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GCSE Maths Coursework Module 4 Number grid

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Introduction

-GCSE Maths Coursework Module 4 Number 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 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 99 100 * A box is drawn round four numbers * Find the product of the top left number and the bottom right number in the box * Do the same with the top right and bottom left numbers * Calculate the difference between these products Investigate further. For my module 4 coursework, I have been given the above investigation to carry out. The grid size is 10 x 10 and the box inside is 2 x 2. The box covers four numbers where I have been instructed to find the product of the top left number and the bottom right number as well as the top right number and the bottom left number. ...read more.

Middle

an r x r box on a 10 x 10 grid: R X R box within a grid 10 numbers across: n n + 1 . . . n + r - 1 . . . n + 10 n + 1 +10 . . . n + r - 1 + 10 . . . . . . . . . . . . . . . . . . n + 10(r - 1) = n + 10r - 10 n + 1 + 10(r - 1) . . . n + r - 1 + 10(r - 1) = N + 11r - 11 . . . From this R x R box I have obtained the equation from the product of top right and bottom left: (n + 10r - 10) x (n + r - 1) I then expanded the brackets and eventually getting an expression containing six terms: n2 + 11nr - 11n + 10r2 - 20r + 10 (Equation 1) I then took the top left and bottom right and multiplied them together: n (n + 11r - 11) = n2 + 11nr - 11n (Equation 2) ...read more.

Conclusion

From the r X s box I the bottom left and top right and multiplied them together: (n + gs - g) x (n + r - 1) I then expanded these brackets to get 9 terms: n2 + nr - n + gsn + gsr - gs - gn - gr + g (Equation 1) Now I took the top left and bottom right and multiply these together: n (n + r + gs - g - 1) = n2 + nr + gsn - gn - n (Equation 2) If then (Equation 2) away from (Equation 1) and simplified it to get: gsr - gs - gr + g g(sr - s - r + 1) The expression in brackets again factorises so I now got: = g (r - 1)(s - 1) Here I have got the equation for the grid size. And changing numbers around will get you different results with this equation. If g=10 this formula becomes the same as the one calculated for the r x s box within a grid 10 numbers across. If g=10 and r=s this formula becomes the same as the one calculated for the r x r box within a grid 10 numbers across. ?? ?? ?? ?? ...read more.

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