• 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
  21. 21
    21
  • Level: GCSE
  • Subject: Maths
  • Word count: 5723

Maths coursework

Extracts from this document...

Introduction

Maths coursework

During my investigation I will be investigating whether there is a relationship between the T-number and the T-total.

The T-shape will look like: (in this example I will be using the numbers 1, 2, 3, 11, 20)

The T-total is the number at the bottom of the T-shape. The T-total is the sum of all the numbers inside the T-shape.

          Throughout my investigation I will use a key to refer to the T-total, T-number and grid size.

For the first part of my investigation I will be investigating whether there is a relationship between T and N for numbers in a G9. On the first grid I have shaded places where N must not go; the reason that N cannot go in these places is because if there was a case where N was in these places then there would not be five numbers in the T-shape. Whilst trying to find the relationship I will move the T-shape systematically through each grid.

To find the relationship I could use:

  • The sequence method
  • Simultaneous equations
  • Graphical methods

However, I will only use two of these methods. But for every relationship I will test whether the formula I conclude is correct, I will do this by randomly putting a T-shape into the grid and apply the formula into the numbers inside the T-shape. Also just to make sure that my conclusions are accurate I will use an algebraic approach; I use this approach because it shows a proof to an outcome.

Part 1, finding the formula relating T and N

The first thing that I notice when looking at T is that the values consistently ascend in 5’s when N ascend in 1’s. This states that there is a linear relationship.

Finding the formula.

...read more.

Middle

        G (grid size)

      T     (t-total)

       G9

       G8

       G7

         T = 5N - 63

         T = 5N - 56

         T = 5N – 49

I have noticed that in all of the formulas it is consistent that 5N is in the formula. Also the second term in the formula is the sum of G × -7.

Therefore I predict that the general formula is T = 5N – 7G

I will now test my prediction by using G10 and grid 11. I will use N = 25

T = (5 × 25) – (7 × 10)

T = 125 – 70

T = 55

Now I will use addition to see if T is the same as when I used the formula

T = 25 + 15 + 4 + 5 + 6 = 55

I can now say that the forula that I predicted is correct, this is because when I used the predicted formula the answer I got to was 55 and when I used addition the answer I got was the same of 55.

However if you look at G10 in grid 11 when N = 25 there is a relationship between T, N and G. this is:

I will now add up all of that is in the t-shape and put it into its simplest form:

T = N + (N – G) + (N – 2G) + (N – 2G + 1) + (N – 2G – 1)

T = 5N – 7G

Therefore this also correlates with the formula that I previously found, therefore the formula of T = 5N – 7G is correct.

Part 3

Here I will investigate the effect of a translation (x/y) on t-total.

Whilst doing this investigation I will use T2 as the new t-total.

Horizontal translation (x/0) for all grid sizes:

Firstly I will use G8 to find the effect of (1/0).

I can say that the formula for the t-shape in grid 3 is 5N – 7G, this is because I proved it in part 2. Now to find the formula in grid 4 compared to 5N – 7G

T in grid 3 = 34

T in grid 4 = 39

Here it shows that (1/0) is 5 more than (0/0). Therefore the formula here is            

T2

...read more.

Conclusion

T = 5N + 5x – 5Gy + 7 – 5d – 5dG

If these are then combined for a translation (c/d) then:

T = 5N +5x – 5Gy + 7 +5c – 5d – 5Gc – 5Gd.

However this is only my prediction, therefore I will now test this by using the formula first to find out the t-total of the rotated and translated shape, and then I will manually add up the five terms inside the rotated and translated shape and if the results both comply then the formula must be correct. I will test this on G10 on grid 10, the original t-shape will have N54 then this will be translated (-2/-1) then this shape will be rotated from the point (2/-1):

T = (5×54) + (5×-2) – (5×10×-1) + 7 + (5×2) – (5×-1) – (5×10×2) – (5×10×-1)

T = 282

Now I will add the five terms inside the rotated shape from the translated shape, and if the sum of this equals 282, then the formula works:

T = 55 + 56 + 57 + 47 + 67

T = 282

This means that the overall formula for a translation (x/y), followed by a rotation of 90º clockwise (c/d) from the new t-total is T = 5N + 5x – 5Gy + 7 + 5c – 5d – 5Gc – 5Gd.

Evaluation:

Therefore overall from my investigation, I have found that:

  • For a translation (0/y) the general formula is T = 5N – 7G – 5Gy
  • For a translation (x/0) the general formula is T = 5N – 7G + 5x
  • For a translation (x/y) the general formula is T = 5N – 7G – 5Gy + 5x
  • For a rotation 90º clockwise about point (c/0) T = 5N + 7 + 5c – 5cG
  • For a rotation 90º clockwise about point (0/d) T = 5N + 7 – 5dG – 5d
  • For a rotation 90º clockwise about point (c/d) T = 5N + 7 – 5dG – 5d – 5Gy + 5x
  • For a translation (x/y),followed by a rotation of 90º clockwise from point (c/d) from the translated t-shape, T = 5N + 5x – 5Gy + 7 + 5c – 5d – 5Gc – 5Gd

However, due to time restriction I could only find the effects of a 90º clockwise rotation, but if time was not of the essence, then I could find the effect of a 180º rotation and 270º rotation and see if the is a connection between them all.

...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. Marked by a teacher

    T-total coursework

    5 star(s)

    because it is one more than (n+(2h+3)w). All the terms contain (2h) because every square is a minimum of (2h) rows (2hw) away from each other. To add these terms together, I must multiply out the brackets: (n+(2h+1)w) + (n+(2h+2)w) + (n+(2h+3)w) + (n+(2h+3)w-1) + (n++(2h+3)w+1) = (n+2hw+w)

  2. T-Shapes Coursework

    5 x 21 = 105 - 63 = 42 Now let us find the T-total and see if our formula works properly. T-total (Tt) = 2 + 3 + 4 + 12 + 21 = 42 It does work! Okay so we have established a formula that works for T-Shapes

  1. T-Shapes Coursework

    n x 5 + 7 = t Lets do some tests to see if this formula actually works: 5 x 33 + 7 = 172 33 + 34 + 26 + 35 + 44 = 172 The formula works. 5 x 65 + 7 = 332 65 + 66 + 67 + 58 + 76 = 332 The formula works.

  2. T-Shapes Coursework

    Here are the results of the 5 calculations for a 3x1 "T" on Width 12 Grid (Fig 2.4): Middle Number Sum of Wing Sum of Tail Total Sum (Wing + Tail) 2 6 14 20 3 9 15 24 4 12 16 28 5 15 17 32 6 18 18 36 (e)

  1. The T-Total Mathematics Coursework Task.

    and Numbers there can be in a 9 by 9 number grid L-number Right of L-shape L-total All numbers in L-shape added L-number Right of L-shape L-total All numbers in L-shape added 29 87 56 222 30 92 57 227 31 97 58 232 32 102 59 237 33 107

  2. T-Totals Maths

    when it it translated to the right therefore adding five more onto the total. For this same reason, five has to be included as the main focus of my algebraic formula. The Algebraic Formula I could then, using the process of elimination and trial and error come up with an algebraic formula.

  1. Maths Coursework- Borders

    Multiply equation 4 by 3 so that 6b can be cancelled out of the equation and we can find out what a is equal to, 4 ? 3 = 18a + 6b = 12 Then to find a we need to subtract equation 5 from equation 4 4 - 5

  2. T-Total Coursework

    I also found another formula of finding out the T-Total. This formula would be: T = N + (N - 9) + (N - 17) + (N - 18) + (N - 19) 31 32 33 41 50 This formula can be used, too because the distance between the numbers in a T-Shape never changes.

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