GCSE: TTotal
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T shapes. Once I have all of the results, I shall work out the nth term and investigate the relationship between the T number and the T total.
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 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
 Word count: 1567

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
 Word count: 2679

3 Step Stairs
e.g. total = number added + ((number of squares x squares right) + (10number of squares x squares up)) 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 Number added = (1+2+3+11+12+21)
 Word count: 1703

TTotal. In order to find the relationship between the Tnumber and the Ttotal I need to show the numbers in the T algebraically
74 75 77 78 79 80 81 82 In order to find the relationship between the Tnumber and the Ttotal I need to show the numbers in the T algebraically as shown in the diagram below. N19 N18 N17 N9 N This is worked out with the grid size because how you get one square up is by taking 9 because it is a 9*9 grid. If I move left I +1 and if you move right you 1. If I add all the numbers together in the diagram above you get 63 and that is the same wherever the T is on a 9*9 grid.
 Word count: 1306

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.
 Word count: 2378

Maths GCSE Coursework: TTotal Investigation
2 3 4 12 21 4 5 6 14 23 7 8 9 17 26 T Number T  Total 20 37 21 42 22 47 23 52 24 57 25 62 The pattern in this table is for the T Number it is plus one every time and for the TTotal it is plus five every time. 7 8 9 17 N The nth term = 5N  63 To find the nth tern I looked at the T  Number value and times it by the gap which is 5 and then subtracted by the first Tnumber to get the gap which in this case was 63.
 Word count: 1077

Maths Coursework: TTotal and TNumber
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 We all ready know the answer to the one in red. To work out the one in green all we have to do is work out the difference in the tnumber and in this case it is 54.
 Word count: 4144

The tshape
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 We all ready know the answer to the one in red. To work out the one in green all we have to do is work out the difference in the tnumber and in this case it is 54.
 Word count: 4139

T Totals. From this 9*9 grid I will collect a number of T Shapes with T Numbers after collecting these I will put them into a table and will investigate to find any relationship between them.
are from the second row: 10 11 12 20 29 T Number = 29 T Total = 82 11 12 13 21 30 T Number = 30 T Total = 87 12 13 14 22 31 T Number = 31 T Total = 92 13 14 15 23 32 T Number = 32 T Total = 97 After collecting these I have put them in a table to see if there is any relationship between the T Number and the T Total: T Number T Total 20 37 21 42 22 47 23 52 T Number T Total 29 82
 Word count: 4075

TShapes Coursework
I have chosen my three Tshapes and have labelled the TNumbers in them appropriately. I am now going to work out the TTotals for each of my Tshape. Tnumber20=20+11+1+2+3=37 Tnumber21=21+12+2+3+4=42 Tnumber22=22+13+3+4+5=47 TNumber TTotal Tnumber20 20+11+1+2+3=37 Tnumber21 21+12+2+3+4=42 Tnumber22 22+13+3+4+5=47 From looking at the table above a clear pattern can be seen that as the Tnumber increases the Ttotal also increases by 5. This is because there is five numbers in a Tshape. The ratio then for the Ttotal is for every Tnumber increase by 1 the Ttotal increases by 5. A ratio of 1:5.
 Word count: 1387

Black and white squares
Formula = 4+N I am going to test this formula with an example. Sequence number = 56 Consistent difference = 4 The number of white squares = 4+56= 60 The black squares I would have take in to thought, that the black squares of a pattern equal the total number of squares in the previous pattern, this helps in the search of a formula. We also know that the difference between the black squares and the total of all the squares is 4.
 Word count: 1874

T total and t number
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 In this grid g = 9.
 Word count: 1729

FINDING THE RELATIONSHIP BETWEEN THE TNUMBER AND TTOTAL USING DIFFERENT SIZED GRIDS.
61 62 63 71 80 8061=19 8062=18 8063=17 8071=9 Since my results have been proven correctly, I will now work out a formula for any TShape on a 9x9 grid. If I give my TNumber a letter (n) to represent it, the formula will be: 1 2 3 11 11 20 n19 n18 n17 n9 n = *THIS FORMULA APPLIES ON ANY TSHAPE ON A 9x9 GRID ONLY.* After this, I decided to work out another formula for the TShape.
 Word count: 1673

Number Stairs
I will work out the total of these steps then I will find the formula for these. I am going to start at number 1 and move from left to right. Position One : 11 1 2 Total of position 1: 1+2+11 = 14 Position Two : 12 2 3 Total of position 2: 2+3+12 = 17 Position Three : 13 3 4 Total of position 3: 3+4+13 = 20 Position Four : 14 4 5 Total of position 4: 4+5+14 = 23 Position Five : 15 5 6 Total of position 5: 5+6+15 = 26 Position Six : 16
 Word count: 3207

Compile a report which will look at, and assess the performance of sales generated by the company DVD Sales
* The proportion of Totals Sales in the three regions? * Does the gender of the manager affect sales in the regions? * Which type of DVD is sold the most by female compared to male managers in the South of England. * The relationship between Advertising and Total sales. * The effect of price increases on Total Sales. * Another variable such as managers' age to see if this affects sales. 3.1 Overall distribution of total sales in the UK Figure 1.
 Word count: 1839

TTotals. Firstly I am going to do a table of 5 x 5 and look at the Ttotals and Tnumbers.
15 + 24 = 57 Ttotal = 57 The Tnumber is 25 6 + 7 + 8 + 16 + 25 = 62 Ttotal = 50 The Tnumber is 26 7 + 8 + 9 + 17 + 26 = 67 Ttotal = 67 The rest of the answers will be put into a table. Tnumber Ttotal Tnumber Ttotal Tnumber Ttotal 20 42 43 157 66 272 21 47 44 162 67 277 22 52 45 167 68 282 23 57 46 172 69 287 24 62 47 177 70 292 25 67 48 182 71 297 26 72 49
 Word count: 4430

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.
 Word count: 2377

TTotal Course Work
the Ttotal and Tnumber and the grid size by using a variety of grids and TShapes at different positions 8x8 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 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 1 2 3 Tnumber = 18 Numbers: 1 2 3 10 18 181 182 183
 Word count: 3772

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.
 Word count: 2322

TTotal. PART 1 Investigate the relationship between the Ttotal & the TNumber.
 23 = 37 21 x 3  23 = 40 20 x 4  43 = 37 20 x 4  43 = 41 20 x 5  63 = 37 21 x 5  63 = 42 22 x 5  63 = 47 23 x 5  63 = 52 24 x 5  63 = 57 25 x 5  63 = 62 26 x 5  63 = 67 37 + 38 + 39 + 47 + 56 = 217 58 + 59 + 60 + 68 + 77 = 322 56 x 5 
 Word count: 1032

See how many squares would be needed in order to construct any crossbuilt up in the way described in the investigation.
For the next pattern I predict the total number of squares would be 41. I am now going to check if my prediction is correct, using the pattern 1+3+5+7+9+7+5+3+1=41. I was right; this could be useful fact in searching for a formula. By gaining this information I will now draw a table of results and write down more patterns, as the moment I have is not conclusive. I have also noticed that to find the number of shaded squares in the next pattern, you have to use the total number of squares from the previous pattern.
 Word count: 1399

TTotals. Aim: To find the relationship between the TTotal and the Tnumber. To find a formula that works for every grid size. To find how rotating the Tshape effects the TTotal To find a formula that works f
I will use the second method to succeed in finding the Constant. Ttotal 1=37 37=(5*20)+C C=375*20 C=37100 C= 63 Tnumber=20 Therefore T=5n63 I will try this formula on TNumber 50: Using my formula, Tnumber=69 so T=(5*69)63 =34563 =282 Now I need to show it is correct: T=50+51+52+60+69 =282 My prediction was correct so my formula is right. This is my first aim. I will now use Grid size 8 to see if there is any difference in the formula I have found for Grid size 9 and if there is to work out the connection between the Grid size and the formula.
 Word count: 1630

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