• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Mathematics Coursework - T Shapes

Extracts from this document...

Introduction

2. Translate the T-shape to different positions.

Using a grid of any size, I will investigate how the original T-number is related to the T-total of the translated T-shape. First, I will use

...read more.

Middle

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

image01.png

image02.png

Here is a table showing the results so far for the different grid sizes, t-numbers, t-totals and the vector.

Vector ((a,b))

(3,0)

(2,0)

(1,0)

Grid Size (g)

9x9

8x8

6x6

Original T-number (n)

20

18

14

Original T-total

37

34

28

Final T-number

23

20

15

Final T-total (T)

52

44

43

image03.png

From this table I can see a pattern. It shows that when you take an Original T-total (37) and add on 5 times the vector a (3) you get the final T-total. In equation form this is:
Final T-total = Original T-total + (5xMovement in Horizontal Direction)
However this equation requires us to know the T-total In advance when we only know the T-number. So I can substitute a previous equation for the Original T-total (5n-7g). This gives me the final equation of:
Final T-total = (5n-7g)+(5a)

Therefore, I have a final formula of:
(T=Final t-total) (n=original T-number) (a=the horizontal direction on the vector)

T = (5n-7g)+5a

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

...read more.

Conclusion

wspan="1">

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

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

Justification
To prove that this formula will always work with any grid size and any T-shape using a horizontal vector I can use this T-shape, Grid and vector:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15image05.png

6

17

18

19

20

21

22

23

24

25

                                
                   First T-shape                                           Final T-shape         

...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-Shapes Coursework

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 So in this test, (g) would become 4, as we are using a 4x4 grid. Tt = (5 x 15) - 7(4) = 75 - 28 = 47 T-Total = 47 We have a

  2. T-Shapes Coursework

    have the same formula as they did for the 9x9. This could mean that I have already found out their 'general formula' (formula for any grid).For the other type of t-shapes e.g. have different formulas from the original. The 9x9 grid formula consisted of n x 5 -(+)

  1. T-Shapes Coursework

    In fact, if we take one constant Middle Number, 25, from each of the above tables, we get the following: Middle Number Wing Width (w) Sum of Wing Sum of Tail Total Sum (Wing + Tail) 25 5 125 35 160 25 7 175 35 210 25 9 225 35

  2. The T-Total Mathematics Coursework Task.

    59 232 22 47 60 237 23 52 61 242 24 57 62 247 25 62 65 262 26 67 66 267 29 82 67 272 30 87 68 277 31 92 69 282 32 97 70 287 33 102 71 292 34 107 74 307 35 112 75 312

  1. T-Total Coursework

    There is also transformation and combinations of transformations. I need to find out the investigation of the relationship between the T-Total, the T-Number, the grid size and the transformations. If I turned the T-Shape around 180 degrees it would look like this. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

  2. Objectives Investigate the relationship between ...

    of T24 is '50' I will now find the algebraic formula for this 10x10 grid, using the T-shape T22. I will find this formula using an equation, to do so I will find the nth term My prediction is '5*n - x = T-total' where n = T-number If I

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

    WRITE YOUR RULE USING ALGEBRA T=5(v+cg+d)+2 v = middle number c = difference (in grid blocks) between the centre and the v number g = grid width d = distance between new v number and the centre of rotation If we use this formula to generate an answer; T=5(41+(3x9)+3)+2 T=5(71)+2

  2. T totals - translations and rotations

    26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 My T-number is 19 as you can see above on my 7by7 grid I will be representing this as N in my equation.

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