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  • Level: GCSE
  • Subject: Maths
  • Word count: 1725

T-totals, Main objective of this project of T-totals coursework is to find an inter-relationship between the T-total and the T-number.

Extracts from this document...

Introduction

Sotirios Kopitsas

Warren Comprehensive School

Candidate number: 7037

Coursework project:  Subject: T-totals and the T-number


Preface

This booklet contains information about GCSE mathematics coursework 2007-2008. Main objective of this project of T-totals coursework is to find an inter-relationship between the T-total and the T-number. The booklet uses methods and tools of analysis required in order to resolve and explore the various objectives of the coursework.

T-totals are used in GCSE mathematics coursework in order to improve the numerical quality in the student’s mind and his/her technical thinking. In this booklet, numbers including the T-number within the t-shape are used to calculate the t-total and eventually to find an overall pattern of the results of the analysis of the t-totals which involves an algebraic rule. This rule is used to prove that the T-total and the grid size follow a specific pattern as it is explained in this booklet.

Furthermore, there are other technical methods that affect the t-total structure.

...read more.

Middle

        Therefore, the rule is 5n-42

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T-number:     T-total:

  1.        24+17+9+10+11=71

            55         55+48+40+41+42=226

            65         65+58+50+51+52=276

            104       104+97+89+90+91=471

Therefore, the rule is 5n-49

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T-number:     T-Total:

       26            26+18+9+10+11=74

       23                23+15+6+7+8=58

       54                54+46+37+38+39=214

       74                74+66+57+58+59=284

Therefore, the rule is 5n-56


Evaluation of Results

1) General rule findings

The above results are generalized in formulas (rules) for each grid size and presented in a following table:

Grid Size:

Rule

6

5n-42

7

5n-49

8

5n-56

9

5n-63


By observation of the above table the general rule applied on the above grid sizes is then: 5n-7g where g=6 to 9.

2) Interrelation between T-totals and Translation vectors

By observation between the T-totals and translation vectors in a typical 9-size grid it appears that the T-totals are directly connected with the T-shape moving sideways and vertically in the grid as follows:

Examples in the following vectors

1        (moving T-shape by one grid horizontally to the right) the T-totals increase by 5

0        each time

-1        (moving T-shape by one grid horizontally to the left) the T-totals decrease by 5    

0        each time        

0        (moving T-shape by one grid vertically down) the T-totals increase by 45 each time

1

...read more.

Conclusion

Rule finding:

From the above observations a general rule may be applied as follows:

0        T-total increase by 45y

y

Similarly

x        T-total increase by 5x

0

Here is an example of the method of translation vectors that I have applied:

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T-number:    T:total:

      30          30+21+11+12+13=87

  1        t: number=31

  0        T-total=31+22+12+13+14=92

  2        t-number=32

  0        T-total=32+23+13+14+1=97

 0        t-number=39

 1        T-total=39+30+21+20+22=132

 0        t-number=48

 2        T-total=48+39+29+30+31=177

By using of the rule 5n-63 in the translation vectors the t-totals calculated as follows for example in the case of T-number=30:

1        5(30)-63+5(1)=87+5

0

2        5(30)-63+5(2)=87+10

0

0        5(30)-63+45(1)=87+45

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0        5(30)-63+45(2)=87+90

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Below we give an example of the application of the rule when T-shape moves horizontally and vertically (right across and downwards) as follows:

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If  T-number=30 and assuming that the T=shape moves according to the below translation vector::

2        5(59)-63+5(2)+45(3)=232+10+135

3

The general rule for the two-dimension movement of the T-shape is the following:

5n-63+5(x)+45(y)

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...read more.

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