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GCSE MATHEMATICS COURSEWORK Introduction My aim is to investigate the relationship between the T-total and the T-number. I will then used grids of different sizes and translated the T-shape to different positions to re-investigate the relationship between the T-total and the T-number. Figure 1. Figure 1.a. 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-19) 1 (T-18) 2 (T-17) 3 10 (T-9) 11 12 19 (T) 20 21 We shall call the grid dimensions 'g'. Figure 1 is drawn on a 9 by 9 grid, so in this case: g = 81 Figure 1 is a T-shape drawn on a number grid where g = 9. The T-total is 1+2+3+11+20=37 The T-number is 20. The Nth term, as taken from figure 1.a. is: T + (T-9) + (T-17) + (T-18) + (T-19) = 5T - 63 5T - 63 = 37 5T = 37 + 63 T = 100 5 T = 20 Figure 2. 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 In this grid g = 9. The T-total is 2+3+4+12+21=42 The T number is 21 The Nth term is will be the same: T + (T-9) +...

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