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GCSE: Number Stairs, Grids and Sequences

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• Marked by Teachers essays 18
1. GCSE Maths questions

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• 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