Investigate the difference of the product of the diagonally opposite corners of a certain shape, drawn on a 10x10 grid with the individual squares numbered off 1 to 100.

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Maths Coursework

Aim: I task is to investigate the difference of the product of the diagonally opposite corners of a certain shape, drawn on a 10x10 grid with the individual squares numbered off 1 to 100

I will start off by working this out on a 2x2 square and from there I will begin to investigate varying the length and width of rectangles and other squares.

I will aim to investigate the differences for different sized rectangles and squares that are aligned differently on the grid.

I will record findings and ideas as I proceed.

Method: To make things easier for me I will break up each investigation in to sections, I will start with:

2x2 square

I will concentrate on one particular aspect at a time.

* What is the difference between the products of the corners?

* Is the difference the same for a square or rectangle the same shape anywhere on the grid?

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2 x 11 = 22

x 12 = 12

Diff = 10

Are all the differences 10?

46 x 55 = 2,530

45 x 56 = 2,520

Diff = 10

It seems so. I now predict that all 2x2 squares will have a difference of 10. I shall test this prediction:

70 x 79 = 5,530

69 x 80 = 5,520

Diff = 10

I am correct; all 2x2 squares have a difference of 10

This brings up the obvious question:

* Is the difference different when the square changes size?

In answer to this I will do a test for a 3x3 square and a 4x4 square

3x3 square

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3 x 21 = 63

x 23 = 23

Diff = 40

46 x 64 = 2,944

44 x 66 = 2,904

Diff = 40

60 x 78 = 4,680

58 x 80 = 4,640

Diff = 40

Here the differences are all 40

4x4 square

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Join now!


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