1. Primary Schools’ Mathematics Challenge 2008 Final Round Questions Here is a selection of questions asked over two rounds. To access answers left click mouse and an automated sequence will appear. The questions may very slightly from those presented and are not in the order they were asked.

2. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL The sum of three consecutive numbers is 15. What is their product? Clue: 97, 98, 99, 100 and 101 are consecutive numbers. The consecutive numbers are 4 5 6 Their product is 4 x 5 x 6 = 20 x 6 = 120

3. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL The top number is the product of the two numbers below The bottom number is the difference between the two numbers above Which numbers could be missing from the grid below? 9 4 45 5 9 4 117 13 Two possible answers

4. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL An oval dog racing track is 240 metres all round. Jack the Flash wins a three lap race in a time of 1 min. 30 seconds. How many metres does the dog run on average per second? The dog travels 720 metres (3 x 240m) in 90 seconds Divide 720m by 90. 720m ÷ 90 = 8m per second on average Quick isn’t he?

5. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL 2 + 610 - 82 x 5 + 9 ÷ 3 + 15 - 9 + A The grid is completed by adding together the boxes as shown by the arrows. Which number fits into box A? 6 X 5 + 40 19 + 23 6 10 8 30 10 13 59 40 19

6. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Which five numbers are missing from this number track? 25 x3 Minus 19Divide by 8 Multiply by 7Add 1 75 56 50497

7. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL The rule for this sequence is find a quarter and add 11. Write in the two missing numbers in the sequence below. 4121414.5 ¼ of 12 is 3. 3 + 11 make 14 ¼ of 14 is 3.5 3.5 + 11 make 14.5

8. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL The rectangle has the same perimeter as the square. What is the length of the shorter side of the rectangle? Square Area 81cm 2 10.75 cm The length of one side is 9cm The perimeter is 36cm (9cm x 4) The perimeter is 36cm Two of the sides total 21.5 cm (10.75 x 2) The other two sides total 36 - 21.5 = 14.5 cm The short side is 14.5cm ÷ 2 The short side is 7.25cm

9. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Tom finds the denominator of a fraction by calculating three-fifths of 25. He finds the numerator by finding a quarter of a half of 16 What is Tom’s fraction? 15 2 2

10. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Here are six number cards. The 12 card must be used in each fraction. 16312489 Use the cards to make two different fractions equivalent to ¾ 12 16 9

11. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL What fraction of the large square is not shaded grey? The denominator is 16. 10 squares are not grey The fraction not shaded is 10/16 or 5/8

12. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Add 0.25 to each of the decimal fractions below. 0.350.050.150.50.55 Rewrite the new decimal fractions in order starting with the largest. 0.350.050.150.50.55 Add 0.25 to each decimal 0.60.30.40.750.8 Rewrite starting with the largest decimal 0.80.750.60.40.3

13. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL This diagram is placed in the middle of a square grid. The new grid is the same height as the diagram shown What percentage of the new large square grid is red? Because the diagram is five squares high the new big square is made up of 25 smaller squares. The diagram fits in the middle. Three out of the 25 squares are red. As a percentage this is 12 out of 100 or 12%

14. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Which mathematics terms are hidden in these anagrams? ALL PALER MYSTERY M ALL CUT ACE Then find your answers on the word search grid. UPATEALY NAAASFET ER`SPAALE LACULTEN ALCTYSYM SEYMMTRY TLCMEINK SLYMEZXP P A R A L L E L S Y M C E T Y R PARALLEL SYMMETRY CALCULATE P A R A L L E L SEYMMTRY LACULTEAC

15. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL A TU R Q L I E R LN U E G E S Q Three mathematical words are mixed up in this circle of letters. Each word must contain the centre letter A once only U R E S Q URESQA E Q U E L Q U E LQUE T L I R N E G TLIRNEG A A

16. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL You have a zero to ninety-nine hundred square. A. How many times does the 9 digit appear? B. Which digit appears the least number of times? 0123456789 10111213141516171819 20212223242526272829 30313233343536373839 40414243444546474849 50515253545556575859 60616263646566676869 70717273747576777879 80818283848586878889 90919293949596979899 9 19 29 39 49 59 69 79 89 99909192939495969798 0 10 20 30 40 50 60 70 80 90 11 times 9 times 10 times 11 + 9 = 20 0 ten times

17. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL All the triangles in this shape are equilateral. The perimeter of the large triangle is 108cm. What is the perimeter of the blue rhombus made by the two equilateral triangles? The side of the large triangle is 108cm ÷ 3 = 36cm One side of the rhombus is 36cm ÷ 2 = 18cm The perimeter of the rhombus is 18cm x 4 = 72cm

18. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Use the symbols = to make these number sentences correct A.( 2 x 19 ) + 15 13 x 4 B.10 x 10 x 10 40 x 25 C.9.9 - 3.3 9.3 - 3.9 38 + 15 = 5352 1000 6.65.4 > = >

19. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL A bag of crisps weights 25g How many bags of crisps are in a box if its contents weigh 2Kg? 2 Kg = 2000 g 2000 g ÷ 25 = 80

20. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL In a sale a shop makes the following offer: Buy one item and get a second item at a 20% discount. The discount applies to the cheaper item bought. Jack buys a football and a pair of trainers. How much does he pay altogether? £25.49 £19.99 £10.50 The football is cheaper so £10.50 ÷ 5 (20%) = £2.10 this is his discount. He pays £10.50 - £2.10 = £8.40 for the football For the trainers and the football Jack pays £25.49 + £8.40 = £33.89 20% is the same as one-fifth

21. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL School starts at 8:50 a.m. Amy arrives 13 minutes early. Ben is late. Ben and Amy arrive 35 minutes apart. What time does Ben arrive at school? Amy arrives at ( 8:50 - 13min. ) 8:37 Ben arrives at ( 8:37 + 35min. ) 9:12

22. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL 18cm Jade has three Russian Dolls. Each doll is 1½ (1.5) times bigger than the previous one. ABC How tall are dolls A and C? Doll A is 12 cm. 18 cm ÷ 1.5 = 12 cm Doll C is 27 cm. 18 cm x 1.5 = 27 cm

23. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL A transit van and its parcels weigh 2.25 Tonnes altogether. The van weighs 1.75 Tonne. Jack loads the van with 125 similar parcels. How much does each parcel weigh? Altogether the parcels weigh 2.25T - 1.75 T = 500 Kg (2250 Kg - 1750 Kg) Each parcel weighs 500 Kg ÷ 125 = 4 Kg

24. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Look at the three separate problems below. A = 19 + yB = y 2 C = (5 x y) - (120 ÷ y) y = 15, what is the answer to each problem? A.19 + 15 = 34 B.15 X 15 = 225 C.75 - 8 = 67

25. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Amy is facing east. She turns anti-clockwise to face north-west Through how many degrees does she turn? E N W N..W. 90 0 45 0 90 0 +45 0 = 135 0

26. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL A B X 80 0 Isosceles triangles A and B are the same size. What is the value of angle X? This angle is 180 0 - (80 0 + 80 0 ) = 180 0 - 160 0 = 20 0 This angle is also 20 0 because the triangles are the same size. Angle X is 180 0 - (20 0 + 20 0 ) = 180 0 - 40 0 = 140 0

27. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL A B C D E Sam is snookered on all the reds. He plays his shot along the line shown by the white dots. Which red is he most likely to hit if the ball bounces off the cushion at a right angle? A

28. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Art gallery ENTRY FEE £1.25 per person 220 people went to the art gallery on Saturday. How much money is this altogether? £1.25 X 220 = £275

29. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Five friends have the weights shown below. Amy 42 Kg, Ben 51 Kg Jade 46Kg Laura 51Kg Tom 47Kg What is the difference in Kg between their modal weight and their median weight? Their modal weight is 51 Kg Their median weight is 47 Kg 51 Kg - 47 Kg = 4 Kg

30. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL 5 4 =60 3 15 7 =7 1 You may use the symbols + - x ÷ once only. Complete these equations (number sentences) - x ÷ +

31. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Here is part of a multiplication problem solved by using the grid method. x30 20 4 What is the answer to the calculation when complete? 700 + 140 = 840 5 600100 120 700 140

32. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Use the rules to find the next number in each sequence Find he sum of your three answers Rule: Add 95 14 23 Rule: Multiply by 44 16 64 Rule: Subtract 8120 112 104 256 96 32 32 + 256 + 96 = 384

33. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Find the total of all the prime numbers between 1 and 20. Multiply your result by three. 23711131719 ++ 5 +++++ Total 77 77 x 3 = 231

34. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL The diagram shows some shapes on a square grid CAB DE a. Which two shapes have the same area as A? b. Which two shapes have the same perimeter as A? Shape A has an area of 3 units. Shapes B and E have the same area Shape A has a perimeter of 4 small units and 2 longer units. Shapes D and E have the same area

35. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Which of these shapes have at least one line of symmetry? CA BD E F A, C, D, F

36. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL Which of the shapes on the grid have more than 1 line of symmetry? ABD C EF G Shapes B D E

37. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL The shape below is rotated 90 0 degrees clockwise Which shape below that shows its new position? ABCDEF

38. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL The top line of the rectangle goes through the centre of each of the three similar circles. The perimeter of the rectangle is 32cm. What is the radius of each circle? 4 cm The longer side of the rectangle is 12 cm The diameter of each circle is 12 cm ÷ 3 = 4cm The radius of each circle is 4 cm ÷ 2 = 2cm

39. PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL x y 0 2468 2 4 6 A. What are the co- ordinates of the centre of the square? B. What are the co- ordinates of the junction of the two straight lines that make a cross ? A ( 3, 4 ) B ( 7, 3 )