• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1573

T-Total. I will be looking at T-shape drawn on different size grids. I will also be comparing and finding link and formulas between T-number and T-total.

Extracts from this document...

Introduction

T-Total

In this investigation, I will be looking at T-shape drawn on different size grids. I will also be comparing and finding link and formulas between T-number and T-total. The different size grid will be: 10 by 10, 9 by 9, 8 by 8, 7 by 7, 6 by 6 and 5 by 5.

I will use grids of different sizes to try out transformation, combinations of transformations and reflection. I will also be making tables to identify formulae.  

image00.png

1.In this experiment I will for the formula of a T, with the T-number facing southwards. My first table is the result from a 10 by 10 grid, this on page 1.

Number

T-total

T-number

1

40

22

2

45

23

3

50

24

4

55

25

5

60

26

6

65

27

Here is the grid formula.

image01.png n + n-10 + n-20 + n-21 + n-19 = 5n-70

and therefore formula for 10 by 10 is 5n-70.

Here is 9 by 9 grids result from page 2.

Number

T-number

T-total

1

20

37

2

21

42

3

22

47

4

23

52

5

24

57

Here is the grid formula

image12.pngn-19 + n-18 + n-17 + n-9 + n =5n-63

and therefore the formula for 9 by 9 grid is 5n-63.

Here is 8 by 8 grids result from page 2.

Number

T-number

T-total

1

18

34

2

19

39

3

20

44

4

21

49

5

22

54

Here is the grid formula

image17.pngn-17 + n-16 + n-15 + n-8 + n = 5n-56

therefore the formula is 5n-56.

...read more.

Middle

T-total

1

10

43

2

11

48

3

12

53

4

13

58

5

14

63

Here is the grid formula for 7 by 7 grid.

image22.pngn-9 + n-2 + n+5 + n-1 + n = 5n-7

From the results above I can predict that the formula for a 6 by 6   and 5 by 5 will be 5n-7.

I was able to find the general formula by looking at grids above.

All t-total with t-number facing eastward will have the formula 5n-7.

I found out the general grid formula which will be:

image23.png

3) This time we will be looking at t-shape with t-number facing north.My first table will 10 by 10 grid from page 7.

Number

T-number

T-total

1

2

80

2

3

85

3

4

90

4

5

95

5

6

100

6

7

105

Here is the grid formula for 10 by 10.

image02.pngn + n +10 + n + 19 + n + 20 + n + 21 = 5n + 70

Here is grid 9 by 9 from page 8:

Number

T-number

T-total

1

2

73

2

3

78

3

4

83

4

5

88

5

6

93

Here formula grid for 9 by 9 grid:

image03.png n + n + 9 + n + 17 + n + 18 + n + 19 = 5n+63

Results of grid 8 by 8 form page 8:

Number

T-number

T-total

1

2

66

2

3

71

3

4

76

4

5

81

5

6

86

Here’s the grid formula for 8 by 8:

image04.png n + n + 8 + n + 15 + n + 16 + n + 17 = 5n+56

Here is the 7 by 7 grid from page 9:

Number

T-number

T-total

1

2

59

2

3

64

3

4

69

4

5

74

5

6

79

The grid formula for 7 by 7 grid is:

image05.pngn + n + 7 + n + 13 + n + 14 + n + 15 = 5n+49

From using information above I am able to find the general formula for any T-shapes with T-number facing. The general formula is 5n+7g (g = grid size, e.g. for 6 by 6 grid the g will be 6).

 The general grid formula for this is: image06.png

4) This fourth experiments is about T-shapes with T-number facing west.

 Here’s the 10 by 10 grid from page 10:

Number

T-number

T-total

1

11

62

2

12

67

3

13

72

4

14

77

5

15

82

6

16

87

Here is the grid formula:

image07.pngn + n + 1 + n + 2 + n – 8 + n + 2 + n + 12 = 5n+7

So the formula for 10 by 10 grid is 5n+7

Here’s 9 by 9 grid from page 11:

Number

T-number

T-total

1

10

57

2

11

62

3

12

67

4

13

72

5

14

77

...read more.

Conclusion

6) conclusion

The general formula for all sides.

The formula for T-shapes with T-number facing southwards is 5n-7g. The general formula for T-shapes with T-number facing northwards is 5n+7g. The general formula for T-shapes with T-number facing eastwards is 5n-7. The general formula T-shapes with T-number facing westwards is 5n+7. You can see from this results that when formula’s of vertically opposite T-shapes are nearly the same except it will be plus or an minus, e.g. the T-shapes with formula’s 5n-7g and 5n+7 are vertically opposite and the only difference is the plus and minus.

Look at these T-shapes I have only named two boxes the T-number and the on the opposite end, from I research I can say that whenever x is bigger than n there will be a plus sign in the formula, if n is bigger than x then there will be a minus sign in the formula. E.g. the T-shape with T-number facing southwards

The T-number is 22 and x is 2, the T-number is bigger than x and the formula is 5n-7g.

image13.pngimage14.pngimage15.pngimage16.png

...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-Total Investigation

    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 Here we can see a rotation of 90

  2. T-Total and the T-Number.

    n-1 + n-2 + n-11 + n+ 7 +n = 5n - 7 = T-Total Above is the formula for a "T" rotated 90 degrees anti-clockwise. After finding the remaining 2 formulas, I shall test each of those formulas to see if they are correct.

  1. In this investigation I will be looking at the relationship between the T-total and ...

    where I looked at the relationship between the t-total and the T-number. I will now take this investigation further by using different grid sizes. I am going to use grid sizes 7 x 7 and 8 x 8 to see if there is any difference in the relationship between the T-total and T-number.

  2. Objectives Investigate the relationship between ...

    5x25-70=55 Just to prove that this is correct: 25+15+5+4+6=52 * T25 180� Rotation 24 25 26 34 35 36 44 45 46 25+35+45+44+46=195 T-shape T-total Increment T25 55 T25 (180�)

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

    This is 9*7=63. The nine in this comes from the size of the grid this one been nine. If the grid size were 10 by 10 then it would be 10*7. At the end of this piece of coursework when we but all the formulas together we realise that the number we minus or plus by is divisible b y seven.

  2. T-shapes. In this project we have found out many ways in which to ...

    This is where we get the seven from. The seven works with all the same sizes. The other method will also work with a different size grid. If we add these two together we have our formula. 5tn-63=t-total Here is an example of using the formula 1 2 3 4

  1. T-Total. I will take steps to find formulae for changing the position of the ...

    51 52 53 54 55 56 57 58 59 60 61 62 63 64 WORKING OUT AND RESULTS Formula: 5x - y - 5zb + 5a Substituting in the relevant information: (5 x 42) - 56 - (5 x 8 x 3)

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

    3 + x - 7 + x - 6 + x - 5 t = 5x - 21 Again the "magic number" is a multiple of 7, thus I can predict the "magic number" for any grid as 27 is the magic number found by 3 x 7 or g x 7.

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