2. Sequences and Formulae

3. 1.Look at the pattern below Copy and complete the table below 4 710 131631 301 3n+1

4. 2.Look at the table arrangements below 5 811 141732 302 3n+2

5. 3.Copy and complete the table below 4312510nHouses Cards 5 9 13 1721 41 4n + 1

6. 4.Copy and complete the following table Term1234510n No12203042 Factors 56 3x4 4x5 5x66x77x8 12x13 156 (n+2)(n+3) n 2 +5n+6

7. 5.Copy and complete the following table Term1234510n No10182840 Factors 54 2x5 3x6 4x75x86x9 11x14 154 (n+1)(n+4) n 2 +5n+4

8. 6.Copy and complete the following table Term1234510n No15284566 Factors 91 3x5 4x7 5x96x117x13 12x23 276 (n+2)(2n+3) 2n 2 +7n+6

9. 7.Copy and complete the following table Term1234510n No4122440 Factors 60 1x4 2x6 3x84x105x12 10x22 220 n(2n+2) 2n 2 +2n

10. 8.Copy and complete the following table Term1234510n No3153563 Factors 99 1x3 3x5 5x77x99x11 19x21 399 (2n-1)(2n+1) 4n 2 - 1

11. E.GMaking x the subject of formula eg 1eg 2

12. E.GMaking x the subject of formula eg 3eg 4

13. ExMake x the subject of formula ex 1ex 2

14. ExMake x the subject of formula ex 3ex 4

15. ExMake x the subject of formula ex 5ex 6

16. ExMake x the subject of formula ex 7ex 8

17. Statistics and Probability

18. Calculate the semi-interquartile range from the Stem and leaf diagram 2 5 2 7 1 0 2 3 1 6 0 2 4 2 1 9 3 4 3 1 8 5 1 2 9 2 8 2 0 2 2 6 3 1 0 4 7 3 1 1 2 0 1 2 2 5 7 3 0 1 2 6 4 1 1 2 3 3 4 8 9 5 0 1 2 2 2 2 2 8 9 6 0 1 1 1 3 3 4 7  Q 2 = (35+1)  2 = 18 th entry  Q 1 = (17+1)  2 = 9 th entry  Q 3 = (17+1)  2 = 27 th entry Q 2 = 49% Q 1 = 32% Q 3 = 59% SIQR = (59 – 32)  2 = 13.5

19. Pupil A scored the following grades in her S1 tests 89%, 61%, 75%, 84%, 99%, 67%, 91%, 62%, 79%, 90%, 64% Draw a box plot to illustrate her grades 61%, 62%, 64%, 67%, 75%, 79%, 84%, 89%, 90%, 91%, 99%  Q 2 = (11+1)  2 = 6 th entry  Q 1 = (5+1)  2 = 3 rd entry  Q 3 = (5+1)  2 = 9 th entry Q 2 = 79% Q 1 = 64% Q 3 = 90%

20. 30 40 50 60 70 80 90 100

21. Pupil B scored the following grades in his S1 tests 59%, 61%, 60%, 51%, 58%, 68%, 49%, 57%, 63%, 56% Draw a box plot to illustrate his grades 49%, 51%, 56%, 57%, 58%, 59%, 60%, 61%, 63%, 68%  Q 2 = (10+1)  2 = 5 th /6 th entry  Q 1 = (5+1)  2 = 3 rd entry  Q 3 = (5+1)  2 = 8 th entry Q 2 = 58.5% Q 1 = 56% Q 3 = 61%

22. 30 40 50 60 70 80 90 100 64 79 90 56 58.5 61 Pupil A Pupil B Observations ? Pupil A interquartile range = 26 Pupil B interquartile range = 5 Pupil A stronger student Pupil B more consistent

23. Copy and complete the table finding the mean and median DonationFrequency Cumulative Frequency Donation x Frequency £52 £104 £155 £2011 £254 2 6 11 22 26 10 40 75 220 100 Total = 445 Mean = 445  26 = £17.12 Median = (26+1)  2 = 13 th /14 th = £20

24. Copy and complete the table finding the mean and median Darts Scores Mid value Frequency Cumulative Frequency Mid score x Frequency 0 – 19107 20 – 39308 40 – 59504 60 – 79703 80 – 99902 7 15 19 22 24 70 240 200 210 180 Total = 900 Mean = 900  24 = 37.5 Median = (24+1)  2 = 12 th /13 th = 20 – 39  30

25. The average range fall was recorded over one week City A 16mm, 30mm, 2mm, 27mm, 26mm, 30mm, 30mm City B 0mm, 2mm, 68mm, 75mm, 9mm, 0mm, 0mm Calculate the mean and standard deviation for both Cities Comment on your results

26. X 16 30 2 27 26 30 -7 7 -21 4 3 7 7 49 441 City A 16mm, 30mm, 2mm, 27mm, 26mm, 30mm, 30mm 16 9 49

27. X 0 2 68 75 9 0 0 -22 -20 46 53 -13 -22 484 400 2116 2809 169 484 City B 0mm, 2mm, 68mm, 75mm, 9mm, 0mm, 0mm

28. Summary City A 16mm, 30mm, 2mm, 27mm, 26mm, 30mm, 30mm City B 0mm, 2mm, 68mm, 75mm, 9mm, 0mm, 0mm OBSERVATIONS? Although both Cities had a similar average rainfall for the week, the higher standard deviation for City B suggests that the rain fall was much more varied.

29. Probability Quick reminder

30. Measured on a scale form 0 to 1 0 1 0.5 50/50 E.g.s unlikelylikely

31. Combined Probabilities

32. H T H T H T HH HT TH TT H T H6

33. Future Expectation Chris plays the game 30 times, how many games should he expect to win? LW L W L 300 people were born in August. How many would you expect to be born on the 1 st ?

34. Relative Frequency ResultFrequency 180 264 346 453 5107 650 Hannah makes a die, rolls it 400 times and records her results a. Calculate the relative frequency of a 2 b. Calculate the relative frequency of a 5 c. What can you deduce about the die? Implies too many fives, perhaps her dice is biased