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  • Level: GCSE
  • Subject: Maths
  • Word count: 1437

T-totals. For my T-totals maths coursework I will investigate the relationship between the T-total and T-number, the T-total and T-number and grid size and the T-shape in different positions.

Extracts from this document...

Introduction

Maths Coursework – T-totals

Introduction

        For my T-totals maths coursework I will investigate the relationship between the T-total and T-number, the T-total and T-number and grid size and the T-shape in different positions.

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Looking at this T-shape drawn on a 9x9 grid,

The total of the numbers inside the T-shape is 2+3+4+12+21=42

This is called the T-total.

The number at the bottom of the shape is the T-number. The T-number for this shape is 21.

Part 1

For the first part of my coursework I must investigate a relationship between the T-total and the T-number. To do this I have chosen the following T-shapes:

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20

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23

     &

I noticed that the difference between each number in the T-shape and the T-number was always the same no matter what T-shape you use.

(N = T-number )

23-4

23-5

23-6

23-14

23

20-1

20-2

20-3

20-11

20

      &
=

With the table set out like this a formula can be worked out to find any T-Total on this size grid. This is done in the working below:

N-19

N-18

N-17

N-9

N

...read more.

Middle

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By doing the same as in the 9 x 9 grid you will get a T-shape like this:

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=

N-13

N-12

N-11

N-6

N

This means that the formula to find the T-number in a 6 x 6 grid is:

T = 5N – 42.

Now we must put this formula to the test,

For example, If I put the T-number 27 into the formula it looks like this:

5 x 27 – 42 = T

135 – 42 = T

T = 93

Therefore, the T-total of a T-shape with a T-number of 27 on a 6 x 6 grid should be 93.

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21

27

T-total = 14+15+16+21+27=93

Therefore my formula was proven correct!

Part 2

In the last part I noticed that not only did the centre column in each T-shape for the 9 x 9 grid go up in 9’s but also the centre columns in each T-shape for the 6 x 6 grid went up by 6. This means that I can work out a formula for any T-total on any grid size by using the calculations below:

N-(2G-1)

N-(2G)

N-(2G+1)

N-G

N

                (G = Grid size)

This means that to find the T-number on any T-shape on any size graph you must use the formula:

T = 5N – 7G

Now I must put this formula to the test

I will use a 5 x 5 grid:

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I will use the T-number 18.

T = 5N – 7G

T = 5 x 18 – 7 x 5

T = 90 – 35

T = 55

This means that the T-total for a T-shape with T-number 18 on a 5 x 5 grid should be 55.

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18

 T = 7+8+9+13+18=55        

I have proven that it works on a square grid but now I will see if it will work on a rectangle grid. I will use a 4 x 6 grid and use the T-number 19.

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T = 5N – 7G

T = 5 x 19 – 7 x 4

T = 95 – 28

T= 67

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19

T = 10+11+12+15+19=67

This means that my formula is correct and now I can make a formula that gives me the T-number if I have the T-total. This formula is:

N = T + 7G

          5

Now I will test this formula using a 4 x 4 grid and using a

T-total of 42.

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...read more.

Conclusion

This relationship will enable me to find formulas for T-shapes in any positions on any grid:

N

N+7

N+13

N+14

N+15

This means that to find the T-total or T-number of an “upside down” T-shape on a grid size 7 x 7 you must use this formula:

T = 5N + 49

Now we must check this. For example, if I use the T-number 33 into the formula it looks like this:

T = 5N + 49

T = 5 x 33 + 49

T = 165 + 49

T = 214

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46

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48

T = 33+40+46+47+48=214

Therefore my formula is correct.

Now I know that to find the formula of the T-shape “upside down” or “opposite” you must turn the mathematical signs opposite I can now find the formula for any size grid without doing much working out:

N

N+G

N+2G+1

N+2G

N+2G-1

This means that the formula to find a T-total of an upside down T-shape on any size grid is:

T = 5N + 7G

Now I must test this formula. I will use a 8 x 8 grid and the T-number 28:

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T = 5N + 7G

T = 5 x 28 + 7 x 8

T = 140 + 56

T = 196

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T = 28+36+43+44+45=196

Therefore my formula is correct.

...read more.

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