• 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. Connect 4 - Maths Investigation.

    As height is the variable I will have to put it into the equation, I have decided to put it at the beginning. To work out the final rule I will have to put that into a current total. For Height4: [H(4L-9)] 4(4L-9)

  1. T-Total Maths coursework

    x 40)-63 = 200-63 = 137 N = 79 T = (5 x 79)-63 = 495-63 = 332 Here is the last equation I will show from the 9 by 9 grid to show that the equation N = 80 T = (5 x 80)-63 = 400-63 = 337 Rotation

  2. To prove that out of town shopping is becoming increasingly popular with shoppers, and ...

    Also generally the woman in a family does the majority of shopping such as food and clothes shopping for the children 3) Area I predict that most shoppers will come from the areas around the Bescot Retail Park and not come from anywhere further that 10 miles radius.

  1. Maths GCSE Coursework – T-Total

    will be so as all numbers are greater than the T-Number as the shape extends downwards. To prove this we can put this into practice. 1 2 3 4 5 6 7 8 9 Working this out using the traditional method the answer is 31 (2 + 5 + 7

  2. Objectives Investigate the relationship between ...

    I have used an equation method to find my formula; I could have used the algebraic difference method, to find it. T20 1 2 3 11 20 Tn n-19 n-18 n-17 n-9 n As you can see from the above T-shape, we now know how to find all the individual values of the T-shape.

  1. T-Shapes Coursework

    81 82 83 84 85 86 87 88 Fig 2.3 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

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

    = 77 Try out the new formula 5tn - 77= t-total 5*24-77=43 The same formula works with only changing the last number in the formula. This will be tried on a smaller grid size to make sure it is not if the grid size is bigger.

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