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

GCSE Mathematics T-Totals

Extracts from this document...

Introduction

GCSE Mathematics T-Total C/W I have been given mathematics coursework on T-totals; the coursework has been set in three tasks. The question is about T-shapes on different grids. The bottom number in the T is called the T-number. All the numbers in the T-shape added together are called the T-total. For each part of the coursework I have to translate the T-shape to different positions on the grid. Key: T-total = T T-number = n Grid Size = G Part 1 For the first part of the coursework, I have to investigate the relationship between T-total and T-number. I will use a 9x9 number grid and start off with the T-shape beginning at the number 1. 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 To understand the relationship between the T-total and T-number we can look at the T-shape drawn on the 9x9 number grid. The total of the numbers inside the T-shape is 37 this is called the T-total. The number at the bottom of the T-shape is called the T-number. ...read more.

Middle

Then I subtracted 34(T-Total) from 90 which gave me 56. Using this formula I found out it worked by testing it on all the T-shapes. 7x7 Grids n 16 17 18 19 T 31 36 41 46 I did a prediction for the next T-shape. I predict this because the T-number is increasing by 1 and the T-Total is increasing by 5. From my findings I concluded a formula linking the T-Number and T-Total which is T=5n-49. I got this formula when I seen that the difference between each T-Total is 5 so the formula had to contain 5n.I used the 5n on my first n in my table and I got 80. Then I subtracted 31(T-Total) from 80 which gave me 49. Using this formula I found out it worked by testing it on all the T-shapes Summary Grid Size Formula 9x9 5n-63 8x8 5n-56 7x7 5n-49 Also I can predict that for a 6x6 grid the formula will be 5n-42. The prediction I have is so because the 5n will remain the same and as the constant goes down by 7 each time I can minus 7 from 49 to give me 42. I have algebraic proof that there is a relationship between T and n. 9x9 grids n-19 n-18 n-17 n-9 n 1 2 3 11 20 (n-19) + (n-18) + (n-17) + (n-9) + (n) = 5n-63 T= 5n-63 7x7 grids n-15 n-14 n-13 n-7 n 1 2 3 9 16 (n-15) ...read more.

Conclusion

Also the T-number has a difference of 3 so 15n�3 is in the formula. 15n�3 can be simplified to 5n. To get to the T-total from 5n you have to add 7. So T= 5n+7 To prove this I have some examples: n=32 (5x32) +7=167 n=29 (5x29) +7=152 This has proven that the formula works for different grid sizes and if I check in the table above I can see my results are correct. For 270� the formula I have found is T= 5n-7 I have found this formula by noticing that the T-total has a difference of 15 which means that 15n is in the formula. Also the T-number has a difference of 3 so 15n�3 is in the formula. 15n�3 can be simplified to 5n. To get to the T-total from 5n you have to subtract 7. So T= 5n-7 To prove this I have some examples: n=30 (5x30) -7=143 n=27 (5x27) -7=128 Also I made a prediction for a 10x10 grid. I predicted that when n=35 for a 90� rotation the T-total will be 182. Here is my working. (5x35)+7=182 Also I predicted that when n=33 for a 270� rotation the T-total will be 158. Here is my working. (5x33)-7=158 I can prove my prediction is correct by showing that 182-158=24. This is significant as for each grid size's T-totals for 90� and 270� have a difference of 24 also, e.g. 8x8 grids 90� T-total=152 270� T-total=128 152-128=24 ?? ?? ?? ?? Imran Kola 11.13 Maths Coursework Page 2 ...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. T-Total Maths coursework

    The formula also works for 8x8 grids. Now I am going to find out this formula works for 7x7 grids. 7x7 Grid size 90� N =10 5N = 5x10 = 50 G = 7 = 7x7 = 49 I now have enough data to prove that my formula works 5N

  2. The T-Total Mathematics Coursework Task.

    one to four to investigate and find any relationships between the L-total and the L-number, I will then compare them to the T-shape to see the resemblance. * After completing the main tasks I will come to an overall conclusion of my work, findings, investigations and relationships.

  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. 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 Coursework:- T-Total

    t + 3 + g(y-3) = new t t + 6 + g(2y) = new t t + 4 + g(-2y) = new t Diagram 2 * On this diagram (2) : X = 0 Y = 2 What I am now going to do is say how I get

  2. Objectives Investigate the relationship between ...

    I will use the T-shape of T35 18 19 20 21 26 27 28 29 34 35 36 37 42 43 44 45 * T35 No rotation 18 19 20 26 27 28 34 35 36 SUM method: 18+19+20+27+35=119 Algebraic Formula (5n-56): 5x35-56 = 119 * T35 90� Rotation 27

  1. T-Shapes Coursework

    The Sum of the Tail equals the Middle Number plus the Grid Width. 5) Generalisation It can be assumed that for all possible locations of the 3x1 "T" on the width g grid, these patterns will be true. Therefore, the following logic can be used to create a formula where:

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

    We can see that by changing the grid size we have had to change the formula but still managing to keep to the rule of how you get the number to minus in the formula. PART 3 In this next section there is change in the size of grid.

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