• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17
  18. 18
    18
  19. 19
    19
  • Level: GCSE
  • Subject: Maths
  • Word count: 2880

My aim is to see if theres a relation between T total and T number and I will then work out the algebraic expressions so that the 50th term would be found out using the formula.

Extracts from this document...

Introduction

MATHS

T – Totals COURSEWORK

MR.UDDIN

T – Totals

PART 1:

My aim is to see if there’s a relation between T – total and T – number and I will then work out the algebraic expressions so that the 50th term would be found out using the formula.

1

2

3

12

22

The total of the numbers inside the T – shape is called the T – total.

The bottom number of the T is called the T – number.

So in this case the T – number would be 22.

The T – total is 22 + 12 + 2 + 1 + 3 = 40

T – Total in a 10 by 10 grid:

2

3

4

13

23

T – Total = 2 + 3 + 4 + 13 + 23 = 45

T – Number = 23

Another try:

3

4

5

14

24

T – Total = 3 + 4 + 5 + 14 + 24 = 50

T – Number = 24

I’ll put it in a table to see the difference:

T – number

T – total

Difference

22

40

23

45

5

24

50

5

As you can see that when the T – number increases by 1 the T – total increases by 5. This is because there are 5 boxes in the T –shape and each number increases by 1 will add up to five extra at the end.

Now I predict that T – total is going to be 55 in a 10 by 10 grid, now to check if it is right from a 10 by 10 grid:

4

5

6

15

25

4 + 5 + 6 + 15 + 25 = 55.

This here shows that my prediction was correct.

For a 10 by 10 grid, this is how the T – shape will look:

T-21

T-20

T-19

T-10

T

...read more.

Middle

th term would be the following:

5 x 50 – 7 = 243

Now I am going to do a 6 by 6 90º anticlockwise:

This would be the same as this:

T + 4

T-2

T - 8

T-1

T

T + 4 + T – 2 + T – 8 + T – 1 + T = 5T -7

16

10

4

11

12

I have to put my formula to the test:

5 x 12 – 7 = 53

I need to test if the formula is right:

16 + 10 + 4 + 11 + 12 = 53

So the 50th term would be the following:

5 x 50 – 7 = 243

Now I am going to put the results in the table and see if there is a difference in the T – Shapes when I changed the grid size and rotated the T – Shape 90º anticlockwise.

Grid Size

Formula

Difference

9 by 9

5T – 7

0

8 by 8

5T - 7

0

7 by 7

5T - 7

0

As you can see that there is no difference on these formulae, this is because when you put it into a T – shape, the right hand box and the left hand box will decrease as the grid size decreases. However this wouldn’t be a problem as both numbers has decreased by 1.

Example:

7 by 7 grid:

T + 5

T-2

T - 9

T-1

T

 5 – 2 – 9 – 1 = -7

6 by 6 grid:

T + 4

T-2

T - 8

T-1

T

4 – 2 – 8 – 1 = -7

Now I am going to rotate the T - shape 90º clockwise to investigate the difference between the T – number and T – total in different size grids.

...read more.

Conclusion

CONCLUSION:

During this coursework I found out many things about the T – shapes, the first thing was that the algebraic expression change as the grid size change, however it’s answer was negative and always was in the 7 times table.

Example: 5T – 70 & 5T - 63

However when the T –shape is rotated 90° anticlockwise, the grid size didn’t make a difference to the algebraic expression, infact it didn’t even change, although the numbers in the algebraic expression was negative.

Example: 5T – 7

In addition when I rotated the grid size 90° clockwise, the algebraic expression didn’t change, however it was a positive number, which is an exact opposite of what I found out when I rotated the T – shape 90° anticlockwise.

Example: 5T + 7

However when I rotated the T – shape 180°, the grid size changed the algebraic expression, however as the first it was always in the 7 times but in this case the number was a positive, because it was an exact opposite of the first one.

Example: 5T + 70 & 5T + 63

Moreover, when I did vector translations in my T- shape I found that if there was a vector as so: image04.png, the number would decrease by 5, however if there was a vector as so: image03.png, the number would increase by 5.  

Example:

image03.png = 5T – 7P + 5a

image04.png= 5T – 7p – 5bP

image02.png = 5T – 7P + 5a – 5bP

...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

    N = 14 T = (5 x 14)-7 = 70-7 = 63 Rotation of 900 8 by 8 T-number and T-total table T-number T-total 9 52 10 57 11 63 12 67 Here I have added a prediction of mine when I realized the pattern of the sequence, which goes up by 5 each time.

  2. T Total and T Number Coursework

    is a pattern: For +90 degrees the formula I have found is 5n+7 For -90 degrees the formula I have found is 5n-7 For +180 degrees the formula I have found is 5n+7g These three formulas work perfectly on this grid size but I shall have to do another grid size to be sure that they are correct.

  1. T-Shapes Coursework

    + 7(9) = 150 + 63 = 213 This is the correct answer. This shows that this formula works, but just to make sure that we can use this formula with any other sized grid; I am going to test it again, this time using an 8x8 grid.

  2. Urban Settlements have much greater accessibility than rural settlements. Is this so?

    up from the residents of 'South Downs' - An OAP's residential area. This explains why there are hardly any pedestrians in most areas of South Darenth. This also explains the lack of traffic. South Downs has its own shop and has its own entertainment.

  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. T-Shapes Coursework

    6) Testing My formula works as shown with the following, previously unused values: 1) Where n = 92 and w = 13 Total Sum = = = = Total Sum = = = = = Wing + Tail (86 + 87 + 88 + 89 + 90 + 91 + 92

  1. Maths Coursework T-Totals

    +3 or -2) and g is the grid width. Combinations (diagonal) For diagonal translation across a grid a combination of horizontal and vertical translations are used, therefore I predict that if I combine my 2 found equations for horizontal and vertical equations, I can generate a general formula for diagonal translations, which is a prediction I need to change.

  2. Given a 10 x 10 table, and a 3 steps stair case, I tried ...

    If we sum up all the values in the staircase in the algebraic table we end up with the same formula: Formula = x + x + 1 + x + 2 + x + 10 + x + 11 + x + 20 = 6x + 44 Which proves

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