• 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

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.

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: , the number would decrease by 5, however if there was a vector as so: , the number would increase by 5.

Example:

= 5T – 7P + 5a

= 5T – 7p – 5bP

= 5T – 7P + 5a – 5bP

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

# 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-Shapes Coursework

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 The table above shows our T-Shape being rotated 270� clockwise.

1. ## T-Shapes Coursework

Justification The formula can be proven to work with algebra in the form of an arithmetic progression. The basic algebraic labelling of the 3xl "T" on a width 10 grid is: n - 1 n n + 1 n + 10 n + (10 + 10)

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

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

1. ## T totals - translations and rotations

The two numbers remaining in my T-shape are N-14-1 and N-14+1. Thus my T-total is: N+ (N-7) + (N-14) + (N-14-1) + (N-14+1) = 5N-49 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

2. ## 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.

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

Towards Dartford... Cars: Vans: Buses: Motorbikes: Pushbikes: |||||||| Total: 8 Total: 0 Total: 0 Total: 0 Total: 0 Overall South Darenth has a relatively low traffic density. Sketch Maps to Show Count Locations (Traffic and Pedestrian): Bexley: 1. 2. 3.

2. ## T Total and T Number Coursework

7g= 7x9- this is from 9x9 so 5n x(7x9)= 5nx56 This is the general formula for any grid size to find the T-total. Testing the General formula On A Different grid Size. Now that I have found my formula and found that it works for a grid size that I

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