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• Level: GCSE
• Subject: Maths
• Word count: 2067

# T Total Investigation

Extracts from this document...

Introduction

 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

T-Total = 2 + 3 + 4 + 11 + 19 = 39

T-Number = 19

T-Total = 3 + 4 + 5 + 12 + 20 = 44

T-Number = 20

T-Total = 4 + 5 + 6 + 13 + 21 = 49

T-Number = 21

T-Total = 5 + 6 + 7 + 14 + 22 = 54

T-Number = 22

T-Total = 6 + 7 + 8 + 15 + 23 = 59

T-Number = 23

T-Total = 7 + 8 + 9 + 16 + 24 = 64

T-Number = 24

## T-Number (n)

19

20

21

22

23

24

T-Total (t)

39

44

49

54

59

64

(        5        5       5        5       5        )

t = 5n – 56

 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

T-Total = 13 + 19 + 20 + 21 + 29 = 102

T-Number = 19

T-Total = 14 + 20 + 21 + 22 + 30 = 107

T-Number = 20

T-Total = 15 + 21 + 22 + 23 + 31 = 112

T-Number = 21

T-Total = 16 + 22 + 23 + 24 + 32 = 117

T-Number = 22

T-Total = 17 + 23 + 24 + 25 + 33 = 122

T-Number = 23

T-Total = 18 + 24 + 25 + 26 + 34 = 127

T-Number = 24

## T-Number (n)

19

20

21

22

23

24

T-Total (t)

102

107

112

117

122

127

(        5        5       5        5       5        )

t = 5n + 7

 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

T-Total = 9 + 17 + 18 + 19 + 25 = 88

T-Number = 19

T-Total = 10 + 18 + 19 + 20 + 26 = 93

T-Number = 20

T-Total = 11 + 19 + 20 + 21 + 27 = 98

T-Number = 21

T-Total = 12 + 20 + 21 + 22 + 28 = 103

T-Number = 22

T-Total = 13 + 21 + 22 + 23 + 29 = 108

T-Number = 23

T-Total = 14 + 22 + 23 + 24 + 30 = 113

T-Number = 24

## T-Number (n)

19

20

21

22

23

24

T-Total (t)

88

93

98

103

108

113

(        5        5       5        5       5        )

t = 5n - 7

 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

T-Total = 19 + 27 + 34 + 35 + 36 = 151

T-Number = 19

T-Total = 20 + 28 + 35 + 36 + 37 = 156

T-Number = 20

T-Total = 21 + 29 + 36 + 37 + 38 = 161

T-Number = 21

T-Total = 22 + 30 + 37 + 38 + 39 = 166

T-Number = 22

T-Total = 23 + 31 + 38 + 39 + 40 = 171

T-Number = 23

T-Total = 24 + 32 + 33 + 34 + 41 = 176

T-Number = 24

## T-Number (n)

19

20

21

22

23

24

T-Total (t)

151

156

161

166

171

176

(        5        5       5        5       5        )

t = 5n + 56

 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

Middle

t = 5n – 63

 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

T-Total = 14 + 21 + 22 + 23 + 32 = 112

T-Number = 21

T-Total = 15 + 22 + 23 + 24 + 33 = 117

T-Number = 22

T-Total = 16 + 23 + 24 + 25 + 34 = 122

T-Number = 23

T-Total = 17 + 24 + 25 + 26 + 35 = 127

T-Number = 24

T-Total = 18 + 25 + 26 + 27 + 36 = 132

T-Number = 25

T-Total = 19 + 26 + 27 + 28 + 37 = 137

T-Number = 26

## T-Number (n)

21

22

23

24

25

26

T-Total (t)

112

117

122

127

132

137

(        5        5       5        5       5        )

t = 5n + 7

 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

T-Total = 10 + 19 + 20 + 21 + 28 = 98

T-Number = 21

T-Total = 11 + 20 + 21 + 22 + 29 = 103

T-Number = 22

T-Total = 12 + 21 + 22 + 23 + 30 = 108

T-Number = 23

T-Total = 13 + 22 + 23 + 24 + 31 = 113

T-Number = 24

T-Total = 14 + 23 + 24 + 25 + 32 = 118

T-Number = 25

T-Total = 15 + 24 + 25 + 26 + 33 = 123

T-Number = 26

## T-Number (n)

21

22

23

24

25

26

T-Total (t)

98

103

108

113

118

123

(        5        5       5        5       5        )

t = 5n - 7

 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

T-Total = 21 + 30 + 38 + 39 + 40 = 168

T-Number = 21

T-Total = 22 + 31 + 39 + 40 + 41 = 173

T-Number = 22

T-Total = 23 + 32 + 40 + 41 + 42 = 178

T-Number = 23

T-Total = 24 + 33 + 41 + 42 + 43 = 183

T-Number = 24

T-Total = 25 + 34 + 42 + 43 + 44 = 188

T-Number = 25

T-Total = 26 + 35 + 43 + 44 + 45 = 193

T-Number = 26

## T-Number (n)

21

22

23

24

25

26

T-Total (t)

168

173

178

183

188

193

(        5        5       5        5       5        )

t = 5n + 63

 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

T-Total = 2 + 3 + 4 + 13 + 23 = 45

T-Number = 23

T-Total = 3 + 4 + 5 + 14 + 24 = 50

Conclusion

For the normal T…

 2 3 4 12 13 14 22 23 24
 Grid size 8x8 9x9 10x10 T Formula 5n - 56 5n - 63 5n - 70

(                     7                    7                     )

5n – 7g

For the T rotated 90 …

 2 3 4 12 13 14 22 23 24
 Grid size 8x8 9x9 10x10 T Formula 5n + 7 5n + 7 5n + 7

(                     0                    0                     )

5n + 7

For the T rotated 180 …

 2 3 4 12 13 14 22 23 24
 Grid size 8x8 9x9 10x10 T Formula 5n + 56 5n + 63 5n + 70

(                     7                    7                    )

5n + 7g

### For the T rotated 270 …

 2 3 4 12 13 14 22 23 24
 Grid size 8x8 9x9 10x10 T Formula 5n - 7 5n - 7 5n - 7

(                     0                    0                     )

5n – 7

Alan Davidson – 11H        Maths GCSE Coursework        T-Totals

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