N.E. LINCS. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2005

1. N.E. LINCS. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2005 Semi-final questions and answers

2. N.E. LINCS. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2005How to use the presentation • Each question is presented twice. • Slides with a red square in the top right corner are the tasks to be performed and are printable for child use. • Click to select the duplicate slide to display the answer. • A mouse will appear on the slide - click once • The slide will then process the answer automatically and where appropriate present a strategy for solving the problem. • When the process is complete a green arrow will appear. • Click the green arrow and the slide will move to the next problem.

3. Printing slides for children’s use. • Select the numbers of slides to be printed • Select Ctrl P. • Type slide numbers in the appropriate box. • Suggest select: • Pure black and white • Frame slides • Scale to fit paper • Select print what: • Highlight number of slides per page, (handouts 2 slides per page) works well. • Select number of copies. • Click OK.

4. Which number will make this number sentence correct? 5 x 4 x ? = 140

5. Which number will make this number sentence correct? 5 x 4 x ? = 140 5 x 4 x7 = 140 Answer

6. Which numbers complete this sequence? -13 3 19 27 35

7. Which numbers complete this sequence? -13 -5 3 11 19 27 35 The sequence is - add 8 to the previous number. To discover the sequence you may have to work backwards and subtract 8. Answer

8. What decimal fraction of this shape is shaded red?

9. What decimal fraction of this shape is shaded red? Ans. 0.25 As a vulgar (ordinary) fraction the answer would be two-eighths or ¼. This is then changed into a decimal. Answer

10. Emily has three regular hexagons like the one below.Each side is 5cm long. She joins them to make a new shape. What is the perimeter of her new shape?

11. Emily has three regular hexagons like the one below.Each side is 5cm long. She joins them to make a new shape. What is the perimeter of her new shape? 10 cm hidden here 10 cm hidden here 70 cm The answer may be found by counting round each line of the shape in 5cm blocks. OR Each hexagon has a perimeter of 30cm. This makes 90 cm altogether. When they are joined 10cm of perimeter is hidden. They are joined twice, 90cm - 20cm = 70cm. Answer

12. Each shape stands for a number.Use the information to work out the value of each shape. = 8 ÷ = - 2 x = 36

13. Each shape stands for a number.Use the information to work out the value of each shape. 48 6 = 8 ÷ = - 48 2 50 6 x 6 = 36 Answer

14. Find the four shapes hidden in the word search CYLINDER KITE SPHERE RHOMBUS S K K Q K H O P X H I I S S P P H H E E R R E E R R T T Y N O T H H L H E E L U M F O O H R H D D M B S M M R R H O N N S P B B Y E M Z J I I V U U M K I E T L L L S S L P F I H Y G Y Y Y V G T C C D J C C

15. Find the four shapes hidden in the word search CYLINDER KITE SPHERE RHOMBUS S K K Q K H O P X H I I S S P P H H E E R R E E R R T T Y N O T H H L H E E L U M F O O H R H D D M B S M M R R H O N N S P B B Y E M Z J I I V U U M K I E T L L L S S L P F I H Y G Y Y Y V G T C C D J C C Answer

16. Which of the blue shapes below has the same area as the shape on the grid? A B C D E

17. Which of the blue shapes below has the same area as the shape on the grid? A 18 B 18 C D D Answer E

18. Which five consecutive even numbers add up to 30?

19. Which five consecutive even numbers add up to 30? 2, 4, 6, 8, 10 Answer

20. Estimate the size if this angle.N.b.this is a sketch of the original and may not be exact size if reproduced.

21. Estimate the size of this angle. 1150 900 250 Leeway 1100 to 1200 Answer

22. The recipe makes 6 Yorkshire puddings.Adjust it for 8 Yorkshire puddings 240 g Flour 3 Eggs 360 ml Water 120 ml Milk

23. The recipe makes 6 Yorkshire puddings.Adjust it for 8 Yorkshire puddings 240 g Flour 3 Eggs 360 ml Water 120 ml Milk 320 g Flour 4 Eggs 480 ml Water 160 ml Milk Two extra people is one third of six people. Find one third of each item and add it to the original amount. Answer

24. A Calculate half of a quarter of 48. B A train leaves the station at 12:35. It arrives after travelling for 100 minutes. What time does it arrive. Answer in 24 hour clock. C Jack receives £3.70 change from £10. He buys 2 items. One cost 50p. What did the other item cost?

25. 6 A Calculate half of a quarter of 48. B A train leaves the station at 12:35. It arrives after travelling for 100 minutes. What time does it arrive. Answer in 24 hour clock. 14:15 C Jack receives £3.70 change from £10. He buys 2 items. One cost 50p. What did the other item cost? £5.80 Answer

26. Each cube weighs the same.The cylinder weighs 0.6 Kg.What is the weight of 1 cube? 6Kg 2Kg

27. Each cube weighs the same.The cylinder weighs 0.6 Kg.What is the weight of 1 cube? 800 grams 800 grams 800 grams 6Kg 2Kg Total weight is 3Kg or 3000 g (on scale) Cylinder weighs 600g (0.6 Kg) Three cubes weigh 3 000g - 600g = 2 400 g altogether. One cube weighs 2 400 g ÷ 3 One cube weighs 800g Answer

28. TRUE OR FALSE? All odd numbers are prime numbers. All rectangles are quadrilaterals. A litre of water weighs 1 Kilogram. All 3-digit numbers are divisible by three without a remainder.

29. TRUE OR FALSE? All odd numbers are prime numbers. All rectangles are quadrilaterals. A litre of water weighs 1 Kilogram. All 3-digit numbers are divisible by three without a remainder. FALSE TRUE TRUE FALSE Answer

30. Jack multiplies 24 by 15 on his calculator.He presses the wrong digits and gets the answer 495 on the display.What is the difference between the correct answer and the one Jack sees on the calculator display?

31. Jack multiplies 24 by 15 on his calculator.He presses the wrong digits and gets the answer 495 on the display.What is the difference between the correct answer and the one Jack sees on the calculator display? 24 x 15 = 360 495 - 360 = 135 Answer

32. Use the information given to put the heights of the five children in order starting with the smallest child. Tom is 8 cm smaller than Jack. Jack is 2 cm taller than Ben. Ben is 1.5 m tall. Jack is 4 cm smaller than Emily. Amy is 10 cm smaller than Ben.

33. Use the information given to put the heights of the five children in order starting with the smallest child. Tom is 8 cm smaller than Jack. Jack is 2 cm taller than Ben. Ben is 1.5 m tall. Jack is 4 cm smaller than Emily. Amy is 10 cm smaller than Ben. AMY 140 cm TOM 144 cm BEN 150 cm JACK 152 cm EMILY 156 cm HINT: Work in cm. Answer

34. Both shapes are regular and have the same perimeter.How long is one side of the triangle? 12 cm

35. Both shapes are regular and have the same perimeter.How long is one side of the triangle? 12 cm Perimeter of equilateral triangle is 60 cm. 1 side is 60 ÷ 3 = 20 cm. Perimeter of regular pentagon is 5 x 12 cm = 60cm Answer

36. The numbers in the pyramid are calculated by adding the two numbers immediately below.Complete the pyramid. 16 2 3 11

37. The numbers in the pyramid are calculated by adding the two numbers immediately below.Complete the pyramid. 61 31 30 15 14 16 2 13 3 11 Answer

38. Each cube has a surface area of 6 square units. The shape below is made from similar cubes What is the total surface area of the new shape?

39. Each cube has a surface area of 6 square units. The shape below is made from similar cubes What is the total surface area of the new shape? 2 square units hidden here and here Or you could just count 2 square units hidden here 18 square units. Total surface area is 6 x 4 = 24. Each join takes away 2 faces or 2 square units. There are three joins so the new area is 24 - 6 = 18 square units Answer

40. It takes 3 of the middle container to fill the large one.It takes six of the small one to fill the middle one.How many millilitres does the small container hold? 450 ml

41. It takes 3 of the middle container to fill the large one.It takes six of the small one to fill the middle one.How many millilitres does the small container hold? ÷3 ÷6 450 ml 150 ml 25 ml Answer

42. Each line in the drawing adds up to 1000.Complete the boxes to make the target total for each line. 550 375 250 150

43. Each line in the drawing adds up to 1000.Complete the boxes to make the target total for each line. 550 475 375 375 250 150 75 Answer

44. Amy makes rectangular shapes by linking three similar rectangles.How many rectangles can you count altogether in Amy’s drawing?

45. Amy makes rectangular shapes by linking three similar rectangles.How many rectangles can you count altogether in Amy’s drawing? 2 3 11 2 4 Answer

46. Below is an EQUATION3n + 9 = 30What does n equal?

47. Below is an EQUATION3n + 9 = 30What does n equal? 3n = 30 - 9 3n = 21 n = 7 Answer

48. A house is bought for £175 000.A year later the house is sold for 10% more than it cost originally.What is the new price?

49. A house is bought for £175 000.A year later the house is sold for 10% more than it cost originally.What is the new price? 10% 0f £175 000 is £17 500. Add together £175 000 and £17 500. New price £192 500. Answer

50. The box is as wide as it is tall.What is the volume of the box? 12 cm 5 cm