# T-Total. PART 1 Investigate the relationship between the T-total & the T-Number.

Extracts from this document...

Introduction

MATHS COURSEWORKT-TOTALS

T-TOTALCOURSEWORK

The number at the bottom of the ‘T’ is the t-number & the total of all of these numbers in the ‘T’ added together is called t-total.

In the example above the t-number is 20 & the t-total is 37.

PART 1

Investigate the relationship between the T-total & the T-Number.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |

28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 |

37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 |

46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 |

55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 |

64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 |

72 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 |

GRIDSIZE9x9

RELATIONSHIP

T-Number | 20 | 21 | 22 | 23 | 24 | 25 | 26 |

T-Total | 37 | 42 | 47 | 52 | 57 | 62 | 67 |

As t-number goes up by 1 the t-total goes up by 5

ROUGHWORK

20 x 2 – 3 = 37

21 x 2 – 3 = 39

20 x 3 – 23 = 37

21 x 3 – 23 = 40

20 x 4 – 43 = 37

20 x 4 – 43 = 41

20 x 5 – 63 = 37

21 x 5 – 63 = 42

22 x 5 – 63 = 47

23 x 5 – 63 = 52

24 x 5 – 63 = 57

25 x 5 – 63 = 62

26 x 5 – 63 = 67

37 + 38 + 39 + 47 + 56 = 217

58 + 59 + 60 + 68 + 77 = 322

56 x 5 – 63 = 217

77 x 5 – 63 = 322

SO THE RELATIONSHIP BETWEEN THE T-NUMBER & THE T-TOTAL IS

T = 5N – 63

To prove formula algebraically, I am going to substitute x for my T-Number

Middle

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |

61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |

71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

## GRID SIZE 10x10

T-Number | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |

T-Total | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 |

As t-number goes up by 1 the t-total goes up by 5

ROUGHWORK

22 x 5 – 63 = 47

22 x 5 – 70 = 40

23 x 5 – 70 = 45

24 x 5 – 70 = 50

25 x 5 – 70 = 55

26 x 5 – 70 = 60

27 x 5 – 70 = 65

28 x 5 – 70 = 70

29 x 5 – 70 = 75

53 + 54 + 55 + 64 + 74 = 300

65 + 66 + 67 + 76 + 86 = 360

74 x 5 – 70 = 300

86 x 5 – 70 = 360

SO THE

Conclusion

There is also a connection between the number that you take away at the end. If you look carefully then you notice that all of those numbers are the multiples of seven. The number that you take away is grid size times 7.

For example; 9 x 7 = 63, 8 x 7 = 56 & 10 x 7 =70.

So from this you can work out the relationship between the T number, T total and the grid size.

Which is:

5n – (grid size x 7)

MOHAMMAD SUHAYB RIAZ

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