# 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

Extracts from this document...

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 |

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 |

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.

This student written piece of work is one of many that can be found in our GCSE T-Total section.

## Found what you're looking for?

- Start learning 29% faster today
- 150,000+ documents available
- Just £6.99 a month