GCSE: TTotal
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 Level: GCSE
 Questions: 75

Ttotal coursework
5 star(s)is (n19) as it has been decreased by 1. The cell to the right of (n18) is (n17) as it is 1 more than (n18). When these 5 terms are added together I get: (n) + (n9) + (n17) + (n18) + (n19) = 5n  63 The calculation above shows that the sum of the 5 terms within the Tshape is 5n  63, therefore I can make a proper formula: T = 5n  63 where T is the Ttotal and n is the Tnumber Tnumber (n) Ttotal (T) Ttotal using formula (5n63) 20 37 (5x20)= 100 10063 = 37 26 67 (5x26)= 130 13063 = 67 50 187 (5x50)= 250 25063 = 187 80 337
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For my investigation, I will be investigating if there is a relationship between ttotal and tnumber. I will first try to find a relationship between Tnumber and TTotal on a 9x9 grid then change the variables such as grid size.
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 First I put the T shape onto my 9x9 grid and translated it right by 1 space each time. As shown above I started on 20 and finished on 25 I then constructed the tale below. TNumber (T) TTotal (N) Difference 20 1+2+3+11+20=37  21 2+3+4+12+21=42 5 22 3+4+5+13+22=47 5 23 4+5+6+14+23=52 5 24 5+6+7+15+24=57 5 25 6+7+8+16+25=62 5 The table above shows the difference between the consecutive TTotals as the TNumber increases by one.
 Word count: 2692

For my investigation, I will be investigating if there is a relationship between ttotal and tnumber. I will first try to find a relationship between Tnumber and TTotal on a 9x9 grid
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 First I put the T shape onto my 9x9 grid and translated it right by 1 space each time. As shown above I started on 20 and finished on 25 I then constructed the tale below. TNumber (T) TTotal (N) Difference 20 1+2+3+11+20=37  21 2+3+4+12+21=42 5 22 3+4+5+13+22=47 5 23 4+5+6+14+23=52 5 24 5+6+7+15+24=57 5 25 6+7+8+16+25=62 5 The table above shows the difference between the consecutive TTotals as the TNumber increases by one.
 Word count: 2692

In this investigation Im going to find out relationships between the grid sizes and T shapes within the relative grids, and state an explanation to generalize the finding using the TNumber
of 30, and the Ttotal (t) adds up to 87 (11+12+13+21+30). With the second T shape with a T number of 31, the Ttotal adds up to 92, by looking at the two results a trend can be seen therefore suggesting the larger the T number the larger the total. By looking at the TShapes we can plot a table of results. TNumber (n) TTotal (t) 30 87 31 92 32 97 33 102 34 107 By looking at my table of results a pattern can be seen between the TNumber and the TTotal, there's also a relationship between the TNumber and the TTotal because a trend occurs as you move it over different parts of the grid and it gives a ratio of 1:5.
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TTotals (A*) Firstly I have chosen to look at the 9 by 9 grid. I will be taking five tnumbers in a row and investigating the ttotals for them. Once I have completed all five, I will then look for a formula to link those five
The ttotal is 32+23+15+13+14 which will give us 97. Tnumber: 32 Ttotal: 97 Number 4: 14 15 16 24 33 The tnumber in this case will be 33. The ttotal is 33+24+14+15+16 which will give us 102. Tnumber: 33 Ttotal: 102 Number 5: 15 16 17 25 34 The tnumber in this case will be 34. The ttotal is 34+25+15+16+17 which will give us 107. Tnumber: 34 Ttotal: 107 Formula: After investigating the tnumbers from 30 to 34 and comparing them with their ttotals, I have noticed that every time I increase the tnumber by one the ttotal goes up by five.
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My aim is to see if theres a relation between T total and T number and I will then work out the algebraic expressions so that the 50th term would be found out using the formula.
I believe this would work because of the following: T21 + T20 + T19 + T10 + T = 5T  70 T = T  number So the 50th value would have the T  number of 50, so the T  Total would be: 5 x 50  70 = 180 I will prove it from another T  Shape: 4 5 6 15 25 Formula: 5T  70 5 x 25 = 125  70 = 55 To check: 4 + 5 + 6 + 15 + 25 = 55 PART 2: Now I want to see whether different grid size would differ the algebraic expression.
 Word count: 2880

specify
I have noticed that after each translation 5 has been added to the Ttotal. This is because when the Tshape is moved across once on the grid, one is added to each number, and because there are 5 numbers in the Tshape, 5 is added all together. I have now used a different Tshape; this is still on a 9 by 9 grid. The total for this Tshape is 4 + 5 + 6 + 14 + 23 = 52. Now, I have moved my Tshape down by one on the grid. The new Ttotal for this shape is 97.
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TTotals. To figure out an equation for different grid sizes, I have to find the relationship between grid sizes and the T total. I will now let S= Grid Size.
I can check whether this works. 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 The totals are the same so my formula seems to work.
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GCSE Mathematics TTotals
The number at the bottom of the Tshape is called the Tnumber. The Tnumber for this Tshape is 20. In order to investigate the relationship between the Ttotal and Tnumber I will translate the Tshape by the vector (1, 0). In order to achieve accurate results I will carry this out 3 times. Here are the three Tshapes I end up with. 1 2 3 11 20 3 4 5 13 22 2 3 4 12 21 I then tabulated the results to look for patterns. n 20 21 22 23 T 37 42 47 52 9x9 Grids I did a prediction for the next Tshape.
 Word count: 2003

t totals gcse grade A
21, 34 and 68 The ttotal is where you add up all the numbers in the tshape e.g. 2+3+4+12+21=42 49+50+51+59+68=276 15+16+17+25+34=97 2 Basic tformulas This is of a 9x9 grid Tnumber ttotal 57 222 58 227 59 232 60 237 61 242 You can see the ttotal in going up 5 every time as the tnumber is going up 1 every time their must be a link? 57x5=285 28563=222 the ttotal What is the link between 63 and 9? 63 is 7x9 So the formula would be Tnumber x 5  (9 x 7) 5xtnumber7x9 3 Algebra in a tformula I am trying to find the number in each cell compared to the tnumber A B C D
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Software Applications
in stock Retail price % Margin Packard Bell PB 100 1123 �999.00 23% PB 110 356 �1,009.00 11% PB 140 17 �1,199.00 25% PB 160 378 �1,230.00 19% PB 180 24 �1,299.00 8% PB 200 65 �1,499.00 33% PB 220 98 �1,530.00 19% PB 260 397 �1,699.00 16% Pb 290 567 �1,799.00 12% PB 390 25 �1,899.00 13% Sub total 18% Sony S100 58 �999.00 25% S200 1287 �1,200.00 8% S300 36 �1,300.00 6% S400 748 �1,399.00 28% S500 38 �1,449.00 23% S600 66 �1,699.00 16% S700 487 �1,799.00 13% S800 101 �1,849.00 6% S900 294 �1,999.00 13% S1000 73
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GCSE Mathematic Coursework Ttotals Aim: to find a pattern that connects the T number with the T total
+ (7 x 9) = 263 Example: 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 p 42 43 44 45 46 47 48 49 p+r 51 52 53 54 55 56 57 p+2r1 p+2r p+2r+1 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 1 2 3 4 5 6 7 8 9 10 11 12
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Maths GCSE Investigation  T Numbers
For example, in the above 6 by 6 square, a Tshape is selected: Tnumber=21 Ttotal=21(Tnumber) + 216(15) + 2112(9) + 21121(8) + 2112+1(10) To create a formula, I will now substitute in X for the Tnumber: Ttotal=X(Tnumber) + X6(15) + X12(9) + X121(8) + X12+1(10) =5X  42 I will now see if my formula works for another Tshape in the same 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 Ttotal = 5X42 = 5*3442 = 17042 =128 21+22+23+28+34=128 My formula works.
 Word count: 2629

This is an investigation to find a relationship between the Ttotals and the Tnumber. The diagram shows a 9x9 grid, with each individual cell having one number in it starting on the
by 1 the Ttotal will increase by 5 as there are five number squares within the Tshape and translating the shape to the next possible arrangement would increase all the numbers in the Tshape by 5. Results Below is a 9x9 grid with each Tshape in the first row overlapping another Tshape to represent each Tshape pattern on row 1. I have tabulated my results to see if there is a pattern emerging. Row 1 (19) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
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Magic E Coursework
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 From this diagram you can see that the total of the numbers in this E is: 2+3+4+10+18+19+20+26+34+35+36 = 207 Instead of drawing out the next E, we can make a table of E's and there etotals. If we call the top left number the enumber (shown as "e") then we can see if there is a pattern between the enumber and etotals.
 Word count: 2114

My task is to find out the relationship between the Ttotal and the Tnumber.
I will show drawing and working out, I will show my results in a table of results, I will look for patterns and rules from my results. I will write my rules in sentences and algebra. Prediction: When I've finished the task I think I will find that if I move my Tshape step by step at a time to the right my Ttotal will increase by 5 and my Tnumber will increase by 1. 11/05/05 T  Totals Prashant Sawlani Coursework Workings: Table of Results: Tnumber 20 21 22 23 24 25 26 Ttotal 37 42 47 52 57
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Number Grid Coursework
81 x 92 7452 91 x 82 7462 Difference 10 Equation Total 9 x 20 180 10 x 19 190 Difference 10 9 10 19 20 There is a pattern; the difference is always 10 for 2x2 squares. To prove these results algebraic equations can be used. When the value of X is replaced by a number the difference will always be 10. x x+1 x+10 x+11 Expression 1 x(x+11)= x2 +11x Expression 2 (x+10) (x+11) = x2 +10x+x+10 = x2 +11x+10 x2 +11x+10  x2 +11x = 10 3x3 squares 2 3 4 12 13 14 22 23 24
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ICT Coursework: Data Management Systems
The advantages of using an ICT solution are that a lot of space is saved (there is no need for lots of loose paper), time is saved (all calculations are done automatically), and the business is much easier to manage. For example, income and expenditure can be easily viewed, and stock is easily managed with the remaining stock kept in the spreadsheet. Also, all data about the business can be accessed easily, and almost anywhere. By backing up to a disk, the spreadsheet can then be viewed from any computer that has a disk drive, and the appropriate software.
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Maths Coursework on TShapes
In this investigation I will first find a formula to find the Ttotal using the Tnumber in a 9x9 grid, I will then use differing grid sizes to see what an affect this has on the formula. Then using this information I will find a formula, which will be true to all grid sizes. Then I will experiment with rotations and reflections on differing grid sizes to see what an affect it has on the formula. Then a Conclusion about Tshapes.
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1) Investigate the relationship between the Ttotal and the Tnumber. 2) Use grid of different sizes. Translate the Tshape to different position. Investigate relationships between the Ttotal, the Tnumbers and the grid size.
Tnumber 20 21 22 23 24 25 26 Ttotal 37 42 47 52 57 62 67 This table clearly shows that the numbers go up by 5 every time the Tnumber goes up by 1. Now I can use trial and error to try to find the formula, I will then test what I believe to be the correct formula to see if it is. Because there is a difference of 5 between the Ttotals I think that it is a logical place to start the formula.
 Word count: 2630

Maths Coursework Borders
I will be working systematically in my investigation because if I work in a particular order it will be easier for to see a pattern and links in the sequences. Finally I will be looking at different ways of getting the formulae and also extending my investigation into 3 dimensions. Part 1 Drawing the crossshapes Pattern 1 Pattern 2 Pattern 3 Pattern 4 Pattern 5 Pattern 6 Pattern 7 Here is my table of results telling me how many black, white and total numbers of squares there are in patterns 1 up to 7.
 Word count: 2004

TTotals  All the things T said
Sample 1) 1 2 3 11 20 TNumber = 20 TTotal = 1+2+3+11+20 = 37 Sample 2) 2 3 4 12 21 TNumber = 21 TTotal = 2+3+4+12+21 = 42 Sample 3) 3 4 5 13 22 TNumber = 22 TTotal = 3+4+5+13+22 = 47 I arrange these samples in the table. TNumber 20 21 22 TTotal 37 42 47 As we notice, when TNumber increases by 1, its TTotal also increases by 5. It shows that there is a certain pattern.
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Investigating the relationship between the Ttotals and the Tnumber.
So in this case the ratio between the Tnumber and the Ttotal is 1:5. This can help me because when I want to translate a Tshape that is in another position. For instance when I the Tshape here. 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
 Word count: 2813

TTotal. I can work out a formula to find the Ttotal on a 9 by 9 grid.
T = N19+N18+N17+N9+N T = 5N63 Time for me to check if this formula works: N means TNumber. N = 20 T = 5x2063 T = 10063 T = 37 To make sure it is not a fluke, I will do 2 more checks on the same grid size. 16 17 18 26 35 T = 112 T = 5x3563 T = 17563 T = 112 48 49 50 58 67 T = 272 T = 5x6763 T = 33563 T = 272 So now you know the formula for the 9 by 9 grid is T =5N63 2. I will now find the formula for a 5 by 5 grid. Here is the 5 by 5 grid.
 Word count: 2271

Number Stairs Investigation
+ 20 x + 10 x + 11 x x + 1 x + 2 The formula for the 3step stair on a 10 x 10 grid is Tx = 6x + 44 The letter "g" represents the grid number, in this case 10. Using this formula I will predict that T = (6 x 4) + 44 T = 24 + 44 T = 68 24 14 15 4 5 6 24+14+15+4+5+6 = 68 I will also predict that T = (6 x 72)
 Word count: 2212