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

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

...read more.

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
...read more.

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.

...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. Black and white squares

    x 3� + b x 3� + c x 3 + -1 25 = a x 27 + b x 9 + 3c - 1 25 = 27a + 9b + 3c - 1 26 = 27a + 9b + 3c I 26 = 27a + 9b + 3c 4

  2. T-Total. I will take steps to find formulae for changing the position of the ...

    The 5zb part of the first formula calculates the movement moving down and the 5a calculates the movement of moving to the right. These are the two movements that are made in the process so are vital and must be in the formula.

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

    Rotation (degrees) Direction Equation 0 Anti-Clockwise t=5v - 2g 90 Anti-Clockwise t=5v - 2 180 Anti-Clockwise t=5v + 2g 270 Anti-Clockwise t=5v + 2 Combinations of translation and rotation EXTEND THE PROJECT - EXPLORE what happens when you CHANGE THE PROBLEM in a SMALL WAY For this section, we can

  2. I am going to investigate how changing the number of tiles at the centre ...

    The quadratic expressions form a pattern, as I thought, 2N( is recurrent, the last number which is added on, is equal to the number of centre tiles in the pattern and the number times by, N, is double that number.

  1. T-Totals. I will take steps to find formulae for changing the position of ...

    5 6 5 6 7 11 12 13 14 15 20 21 22 23 24 When the T is moved across one square, 5 is added to the T total because there are 5 squares in the T shape meaning 1 has been added to each number in the T adding up to a total of 5.

  2. T-Totals. Firstly I am going to do a table of 5 x 5 and ...

    T-Number is 12 Now I am going to put the T-shape in another location 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 The T-number is 13 The T-total for this T-shape is 2

  1. T-Total Course Work

    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 1 2 3 T-number = 20 Numbers: 1 2 3 11 20 20-1 20-2 20-3 20-11 20 T-19 T-18 T-17 T-9 T T-total

  2. Football League - mathematics investigation.

    A C v B -------- C v D C v E C v F D D v A D v B D v C -------- D v E D v F E E v A E v B E v C E v D -------- E v F F F

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