14 biscuits. Sapna has 2 more biscuits than Robbie. How many biscuits does Robbie have? Click for a solution Sapna (R + 2) Robbie Total biscuits 2 0 2 3 1 4 4 2 6 5 3 8 6 4 10 7 5 12 8 6 14
39. 39. 2005 Mathematics Paper B Q14 Next Page 1. This pattern is made by turning a shape clockwise through 90° each time. Draw the two missing triangles on the last shape. Pen tool Word file
40. 40. 2005 Mathematics Paper B Q15 Next Page The diagram shows two identical squares. A is the point (10,10) What are the coordinates of B and C ? Firstly, what is the first value for B?
41. 41. 2005 Mathematics Paper B Q15 Next Page The diagram shows two identical squares. A is the point (10,10) What are the coordinates of B and C ? Firstly, what is the second value for B? B = (0,?)
42. 42. 2005 Mathematics Paper B Q15 Next Page The diagram shows two identical squares. A is the point (10,10) What are the coordinates of B and C ? Firstly, what is the first value for C? B = (0,10) C = (?,_)
43. 43. 2005 Mathematics Paper B Q15 Next Page The diagram shows two identical squares. A is the point (10,10) What are the coordinates of B and C ? Firstly, what is the second value for C? B = (0,10) C = (10,?) Co-ord. PPT
44. 44. 2005 Mathematics Paper B Q16 Next Page <ul><ul><ul><ul><ul><li>Choose all the factors of 30 which are also factors of 20 </li></ul></ul></ul></ul></ul><ul><li>1 </li></ul><ul><li>2 </li></ul><ul><li>4 </li></ul><ul><li>5 </li></ul><ul><li>6 </li></ul><ul><li>10 </li></ul>
45. 45. 2005 Mathematics Paper B Q16 Next Page <ul><ul><ul><ul><ul><li>Choose all the factors of 30 which are also factors of 20 </li></ul></ul></ul></ul></ul><ul><li>1 </li></ul><ul><li>2 </li></ul><ul><li>4 </li></ul><ul><li>5 </li></ul><ul><li>6 </li></ul><ul><li>10 </li></ul>Factors are numbers which share into another number without any remainder e.g. the factors of 6 are: 1 2 3
46. 46. 2005 Mathematics Paper B Q17 Next Page 17 multiplied by itself gives a 3-digit answer. What is the smallest 2-digit number that can be multiplied by itself to give a 4-digit answer? XL file
47. 47. 2005 Mathematics Paper B Q18 Next Page All the children at Park School chose their favourite soup. The graph shows the results. How many more children chose chicken soup than mushroom soup?
48. 48. 2005 Mathematics Paper B Q18 Next Page Answer key All the children at Park School chose their favourite soup. The graph shows the results. Robbie says, ‘ More than half of the children chose tomato soup’. Is he correct? Yes or No. Explain how you can tell from the graph.
49. 49. 2005 Mathematics Paper B Q18 Next Page Robbie says, ‘ More than half of the children chose tomato soup’. Is he correct? Yes or No. Explain how you can tell from the graph. How many more children chose chicken soup than mushroom soup? (a) Answer in the range 14 to 16 inclusive. <ul><li>(b) An explanation which recognises that the bar for tomato is shorter than the other two bars added together, eg </li></ul><ul><ul><li>· ‘Because there are 300 children altogether and only 135 chose tomato’; </li></ul></ul><ul><ul><li>· ‘Because 165 is more than 135’; </li></ul></ul><ul><ul><li>· ‘Because double 135 is 270 and there are more children than that altogether’; </li></ul></ul><ul><ul><li>· ‘Because half of 300 is 150’; </li></ul></ul><ul><ul><li>· ‘Because tomato is less than mushroom add chicken’. </li></ul></ul><ul><ul><ul><li>No mark is awarded for writing ‘No’ alone. </li></ul></ul></ul><ul><ul><ul><li>Do not accept vague or arbitrary explanations, eg </li></ul></ul></ul><ul><ul><ul><li>· ‘Because most of the children chose tomato’; </li></ul></ul></ul><ul><ul><ul><li>· ‘Because 135 children chose tomato’; </li></ul></ul></ul><ul><ul><ul><li>· ‘Because 75 + 135 + 90 = 300’. </li></ul></ul></ul><ul><ul><ul><li>If ‘Yes’ is circled but a correct, unambiguous explanation is given then award the mark. </li></ul></ul></ul>
50. 50. 2005 Mathematics Paper B Q19 Next Page Answer Key Sapna makes a fruit salad using bananas, oranges and apples. For every one banana, she uses 2 oranges and 3 apples. Sapna uses 24 fruits. How many oranges does she use?
51. 51. 2005 Mathematics Paper B Q19 Next Page Sapna makes a fruit salad using bananas, oranges and apples. For every one banana, she uses 2 oranges and 3 apples. Sapna uses 24 fruits. How many oranges does she use? Award TWO marks for the correct answer of 8 up to 2 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 1 + 2 + 3 = 6 24 ÷ 6 = 4 4 x 2 OR 6 fruits 2 oranges 12 fruits 4 oranges 18 fruits 6 oranges 24 fruits wrong answer Answer need not be obtained for the award of ONE mark. XL File
52. 52. 2005 Mathematics Paper B Q20 Next Page Answers Which two of these numbers, when multiplied together, have the answer closest to 70? <ul><li>7.4 </li></ul><ul><li>8.1 </li></ul><ul><li>9.4 </li></ul><ul><li>10 </li></ul>
53. 53. 2005 Mathematics Paper B Q20 Next Page Answers Which two of these numbers, when multiplied together, have the answer closest to 70? <ul><li>7.4 </li></ul><ul><li>8.1 </li></ul><ul><li>9.4 </li></ul><ul><li>10 </li></ul>7.4 x 9.4 = 69.56
54. 54. 2005 Mathematics Paper B Q21 Next Page answers Here is an isosceles triangle. Calculate the size of angle x - do not use a protractor (angle measurer).
55. 55. 2005 Mathematics Paper B Q21 Next Page Here is an isosceles triangle. Calculate the size of angle x - do not use a protractor (angle measurer). Relevant facts: In all triangles the internal angles add up to?
56. 56. 2005 Mathematics Paper B Q21 Next Page Here is an isosceles triangle. Calculate the size of angle x - do not use a protractor (angle measurer). Relevant facts: In all triangles the internal angles add up to? In an isosceles triangle how many sides are equal to each other?
57. 57. 2005 Mathematics Paper B Q21 Next Page Here is an isosceles triangle. Calculate the size of angle x - do not use a protractor (angle measurer). Relevant facts: In all triangles the internal angles add up to? In an isosceles triangle how many sides are equal to each other? x = x (shown above) So internal angles = 180 º 180º = 110º + xº + xº Therefore xº + xº = 70 º xº = 35 º Investigation – are two of the internal angles in an isosceles triangle always equal? Internet activity
58. 58. 2005 Mathematics Paper B Q22 Next Page On Monday all the children at Grange School each play one sport. They choose either hockey or rounders. There are 103 children altogether in the school. 27 girls choose hockey. Write all this information in the table. Then complete the table. What number goes here?   hockey rounders Total boys 22 girls 53 Total
59. 59. 2005 Mathematics Paper B Q22 Next Page On Monday all the children at Grange School each play one sport. They choose either hockey or rounders. There are 103 children altogether in the school. 27 girls choose hockey. Write all this information in the table. Then complete the table. What number goes here?   hockey rounders Total boys 22 girls 27 53 Total
60. 60. 2005 Mathematics Paper B Q22 Next Page On Monday all the children at Grange School each play one sport. They choose either hockey or rounders. There are 103 children altogether in the school. 27 girls choose hockey. Write all this information in the table. Then complete the table. What number goes here?   hockey rounders Total boys 22 girls 27 53 Total 103
61. 61. 2005 Mathematics Paper B Q22 Next Page On Monday all the children at Grange School each play one sport. They choose either hockey or rounders. There are 103 children altogether in the school. 27 girls choose hockey. Write all this information in the table. Then complete the table. What number goes here?   hockey rounders Total boys 22 50 girls 27 53 Total 103
62. 62. 2005 Mathematics Paper B Q22 Next Page On Monday all the children at Grange School each play one sport. They choose either hockey or rounders. There are 103 children altogether in the school. 27 girls choose hockey. Write all this information in the table. Then complete the table. What number goes here?   hockey rounders Total boys 22 50 girls 27 26 53 Total 103
63. 63. 2005 Mathematics Paper B Q22 Next Page On Monday all the children at Grange School each play one sport. They choose either hockey or rounders. There are 103 children altogether in the school. 27 girls choose hockey. Write all this information in the table. Then complete the table. What number goes here?   hockey rounders Total boys 22 28 50 girls 27 26 53 Total 103
64. 64. 2005 Mathematics Paper B Q22 Next Page On Monday all the children at Grange School each play one sport. They choose either hockey or rounders. There are 103 children altogether in the school. 27 girls choose hockey. Write all this information in the table. Then complete the table. What number goes here?   hockey rounders Total boys 22 28 50 girls 27 26 53 Total 54 103
65. 65. 2005 Mathematics Paper B Q22 Next Page On Monday all the children at Grange School each play one sport. They choose either hockey or rounders. There are 103 children altogether in the school. 27 girls choose hockey. Write all this information in the table. Then complete the table.   hockey rounders Total boys 22 28 50 girls 27 26 53 Total 49 54 103
66. 66. Next page 30% of 60 is 2005 Mathematics Paper B Q22a
67. 67. Next page Answer Key 30% of is 60? 2005 Mathematics Paper B Q22b
68. 68. Next page – methods of solving 22a 30% of is 60? 2005 Mathematics Paper B Q22a 30% of 60 is (a) 18 Do not accept 18% (b) 200 Do not accept 200% If the answer for 23a is 18% AND the answer for 23b is 200%, award ONE mark only in the 23b box.
69. 69. Next page – methods of solving 22b 2005 Mathematics Paper B Q22a 30% of 60 is (a) 18 Do not accept 18% Method 1: use decimal fractions & calculator 30% = 0.30 0.30 x 60 = 18 Method 2: Find 1% and multiply 1% of 60 = 0.6 30 lots of 1% = 30 x 0.6 = 18
70. 70. Next page 2005 Mathematics Paper B Q22a (b) 200 Method 1: use decimal fractions & calculator 30% = 0.30 0.30 x ?? = 60 rearrange  0.30 x 60 = ?? = 200 Method 2: Find 1% and multiply 30% = 60 so 10% = 20 and 1% = 2 100 lots of 1% = 2 x 100 = 200 30% of is 60?
71. 71. 2005 Mathematics Paper B Q24 Next Page Answers Here is a rectangle with a width of 15.7 centimetres. The perimeter of this rectangle is 85 centimetres. Calculate the length of the rectangle in cm.
72. 72. 2005 Mathematics Paper B Q24 Next Page Here is a rectangle with a width of 15.7 centimetres. The perimeter of this rectangle is 85 centimetres. Calculate the length of the rectangle in cm. Rectangle Facts: opposite sides are equal; perimeter = distance all the way round = (width x 2)+(length x 2) 85 cm = (15.7cm + 15.7cm) +(length x 2) 85cm = 31.4cm + (length x 2) 85cm – 31.4cm = length x 2 53.6cm = length x 2 so half of 53,6cm = length = 26.8cm
73. 73. 2005 Mathematics Paper B Q25 Next Page A box contains 220 matches and weighs 45 grams. The empty box weighs 12 grams. Calculate the weight of one match.
74. 74. 2005 Mathematics Paper B Q25 End of paper A box contains 220 matches and weighs 45 grams. The empty box weighs 12 grams. Calculate the weight of one match. Total weight = box + matches Matches = total weight – box Matches = 45g – 12g = 33g 220 matches = 33g 1 match = 33g ÷220 = 0.15g