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# GCSE: T-Total

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1. ## GCSE Maths questions

• Develop your confidence and skills in GCSE Maths using our free interactive questions with teacher feedback to guide you at every stage.
• Level: GCSE
• Questions: 75
2.  ## T-total coursework

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is (n-19) as it has been decreased by 1. The cell to the right of (n-18) is (n-17) as it is 1 more than (n-18). When these 5 terms are added together I get: (n) + (n-9) + (n-17) + (n-18) + (n-19) = 5n - 63 The calculation above shows that the sum of the 5 terms within the T-shape is 5n - 63, therefore I can make a proper formula: T = 5n - 63 where T is the T-total and n is the T-number T-number (n) T-total (T) T-total using formula (5n-63) 20 37 (5x20)= 100 100-63 = 37 26 67 (5x26)= 130 130-63 = 67 50 187 (5x50)= 250 250-63 = 187 80 337

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3. ## For my investigation, I will be investigating if there is a relationship between t-total and t-number. I will first try to find a relationship between T-number and T-Total 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. T-Number (T) T-Total (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 T-Totals as the T-Number increases by one.

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4. ## For my investigation, I will be investigating if there is a relationship between t-total and t-number. I will first try to find a relationship between T-number and T-Total 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. T-Number (T) T-Total (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 T-Totals as the T-Number increases by one.

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5. ## 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 T-Number

of 30, and the T-total (t) adds up to 87 (11+12+13+21+30). With the second T shape with a T number of 31, the T-total 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 T-Shapes we can plot a table of results. T-Number (n) T-Total (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 T-Number and the T-Total, there's also a relationship between the T-Number and the T-Total 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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6. ## T-Totals (A*) Firstly I have chosen to look at the 9 by 9 grid. I will be taking five t-numbers in a row and investigating the t-totals for them. Once I have completed all five, I will then look for a formula to link those five

The t-total is 32+23+15+13+14 which will give us 97. T-number: 32 T-total: 97 Number 4: 14 15 16 24 33 The t-number in this case will be 33. The t-total is 33+24+14+15+16 which will give us 102. T-number: 33 T-total: 102 Number 5: 15 16 17 25 34 The t-number in this case will be 34. The t-total is 34+25+15+16+17 which will give us 107. T-number: 34 T-total: 107 Formula: After investigating the t-numbers from 30 to 34 and comparing them with their t-totals, I have noticed that every time I increase the t-number by one the t-total goes up by five.

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7. ## 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: T-21 + T-20 + T-19 + T-10 + 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.

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8. ## specify

I have noticed that after each translation 5 has been added to the T-total. This is because when the T-shape is moved across once on the grid, one is added to each number, and because there are 5 numbers in the T-shape, 5 is added all together. I have now used a different T-shape; this is still on a 9 by 9 grid. The total for this T-shape is 4 + 5 + 6 + 14 + 23 = 52. Now, I have moved my T-shape down by one on the grid. The new T-total for this shape is 97.

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9. ## T-Totals. 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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10. ## GCSE Mathematics T-Totals

The number at the bottom of the T-shape is called the T-number. The T-number for this T-shape is 20. In order to investigate the relationship between the T-total and T-number I will translate the T-shape by the vector (1, 0). In order to achieve accurate results I will carry this out 3 times. Here are the three T-shapes 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 T-shape.

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11. ## t totals gcse grade A

21, 34 and 68 The t-total is where you add up all the numbers in the t-shape e.g. 2+3+4+12+21=42 49+50+51+59+68=276 15+16+17+25+34=97 2 Basic t-formulas This is of a 9x9 grid T-number t-total 57 222 58 227 59 232 60 237 61 242 You can see the t-total in going up 5 every time as the t-number is going up 1 every time their must be a link? 57x5=285 285-63=222 the t-total What is the link between 63 and 9? 63 is 7x9 So the formula would be T-number x 5 - (9 x 7) 5xt-number-7x9 3 Algebra in a t-formula I am trying to find the number in each cell compared to the t-number A B C D

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12. ## 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 S-100 58 �999.00 25% S-200 1287 �1,200.00 8% S-300 36 �1,300.00 6% S-400 748 �1,399.00 28% S-500 38 �1,449.00 23% S-600 66 �1,699.00 16% S-700 487 �1,799.00 13% S-800 101 �1,849.00 6% S-900 294 �1,999.00 13% S-1000 73

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13. ## GCSE Mathematic Coursework T-totals 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+2r-1 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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14. ## Maths GCSE Investigation - T Numbers

For example, in the above 6 by 6 square, a T-shape is selected: T-number=21 T-total=21(T-number) + 21-6(15) + 21-12(9) + 21-12-1(8) + 21-12+1(10) To create a formula, I will now substitute in X for the T-number: T-total=X(T-number) + X-6(15) + X-12(9) + X-12-1(8) + X-12+1(10) =5X - 42 I will now see if my formula works for another T-shape 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 T-total = 5X-42 = 5*34-42 = 170-42 =128 21+22+23+28+34=128 My formula works.

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15. ## This is an investigation to find a relationship between the T-totals and the T-number. The diagram shows a 9x9 grid, with each individual cell having one number in it starting on the

by 1 the T-total will increase by 5 as there are five number squares within the T-shape and translating the shape to the next possible arrangement would increase all the numbers in the T-shape by 5. Results Below is a 9x9 grid with each T-shape in the first row overlapping another T-shape to represent each T-shape pattern on row 1. I have tabulated my results to see if there is a pattern emerging. Row 1 (1-9) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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16. ## 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 e-totals. If we call the top left number the e-number (shown as "e") then we can see if there is a pattern between the e-number and e-totals.

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17. ## My task is to find out the relationship between the T-total and the T-number.

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 T-shape step by step at a time to the right my T-total will increase by 5 and my T-number will increase by 1. 11/05/05 T - Totals Prashant Sawlani Coursework Workings: Table of Results: T-number 20 21 22 23 24 25 26 T-total 37 42 47 52 57

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18. ## 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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19. ## 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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20. ## Maths Coursework on T-Shapes

In this investigation I will first find a formula to find the T-total using the T-number 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 T-shapes.

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21. ## 1) Investigate the relationship between the T-total and the T-number. 2) Use grid of different sizes. Translate the T-shape to different position. Investigate relationships between the T-total, the T-numbers and the grid size.

T-number 20 21 22 23 24 25 26 T-total 37 42 47 52 57 62 67 This table clearly shows that the numbers go up by 5 every time the T-number 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 T-totals I think that it is a logical place to start the formula.

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22. ## 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 cross-shapes 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.

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23. ## T-Totals - All the things T said

Sample 1) 1 2 3 11 20 T-Number = 20 T-Total = 1+2+3+11+20 = 37 Sample 2) 2 3 4 12 21 T-Number = 21 T-Total = 2+3+4+12+21 = 42 Sample 3) 3 4 5 13 22 T-Number = 22 T-Total = 3+4+5+13+22 = 47 -I arrange these samples in the table. T-Number 20 21 22 T-Total 37 42 47 -As we notice, when T-Number increases by 1, its T-Total also increases by 5. It shows that there is a certain pattern.

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24. ## Investigating the relationship between the T-totals and the T-number.

So in this case the ratio between the T-number and the T-total is 1:5. This can help me because when I want to translate a T-shape that is in another position. For instance when I the T-shape 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

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25. ## T-Total. I can work out a formula to find the T-total on a 9 by 9 grid.

T = N-19+N-18+N-17+N-9+N T = 5N-63 Time for me to check if this formula works: N means T-Number. N = 20 T = 5x20-63 T = 100-63 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 = 5x35-63 T = 175-63 T = 112 48 49 50 58 67 T = 272 T = 5x67-63 T = 335-63 T = 272 So now you know the formula for the 9 by 9 grid is T =5N-63 2. I will now find the formula for a 5 by 5 grid. Here is the 5 by 5 grid.

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26. ## Number Stairs Investigation

+ 20 x + 10 x + 11 x x + 1 x + 2 The formula for the 3-step 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)

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