Maths Investigation

1
Maths Investigation
2
Opposite corners
10(n-1)2 is the equation for finding what the two
opposing numbers in a grid e.g. ( x 1)( x
10) x x10x10x²11x10 x( x
11)x² 11x x ²11x10-x²11 10 10 x (n-1)² e.g.
10 x (2-1)² 1 x 1 x 10 10
3
Opposite corners continued
10(n-1) ² is the formula for finding what the
opposite corners which are multiplied together
(shown in the last slide) and taken away from
each other (also shown in the last slide) e.g. 10
x (3-1)² 2² x 10 40 and for a 5 by 5 grid it
would be 10(5-1)² 4² x 10 16 x 10 160
4
Each opposite squares
5
3 x 3 grid
If you times 1 and 23 it 23 Then times 3 and 21
it 63 so the difference is 40 So 2x2 grid
difference is 10 and 3x3 grid difference is 40
My proof is using x First x(x22) x² 22x Then
(x2)(x20) using FOIL method x² 22x 40
6
4 by 4
4 by 4 grids have a difference of ninety 1 times
34 34 4 times 31 124 Difference of 34 and 124
90
I shall prove my answer with x x(x33) x²
33x (x3)(x30) Using FOIL Method x² 33x
90 difference 90
7
5 by 5 grids have a higher difference then 4 by
4, 3 by 3 or 2 by 2. 5 by 5 have a difference
of 160 First 1 times 45 45 Then 5 times 41
205 The difference is 160 between these numbers
5 by 5
The Proof I have will again be x x(x44)x² 44x
(x4)(x40) x² 44x 160 The
difference is 160
8
6 by 6
6 by 6 goes up from 160 in 5 by 5 to 250
increasing by 90 1 times 56 56 6 times 51
306 The difference is 250
To prove that Im right I shall use x First
x(x55) x² 55x Then (x5)(x50) x² 55x
250
9
Proving with x is important so I shall x(x66)
x² 66x (x6)(x60)x² 66x 360
7 by 7
7 by 7 360 a total 110 above 6 by 6 1 times 67
67 7 times 61 427 Total difference 360
10
8 by 8 difference is 490 1 x 78 78 8 x 71
568 Difference is 490
8 by 8
The proof x(x77)x² 77x (x7)(x70)x² 77x
490
11
Thank you for watching my algebraic
slide Pictures 1-Richard Humphreys 2 i)
Internet ii) Internet iii) Internet 3-Internet 4-R
ichard Humphreys 5-Richard Humphreys 6-Richard
Humphreys 7-Richard Humphreys 8-Richard
Humphreys Information Most- Mr. Seward Little-
Piece of paper Slide animation Richard
Humphreys