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  • Level: GCSE
  • Subject: Maths
  • Word count: 1387

T-Shapes Coursework

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Introduction

T-Shapes Coursework

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In this coursework I am going to look at a series of grids and within the grids look at certain T-shapes. The first thing I am going to do in this investigation is pick three T-Shapes from the grid below.

 Above is my 9x9 Grid the numbers ranging from 1-81. I have chosen my first T-shape to be located in the top left of the grid, and my T-number will be 20 The T-shape above has been highlighted in red. Because my choice was the number at the bottom of the T-shape I am going to be consistent with future T-shapes chosen. I have highlighted the T-number with a light blue colour.

I have chosen my three T-shapes and have labelled the T-Numbers in them appropriately. I am now going to work out the T-Totals for each of my T-shape.

T-number-20=20+11+1+2+3=37

T-number-21=21+12+2+3+4=42

T-number-22=22+13+3+4+5=47

T-Number

T-Total

T-number-20

20+11+1+2+3=37

T-number-21

21+12+2+3+4=42

T-number-22

22+13+3+4+5=47

...read more.

Middle

          = 47

The above calculations show that the formula is correct.

I am now going to test this formula on a different sized grid. The size grid I have chosen to do next is an 11x11 grid.

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T-total = 1+2+3+13+24 = 43

T-number = 24

The T-Total and the T-Number have risen even though the T-Shape looks to be in the same place. The T-Number has risen by four and the T-Total has risen by six.

...read more.

Conclusion

                        T-total = 5 x 69 – 63

                                                 = 345 – 63

                                                          = 282

I will now check my calculations by drawing the appropriate T-shape.

T-Total= 50+51+52+60+69=282

My formula has been proved to work and my calculations correct.

By looking at my previous results, I have now decided that I am going to try and generalise for a G x G grid.

T-Total = T-2g-1 + T-2g + T-2g+1 + T-G + T

                           = 5T-7G

I will now use my general formula to predict the T-Total of T-Number 24 on a 7 x 7 grid.

        T= 24        G=7

        T-Total  = 5 x 24 – 7 x 7

                                = 120 – 49

                                =  71

I will check this by drawing the appropriate T-shape and adding up the numbers within.

I am now going to increase the size of my T-shape and also choose a different size grid for this larger T-Shape.

The grid size I have chosen to do is a 10 x 10 grid. I am going to enlarge my T-shape to see if my formula will still work on a larger T-shape.

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Oliver Mason year 11

...read more.

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