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 How would you write the number below to 1 decimal place? 4.8635

4. Back to board How would you write the number below to 1 decimal place? 4.8635 4.9 Explain?

5. Back to board How would you write the number below to 1 decimal place? 4.8635 5 or bigger ? 4.9  So round up

6. Back to board Answer Simon and Jenny share the bar of chocolate in the ratio 3 : 4. How many pieces do they each receive?

7. Back to board Simon gets 9 pieces Jenny gets 12 pieces Simon and Jenny share the bar of chocolate in the ratio 3 : 4. How many pieces do they each receive? Explain?

8. Back to board 21 pieces 3 + 4 = 7 parts Simon and Jenny share the bar of chocolate in the ratio 3 : 4. How many pieces do they each receive? Simon gets 9 pieces Jenny gets 12 pieces 3 Simon gets 7 of 21 = 9 (3 parts out of 7) Jenny gets 4 7 of 21 = 12 (4 parts out of 7)

9. Back to board Answer A portable television is on sale for £124.00. A special offer gives a 30% discount on the total price when you buy two. Jenny buys two televisions. How much does she pay? £124.00 SPECIAL OFFER: Buy 2 and get a 30% discount on the total price. £124.00

10. Back to board Explain? £124.00 SPECIAL OFFER: Buy 2 and get a 30% discount on the total price. £124.00 A portable television is on sale for £124.00. A special offer gives a 30% discount on the total price when you buy two. Jenny buys two televisions. How much does she pay? £173.60

11. Back to board £124.00 SPECIAL OFFER: Buy 2 and get a 30% discount on the total price. £124.00 A portable television is on sale for £124.00. A special offer gives a 30% discount on the total price when you buy two. Jenny buys two televisions. How much does she pay? £173.60 Final cost = £248 - 30% = £248 - £74.40 = £173.60 Or, more efficiently, 0.7 x £248 = £173.60

12. Back to board Answer Evaluate:

13. Back to board Explain? Evaluate:

14. Back to board Evaluate:

15. Back to board Answer How many small cubes would there be in the next diagram? 1 8 27 ?

16. Back to board 1 8 27 ? 64 Explain? How many small cubes would there be in the next diagram?

17. Back to board 1 8 27 ? 64 These are cube numbers. 1 3 = 1, 2 3 = 8, 3 3 = 27, 4 3 = 64 How many small cubes would there be in the next diagram?

18. Back to board Answer x-3-20123 y y = 3x - 1 The graph of y = 3x - 1 is to be drawn. Calculate the y values for each x value shown.

19. Back to board x-3-20123 y y = 3x - 1 x-3-20123 y-10-7-4258 The graph of y = 3x - 1 is to be drawn. Calculate the y values for each x value shown.

20. Back to board Answer Solve the simultaneous equations: x + y = 6 2x - 3y = 2

21. Back to board Explain? Solve the simultaneous equations: x = 4 and y = 2 x + y = 6 2x - 3y = 2

22. Back to board Solve the simultaneous equations: EQ 1 x 3 gives the equivalent pair. x = 4 and y = 2 Adding EQ 3 and EQ 2 gives. 5x = 20 so x = 4 Substituting x = 4 in EQ 1 gives. x + y = 6 2x - 3y = 2 1 2 3x + 3y = 18 2x - 3y = 2 3 2 4 + y = 6  y = 2

23. Back to board Answer Work out the answer to the question below in your head using an algebraic identity to help you. 67 2 - 33 2

24. Back to board Explain? 3400 67 2 - 33 2 Work out the answer to the question below in your head using an algebraic identity to help you.

25. Back to board 3400 = (67 + 33)(67 - 33) = 100 x 34 Remember: The difference of two squares states that a 2 – b 2 = (a + b)(a – b) 67 2 - 33 2 Work out the answer to the question below in your head using an algebraic identity to help you.

26. Back to board Answer 48 0 a Calculate angle a giving a reason for your answer.

27. Back to board 48 0 a Calculate angle a giving a reason for your answer. 132 o Explain?

28. Back to board 48 0 a Calculate angle a giving a reason for your answer. Angles on a straight line add to 180 0 132 o 180 0 - 48 o = 132 o

29. Back to board Answer 50 cm Calculate the approximate circumference C, of the table top by taking a value of  = 3.

30. Back to board 50 cm Calculate the approximate circumference C, of the table top by taking a value of  = 3. C = 300 cm Explain?

31. Back to board 50 cm Calculate the approximate circumference C, of the table top by taking a value of  = 3. C = 300 cm C = 2  r C = 2 x 3 x 50

32. Back to board Answer What is the scale factor of enlargement that maps triangle A onto triangle B? A B

33. Back to board Explain? What is the scale factor of enlargement that maps triangle A onto triangle B? A B x1/3

34. Back to board What is the scale factor of enlargement that maps triangle A onto triangle B? A B 9 12 3 4 x1/3 All lengths on triangle B are 1/3 of those on triangle A.

35. Back to board Answer o A B 88 o yoyo Calculate angle y. Diagrams not accurately drawn.

36. Back to board Explain? o A B 88 o yoyo Calculate angle y. 44 o Diagrams not accurately drawn.

37. Back to board o A B 88 o yoyo Calculate angle y. 44 o The angle at the centre is twice the angle at the circumference. Diagrams not accurately drawn.

38. Back to board Answer 10 30 20 40 50 6070 0 80 90 100 120 160 Kilometres (km) 140 Miles 80 60 40 20 Use the conversion graph to convert 80 miles to km.

39. Back to board 10 30 20 40 50 6070 0 80 90 100 120 160 Kilometres (km) 140 Miles 80 60 40 20 Use the conversion graph to convert 80 miles to km. 128 km Explain?

40. Back to board 10 30 20 40 50 6070 0 80 90 100 120 160 Kilometres (km) 140 Miles 80 60 40 20 Use the conversion graph to convert 80 miles to km. 128 km

41. Back to board Answer (a)On how many days were visitor numbers recorded? (b)What type of correlation is shown? 12 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors0 The scatter graph shows information on the number of daily visitors to a museum last summer.

42. Back to board Explain? The scatter graph shows information on the number of daily visitors to a museum last summer. 12 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors0 (a)10 (a)On how many days were visitor numbers recorded? (b)What type of correlation is shown? (b) negative

43. Back to board 12 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors0 The scatter graph shows information on the number of daily visitors to a museum last summer. (a)On how many days were visitor numbers recorded? (b)What type of correlation is shown? As one quantity increases (sunshine), the other quantity decreases (visitors) so there is a negative correlation between the data. (a)10 (b) negative

44. Back to board Twenty people threw darts at a dartboard until they hit triple twenty. Work out an estimate for the mean number of darts thrown by each person. Answer Number of darts thrown FrequencyMidpoint Midpoint x Frequency 1 - 55 6 - 108 11 - 154 16 - 203

45. Back to board Explain? 9 darts Number of darts thrown FrequencyMidpoint Midpoint x Frequency 1 - 55 6 - 108 11 - 154 16 - 203 Twenty people threw darts at a dartboard until they hit triple twenty. Work out an estimate for the mean number of darts thrown by each person.

46. Back to board 9 darts Number of darts thrown FrequencyMidpoint Midpoint x Frequency 1 - 55 6 - 108 11 - 154 16 - 203 3 8 13 18 15 64 52 54 20 185 Mean estimate = 185/20 = 9.25 Twenty people threw darts at a dartboard until they hit triple twenty. Work out an estimate for the mean number of darts thrown by each person.

47. Back to board Answer red blue red blue red blue The tree diagram shows the probabilities for removing two coloured cubes from a bag of ten. The first cube is replaced. What is the probability of selecting a red cube followed by a blue cube?

48. Back to board Explain? red blue red blue red blue 21/100 The tree diagram shows the probabilities for removing two coloured cubes from a bag of ten. The first cube is replaced. What is the probability of selecting a red cube followed by a blue cube?

49. Back to board red blue red blue red blue 21/100 The tree diagram shows the probabilities for removing two coloured cubes from a bag of ten. The first cube is replaced. What is the probability of selecting a red cube followed by a blue cube?