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  • Level: GCSE
  • Subject: Maths
  • Word count: 2195

For this piece of GCSE maths coursework, I am aiming to find out the relationship between the T-Number and T-Total. To do this I am first going to use the 9 by 9 grid. After that, I am going to try out my rule by using different grids, 8 by 8, 6 by 6 etc

Extracts from this document...

Introduction

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For this piece of GCSE maths coursework, I am aiming to find out the relationship between the T-Number and T-Total. To do this I am first going to use the 9 by 9 grid. After that, I am going to try out my rule by using different grids, 8 by 8, 6 by 6 etc

Now I am going to do my first investigation, which is the 9 by 9 grid, and for this,             I am trying to find out the T-number and T-total.

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N=65                                                         N=66

T=46+47+48+56+65=262                        T=47+48+49+57+66=267                                                      

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68

N=67N=68

T=49+50+51+59+68=277                                           T=48+49+50+58+67=272                    

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N=69                                                            N=70                          T=50+51+52+60+69=282                       T=51+52+53+61+70=287

                                                                                         Key: - N= T-Number

T= T-Total

Now I am going to see the pattern that I made with the T-Number and the T-Total

T-Number

T-Total

Pattern

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262

5

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267

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272

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68

277

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282

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70

287

5


I have found out that every time you move to the right, you add 5 and every time you move to the left, you subtract 5. I know this just by looking at the pattern grid above.

Now I am going to put my result into tables because I want to find the rule and the relation between the T-Total and the T-Numbers. In addition, my work would be neat, easier to read and it gives a good presentation of my work. It is also easy for me to conclude the results.

T-Number

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70

T-Total

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277

282

287

                                                                                                                              I am going up by one

I am going up by five  

...read more.

Middle

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Rule in Algebra:-

N-19

N-18

N-17

 N-9

  N

74-55

74-56

74-57

74-65

74=N

My aim was to find the T-Number for each of the numbers above. The first thing that I did was to find out the T-Number, which is eventually at the bottom of the T-shape. Then I subtracted the T-Number by the other numbers inside the T-Shape, for example, I subtracted 65 from 74, which gave the answers N-9+N-18+N-17+N-9+N, and this is how I found the T-Number for the entire number grid. I have noticed that the middle column is going up in nine and I think this is because of the size of the grid. I think that in every other grids which I would do the T-Number is going to gain on the grid size and go up in multiples e.g. 9 by 9 grid, the T-Number is going to go up in nine’s. I concentrated on the number 74 because it was the T-Number.                                                                                                                                       This is the formula for the T-Total= N-19+N-18+N-17+N-9+N= 5N-63                                                                                          

Now I am going to test my theory to see if it works with other T-Numbers.

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                                                                           Key: - N= T-Number

T= T-Total

T =1+2+3+11+20=37                                          T=16+17+18+26+35=112                                                                   T-Total= N-19+N-18+N-17+N-9+N=5N-63      T-Total=N-19+N-18+N-17+N-9+N=5N-63 T=5x20-63=37                                                    T= 5x35-63=112

I have found out the formula 5N-63 works anywhere in the grid, I know this because I tested the formula two times for different T-Numbers and the formula works.                                                                                                                             The full formula for the nine by nine grid is: - T=5N-63

Now I am going to find out by using different grids the rule in algebra, I am doing this because I want to find out does the grid size matter and if it does how. I am going to do an eight by eight grid to start.

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N-17

N-16

N-15

 N-8

  N

The formula for the T-Total is:-

T-Total = N-17+N-16+N-15+N-8+N=5N-56

T= 5x35-56=119

Now I am going to test this formula to see if it works

                                                                                             Key: - N= T-Number

T= T-Total

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T =9+10+11+18+26=74                                       T=30+31+32+39+47=179                                                                   T-Total= N-17+N-16+N-15+N-8+N=5N-56       T-Total= N-17+N-16+N-15+N-8+N=5N-56                                                          T= 5x26-56=74                                                    T= 5x47-56=179

I have found out that the formula 5N-56 works anywhere in 8 by 8 grid, I have tested the formula two times and this proves that my result does not have in faults in it.                                                                                                                                  The formula for the 8 by 8 grid is: - T=5N-56

Now I am going to do a seven by seven grid to find out the Algebraic rule

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N-15

N-14

N-13

 N-7

  N

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The formula for the T-Total is:-

T-Total = N-15+N-14+N-13+N-7+N=5N-49

T= 5x16-49=31

Now I am going to test this formula to see if it works

                                                                                            Key: - N= T-Number

T= T-Total

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...read more.

Conclusion

5N-7x6

5N-42

7 by 7

5N- 7x7

5N-49

8 by 8

5N- 7x8

5N-56

9 by 9

5N- 7x9

5N-63

10 by 10

5N- 7x10

5N-70

Overall, the general rule for the T-Total is 5N-7G, where the N is T-Number and the G is grid number.

I recognised that if I multiply the number of grids by 7 I would get the T-Total.

General Rule: 5N-7G

Now I am going to test my general rule with two examples and then prove that I was right:-

N-2G-1

N-2G

N-2G+1

N-G

  N

General rule in algebraic form

now I will add the numbers to find the General rule, N-2G-1+N-2G+N-2G+1+N-G+N                                     I got the N-G because the middle square is the same as the grid number.

Using my rule that I found out I predict that if the grid size is 5 by 5 the rule is: 5N-35                  Now I am going to prove it 5N- 7G is 5N-7x5, so the rule is 5N-35.

Now I am going to predict and prove it for a 4 by 4 grid just to make sure that my general rule is correct. Therefore, the rule for a 4 by 4 grid is going to be 5N-28. Now I am going to prove it; 5N-7G is 5N-7x4, so the rule is 5N-28.

I have predicted and proved it twice to see if my general rule is 5N-7G and by my prediction, I have proved that my rule is correct.

THIS DOCUMENT WAS DOWNLOADED FROM COURSEWORK.INFO - THE UK'S COURSEWORK DATABASE - HTTP://WWW.COURSEWORK.INFO/

...read more.

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