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  • Level: GCSE
  • Subject: Maths
  • Word count: 2722

Investigate the relationship between the T-total and the T-number.

Extracts from this document...

Introduction

Mohammed Panchbhaya

GCSE Math’s

Investigation

Introduction

In this investigation I’m going to investigate the relationship between the T-total and the T-number. What I’m going to do is use different sizes of grids for example 9*9, 8*8, 7*7, 6*6, 5*5 and 4*4. To compare the answers I will have to investigate each grid for a few times for example 9*9 grid will be investigated for at list three times. I will have to make predictions for each of the grids. I will also have to translate and compare different positions of the T-shape and the T-numbers. After I have finished the investigation I will then evaluate and compare the relationships between different sizes of grids.

The first grid I will investigate will be the 9*9 grid.

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T-number = 20

T-Total = 1+2+3+11+20=37image14.png

T20=37

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 n

                                                                             T-number = n

                                                                             T-Total = n+n-9+n-17+n-18+n-19image16.png

Tn = 5n-63
 
image17.pngimage46.png

image20.png

        T-number = 20image02.pngimage02.png

                                   Tn = 5n-63 image03.pngimage04.pngimage05.png

        20 * 5 = 100image06.png

                                                                -63image07.png

                                                                  37image08.pngimage09.png

Here is another 9*9 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.  

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image00.pngimage13.png

T-number = 22

T-Total = 3+4+5+13+22=47image14.png

T20=47

n-19

n-18

n-17

n-9

image15.png

 n

                                                                             T-number = n

                                                                             T-Total = n+n-9+n-17+n-18+n-19image16.png

Tn = 5n-63
 
image18.pngimage17.png

image19.png

image20.png

...read more.

Middle

                                                                             T-total = n+n-8+n-15+n-16+n-17image39.png

Tn = 5n-56

                                                            T-number = 19

                                                            Tn = 5n-56

                                                            19*5=95

                                                                     -56

39image40.pngimage41.pngimage42.png

Here is another 8*8 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.

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 43

T-number = 43

T-total = 26+27+28+35+43=159

T19 = 159

n-17

n-16

n-15image44.png

n-8

 n



                                                                            T-number = n

                                                                             T-total = n+n-8+n-15+n-16+n-17image45.png

Tn = 5n-56

image47.png

                                                            T-number = 43

                                                            Tn = 5n-56

                                                            43*5=215

                                                                       -56image09.png

159image48.pngimage41.png

image49.png

Here is another 8*8 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.

image37.png

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T-number = 18

T-total = 1+2+3+10+18=34

T19 = 34

n-17

n-16

n-15image44.png

n-8

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                                                                            T-number = n

                                                                             T-total = n+n-8+n-15+n-16+n-17image45.png

Tn = 5n-56

image51.png

                                                            T-number = 18

                                                            Tn = 5n-56

                                                            18*5= 90

                                                                       -56image09.png

 34image41.pngimage48.png

As you have seen from the above diagram and from the diagram on the first page as well the second page, the Tn answer is the same, Tn = 5n-63, so my prediction on this was correct and in this case it also makes it clear that all the other 8*8 grids will produce the same answers.

...read more.

Conclusion

8+n-9

Tn = 5n-28

                                                            T-number = 10

                                                            Tn = 5n-28

                                                            10*5=50

                                                                     -28

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Here is another 4*4 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.

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T-number = 14

T-total = 5+6+7+10+14=42

Tn = 42



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                                                                            T-number = n

                                                                             T-total = n+n-4+n-7+n-8+n-9

Tn = 5n-28

                                                            T-number = 14

                                                            Tn = 5n-28

                                                            14*5=70

                                                                     -28

42

As you have seen from the above diagram and from the diagram on the first page the Tn answer is the same, Tn = 5n-28 so my prediction on the third diagram is that I think the Tn algebra will still remain the same.

Here is another 4*4 grid I will use the similar method just like the one on the first page and second page. There is no difference between them apart from the T-numbers in the T-shape.

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T-number = 15

T-total = 6+7+8+11+15=47

Tn = 47



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                                                                            T-number = n

                                                                             T-total = n+n-4+n-7+n-8+n-9

Tn = 5n-28

                                                            T-number = 115

                                                            Tn = 5n-28

                                                            15*5=75

                                                                     -28

47

As you have seen from the above diagram and from the diagram on the first page as well the second page, the Tn answer is the same, Tn = 5n-28, this perfectly makes my prediction correct and it also proves that all the 4*4 grids will have the same answers no matter what the numbers.

...read more.

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