• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 3136

To investigate and discover an equation, numerically and algebraically.

Extracts from this document...

Introduction

Maths coursework: January 2001. Aim: To investigate and discover an equation, numerically and algebraically. 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 Method: We experimented with different grid sizes, including 9 and 7. We found out the total of the numbers inside the t-shape. (Red) T = 1+2+3+11+10 = 37 If I move the T across I can investigate the relationship by comparing the various t-totals. 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 T= total G= grid size N= t number (e.g.) 20 N G T Difference 20 9 37 5 21 9 42 5 22 9 47 5 To try and find a formula for the red T, I used the difference, 5 and multiplied it by the N number. ...read more.

Middle

65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 N becomes 8: T= 8+9+10+3+17= 47 When N= 9 T= 9+10+11+4+18= 52 When N= 10 T= 10+11+12+5+19= 57 G N T Diff 7 8 47 5 7 9 52 5 7 10 57 5 N=8 Nx5= 40 +7 = 47 N=9 Nx5= 45 +7= 52 N=10 Nx5 = 50 +7= 57. The formula has been found to be the same as on Grid size 9: T=5N+7 Again, if we mirror the image the formula can be predicted to be: T=5N-7. First lets try Grid size 9. 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 N=12 G N T Diff 9 12 53 5 9 13 58 5 9 14 63 5 T= 12+11+10+1+19= 53 N= 13 T= 13+12+11+2+20= 58 N= 14 T= 14+13+12+3+21= 63 Predicted Formula: T= 5N-7 When N=12 5xN= 60 60-7= 53 When N= 13 5x13= 65 65-7= 58 When N= 14 5x14= 70 70-7= 63 So we have found that when a T-shape N number is placed upright and facing to the right, the outcome is positive. ...read more.

Conclusion

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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 N= 23 G N T Diff 7 23 73 5 7 24 78 5 7 25 83 5 T= 23+17+11+3+19= 73 N= 24 T= 24+18+12+4+20= 78 N= 25 T= 25+19+13+5+21= 83 When the Grid size was nine and the shape was in the same rotation, the formula was: T= 5N-56 but will it be the same for when G= 7? When N= 23 5N= 115 115 -73 42 This gives us a possibility for a formula: T= 5N-42. 42 is 6x7 or 6G so why can't G be involved in the formula? G cannot be involved because it does not work for grid size nine. 6x9= 54 and the formula for when G= 9 is: T= 5N-56. So, we have found a numerical formula now I have to test it. Formula: T= 5N-42 When N= 24 5N= 120 120-42= 78 When N= 25 5N= 125 125-42= 83 This proves the formula to be successful. Evaluation: From this study I have been able to deduce that for shapes that are mirrored the formulas will be the same but the signs will be opposite. Also G can only be involved when the shape was upright or upside down. G could have been involved more if we were only using grid size seven but then the formula would be specific. It could not have been a general algebraic formula. ...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

    I will carry on and test T-shape I know N = 18 T = (5x18)-56 = 90-56 = 34 As expected, the equation has produced yet another correct answer. Another example is below. N =19 T = (5x19)-56 = 95-56 = 39 N = 37 T = (5 x 37)-56

  2. T-Shapes Coursework

    for the Total Sum: Total Sum = wn + 1/2 l {2n + g(l + 1)} This is a combination of the formulas for the Sum of the Wing and the Sum of the Tail on any grid width that were created in the Data Analysis.

  1. Objectives Investigate the relationship between ...

    substitute my values it will get: 5*22 - x = 40 110 - x = 40 110 - 40 = x 70 = x Therefore '5n - 70 = T-Total' is my formula for finding the T-total of any t-shape.

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

    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

  1. Maths Coursework T-Totals

    of any Grid save, regular (e.g. 5x5) or irregular (e.g. 5x101), with the two variables of grid width (g) and the T-Number (x). Finding relationship between T-Number and T-Total, with different sized grid and different translation, enlargements and rotations of the T-Shape For this section we will have to keep

  2. Beam 82

    Beam 84 Total UDL = 5.42 + 0.7 = 6.12 KN/m Total load of Trapezium = (1/2 x 1.5 x 18) + (18 x 1) = 45 KN/m Reaction at A RA = 45 + (6.12 x 4) = 69.48 = 34.74 KN 2 2 The beam is simply supported

  1. T-Total Course Work

    Below is a t-shape, and in each cell how the number is connected with T on a 10x10 grid T-21 T-20 T-19 T-10 T Check the formula: (T-21) + (T-19) + (T-20) + (T-10) + (T) =5T-70 So this is correct After finding out the similarity of the 8 x

  2. For this task we were required to create a model that can be used ...

    First, I placed all of the data in alphabetical order, so that it is easier to find electrical appliances that you need. I did this by highlighting the table - Data - Sort - Sort by column A - Ascending.

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