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GCSE: Number Stairs, Grids and Sequences

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  • Marked by Teachers essays 18
  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. Marked by a teacher

    opposite corners

    5 star(s)

    I predict that once again all answers will be the same. 3 X 3 Square 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 (3 x 21) - (1 x 23) = 40 (6 x 24) - (4 x 26) = 40 (10 x 28) - (8 x 30) = 40 I believe the answer will always be 40 for a 3 x 3 square on this grid.

    • Word count: 1638
  3. Marked by a teacher

    I am going to investigate the difference between the products of the numbers in the opposite corners of any rectangle that can be drawn on a 100 square (10x10) grid

    4 star(s)

    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 This is a 10x10 grid. On it (outlines in red) is a 2x2 square. Firstly, I?m going to see what the difference between the products of the corners is (D): 55x64=3520 54x65= 3510 3520-3510=10, D=10 Now: What if the same sized rectangle was placed in a different area of the grid?

    • Word count: 1629
  4. Marked by a teacher

    Number grids. In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid.

    4 star(s)

    61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a 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

    • Word count: 941
  5. Marked by a teacher

    Opposite Corners. In this coursework, to find a formula from a set of numbers with different square sizes in opposite corners is the aim. The discovery of the formula will help in finding solutions to the tasks ahead as well as patterns involving Opposite

    4 star(s)

    10 by 10 grid above), 7 � 18 = 126 8 � 17 = 136 The difference between the products above is 10 Tasks: Investigations to see if any rules or patterns connecting the size of square chosen and the difference can be found. When a rule has been discovered, it will be used to predict the difference for larger squares. A test of the rule will be done by looking at squares like 8 � 8 or 9 � 9 X ?

    • Word count: 2865
  6. Marked by a teacher

    Opposite Corners

    4 star(s)

    3 4 5 3 5 1 2 3 3 1 13 14 15 * 25 * 23 11 12 13 * 21 * 23 23 24 25 75 115 21 22 23 63 23 115-75=40 Difference = 40 63-23=40 Opposite corners These answers are the same; just as the answer for the 2*2 squares are the same. I think that any 3*3 square would have a difference of 40. To prove this I will use algebra. z z+1 z+2 z(z+22)=z�+22zz z+10 z+11z+12 (z+2)(z=20)=z�+22z+40 z+20 z+21z+22 (z�+22z+40)-(z�+22z)=40 This proves that with any 3*3 square the corners multiplied the subtracted always = 40 Now I am going to further my investigations again.

    • Word count: 2183
  7. Marked by a teacher

    I am going to investigate by taking a square shape of numbers from a grid, and then I multiply the opposite corners to find the difference of these two results. Firstly I am going to start with a 10x10 grid

    4 star(s)

    I predict if I move the 4x4 square up, I will get the same answer. 12 52x85=4420 55x82=4510 90 My prediction is right. I am going to use algebra to test my results. n n+3 n+30 n+33 (n+3)(n+30)=n�+90+33n n(n+33)=n�+33n Products difference is equal to (n�+90+33n) - (n�+33n) =90 In the same grid I will now work out a 5x5 square. number Left corner x right corner Right corner x left corner Products difference 13 6x50=300 10x46=460 160 14 16x60=960 20x56=1120 160 15 15x59=885 19x55=1045 160 I have noticed that the products difference of 5x5 squares in a 10x10 grid equal to 160.

    • Word count: 3671

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