1. SEMI-FINAL ROUND QUESTIONS WITH ANSWERS POWERPOINT

2. Some of the questions have been modified and may appear slightly different from those in the actual competition. To access answers simply left click the mouse and an automatic answer sequence will appear with an explanation where appropriate HAVE FUN

3. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Each arm of the cross totals 50 19 17 13 Which two numbers are missing from the empty boxes? 1815

4. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Find the mathematical terms mixed up in the capital letter strings written below. A clue is given for each one MATURE PETER - can be measured SO LESS ICE – can be shapely TEMPERATURE ISOSCELES

5. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Emily multiplies three different numbers together. Each number is greater than one. Her answer is 24. What could her numbers have been? 234 XX 64 X= 24

6. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Apples cost 15p each. Jack buys seven apples How much change does Jack receive from £2.00? Buy 2 for 25p. Two apples can be bought for 25p Six apples can be bought for 75p Add the cost of a single apple to 75p 75p + 15p = 90p £2.00 - 90p = £1.10 £1.10

7. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL The perimeter of this regular pentagon is 40 cm Amy joins two congruent pentagons together What is the perimeter of Amy’s new shape? One side measures 40 cm ÷ 5 = 8cm There are 8 sides to Amy’s new shape The new perimeter is 8cm x 8 = 64cm

8. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL True or false? Look at the statements below and say whether each is true (T) or false (F) A. All quadrilaterals have four right angles B. All quadrilaterals have at least one line of symmetry C. A right angle triangle may be isosceles T F F

9. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL This shape has been rotated 90 0 clockwise at point A. Which shape below shows its original position? ABC D E D A

10. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Laura says that 20% of the number she is thinking of is 36. She asks Ben to find out what her number is and then make his answer up to 225. What is the number that Ben should add to Laura’s number to make 225? 20% is equal to one-fifth Laura’s original number is 36 x 5 = 180 Ben subtracts 180 from 225 to find his number 225 - 180 = 45 45

11. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL A football team scores 45 goals in a season. Adam scores 18 goals. Tom scores one-third of them. Nick scores three. How many goals were scored by other team members? 1/3 of 45 is 15 The three players score 18 + 15 + 3 = 36 The other players score 45 - 36 = 9 goals 9

12. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Carpet cost £15 per m 2. Jason has a room like the plan in the drawing. Jason covers the floor with carpet. How much does the carpet for the room cost altogether? 3m 5 m 2 m 6 m Split the room into two rectangles to find the total area Area A is 6m x 3m = 18m 2 Area B is 3m x 2m = 6m 2 The total area is 24m 2 The total cost is 24m 2 x £15 = £360 A B

13. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Ben draw square with sides 6.5 cm long. Amy draws a square with sides twice as long as Ben’s square. What is the area of Amy’s square? 6.5 cm 13 cm The area of the new square is 13cm x 13cm = 169cm 2

14. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL This sequence follows the pattern of double and add one 112347191 Which three numbers are missing from the sequence? 5 95383 Subtract one from 11 and halve the answer Double the previous number and add 1

15. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL The missing numbers above the blue boxes are found by adding the two numbers in the boxes directly below The missing numbers below the blue boxes are found by multiplying the two numbers in the boxes directly above 532 Write in the missing numbers on the drawing 85 13 156 90

16. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL What is one-third of 25% of a half of 4800? Half of 4800 is 2400 25% (or ¼) of 2400 is 600 1/3 of 600 is 200 200

17. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL The area of the triangle A in this drawing is 80cm 2. The total area of the whole drawing is 130 cm 2 The two squares are the same size. What is the length of one side of each square? A The area of the two squares is 130 - 80cm 2 = 50cm 2 The area of one square is 50cm 2 ÷ 2 = 25cm 2 The length of one side of each square is 5cm

18. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL George bought a sports car for £15 000. When he sold it two years later he received 11% less than he paid for it. What was the price he sold his car for? Partition 11% into 10% and 1% 10% of £15 000 is £1 500 (£15 000 ÷ 10) 1% of £15 000 is £1 500 divided by 10 or £15 000 ÷ 100 1% of £1 500 is £150 11% of £15 000 is £1 500 + £150 = £1 650 George sells the car for £15 000 - £1 650 = £13 350

19. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL The cost of Sunday lunch at a restaurant is £12.50 for two courses and £15.75 for three courses. Five people in a party book Sunday lunch. Two have three courses and three have two courses. How much is left out of £100 when the bill has been paid? 2 x £15.75 = £31.50 3 x £12.50 = £37.50 £31.50 + £37.50 = £69 £100 - £69 = £31 left over

20. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL a = 5, b = 3, c = 4, d = 6 Amy uses the numbers to calculate the fraction shown below c x b a x d Write the fraction shown in Amy’s problem in its lowest terms 4 x 3 = 12 6 x 5 = 30 12 30 = 2 5

21. What weight must be added to the left side of the scales to balance them up with the right side? 2.5Kg 750g 2 500g (2.5 Kg) - 750g = 1 750g 1 750g or 1.75Kg or 1Kg 750g PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL

22. Jody has the money shown. She buys 3 packets of crisps and 2 bars of chocolate 32p 47p How much money will Jody have left? 3 packets of crisps 32p x 3 = 96p 2 bars of chocolate 47p x 2 = 94p 96p + 94p £1.90 There is £5.17 in coins £5.17 - £1.90 = £3.27

23. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Jack has three different rectangles each with an area of 24cm 2 Each side of his rectangles is bigger than 1cm. Each side is a whole number of centimetres long. What are the possible perimeters of his three rectangles? 3cm 2cm 12cm 6cm 4cm 8cm Perimeter 28cmPerimeter 22cmPerimeter 20cm Find the lengths of the sides of each rectangle using the area as a starting point The three rectangles may be used to help you with any calculation you may need

24. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL A single cube has sides 13 mm long. Ellie makes a chain of attached cubes like the one shown. What is the length of Ellie’s chain of cubes when it is rounded to the nearest centimetre? There are 19 cubes The total length of the cubes is 19 x 13mm = 247mm 247mm = 24.7cm 24.7cm rounded to the nearest centimetre is 25cm

25. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Tom works out this brackets problem. What is his answer? ( 7 x 5 ) + ( 55 ÷ 5 ) + ( 9 x 4 ) + ( 108 ÷ 6 ) 35113618 35 + 11 + 36 + 18 = 100

26. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Lucy enters the number 4327.5 into her calculator. She meant to enter 4523.7 What is the difference between the number she wanted to put in and the number she put in? 4523.7 - 4327.5 = 196.2

27. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL The difference between two numbers is 25. Their product is 150. Their total is 35. What is the answer when one number is divided by the other? The two numbers are 5 and 30 30 - 5 = 25 30 x 5 = 150 30 + 5 = 35 30 ÷ 5 = 6 Or possibly 5 ÷ 30 = 1/6

28. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL James draws some shapes on a grid. Each grid square is 1cm long and 1cm wide. 3 2 1 5 4 A. Which shapes have only one acute angle? B. Which shape has only right angles? C. Which shapes each have an area of 12.5cm 2 ? 3 and 4 5 1 and 4

29. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Tom earns £1.50 for working on day one and double this amount on day two. On days three, four and five he continues to earn double the amount earned on the previous day. How much has Tom earned altogether over the five days he works? Day 1£1.50 Day 2£3.00 Day 3£6.00 Day 4£12.00 Day 5£24.00 Total £46.50

30. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Kayleigh finds the sum of the non-prime numbers between 40 and 50. She then adds the digits of her answer together. What is the total of the digits? The numbers are 42, 44, 45, 46, 48 and 49 The total is 274 The sum of the digits is 13

31. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL The area of each circle is 124cm 2. The red square has sides of 12cm. What is the area of the part of the drawing shaded yellow? The two semi-circles are the same area as one large circle, i.e. 124cm 2 The area of the whole square is 12cm x 12cm = 144cm 2 The area of the yellow part is 144cm 2 - 124cm 2 = 20cm 2

32. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Fred’s teacher asks him to add together each pair of corner numbers in this target board. Write down Fred’s answers. 19122117 11241413 4032930 16181015 There are six possible combinations 15 + 16 = 31 15 + 17 = 32 16 + 17 = 33 19 + 15 = 34 19 + 16 = 35 19 + 17 = 36

33. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL A B -xx y 0 The interval on the grid is 1 or -1. Jade translates her shape to the second quadrant. One new line has been drawn for you What are the co-ordinates of the new position of the points A and B? A (- 5, 6) B (- 2, 1)

34. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL 0.5 Tom follows the route around the drawing as shown by the arrows and finishes in the yellow middle square. Every time he enters a circle he adds 0.5. Every time he enters a square he subtracts 0.2 What number does he finish with in the yellow square? 0.8 1.1 1.4 1.7 0.30.6 0.91.2 1.5

35. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL Look at the number grid below and read it from left to right in all questions 2345678910111213141516 171819202122232425262728293031 323334353637383940414243444546 474849505152535455565758596061 Row 1 Row 2 Row 3 Row 4 A.What is the total of all the numbers in row 1? B.Find the product of the first and last prime numbers in row 3 ? C.In row 2 which pair of numbers have a product of 475 ? D.In row 4 which five consecutive numbers total 250? 18 x 7 = 126 126 + 9 = 135 3743 37 x 43 = 1591 19 x 25 = 475 48, 49, 50, 51, 52 1925 48495051524849