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• Level: GCSE
• Subject: Maths
• Word count: 1030

# T-Total Investigation

Extracts from this document...

Introduction

 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

Firstly I looked at how the T-shapes would overlap each other   -

Then I experimented with a 9X9 grid and realized

the following points;

1. Sum of T2=T+5
2. Difference between T-total and

T-number goes up in 4

1. Difference between each T-total is 5

I thought of an equation that would be able to tell a person the T-total of

the second T just by using the first T.

## T is made up of 5 squares and moves across 1 to make T2

Squares in T X Movement = 5 ∆ Second T = T + 5

ST X M = 5 ∆T2 = T + 5

## This proved to be unnecessary in my investigation

Middle

This table shows that when 20 is taken from any T-number and then the answer is multiplied by 5 and 37 is added, you will get the T-total. I had to test this method with a few other numbers to check that it worked.

I could now make an equation to summarize my work on task 1

5(n-20)+37

This can be simplified to: 5n-63

Now I had completed task1 I felt I had more of a feel to the investigation and was confident in successful completion. I would now begin to experiment with different grid sizes and investigate the relation of this alteration to the T-total and T-number.

Conclusion

2n+2+(n+2)+6(you add six because the top bar of the T will always be 1,2 and 3 which equal six when added together)

Because there are so many digits scattered everywhere you can simplify this equation to:

3n+10 (where n equals grid size)

I had already found a formula using the 7X7 grid so I began using the 11X11 grid; I decided to draw a table as I had done for the other grid sizes to make my investigation easier.

 T-number T-total Difference (between T-totals) 24 43 + 1st total 25 48 5 26 53 5 27 58 5 28 63 5 29 68 5

In every table I had looked at, the difference between T-totals was always 5.

This student written piece of work is one of many that can be found in our GCSE T-Total section.

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# Related GCSE T-Total essays

1. ## T-Totals Investigation.

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2. ## T-Shape investigation.

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1. ## T-total Investigation

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