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GCSE: Number Stairs, Grids and Sequences

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  1. Squares and columns Investigation

    = 16 11 12 13 14 15 2 (2+3+7+8) = 20 16 17 18 19 20 3 (3+4+8+9) = 24 21 22 23 24 25 4 (4+5+9+10) = 28 5 (5+6+10+11) = 32 6 (6+7+11+12) = 36 7 (7+8+12+13) = 40 This is the step size they are all going up in fours The reason I put number 5 in as a different colour is because it doesn't really exist because its on the end row, also numbers 10, 15, 20 and 25 don't exist, they would only exist if I added another number to the end of the row, it also shows what it would be anyway so it keeps the pattern going.

    • Word count: 528
  2. Number Grid.

    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

    • Word count: 358
  3. Diagonal Differences

    This is equal to the number of rows. Once I noticed this I realised that the 3X3 grids diagonal difference was equal to the number of rows X4. Also the number of rows in the 4X4 square are timed by 9 And in a 5X5 square the rows are timed by 16.

    • Word count: 570
  4. Investigation 1-Square shaped pieces of card

    Height is also the same as to the size of the cut-out corners of an open box. I am going to begin by investigating a square with a side length of 12 cm. Using this side length, the maximum whole number I can cut off each corner is 5cm, as otherwise I would not have any box left. I am going to begin by looking into whole numbers being cut out of the box corners.

    • Word count: 499
  5. To Find the Diagonal Difference Taken From Small Nxn Grids, Like 3x3.

    The investigation I will start my investigation with the 2x2 grids. As there are many values for the smaller grids like 2x2 I will take my values from the larger grid in a distinct fashion. That is starting from the lowest value, top left, then moving down and right towards the bottom right. With grids like the 7x7 once I have taken the values from one angle I will then take them from the opposite angle. Like illustrated below. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

    • Word count: 2494
  6. Opposite Corners coursework

    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 Highlight any 2x2 square within this grid.

    • Word count: 304
  7. To investigate the difference between the products of the numbers in the opposite corners of any rectangles that can be drawn on a one hundred square

    88 89 " 88 x 99 = 8712 8722 - 8712 = 10 98 99 98 x 89 = 8722 From these results I can conclude that every 2 x 2 rectangle has a difference of 10. I am now going to try rectangles of size 2 x m (where m is the other side). 2 x 3: 1 3 " 33 - 11 = 20 11 13 4 4 " 84 - 64 = 20 14 16 7 9 " 153 - 133 = 20 17 19 This shows that all 2 x 3 rectangles have a difference of

    • Word count: 1742
  8. Number Stairs Investigation – Course Work

    I can say the total for square n (Tn) is, "n + n + 1 + n + 2 + n + 3 + n + 10 + n + 11 + n + 20", because where ever n is on the grid, the number of the square: � One place right of it will be n +1 � Two places right of it will be n +2 � One place above it will be n +10 � One place above it then one place to the right will be n + 10 + 1 = n + 11 �

    • Word count: 1362
  9. The Open Box Problem

    I should also be able to come up with a formula to ..... INVESTIGATING SQUARE SHEETS OF CARD 1. For any sized square sheet of card, investigate the size of the cut out square which makes an open box of the largest volume. USING A 100MM SQUARE SHEET OF CARD I will begin this investigation by working out the size of the square cut which makes an open box of the largest volume, using a 100mm square sheet of card .

    • Word count: 268
  10. GCSE Maths coursework - Cross Numbers

    and the number on the right always = (X+1). Therefore I predict this is a master formula for every number I pick. X-g (X-1) X (X+1) X+g Algebraic Investigation I am going to investigate 3 different formulas on a shape, for 3 grid sizes using the assigned cross shape. a) X-g (X-1) X (X+1) X+g [(X-1) (X+1)] - [(X+g) (X-g) = (X�-1) - (X�-g�) = X�-1-x�+g� = g�-1 b) X-g (X-1) X (X+1) X+g [(X-1) + (X+1)] + [(X-g) + (X+g)] = X-1 + X+1 + X-g + X+g = 4x X-g (X-1)

    • Word count: 3674
  11. Maximum Box Investigation

    First of all, I'm going to try a perfect cube, which i predict to be the best shape. With no lid, the cube has 5 sides, so the 576cm� must be divided by 5. This gives us 115.2cm� for each of the cube's faces. The square root of 115.2cm� is 10.73cm, and this gives us the length of each of the edges in the cube.

    • Word count: 477
  12. Maths Patterns Investigation

    This shape follows the same pattern in the shape before except there is an extra row. This is the last and biggest shape, this shape also has the same pattern nut also has one extra row. This shape follows the same pattern as the shape before but there is an extra row. This shape follows the same pattern as the shape before but there is an extra row. Now that I have got my shapes I am going to make a table to record there amount off boxes in the pyramid and also to find out there first and second differences.

    • Word count: 1482
  13. By using a variety of sources and my visit to Brunswick Square I will show that it was built for the upper classes and that there was a demand of many different factors.

    These two landmarks helped the growth of Brunswick Square and Brighton itself. Dr. Russell Dr. Richard Russell and the sea water cure Brighthelmstone (as Brighton was originally called) was transformed from a small fishing town into a fashionable resort in the mid-18th century through the discovery of the therapeutic effects of bathing in and drinking seawater. The success of this cure, promoted by Dr Richard Russell, drew fashionable society to the town to take the waters. Sea water cure Dr.

    • Word count: 1780

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