• 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
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17
  18. 18
    18
  19. 19
    19
  20. 20
    20
  • Level: GCSE
  • Subject: Maths
  • Word count: 8074

Maths GCSE Coursework – T-Total

Extracts from this document...

Introduction

Maths GCSE Coursework 2000 - T-Total Introduction In this investigation I aim to find out relationships between grid sizes and T shapes within the relative grids, and state and explain all generalizations I can find, using the T-Number (x) (the number at the bottom of the T-Shape), the grid size (g) to find the T-Total (t) (Total of all number added together in the T-Shape), with different grid sizes, translations, rotations, enlargements and combinations of all of the stated. Relations ships between T-number (x) and T-Total (t) on a 9x9 grid 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 From this we can see that the first T shape has a T number of 50 (highlighted), and the T-total (t) adds up to 187 (50 + 41 + 31 + 32 + 33). With the second T shape with a T number of 80, the T-total adds up to 337, straight away a trend can be seen of the larger the T number the larger the 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 From these Extra T Shapes we can plot a table of results. ...read more.

Middle

We know with will not make a difference to the final answer as proved in question 2. 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 As we can see, we have a horizontal translation of the first T-Shape (where v =17) by +4. Where v = 17, t = 63, and where v = 21, t = 83 (both found by using t = 5v - 2g), if be draw up a table in the same format as the one we used for the 9x9 grid, we should be able to find some relationships (from 21 to 17). Middle number (v) T-Total (t) Equation used Difference 21 83 t = (5 x 21) + ( 2 x 11 ) 5 (83 - 78) 20 78 t = (5 x 20) + ( 2 x 11 ) 5 (78 - 73) 19 73 t = (5 x 19) + ( 2 x 11 ) 5 (73 - 68) 18 68 t = (5 x 18) + ( 2 x 11 ) 5 (68 - 63) 17 63 t = (5 x 17) + ( 2 x 11 ) N/a From this we can see that 5 is the "magic" number again as for a grid width of 9 for horizontal translations. From this an obvious relation ship can bee seen that for all grid sizes, a horizontal translation of a T-Shape by +1, makes the T-Total +5 larger, but this is only a prediction. To verify this we can see what the "magic" number is on a grid width of 10. 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 ...read more.

Conclusion

Using the formula we get; T=5(36+2x10+0)+2 T=5(56)+2 T=282 Thus proving this formula works and it is obvious that it will work in the same fashion as my static (middle number as the centre) rotations, as they both find the position as the new V number then generate the t-total based on that number, therefore I can state; The T-Total of any rotation of a T-Shape with any centre of rotation on any grid size can be found by using the formula of t=5(c+d(g)+b)+y were t is the T-Total, c is the centre of rotation (grid value) d is the horizontal difference of v from the relative centre of rotation , is the grid width, and b is the vertical difference of v from the relative central number. y is to be substituted by the ending required by the type of rotation, these are : Rotation (degrees) Direction Ending (y) 0 Clockwise - 2g 90 Clockwise + 2 180 Clockwise + 2g 270 Clockwise - 2 0 Anti-Clockwise - 2g 90 Anti-Clockwise - 2 180 Anti-Clockwise + 2g 270 Anti-Clockwise + 2 In terms of x (T-Number); The T-Total of any rotation of a T-Shape with any centre of rotation on any grid size can be found by using the formula of t=5(c+d(g)+b)+y were t is the T-Total, c is the centre of rotation (grid value) d is the horizontal difference of x from the relative centre of rotation, g is the grid width, and b is the vertical difference of x from the relative centre of rotation. y is to be substituted by the ending required by the type of rotation, these are : Rotation (degrees) Direction Ending (y) 0 Clockwise - 7g 90 Clockwise + 7 180 Clockwise + 7g 270 Clockwise - 7 0 Anti-Clockwise - 7g 90 Anti-Clockwise - 7 180 Anti-Clockwise + 7g 270 Anti-Clockwise + 7 [PP1]i 1 Philip Price 30/04/07 ...read more.

The above preview is unformatted text

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. Marked by a teacher

    T-total coursework

    5 star(s)

    The (n-2w-1) equivalent would be (n-2w+2h+3-1), and the (n-2w+1) equivalent is (n-2w+2h+3+1). Effectively, all the terms in the original T-shape have had (2h+3) added to them, so that they move across by this amount. There is no vertical movement, which is why there are no (hw) in the new terms.

  2. Connect 4 - Maths Investigation.

    I have decided to use the grid 8 x 4. H (4L - 9) - 9L + 18 H = 8, L = 4 8 (4L - 9) - 9L +18 32L - 72 - 9L +18 = 23L - 54 23 x 4 - 54 = 38 From this

  1. Magic E Coursework

    + (e + 2) + (e + 8) + (e + 16) + (e + 17) + (e + 18) + (e + 24) + (e + 32) + (e + 33) + (e + 34) E-total = 11e + 185 To prove this formula correct we need to try it on a random e-number, for example 9.

  2. T-Totals. Aim: To find the ...

    This is what I will find out next. Grid size 6 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 There is a

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

    252 5(49)+7=252 308 5(49)+7(9)=308 238 5(49)-7=238 8�8 20 107 5(20)+7=107 156 5(20)+7(8)=156 93 5(20)-7=93 28 147 5(28)+7=147 196 5(28)+7(8)=196 133 5(28)-7=133 36 187 5(36)+7=187 236 5(36)+7(8)=236 173 5(36)-7=173 10�10 45 232 5(45)+7=232 295 5(45)+7(10)=295 218 5(45)-7=218 55 282 5(55)+7=282 345 5(55)+7(10)=345 268 5(55)-7=268 65 332 5(65)+7=332 395 5(65)+7(10)=395 318 5(65)-7=318

  2. Objectives Investigate the relationship between ...

    x = current T-total + 63 (where 'x' is the new T-total to be found...) Now I will find an algebraic formula for finding the T-total of any 90� rotated T-shape. To find this algebraic formula, I will find out a way to find the individual values in the T-shape:

  1. 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)

  2. Investigate the relationship between the T-total and the T-number in the 9 by 9 ...

    To find out the formula for the T-number you rearrange the formula to get n = (t - 7)/ 5 In this case the restraints would also be different. The n would have to be in or between the columns '1' to 'w-3' and in the rows '2' to 'w-1'.

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