2. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 12 x 5 ÷ 4 Which number must go into the box on the right side of the scales to balance them with the left side? Answer 240 12 X 5 = 60 240 ÷ 4 = 60

3. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Amy has 6 different coins in her purse. She has £2.68 altogether Which six coins does she have? Write your answer starting with the smallest coin. 1p, 2p, 5p, 10p, 50p, £2

4. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Jack colours the empty triangles on this shape red How many sixteenths does he shade red? 10 16 5858 X 2 = 10 16

5. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 00C00C -20 0 C The arrow indicates the temperature in a town at 9:00 a.m. By mid-afternoon the temperature has risen by 7 0 C. The temperature then falls by 13 0 C. What is the new temperature? 20 0 C - 1 0 C 12 0 C -1 0 C

6. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 In his cricket innings Tom scores 47 runs. His score is made up of: two sixes, three fours, one three and seven twos. The rest he scores in singles. How many singles does he score in his innings? 6 singles 2 x 6 = 12 3 x 4 = 12 1 x 3 = 3 7 x 2 = 14 Total 41 47 - 41 = 6

7. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The short side of the rectangle is the same length as the diameter of the circle. The radius of the circle is 9.5 cm. What is the perimeter of the rectangle? 24cm 86cm Diameter is 9.5cm x 2 = 19cm 19cm 24cm 19cm + 24cm = 43cm 43cm x 2 = 86cm

8. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The shape above is rotated one quarter turn to the right. Draw the shape in its new position below.

9. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Jason subtracts 0.25 from each of these decimals. Rewrite the new decimals in order starting with the smallest 0.550.51.80.351.5 0.30.251.550.11.25 0.10.250.31.251.55

10. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 At sports day Joe makes a standing jump of 1.8 m. Jade jumps 25 cm more than Holly. Tom jumps 10 cm more than Jade. Holly jumps 15 cm less than Joe. How far does Tom jump? 2m or 200cm Joe 1.8m Holly 1.65m Jade 1.9m Tom 2.0m

11. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 It takes Amy 25 minutes to walk to school. School starts at 8:55 a.m. She likes to arrive 10 minutes early. What time does Amy normally set off for school? 8:20 a.m., 08:20, twenty past eight 8:55 - 10 min. = 8:45 8:45 - 25 min. = 8:20

12. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Three different children do the calculations below. They then add up their answers. What is the total of their three answers? Ben calculates a quarter of 464 Amy calculates 20% of 900 Alex calculates the product of 7 and 45 116 180 315 611

13. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 How many different rectangles are there in this drawing? 10

14. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Each face of this cube has a surface area of 81cm 2 Chelsey wants to build a tower of cubes 216cm tall. How many cubes does she need? 24 cubes The edge of one face is √81cm 2 = 9cm 216cm ÷ 9 = 24

15. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The rule for the sequence below is find a quarter and add two. Which two numbers complete the sequence? 2484 8432¾ 4÷ 4 = 1 1 + 2 = 3 3 ÷ 4 = ¾ ¾ + 2 = 2¾

16. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 1 QUESTION NUMBER 20 Calculate one eighth of a quarter of a third of one-half of 72 Your answer will be a fraction. 3/8 72 ÷ 2 = 36 36 ÷ 3 = 12 12 ÷ 4 = 3 3 ÷ 8 = 3/8

17. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The product of three numbers is 48. Two of the numbers are 2 and 3. What is the third number? 8 2 x 3 = 6 48 ÷ 6 = 8

18. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Joe has one of each coin up to and including £2. How much less than £10 does he have? £6.12 £2 + £1 + 50p + 20p + 10p + 5p + 2p + 1p = £3.88 £10 - £3.88 = £6.12

19. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 15 sheets of paper weigh 7.5 grams. How much does one sheet of paper weigh? 0.5g 7.5g ÷ 15 = 0.5

20. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A B C 70 0 In the sketch the isosceles triangles A, B and C are the same size. Calculate angle X X 60 0 70 0 40 0 60 0

21. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 91394321 37273593 63511929 49618515 Identify the five prime numbers located in the grid. What is the total of the five numbers? 43 37 1929 61 189

22. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 492 The top number in this puzzle is found by adding all the digits below together. The bottom number is the product of the three numbers above. Calculate the two answers needed to complete the puzzle and add together your two answers. 15 72 87

23. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 2 QUESTION NUMBER 8 The area of this square is 64cm 2. The drawing below is made up of squares the same as this one. What is the perimeter of the new shape? 80 cm 8cm 12 sides each 4cm 4cm x 12 = 48cm 8cm x 4 = 32cm 48cm + 32cm = 80cm

24. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 By Christmas a football team has scored 18 goals. This is 25% of their final total for the season. Jack scores 1/3 of the season’s total goals. Tom scores five less than Jack. 13 goals were scored in January. How many goals were scored by the rest of the team? 29 Irrelevant The team scores 18 x 4 goals a season. Total 72 Jack scores 72 ÷ 3 = 24 goals Tom scores 24 - 5 = 19 goals Jack and Tom score 24 + 19 = 43 goals The rest score 72 - 43 = 29 goals

25. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 85 63 57 45 The numbers in the squares are the sum of each number in the circles on each side. Which numbers are missing from the blank shapes? 102 28 46 18

26. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 AYTOWNBETOWNCETOWN 180km360km Train X sets off from Aytown at 11:30 and travels at 90km per hour. Train Y sets off from Cetown at 12:15 and travels at 80km per hour. How much later does train Y arrive at Betown than train X? 3hrs 15min, 3 ¼ hours, 195 minutes

27. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A litre of water weighs 1kg. Jack fills a plastic bottle with 0.75L of water. Together the bottle and water weigh 835g. What is the weight of the bottle? 85 g Subtract the weight of water from the combined weight of the water and the bottle. The water weighs 750g The bottle weighs 835g - 750g = 85g

28. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A palindrome number is one that reads the same backwards as it does forwards, e.g. 8558. Which of the calculations below produce palindrome numbers? A 29 X 24 B 30 X 30 C 11 X 11 X 11 D 1437 + 2006 E 232 + 1001 696 1331 3443 900 1233 A, C, D

29. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The area of each circle is 38cm 2 The diameter of each circle is 7cm. What is the area of the grey shaded background? 44cm 2 14cm Area of the grey square 14cm x 14cm = 196 cm 2 Area of the four circles 152 cm 2

30. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Say whether these statements are true or false A All three digit numbers are divisible by 3 without a remainder B If you add the digits of a four digit number your answer will be an even number C All prime numbers are odd D A square number cannot also be a triangular number E Numbers ending in 0 are multiples of only 5 and 10. All are FALSE

31. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 What fraction of the large square is shaded grey? Answer in lowest terms 10/16 5/8

32. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The area of this square is 64cm 2. The drawing below is made up of squares the same as this one. What is the area of the new shape? 208cm 2 ¼ of a large square is 16cm 2 There are two whole squares 64cm 2 x 2 = 128cm 2 There are 5 quarter squares. Area is 16cm 2 x 5 = 80cm 2 128cm 2 + 80cm 2 = 208cm 2 Alternatively

33. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The area of this square is 64cm 2. The drawing below is made up of squares similar to this one. What is the area of the new shape? 208cm 2 ¼ of a large square is 16cm 2 There are13 quarter squares. Area is 16cm 2 x 13 = 208cm 2 Insert lines to make each large square into quarters

34. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 2 QUESTION NUMBER 19 40% of a number is 120. What is one-third of the number? 100 10% of the number is 120 ÷ 4 = 30 100% - the whole number - is 30 x 10 = 300 One-third of 300 is 100

36. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 12 x 5 ÷ 4 Which number must go into the box on the right side of the scales to balance them with the left side?

37. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Amy has 6 different coins in her purse. She has £2.68 altogether Which six coins does she have? Write your answer starting with the smallest coin.

38. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Jack colours the empty triangles on this shape red How many sixteenths does he shade red?

39. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 00C00C -20 0 C The arrow indicates the temperature in a town at 9:00 a.m. By mid-afternoon the temperature has risen by 7 0 C. The temperature then falls by 13 0 C. What is the new temperature? 20 0 C

40. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 In his cricket innings Tom scores 47 runs. His score is made up of: two sixes, three fours, one three and seven twos. The rest he scores in singles. How many singles does he score in his innings?

41. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The short side of the rectangle is the same length as the diameter of the circle. The radius of the circle is 9.5 cm. What is the perimeter of the rectangle? 24cm

42. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The shape above is rotated one quarter turn to the right. On the shape below draw the missing pieces in their new position to complete the drawing.

43. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Jason subtracts 0.25 from each of these decimals. Rewrite the new decimals in order starting with the smallest 0.550.51.80.351.5

44. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 At sports day Joe makes a standing jump of 1.8 m. Jade jumps 25 cm more than Holly. Tom jumps 10 cm more than Jade. Holly jumps 15 cm less than Joe. How far does Tom jump?

45. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 It takes Amy 25 minutes to walk to school. School starts at 8:55 a.m. She likes to arrive 10 minutes early. What time does Amy normally set off for school?

46. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Three different children do the calculations below. They then add up their answers. What is the total of their three answers? Ben calculates a quarter of 464 Amy calculates 20% of 900 Alex calculates the product of 7 and 45

47. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 How many different rectangles are there in this drawing?

48. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Each face of this cube has a surface area of 81cm 2 Chelsey wants to build a tower of cubes 216cm tall. How many cubes does she need?

49. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The rule for the sequence below is find a quarter and add two. Which two numbers complete the sequence? 2484 84

50. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 1 QUESTION NUMBER 20 Calculate one eighth of a quarter of a third of one-half of 72 Your answer will be a fraction.

51. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The product of three numbers is 48. Two of the numbers are 2 and 3. What is the third number?

52. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Joe has one of each coin up to and including £2. How much less than £10 does he have?

53. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 15 sheets of paper weigh 7.5 grams. How much does one sheet of paper weigh?

54. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A B C 70 0 In the sketch the isosceles triangles A, B and C are the same size. Calculate angle X X

55. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 91394321 37273593 63511929 49618515 Identify the five prime numbers located in the grid. What is the total of the five numbers?

56. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 492 The top number in this puzzle is found by adding all the digits below together. The bottom number is the product of the three numbers above. Calculate the two answers needed to complete the puzzle and add together your two answers.

57. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 2 QUESTION NUMBER 8 The area of this square is 64cm 2. The drawing below is made up of squares similar to this one. What is the perimeter of the new shape?

58. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 By Christmas a football team has scored 18 goals. This is 25% of their final total for the season. Jack scores 1/3 of the season’s total goals. Tom scores five less than Jack. 13 goals were scored in January. How many goals were scored by the rest of the team?

59. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 85 63 57 45 The numbers in the squares are the sum of each number in the circles on each side. Which numbers are missing from the blank shapes?

60. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 AYTOWNBETOWNCETOWN 180km360km Train X sets off from Aytown at 11:30 and travels at 90km per hour. Train Y sets off from Cetown at 12:15 and travels at 80km per hour. How much later does train Y arrive at Betown than train X?

61. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A litre of water weighs 1kg. Jack fills a plastic bottle with 0.75L of water. Together the bottle and water weigh 835g. What is the weight of the bottle?

62. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A palindrome number is one that reads the same backwards as it does forwards, e.g. 8558. Which of the calculations below produce palindrome numbers? A 29 X 24 B 30 X 30 C 11 X 11 X 11 D 1437 + 2006 E 232 + 1001

63. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The area of each circle is 38cm 2 The diameter of each circle is 7cm. What is the area of the grey shaded background?

64. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Say whether these statements are true or false A All three digit numbers are divisible by 3 without a remainder B If you add the digits of a four digit number your answer will be an even number C All prime numbers are odd D A square number cannot also be a triangular number E Numbers ending in 0 are multiples of only 5 and 10.

65. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 What fraction of the large square is shaded grey? Answer in lowest terms

66. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The area of this square is 64cm 2. The drawing below is made up of squares similar to this one. What is the area of the new shape?

67. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 2 QUESTION NUMBER 19 40% of a number is 120. What is one-third of the number?