• 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
• Level: GCSE
• Subject: Maths
• Word count: 2195

# For this piece of GCSE maths coursework, I am aiming to find out the relationship between the T-Number and T-Total. To do this I am first going to use the 9 by 9 grid. After that, I am going to try out my rule by using different grids, 8 by 8, 6 by 6 etc

Extracts from this document...

Introduction

THIS DOCUMENT WAS DOWNLOADED FROM COURSEWORK.INFO - THE UK'S COURSEWORK DATABASE - HTTP://WWW.COURSEWORK.INFO/

For this piece of GCSE maths coursework, I am aiming to find out the relationship between the T-Number and T-Total. To do this I am first going to use the 9 by 9 grid. After that, I am going to try out my rule by using different grids, 8 by 8, 6 by 6 etc

Now I am going to do my first investigation, which is the 9 by 9 grid, and for this,             I am trying to find out the T-number and T-total.

 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 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
 47 48 49 57 66 46 47 48 56 65

N=65                                                         N=66

T=46+47+48+56+65=262                        T=47+48+49+57+66=267

 48 49 50 58 20 49 50 51 59 68

N=67N=68

T=49+50+51+59+68=277                                           T=48+49+50+58+67=272

 51 52 53 61 70
 50 51 52 60 69

N=69                                                            N=70                          T=50+51+52+60+69=282                       T=51+52+53+61+70=287

Key: - N= T-Number

T= T-Total

Now I am going to see the pattern that I made with the T-Number and the T-Total

 T-Number T-Total Pattern 65 262 5 66 267 5 67 272 5 68 277 5 69 282 5 70 287 5

I have found out that every time you move to the right, you add 5 and every time you move to the left, you subtract 5. I know this just by looking at the pattern grid above.

Now I am going to put my result into tables because I want to find the rule and the relation between the T-Total and the T-Numbers. In addition, my work would be neat, easier to read and it gives a good presentation of my work. It is also easy for me to conclude the results.

 T-Number 65 66 67 68 69 70 T-Total 262 267 272 277 282 287

I am going up by one

I am going up by five

...read more.

Middle

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

74

75

76

77

78

79

80

81

Rule in Algebra:-

 N-19 N-18 N-17 N-9 N 74-55 74-56 74-57 74-65 74=N

My aim was to find the T-Number for each of the numbers above. The first thing that I did was to find out the T-Number, which is eventually at the bottom of the T-shape. Then I subtracted the T-Number by the other numbers inside the T-Shape, for example, I subtracted 65 from 74, which gave the answers N-9+N-18+N-17+N-9+N, and this is how I found the T-Number for the entire number grid. I have noticed that the middle column is going up in nine and I think this is because of the size of the grid. I think that in every other grids which I would do the T-Number is going to gain on the grid size and go up in multiples e.g. 9 by 9 grid, the T-Number is going to go up in nine’s. I concentrated on the number 74 because it was the T-Number.                                                                                                                                       This is the formula for the T-Total= N-19+N-18+N-17+N-9+N= 5N-63

Now I am going to test my theory to see if it works with other T-Numbers.

 1 2 3 11 20 16 17 18 26 35

Key: - N= T-Number

T= T-Total

T =1+2+3+11+20=37                                          T=16+17+18+26+35=112                                                                   T-Total= N-19+N-18+N-17+N-9+N=5N-63      T-Total=N-19+N-18+N-17+N-9+N=5N-63 T=5x20-63=37                                                    T= 5x35-63=112

I have found out the formula 5N-63 works anywhere in the grid, I know this because I tested the formula two times for different T-Numbers and the formula works.                                                                                                                             The full formula for the nine by nine grid is: - T=5N-63

Now I am going to find out by using different grids the rule in algebra, I am doing this because I want to find out does the grid size matter and if it does how. I am going to do an eight by eight grid to start.

 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 51 52 53 54 55 56 57 58 59 60 61 62 63 64
 18 19 20 27 35 N-17 N-16 N-15 N-8 N

The formula for the T-Total is:-

T-Total = N-17+N-16+N-15+N-8+N=5N-56

T= 5x35-56=119

Now I am going to test this formula to see if it works

Key: - N= T-Number

T= T-Total

 9 10 11 18 26 30 31 32 39 47

T =9+10+11+18+26=74                                       T=30+31+32+39+47=179                                                                   T-Total= N-17+N-16+N-15+N-8+N=5N-56       T-Total= N-17+N-16+N-15+N-8+N=5N-56                                                          T= 5x26-56=74                                                    T= 5x47-56=179

I have found out that the formula 5N-56 works anywhere in 8 by 8 grid, I have tested the formula two times and this proves that my result does not have in faults in it.                                                                                                                                  The formula for the 8 by 8 grid is: - T=5N-56

Now I am going to do a seven by seven grid to find out the Algebraic rule

 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
 N-15 N-14 N-13 N-7 N 1 2 3 9 16

The formula for the T-Total is:-

T-Total = N-15+N-14+N-13+N-7+N=5N-49

T= 5x16-49=31

Now I am going to test this formula to see if it works

Key: - N= T-Number

T= T-Total

 11 12 13 19 26 17 18 19 25 32
...read more.

Conclusion

5N-7x6

5N-42

7 by 7

5N- 7x7

5N-49

8 by 8

5N- 7x8

5N-56

9 by 9

5N- 7x9

5N-63

10 by 10

5N- 7x10

5N-70

Overall, the general rule for the T-Total is 5N-7G, where the N is T-Number and the G is grid number.

I recognised that if I multiply the number of grids by 7 I would get the T-Total.

General Rule: 5N-7G

Now I am going to test my general rule with two examples and then prove that I was right:-

 N-2G-1 N-2G N-2G+1 N-G N

General rule in algebraic form

now I will add the numbers to find the General rule, N-2G-1+N-2G+N-2G+1+N-G+N                                     I got the N-G because the middle square is the same as the grid number.

Using my rule that I found out I predict that if the grid size is 5 by 5 the rule is: 5N-35                  Now I am going to prove it 5N- 7G is 5N-7x5, so the rule is 5N-35.

Now I am going to predict and prove it for a 4 by 4 grid just to make sure that my general rule is correct. Therefore, the rule for a 4 by 4 grid is going to be 5N-28. Now I am going to prove it; 5N-7G is 5N-7x4, so the rule is 5N-28.

I have predicted and proved it twice to see if my general rule is 5N-7G and by my prediction, I have proved that my rule is correct.

THIS DOCUMENT WAS DOWNLOADED FROM COURSEWORK.INFO - THE UK'S COURSEWORK DATABASE - HTTP://WWW.COURSEWORK.INFO/

...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

# Related GCSE T-Total essays

1. ## Connect 4 - Maths Investigation.

Height Total 3 6L - 10 4 10L - 16 5 14L - 22 From the results I can see that the difference between the totals are 4L - 6. As height is the variable I will have to put it into the equation, I have decided to put it at the beginning.

2. ## T-Total Maths coursework

T=5N-7 I tested that when: T-number=62 T-total=353 N = 12 13 14 15 T = 53 58 63 68 T-number T = (5x12) -7 = 60-7 T = 53 T-total This equation has produced its first correct answer. I will carry on and test T-shape I know the T-total for N = 13 T = (5 x 13)

1. ## T Total and T Number Coursework

Translating the T and the effect it has on the T-total. Now that I have found the general formula for the t-total on any grid size I must take the investigation one step further. I must now investigate the effect of translating the shape to a different point on the grid.

2. ## Magic E Coursework

X = 5 e e+1 e+2 e+3 e+4 The last square in the row will be e + (x-1) due the last square being e plus the width. The first square is e + 0 so 1 must be taken off of the total width.

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

We should now try and find the rule that governs the "magic number" that has to be taken from 5x to gain t. If we say g is the grid size (e.g. 4 for 4x4 or 5 for 5x5). 1 2 3 4 5 6 7 8 9 If we

2. ## T-totals. I am going to investigate the relationship between the t-total, T, and ...

(1 + g) - (d - b) (g - 1) + a - bg } - 7 Validation To thoroughly validate these formulae, all forms of and need to be tested. As there are sixteen combinations of the two vectors, using only an 11�11 grid will be sufficient for our test.

1. ## Objectives Investigate the relationship between ...

And highlight their relationships. Formula(8x8) Formula(9x9) Formula(10x10) What it solves? 5n-56 5n-63 5n-70 Works out the T-total of any T-shape translated horizontally or vertically, (left/right/up/down) 5n+7 5n+7 5n+7 Works out the T-total of any T-shape rotated in a 90� angle 5n+56 5n+63 5n+70 Works out the T-total of any T-shape

2. ## T-Shapes Coursework

Using Pattern 1 above, we can say that the Sum of the Tail = n + g 2) Using the patterns from Section 1, we can still say that the Sum of the Wing = 3n 3)

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