• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

GCSE Maths Coursework Module 4 Number grid

Extracts from this document...

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.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences 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 Number Stairs, Grids and Sequences essays

  1. Marked by a teacher

    Mathematics Coursework: problem solving tasks

    3 star(s)

    I have displayed my results in a small table below and over the page I have drew out my 12 x 9 tile design. L = 4 T = 2(W - 1) + 2 (H - 1) + = (W - 1)

  2. GCSE Maths Sequences Coursework

    1) 12+2b+c=7 2) 27+3b+c=19 2-1 is 15+b=12 b=-3 To find c: 12-6+c=7 c=1 Nth term for Unshaded = 3n�-3n+1 Total Total is equal to Shaded plus Unshaded so; 6N + 3n�-3n+1 3n�+3n+1 Nth term for Total = 3n�+3n+1 Predictions The formulae I have found are: Perimeter 12N+6 Shaded Squares 6N Unshaded Squares 3n�-3n+1

  1. Investigate the number of winning lines in the game Connect 4.

    The table shows the results I tabulated from the grids I decide to alter the size of on the previous page. Height (h) Width (w) No. of winning lines h 2 2x as many h 3 3x as many h 4 4x as many h w wx as many If

  2. Number Grid Coursework

    Product 2 (TR x BL) Difference (P'duct 2 - P'duct 1) 3 207 567 360 11 847 1207 360 23 2047 2407 360 31 3007 3367 360 34 3400 3760 360 4) Data Analysis From tables (a)-(e), it is possible to see that all the differences of the products tested are multiples of 10.

  1. Number Grids Investigation Coursework

    for the difference between the products of opposite corners would be: (top right x bottom left) - (top left x bottom right) = (a + 4) (a + 40) - a (a + 44) = a2 + 4a + 40a + 160 - a2 - 44a = a2 + 44a

  2. Number Grid Investigation.

    = 1080. 9Z (n-1)(d-1) 90 (5-1)(4-1) = 1080. The formula is correct. I can now work out the product differences of grids of all multiples with any sized square within them. Multiples of: 4 5 6 7 8 5 X 4 square PD's: 1920 3000 4320 5880 7680 I will now try some of the above just to double check.

  1. Investigation of diagonal difference.

    21 22 31 32 41 42 n n + 1 n + 4G n + 4G + 1 I theorise that every time I increase the width by one, the difference increases by 10. I predict that the 2 x 6 rectangle will have a diagonal difference of 50.

  2. Open Box Problem.

    maximum, volume, which is 23cm, and the cut equalling to 100/4, which is 25cm. The divisor for this open box, which calculated the cut of x, which in turn gives this open box, its maximum volume is around 4.3. Notice that even thought the values of the same ratio gets larger, the divisor is staying in the same region.

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