• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

T-Total Investigation

Extracts from this document...

Introduction

Maths Coursework – T-Total

I have looked at the T-Number and I called it N. Then I saw how much difference there was between the T-Number and the other numbers in the T. when I did this the numbers came out like this:        20, 20-9, 20-19, 20-18, 20-17. These sums when added together will come out with the T-Total. The T-Total is 37. I have tried out this method with other T-Numbers and the results ended up like this.

T-Number                T-Total

  1. 37
  2. 42
  3. 47
  4. 52
  5. 57
  6. 62
  7. 67
  8. 72
  9. 77
  10. 82

This rule showed a pattern. The next T-Total has 5 added to it. This means that there has to be a 5 in the algebraic rule. Because there are 5 squares in a T the 5 in the rule will be 5N. 5N for the first T-Number is 100. To get to the proven T-Total for this T-Number I have to minus 63. So the rule for this T-Number is 5N – 63. I will now test whether this rule works for the other

T-Numbers.

...read more.

Middle

22, 22-10, 22-20, 20-21, 20-19. This ends up minusing 70 from the 5N.The final T-Total now is 40. I will now try this for other T-Numbers. 5 times 25 is 125, then minus 70 is 55. I tested this and it is correct. 5 times 26 is 130 then minus 70 is 60. This is correct aswell.

The Nth Term for finding out the T-Total on a 10x10 grid is 5N – 70.

I will now try on an 8x8 grid. I will start off with the T-Number 30. 30 times 5 is 150. Now I will do the same as before to get the T-Total. 30, 30-8, 30-16, 30-17, 30-15. Now I have to minus 56. This comes out with 94. I added up the numbers and they do equal 94. I tried this for other T-Numbers and it worked.

The Nth Term for finding out the T-Total on an 8x8 grid is 5N – 56.

I have looked at all of the Nth Terms and I can see a pattern. The number needed to minus to get the T-Total is related to the grid size. The grid size times 7 equals the number. 7x8=56. 7x9=63. 7x10=70.

...read more.

Conclusion

The Nth Term for the T on its side facing left on a 9x9 grid is 5N + 7.

I will now try it on a 10x10 grid facing right with the T-Number 13. 13, 13-1, 13-2, 13-12, 13+8. It is again 5N – 7. So I predict that it will be the opposite for the facing left. I will test it with the T-Number 15. 15, 15+1, 15+2, 15+12, 15-8. It does come out as 5N + 7.  Because the rule is the same for the grid sizes 9x9 and 10x10 grid that it will be the same again for the grid size 8x8. I will now test it with the T facing left with the T-Number 9. 9, 9+1, 9+2, 9-6, 9+10. This adds up to 5N + 7. Now I will try it facing right with the T-Number 11. 11, 11-1, 11-2, 11+6, 11-10. I adds up to 5N – 7 again.

The overall Nth Term for the T on its side facing left on is 5N + 7.

The overall Nth Term for the T on its side facing right on is 5N - 7.

...read more.

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

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE T-Total essays

  1. T-Total Maths

    Formula: T=5N+7 I tested that when: T-number=54 T-total=357 Below is a T-shape, and in each cell how number is connected with T-number on a 9 by 9 number grid. To prove the formula: T= N+N-1+N-10+N-2+N+6 T= 5N+7 How the formula works there are some example shown in below are: Formula:

  2. T-total Investigation

    This is what I did: 23 x 7 = 161 161 - 51 = 110 24 x 7 = 168 168 - 58 = 110 25 x 7 = 175 175 - 65 = 110 My formula for a 7by2 T on 10by10 grid is now 7T - 110 I

  1. T-Shapes Coursework

    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

  2. T-Shapes Coursework

    51 52 53 54 55 56 57 58 59 60 61 62 63 64 The table above shows our T-Shape being rotated 180�. T-Number of rotated T-Shape: 36 T-Total of rotated T-Shape: 36 + 44 + 51 + 52 + 53 = 236 So let us try the general formula we have just discovered: Tt =5 x 36 + 7(8)

  1. T totals. In this investigation I aim to find out relationships between grid sizes ...

    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

  2. T-Total Maths coursework

    For an 8x8 grid use the number 8. E.g. 5n + (7x8) The results compare the findings from the formula n=5n-7g with, I can start to substitute the numbers into the formula, to find out if the formula works.

  1. Maths Coursework T-Totals

    width of 9 the T-Total (t) is -5 smaller than the previous T-Total (t) (the origin) As when v = 32, t = 142 and with a translation horizontally by -1 v = 31, t = 137, and 137 - 142 = -5, therefore the above statement it correct.

  2. Maths coursework

    this is: I will now add up all of that is in the t-shape and put it into its simplest form: T = N + (N - G) + (N - 2G) + (N - 2G + 1) + (N - 2G - 1)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work