• 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
• Level: GCSE
• Subject: Maths
• Word count: 1037

# 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.

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.

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.

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

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

(7 x 23) - (11 x 10) = 51 161 - 110 = 51 1 + 2 + 3 + 4 + 5 + 13 + 23 = 51 I found out that the formula for a 5by2 on a 10by10 grid is correct. I will now do the same on a 9by9 grid.

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

In South Darenth, one bus, the 414 takes passengers to Bluewater, where they can catch connecting buses. In Bexley's case this is not so. There are 7 bus routes linking Bexley to the adjoining communities. All but one of the town's buses goes or terminates at Bexleyheath, where more buses can be caught (including Night Buses)

2. ## Maths GCSE Coursework &amp;amp;#150; T-Total

One simple change needs to be made to my horizontal translation equation, that as "a" was also used for the figure by which to translate (the same as the vertical translation), we have to substitute "a" with "b" in the horizontal equation otherwise we can only move the T-Shape, is fixed diagonal positions.

1. ## In this section there is an investigation between the t-total and the t-number.

For the number 38 we have a grid movement of two so we get (tn+2gm). For the numbers 46, 47 and 48 we have a grid movement of three and a total of three numbers, se we get 3(tn+3gm). The total of all of them together is (5tn +12*gridsize)

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

Rotation (degrees) Direction T-Total (t) Difference compared to original T-Total 14 0 N/a 52 0 14 90 Clockwise 72 +20 14 180 Clockwise 88 +36 14 270 Clockwise 68 +16 MAKE A TABLE and LOOK FOR PATTERNS and TRY TO FIND A RULE It is hard to make any immediate

1. ## Maths Coursework T-Totals

We now need to use the same method with different grid size to make a universal equation. I have chosen a grid width of 11 as that has a central number as does a grid width of 9, but make it vertically shorter as we do not need the lower number as they will not be used.

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

Table 2 Pattern: N 1 2 3 4 5 Total Tiles: T 17 33 53 75 105 +16 +20 +24 +28 +4 +4 +4 Table two shows the pattern number and total amount of tiles in that particular pattern. There is no constant first difference until the second difference (which is constant).

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