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GCSE Mathematic Coursework T-totals Aim: to find a pattern that connects the T- number with the T- total
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GCSE Mathematic Coursework T-totals Aim: to find a pattern that connects the T- number with the T- total. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 p 41 42 43 44 45 46 47 48 p+r 50 51 52 53 54 55 56 p+2r-1 p+2r p+2r+1 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 T- number = T 40 p = T-number T- total = 263 q = T-total Grid size = 9 x 9 r = grid size Calculations: p + p + p + p + p = 5p r + 2r + 2r + 2r = 7r -1 + 1 = 0 Formula for T-shape: q = 5p + 7r Justification: (5 x 40) + (7 x 9) = 263 Example: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 p 42 43 44 45 46 47 48 49 p+r 51 52 53 54 55 56 57 p+2r-1 p+2r p+2r+1 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 T- number = T41 p = T-number T- total = 268 q = T-total Grid size = 9 x 9 r = grid size Calculations: p + p + p + p + p = 5p r + 2r + 2r + 2r = 7r -1 + 1 = 0 Formula for T-shape: q = 5p + 7r Justification: (5 x 41) + (7 x 9) = 268 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 Example: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 p 40 41 42 43 44 45 46 47 p+r 49 50 51 52 53 54 55 p+2r-1 p+2r p+2r+1 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 T- number = T39 p = T-number T- total = 258 q =...
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