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GCSE: Number Stairs, Grids and Sequences

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Meet our team of inspirational teachers Get help from 80+ teachers and hundreds of thousands of student written documents • 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.  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

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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
3.  Opposite Corners

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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
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Step 1 L T + 1 x 1 4 0 0 2 x 2 4 4 1 3 x 3 4 8 4 4 x 4 4 12 9 5 x 5 4 16 16 From the information depicted in the table above it would appear that my prediction stating that the number of L shape spacers needed is always 4, is indeed correct. The obvious reason for this is; because squares and rectangles reliably consist of four corners. So L = 4.

• Word count: 2504
5.  I am going to investigate taking a square of numbers from a grid, multiplying the opposite corners and finding the difference of these two results. To start I used a 5x5 grid:

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So I can see like in the 5x5 grid there is a pattern. If I am right every 2x2 square in a 6x6 grid should have a difference of 6. To check if I am right I will take one more square out of the grid. 16 17 22 23 16 x 23 = 368 17 x 22 = 374 374 - 368 = 6 This shows that my hypothesis is right and every 2x2 square in a 6x6 grid will have a difference of 6.

• Word count: 2963
6.  In this piece course work I am going to investigate opposite corners in grids

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7x7 Grid Here is a grid of numbers in sevens. It is called a seven grid. In this section I will multiply the opposite corners and then subtract them. 2x2 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 In my 7x7 grid I have highlighted three 2x2 grids. I will multiply and subtract the opposite corners now.

• Word count: 2254