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GCSE Mathematics T-Totals

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Introduction

GCSE Mathematics T-Total C/W I have been given mathematics coursework on T-totals; the coursework has been set in three tasks. The question is about T-shapes on different grids. The bottom number in the T is called the T-number. All the numbers in the T-shape added together are called the T-total. For each part of the coursework I have to translate the T-shape to different positions on the grid. Key: T-total = T T-number = n Grid Size = G Part 1 For the first part of the coursework, I have to investigate the relationship between T-total and T-number. I will use a 9x9 number grid and start off with the T-shape beginning at the number 1. 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 To understand the relationship between the T-total and T-number we can look at the T-shape drawn on the 9x9 number grid. The total of the numbers inside the T-shape is 37 this is called the T-total. The number at the bottom of the T-shape is called the T-number. ...read more.

Middle

Then I subtracted 34(T-Total) from 90 which gave me 56. Using this formula I found out it worked by testing it on all the T-shapes. 7x7 Grids n 16 17 18 19 T 31 36 41 46 I did a prediction for the next T-shape. I predict this because the T-number is increasing by 1 and the T-Total is increasing by 5. From my findings I concluded a formula linking the T-Number and T-Total which is T=5n-49. I got this formula when I seen that the difference between each T-Total is 5 so the formula had to contain 5n.I used the 5n on my first n in my table and I got 80. Then I subtracted 31(T-Total) from 80 which gave me 49. Using this formula I found out it worked by testing it on all the T-shapes Summary Grid Size Formula 9x9 5n-63 8x8 5n-56 7x7 5n-49 Also I can predict that for a 6x6 grid the formula will be 5n-42. The prediction I have is so because the 5n will remain the same and as the constant goes down by 7 each time I can minus 7 from 49 to give me 42. I have algebraic proof that there is a relationship between T and n. 9x9 grids n-19 n-18 n-17 n-9 n 1 2 3 11 20 (n-19) + (n-18) + (n-17) + (n-9) + (n) = 5n-63 T= 5n-63 7x7 grids n-15 n-14 n-13 n-7 n 1 2 3 9 16 (n-15) ...read more.

Conclusion

Also the T-number has a difference of 3 so 15n�3 is in the formula. 15n�3 can be simplified to 5n. To get to the T-total from 5n you have to add 7. So T= 5n+7 To prove this I have some examples: n=32 (5x32) +7=167 n=29 (5x29) +7=152 This has proven that the formula works for different grid sizes and if I check in the table above I can see my results are correct. For 270� the formula I have found is T= 5n-7 I have found this formula by noticing that the T-total has a difference of 15 which means that 15n is in the formula. Also the T-number has a difference of 3 so 15n�3 is in the formula. 15n�3 can be simplified to 5n. To get to the T-total from 5n you have to subtract 7. So T= 5n-7 To prove this I have some examples: n=30 (5x30) -7=143 n=27 (5x27) -7=128 Also I made a prediction for a 10x10 grid. I predicted that when n=35 for a 90� rotation the T-total will be 182. Here is my working. (5x35)+7=182 Also I predicted that when n=33 for a 270� rotation the T-total will be 158. Here is my working. (5x33)-7=158 I can prove my prediction is correct by showing that 182-158=24. This is significant as for each grid size's T-totals for 90� and 270� have a difference of 24 also, e.g. 8x8 grids 90� T-total=152 270� T-total=128 152-128=24 ?? ?? ?? ?? Imran Kola 11.13 Maths Coursework Page 2 ...read more.

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