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T-Total. I rotated the T round 180 and took another four readings and worked out that the Equation for this position was N=5N+63

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Introduction

Mathematics G.C.S.E.

T-Total

To start off with the task in hand, I set about the first question, by using the original grid of 9 squares using the first t-shape pictured. After this I took 4 readings on the original shape and worked out an algebraic relationship between the T-total (TT) and the T-number (N).

After these readings I worked out:

N=5N-63

After this I rotated the T round 180° and took another four readings and worked out that the Equation for this position was

N=5N+63

To prove this formula, I worked out every number in the T in terms of N and came up with:

N-19

N-18
N-17
N-9
N

This helps you to work out T numbers when you know only N

 After this, to try to get some work done I tried to work out some proof for the ‘other’ T shapes rotations these were:

N
N+9
N+17
N+18
N+19

...read more.

Middle

5N+77

90°

5N+7

270°

5N-7

 After compiling this table I worked out a formula for any regulation sized T in any grid at 180° and 0° this was:

5N+OR-7G

The G in this equation stands for Grid type i.e. 9,10,or 11.

For the 90° and 270° the Equation is the same;

5N+OR-7

After another look at the equation, I worked out that the five was in relationship with the number of squares in the T so  (letting x be the number or squares) the equation is

XN+or-7G

To test this theory, I tested it on a 6-squared T, thus changing the form of the T so that it looked like:

N

∴ 6*21-7*9 = 63

This, Unfortunately Didn’t work, however, I made a table using only this type of T, the results were:

Grid Type

Angle

Formula

No of Squares

9

0°

6N-83

6

180°

6N+83

90°

6N+45

270°

6N-45

10

0°

6N-92

180°

6N+92

90°

6N+11

270°

6N-11

11

0°

6N-101

180°

6N+101

90°

6N+31

270°

6N-31

I tried to work out a formula for this type of T shape on 0° and 180° and came up with:

6N+or-9G+2

This time, however, the 90° and 270° were not constant and so I tried to work out a formula however there were no set formulas.

Now I moved further on into the depths of question 3, I used proportional change to see if I could find any relationship between the similar shapes,

So I tried:

N
...read more.

Conclusion

I am now moving on to the other ideas of spreading the lower middle strand of the T to try and find a formula.

Grid Type

No of squares

Formula

9

5

5N-63

9

6

6N-108

9

7

7N-162

9

8

8N-225

63                108                162                225

        45                54                63

                9x                9x

So after this I can say that the answer works out as 4.5x

Conclusion

For me this has been an exiting investigation. However I think I have not worked out enough of the formulas or explored deep enough. I got on to investigating question 3 but I worked on it with basic T shapes and with not such sophisticated advanced methods. However I feel I could have tried to work a bit quicker and found more time. I worked on questions one and two with efficiency and I believe that my work was detailed and well structured however, I got mixed up and never really had any structure to my investigation. I worked out the fundamentals involved in question three well and found sufficient answers.

...read more.

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