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Primary Mathematics Challenge

Primary Mathematics Challenge. A selection of questions 2007. Sample semi-final question. Look at the continuous sequence of squares below. 53 rd square. What colour will the fifty-third square be?. Answer - red. Answer sequence. Sample semi-final question.

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Primary Mathematics Challenge

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  1. Primary Mathematics Challenge A selection of questions 2007 N. E. Lincolnshire Mathematics Team

  2. Sample semi-final question Look at the continuous sequence of squares below 53rd square What colour will the fifty-third square be? Answer - red Answer sequence N. E. Lincolnshire Mathematics Team

  3. Sample semi-final question The sum of two numbers is 15 Their difference is three. What is their product? 54 9 + 6 = 15 is their sum or total 9 - 6 = 3 is their difference 9 x 6 = 54 is their product (multiplied together) Answer sequence N. E. Lincolnshire Mathematics Team

  4. Sample semi-final question Jack draws the shape below 16 3 7 6 How many rectangles can be found in the drawing? Answer sequence N. E. Lincolnshire Mathematics Team

  5. Sample semi-final question In a box of dominoes there are seven ‘double’ tiles What is the total number of spots on the seven doubles tiles altogether? 42 Answer sequence N. E. Lincolnshire Mathematics Team

  6. Sample semi-final question The perimeter of this rectangle (oblong) is 48 cm. The rectangle is three times as long as it is wide 18 cm long 6 cm wide How long and how wide is the rectangle? The width and length shown in blue are 24 cm long altogether The width is a quarter of 24 cm and the length three-quarters of 24 cm Answer sequence N. E. Lincolnshire Mathematics Team

  7. Sample semi-final question Shirt £12.99 Sports shoes £16.49 Cap £9.50 Tom buys a cap, Amy buys shoes and Jack buys a shirt. Each child pays with a £20 note. How much change does each child receive? Jack £7.01 Amy £3.51 Tom £10.50 Subtract each price from £20. Answer sequence N. E. Lincolnshire Mathematics Team

  8. Sample semi-final question Joe thinks of two 2-digit numbers both less than seventy-five. Both numbers have 6, 3 and 5 as factors. One number is half the size of the other. 30 60 What are the two numbers? Answer sequence N. E. Lincolnshire Mathematics Team

  9. Sample semi-final question To score a total of 10 on two standard dice you would need to throw a 6 and a 4 or two fives. If you had three dice what are the combinations of scores you could throw to make a total of 10? 2 2 6 3 3 4 These may be thrown in any order 1 5 4 2 4 4 3 1 6 5 3 2 Answer sequence N. E. Lincolnshire Mathematics Team

  10. Sample semi-final question The graph shows the percentage scored by 7 children in a test Jade A. Chelsey Paul Lee B. 35% (½ of 70%) Amy Jack C. Tom and Jade Tom Chelsey 0 10 20 30 40 50 60 70 80 90 100 A. Who scored exactly 30% less than Amy? B. What did Paul score in his last test if this score was double his last score? C. Which two children scored exactly 55%between them? Answer sequence N. E. Lincolnshire Mathematics Team

  11. Sample semi-final question The radius of the yellow circle is 12 cm and x is the centre of the circle 288 cm2 x What is the area of the red rectangle (oblong)? The width of the rectangle equals the radius of the circle 12 cm The length of the rectangle is twice the radius of the circle 24 cm The area of the rectangle is 12 cm x 24 cm = 288 cm2 Answer sequence N. E. Lincolnshire Mathematics Team

  12. Sample semi-final question The circumference of a bicycle wheel is 140 cm How far in metres does the wheel travel in thirty revolutions? 42 m The wheel travels 140 cm x 30 = 4200 cm 4200 cm is the same distance as 42 metres Answer sequence N. E. Lincolnshire Mathematics Team

  13. Sample semi-final question Chloe makes a square with four sticks She then uses some more sticks to make another square on the side 6 She continues the pattern in the same way adding more squares. She uses 19 sticks altogether How many squares are there in her completed sequence? 4 7 10 13 16 19 Answer sequence N. E. Lincolnshire Mathematics Team

  14. Sample semi-final question Three-fifths of a number is 45 25 What is one-third of the same number? If three-fifths of the number is 45 then one-fifth is 45 ÷ 3 = 15 Number Three-fifths 45 15 15 15 15 Two-fifths 15 The whole number is 15 multiplied by 5 = 75. 75 One-third of the number is 75 ÷ 3 = 25 . 75 25 25 25 Answer sequence N. E. Lincolnshire Mathematics Team

  15. Sample semi-final question Triangle ABC is equilateral A X 1200 B C What is the value of angle X? There are many different ways to find this answer. How many can you find? Answer sequence N. E. Lincolnshire Mathematics Team

  16. Sample semi-final question Which numbers are missing from these number sentences? A. - 7 = 35 42 B. X 7 = 35 5 28 C. + 7 = 35 63 D. ÷ 7 = 9 Answer sequence N. E. Lincolnshire Mathematics Team

  17. Sample semi-final question These shapes each have properties in common. Identify 2 common properties Some possibilities All quadrilaterals All have parallel lines All have at least one line of symmetry Answer sequence N. E. Lincolnshire Mathematics Team

  18. Sample semi-final question Jack makes five statements. Some are true, some are false. T A. All squares are rectangles, but not all rectangles are squares F B. An isosceles triangle has two right angles F C. To multiply any number by 10 just put a zero on the end T D. For every decimal fraction there is an equivalent ‘ordinary’ fraction T E. A regular pentagon has five lines of symmetry Write T or F next to each statement Answer sequence N. E. Lincolnshire Mathematics Team

  19. Sample semi-final question Jade starts with an even number. She doubles it. She continues to double until she reaches 144. What are the other numbers in her sequence before she reaches her total? Start with 144 and continue halving until she reaches her starting number. 18 36 72 144 Answer sequence N. E. Lincolnshire Mathematics Team

  20. Sample semi-final question 8 How many different triangles can you find in this drawing? 2 3 1 4 Answer sequence N. E. Lincolnshire Mathematics Team

  21. Sample semi-final question Two of these nets will not make a closed cube. A B C D E Write the letters of the nets that will make a closed cube Answer sequence N. E. Lincolnshire Mathematics Team

  22. Sample semi-final question In a football match the score at half time is 1 – 0 to the home side. In the second half three more goals are scored. What are the possible full-time results? Include both home and away possibilities. 4 - 0 3 - 1 2 - 2 1 - 3 Answer sequence N. E. Lincolnshire Mathematics Team

  23. Sample semi-final question A ream of A4 paper is 500 sheets. The height of a ream is 5.5 cm 0.11 mm What is the thickness of one sheet of paper in millimetres? Change 5.5 cm to 55 mm. Divide 55m by 500 = 0.11mm Answer sequence N. E. Lincolnshire Mathematics Team

  24. Sample semi-final question Here are some lists. Which is the odd one out in each list? 1a 0.4 b. Two-fifths c. 40% d.16 e. 4% 40 2a 25 x 15 b. 750 ÷ 0.5 c. 250 + 125 d.750e. 1000 - 625 2 3a rhombus 3b pollygon 3c paralellogram 3d isocseles 3e trapesium Answer sequence N. E. Lincolnshire Mathematics Team

  25. Sample semi-final question Each apex of the red equilateral triangle is in the centre of a circle. The circles are the same size. The perimeter of the triangle is 45 cm 7.5 cm Each side of the triangle is 15 cm. The radius of these circles is half the length of one side of the triangle 15 cm ÷ 2 = 7.5 cm What is the radius of each of the circles? Answer sequence N. E. Lincolnshire Mathematics Team

  26. Sample semi-final question A shop reduces the price of sports shoes by 20% The new price is £60 £75 What was the original price of the shoes? The new price is four-fifths of the old price. The new price is four parts of the old price, this is £60 ÷ 4 = £15 So the original price was £60 + £15 = £75 Answer sequence N. E. Lincolnshire Mathematics Team

  27. Sample semi-final question There are three prime numbers between 80 and 100 269 What is their total? None of the even numbers can be prime in this case. This leaves - 81 83 85 87 89 91 93 95 97 99 Can be divided by 3, 5 or 7 so are not prime numbers. Are prime numbers. 83 + 89 + 97 = 269. Answer sequence N. E. Lincolnshire Mathematics Team

  28. Sample semi-final question The two triangles are isosceles and the same size. They each have a perimeter of 20.5 cm. 17 cm B The third side is the perimeter of the triangles 20.5cm - 12 cm (the total length of the equal sides) = 8.5 cm The two equal sides of each triangle are 6 am long because they are the same length as the short side of the rectangle. 6 cm Line AB is 2 x 8.5 cm = 17 cm A How long is line AB? Answer sequence N. E. Lincolnshire Mathematics Team

  29. Sample final question Two straight lines cross as shown in the drawing 1050 A 750 What is the size of angle A and angle B? B 1050 Angle A is 1800 - 1050 = 750 Angle B is 1800 - 750 = 1050 Answer sequence N. E. Lincolnshire Mathematics Team

  30. Sample final question The sum of the edges of each of these squares is 1000 450 Which three numbers are missing? 150 775 B A 400 50 100 125 555 395 C Answer sequence N. E. Lincolnshire Mathematics Team

  31. Sample final question Six people play each other once at golf. 15 How many games are played altogether? Player E Player F Player D Player B 1 Game Player F Player C Player E Player C 2 Games Player D Player F Player A Player D 3 Games Player E Player E Player F Player F 4 Games 5 Games Answer sequence N. E. Lincolnshire Mathematics Team

  32. Sample final question Gavin weighs one-third more than Sally. Mum weighs twice as much as Gavin. Mum and dad weigh 140kg altogether. Sally weighs 24kg. How much do mum and dad each weigh? Mum weighs 64kg. Dad weighs 76kg. Gavin weighs 24kg + 8kg = 32kg. Mum weighs 32kg x 2 = 64kg. Dad weighs 140kg - 64kg = 76kg. Answer sequence N. E. Lincolnshire Mathematics Team

  33. Sample final question Jade uses five 5s to write a number sentence. She uses two + signs and one x sign. The answer to her sentence is 555. What could her number sentence have been? (5 + 5) x 55 + 5 = 555 The 5s in her answer are not part of the five 5s she uses to work out her problem. Answer sequence N. E. Lincolnshire Mathematics Team

  34. Sample final question The drawing shows part of number grid six columns wide. 5 10 15 0 5 10 15 20 25 30 35 40 45 45 65 70 70 85 110 110 A B 130 130 Which numbers are missing from squares A and B? Answer sequence N. E. Lincolnshire Mathematics Team

  35. Sample final question The area of this square is 64cm2 Joe uses similar squares to make a new shape. 80cm The area is 64cm2 so each side is 8cm. There are ten sides to the new shape. 10 x 8cm = 80 cm What is the perimeter of the new shape? Answer sequence N. E. Lincolnshire Mathematics Team

  36. Sample final question Amy and Jade live in different villages. Their villages are both 90km away from the town. They agree to meet in the town at noon. Amy travels at a speed of 40km per hour and Jade travels at a speed of 60km per hour. At what time should they each set off from their villages to arrive in the town at noon? Amy sets off at 9:45 a.m. Jade sets off at 10:30 Amy’s journey time is 2¼ hours. Jade’s journey time is 1½ hours. Answer sequence N. E. Lincolnshire Mathematics Team

  37. Sample final question There are three mathematical terms jumbled in this sequence of letters. S M S U U Y B L M T T M R I E A P T C L R T Y Y SMSUUYBLMTTMRIEAPTCL RTYY SU B T RAC T M U L T I P L Y SYMMETRY What are the three terms? SUBTRACT MULTIPLY SYMMETRY Answer sequence N. E. Lincolnshire Mathematics Team

  38. Sample final question Fred cuts discs this size from a sheet of metal as shown below. Each disc has a diameter of 3cm. The sheet is 4 discs (12cm) long The area of the sheet is 9cm x 12cm = 108cm2 The sheet is 3 discs (9cm) wide What is the area of the sheet of metal? 108cm2 Answer sequence N. E. Lincolnshire Mathematics Team

  39. Sample final question Five children run 50m in a race. Their finishing times are: 7.65 sec 7.5 sec., 8.00., 7.75., 8.5 sec. and 6.5 sec. What is their average (mean) time for running 50m? 7.5 + 8.00 + 7.75 + 8.5 + 6.5 = 38.25sec 38.25 ÷ 5 = 7.65 sec. Answer sequence N. E. Lincolnshire Mathematics Team

  40. Sample final question Chloe takes the number 2. She then applies a rule (does something to it) and gets the answer 8. She uses the same rule with some other numbers. Start number 4 finish number 18 Start number 3 finish number 13 Start number 6 finish number 28 Start number 1 finish number 3 Can you work out what her rule is? Multiply the start number by 5 then subtract 2 Answer sequence N. E. Lincolnshire Mathematics Team

  41. Sample final question Calculate the outcome if Tom puts the following sequence into his calculator 7 + 9 4 x 0 - 3 + 12 = ÷ √ 3 Answer sequence N. E. Lincolnshire Mathematics Team

  42. Sample final question The number shown by A in the centre of the drawing is the product of the numbers linked by the arrows opposite each other. 15 What are the values of A and B? B 40 A 120 3 8 Answer sequence N. E. Lincolnshire Mathematics Team

  43. Sample final question The numbers in this sequence start at 27 and reduce by the same number each time. 27 ? 24 ? 21 ? 18 ? 15 12 Which numbers are missing from the sequence? The sequence decreases by 3 from left to right. The sequence increases by 3 from right to left. Answer sequence N. E. Lincolnshire Mathematics Team

  44. Sample final question One person sits on each side of a square table Jack has five similar tables that he joins together to make one long table. 12 How many people can be seated around the new table? Answer sequence N. E. Lincolnshire Mathematics Team

  45. Sample final question In a family each boy has one sister and each girl has one brother. How may people are in the family including mum and dad? 4 Answer sequence N. E. Lincolnshire Mathematics Team

  46. Sample final question What is 25% of one-third of 240? One-third of 240 is 80 25 % (or ¼) of 80 is 20 20 Answer sequence N. E. Lincolnshire Mathematics Team

  47. Sample final question In championship tennis the balls are new at the start of the match. They are changed after the first seven games and then every nine games after that. 5 Roger Federer beats Tim Henman 6 – 3, 7 – 6, 2 – 6, 6 - 4 How many sets of new balls are used in the match? 40 games are played. Subtract 7 (1st set of balls) leaves 33 33 games ÷ 9 uses 3 sets of balls (27 games) with 6 extra games left. An extra set is needed for the six games. 3 + 1 + 1 = 5 Answer sequence N. E. Lincolnshire Mathematics Team

  48. Sample final question Inside the drawing of a square there are 3 shapes. Points A and B are the middle of the sides of the square. The length of each side of the square is 8cm. What is the area of each shape? 1 1. 16cm2 2. 32cm2 3. 16cm2 2 A 3 The area of the square 8cm x 8cm = 64 cm2 Shape 1 is ¼, shape 2 is ½ and shape 3 is ¼ of the square B Answer sequence N. E. Lincolnshire Mathematics Team

  49. Sample final question The sum of three single-digit numbers is 10. Their product is 30. What are the three numbers? 2 3 5 Answer sequence N. E. Lincolnshire Mathematics Team

  50. Sample final question A large rectangle is divided into smaller rectangles The perimeter of this rectangle is 18 cm. 3cm 6cm 42cm2 7cm 7cm What is the area of the pink rectangle? The pink rectangle is 7cm by 6cm = 42 cm2 Answer sequence N. E. Lincolnshire Mathematics Team

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