1. Whiteboardmaths.com © 2004 All rights reserved 5 7 2 1

2. BBBB EEEE DDDD BBBB DDDD CCCC EEEE BBBB DDDD CCCC DDDD CCCC EEEE BBBB CCCC EEEE ALGEBRA NUMBER SHAPE SPACE & M SPACE & M HANDLING DATA

3. Back to board Answer Three parts of the regular pentagon are coloured blue. What is: (a) the fraction, (b) the decimal and (c) the percentage of the shape that is coloured blue?

4. Back to board 3/5 0.6 60% Three parts of the regular pentagon are coloured blue. What is: (a) the fraction, (b) the decimal and (c) the percentage of the shape that is coloured blue? Explain?

5. Back to board 3/5 0.6 60% Three parts of the regular pentagon are coloured blue. What is: (a) the fraction, (b) the decimal and (c) the percentage of the shape that is coloured blue? 3 parts out of a total of 5 parts are coloured blue. 3 5 = 6 10 = 60 100

6. Back to board Answer The exact attendance at a football match is shown below. Write this number to 2 significant figures. 24 684

7. Back to board 25 000 24 684 The exact attendance at a football match is shown below. Write this number to 2 significant figures. Explain?

8. Back to board 25 000 24 684 The exact attendance at a football match is shown below. Write this number to 2 significant figures. So round up and add the zeros. 5 or bigger ? 

9. Back to board Answer If the cost of 8 apples is £1.44. Find the cost of 23 apples.

10. Back to board Explain? £4.14 If the cost of 8 apples is £1.44. Find the cost of 23 apples.

11. Back to board £4.14 144p 8 x 23 If the cost of 8 apples is £1.44. Find the cost of 23 apples. = 18 x 23 = 414p Cost of 1 apple

12. Back to board Answer Rewrite as a single power of 5 then evaluate. 5 3 x 5 4 x 5 5 5858

13. Back to board Explain? 5 4 = 625 Rewrite as a single power of 5 then evaluate. 5 3 x 5 4 x 5 5 5858

14. Back to board Rewrite as a single power of 5 then evaluate. 5 12 = 5858 = 5 4 5 3 x 5 4 x 5 5 5858 5 4 = 625 Remember: Add the indices when multiplying numbers in the same base and subtract when dividing.

15. Back to board Answer Work out the value of V when p = 7. V = 3p - 4

16. Back to board V = 17 Work out the value of V when p = 7. V = 3p - 4 Explain?

17. Back to board V = 17 Work out the value of V when p = 7. V = 3p - 4 V = 3 x 7 - 4 = 17

18. Back to board Answer 6x -2y 6x - 2y 4y The expression in each white triangle is found by adding those in the two triangles beneath. Find the expression for the top triangle. ?

19. Back to board 6x -2y 6x - 2y 4y The expression in each white triangle is found by adding those in the two triangles beneath. Find the expression for the top triangle. 12x + 2y ? Explain?

20. Back to board 6x -2y 6x - 2y 4y The expression in each white triangle is found by adding those in the two triangles beneath. Find the expression for the top triangle. 12x + 2y ? 6x + 4y 6x + 4y + 6x - 2y = 12x + 2y

21. Back to board Answer (a) Find the rule for the n th term, (t n ) in the sequence below. (b) Use your rule to calculate the 7 th term (t 7 ). 0, 3, 8, 15, 24,…..

22. Back to board Explain? (a) t n = n 2 - 1 (b) t 7 = 48 (a) Find the rule for the n th term, (t n ) in the sequence below. (b) Use your rule to calculate the 7 th term (t 7 ). 0, 3, 8, 15, 24,…..

23. Back to board (a) t n = n 2 - 1 (b) t 7 = 48 (a) The term number 2 - 1 gives the rule. (a) Find the rule for the n th term, (t n ) in the sequence below. (b) Use your rule to calculate the 7 th term (t 7 ). (b) t 7 = 7 2 - 1 = 48. 1 2 3 4 5 n Term numbers 0, 3, 8, 15, 24,…..

24. Back to board Answer Expand the bracket below. 4q(qp 2 – 3pq 3 )

25. Back to board Explain? 4q 2 p 2 -12pq 4 Expand the bracket below. 4q(qp 2 – 3pq 3 )

26. Back to board Expand the bracket below. 4q x qp 2 = 4q 2 p 2 4q x -3pq 3 = -12pq 4 4q(qp 2 – 3pq 3 ) 4q 2 p 2 -12pq 4

27. Back to board Answer How many centimetres are there in the number of metres shown? 5½ m

28. Back to board How many centimetres are there in the number of metres shown? 550 Explain? 5½ m

29. Back to board How many centimetres are there in the number of metres shown? 550 1 m = 100 cm 5½ x 100 = 550 5½ m

30. Back to board Answer Front Elevation Side Elevation Plan View Decide which of the three views of the object below show the plan, side and front elevations.

31. Back to board Front Elevation Side Elevation Plan Front Elevation Side Elevation Plan View Decide which of the three views of the object below show the plan, side and front elevations.

32. Back to board Answer 35 36 37 10 miles 12 miles A lorry travels along a motorway from junction 35 to junction 37. The journey time is 20 minutes. Find its average speed in mph.

33. Back to board Explain? 35 36 37 10 miles 12 miles A lorry travels along a motorway from junction 35 to junction 37. The journey time is 20 minutes. Find its average speed in mph. 66 mph

34. Back to board 35 36 37 10 miles 12 miles A lorry travels along a motorway from junction 35 to junction 37. The journey time is 20 minutes. Find its average speed in mph. 66 mph Speed = Distance Time Speed = 22 = 66 1 3

35. Back to board Answer 8.3 cm 3.2 cm The length and width of the rectangle below are measured to the nearest mm. What is the minimum perimeter that the rectangle could be.

36. Back to board Explain? 22.8 cm 8.3 cm 3.2 cm The length and width of the rectangle below are measured to the nearest mm. What is the minimum perimeter that the rectangle could be.

37. Back to board 2(3.15 + 8.25) = Remember: Any measurement is only accurate to  ½ the degree of accuracy centred on the measurement. 8.3 cm 3.2 cm The length and width of the rectangle below are measured to the nearest mm. What is the minimum perimeter that the rectangle could be. 22.8 cm

38. Back to board Answer Prof and Beaky are playing a game of cards. Beaky asks Prof to take a card at random from her hand. What is the probability that Prof takes a card that is not a diamond? Beaky’s Hand

39. Back to board 7 8 Explain? Prof and Beaky are playing a game of cards. Beaky asks Prof to take a card at random from her hand. What is the probability that Prof takes a card that is not a diamond? Beaky’s Hand

40. Back to board 7 of the cards are “not diamonds” Out of a total of 8 cards. 7 8 Prof and Beaky are playing a game of cards. Beaky asks Prof to take a card at random from her hand. What is the probability that Prof takes a card that is not a diamond? Beaky’s Hand

41. Back to board Answer The probability of scoring a treble 20 with the throw of a single dart is 1 in 25. How many treble 20’s would you expect to get in 200 throws?

42. Back to board 8 Explain? The probability of scoring a treble 20 with the throw of a single dart is 1 in 25. How many treble 20’s would you expect to get in 200 throws?

43. Back to board 8 200/25 = 8 The probability of scoring a treble 20 with the throw of a single dart is 1 in 25. How many treble 20’s would you expect to get in 200 throws?

44. Back to board Answer 10 0 5 15 20 3040 50 Frequency Time in minutes 60 Time Taken for Race Use the histogram and frequency polygon to estimate the mean time taken for the 50 runners to complete the race.

45. Back to board Explain? 33.6 mins 10 0 5 15 20 3040 50 Frequency Time in minutes 60 Time Taken for Race Use the histogram and frequency polygon to estimate the mean time taken for the 50 runners to complete the race.

46. Back to board 33.6 mins 7 x 15 + 10 x 25 + 20 x 35 + 9 x 45 + 4 x 55 50 = 33.6 10 0 5 15 20 3040 50 Frequency Time in minutes 60 Time Taken for Race Use the histogram and frequency polygon to estimate the mean time taken for the 50 runners to complete the race. Numbers in blue are the midpoints of the intervals.

47. Back to board Answer Simon Jenny Simon lays a card at random from his hand on the table. Jenny then lays her card. What is the probability that they are both hearts? (heart)

48. Back to board Explain? Simon Jenny Simon lays a card at random from his hand on the table. Jenny then lays her card. What is the probability that they are both hearts? 8/56 = 1/7 (heart)

49. Back to board Simon Jenny Simon lays a card at random from his hand on the table. Jenny then lays her card. What is the probability that they are both hearts? 8/56 = 1/7 2/8 x 4/7 = 8/56 (heart)