Maths Coursework
Part 1
Introduction
I am to conduct an investigation involving a number grid. The first
part of the investigation will involve me:
ü Drawing a box around various random numbers on a number grid
i.e. 2 x 2 numbers, 3 x 3 numbers, 4 x 4 numbers.
ü I will then find the product of the top left number and the
bottom right number in the boxes by multiplying them.
ü I will then do the same with the top right and bottom left
numbers.
ü I am then going to calculate the difference between these
products
10x10 Grid
ü 2x2 Boxes
Box 1
52
53
X
X+1
62
63
X+10
X+11
[image001.gif] [image002.gif] 52 x 63 = 3276 x
(x + 11) x2 + 11x
[image003.gif] 62 x 53 = 3286 (x + 1) (x +
10) x2 + 11x + 10
= (x2 + 11x + 10) -
(x2 + 11x) = 10
3286 - 3276 = 10
The difference between the two numbers is 10
Box 2
81
82
91
92
[image004.gif] 81 x 92 = 7452
91 x 82 = 7462
7462 - 7452 = 10
The difference between the two numbers is 10
Box 3
69
70
79
80
[image005.gif] 69 x 80 = 5520
79 x 70 = 5530
5530 - 5520 = 10
The difference between the two numbers is 10
ü 3x3 Boxes
Box 1
8
9
10
X
X+1
X+2
18
19
20
X+10
X+11
X+12
28
29
30
X+20
X+21
X+22
[image006.gif] [image007.gif] 8 x 30 =
240 x (x + 22) x2 + 22x
[image008.gif] 28 x 10 = 280 (x + 2) (x +
20) x2 + 20x + 2x + 40
= (x2 + 22x + 40) -
(x2 + 22x) = 40
280 - 240 = 40
The difference between the two numbers is 40
Box 2
34
35
36
44
45
46
54
55
56
[image009.gif] 34 x 56 = 1904
54 x 36 = 1944
1944 - 1904 = 40
The difference between the two numbers is 40
Box 3
75
76
77
85
86
87
95
96
97
[image010.gif] 75 x 97 = 7275
95 x 77 = 7315
7315 - 7275 = 40
The difference between the two numbers is 40
ü 4 x 4 Boxes
Box 1
17
18
19
20
X
X+1
X+2
X+3
27
28
29
30
X+10
X+11
X+12
X+13
37
38
39
40
X+20
X+21
X+22
X+23
47
48
49
50
X+30
X+31
X+32
X+33
[image003.gif] [image011.gif] 17 x 50 = 850
x (x + 33) x2 + 33x
[image012.gif] 47 x 20 = 940 (x + 3) (x +
30) x2 + 30x + 3x + 90
=(x2 + 33x + 90) - (x2
+ 33x) = 90
940 - 850 = 90
The difference between the two numbers is 90
Box 2
1
2
3
4
11
12
13
14
21
22
23
24
31
32
33
34
[image013.gif] 1 x 34 = 34
31 x 4 = 124
124 - 34 = 90
The difference between the two numbers is 90
Box 3
64
65
66
67
74
75
76
77
84
85
86
87
94
95
96
97
[image014.gif] 64 x 97 = 6208
94 x 67 = 6298
6298 - 6208 = 90
The difference between the two numbers is 90
ü 5 x 5 Boxes (Prediction)
I am now going to predict the outcome of a 5 x 5 box. From doing
these boxes I have discovered that each of the differences i.e. 10, 40
and 90 are square numbers that are multiplied by 10. For every box
Part 1
Introduction
I am to conduct an investigation involving a number grid. The first
part of the investigation will involve me:
ü Drawing a box around various random numbers on a number grid
i.e. 2 x 2 numbers, 3 x 3 numbers, 4 x 4 numbers.
ü I will then find the product of the top left number and the
bottom right number in the boxes by multiplying them.
ü I will then do the same with the top right and bottom left
numbers.
ü I am then going to calculate the difference between these
products
10x10 Grid
ü 2x2 Boxes
Box 1
52
53
X
X+1
62
63
X+10
X+11
[image001.gif] [image002.gif] 52 x 63 = 3276 x
(x + 11) x2 + 11x
[image003.gif] 62 x 53 = 3286 (x + 1) (x +
10) x2 + 11x + 10
= (x2 + 11x + 10) -
(x2 + 11x) = 10
3286 - 3276 = 10
The difference between the two numbers is 10
Box 2
81
82
91
92
[image004.gif] 81 x 92 = 7452
91 x 82 = 7462
7462 - 7452 = 10
The difference between the two numbers is 10
Box 3
69
70
79
80
[image005.gif] 69 x 80 = 5520
79 x 70 = 5530
5530 - 5520 = 10
The difference between the two numbers is 10
ü 3x3 Boxes
Box 1
8
9
10
X
X+1
X+2
18
19
20
X+10
X+11
X+12
28
29
30
X+20
X+21
X+22
[image006.gif] [image007.gif] 8 x 30 =
240 x (x + 22) x2 + 22x
[image008.gif] 28 x 10 = 280 (x + 2) (x +
20) x2 + 20x + 2x + 40
= (x2 + 22x + 40) -
(x2 + 22x) = 40
280 - 240 = 40
The difference between the two numbers is 40
Box 2
34
35
36
44
45
46
54
55
56
[image009.gif] 34 x 56 = 1904
54 x 36 = 1944
1944 - 1904 = 40
The difference between the two numbers is 40
Box 3
75
76
77
85
86
87
95
96
97
[image010.gif] 75 x 97 = 7275
95 x 77 = 7315
7315 - 7275 = 40
The difference between the two numbers is 40
ü 4 x 4 Boxes
Box 1
17
18
19
20
X
X+1
X+2
X+3
27
28
29
30
X+10
X+11
X+12
X+13
37
38
39
40
X+20
X+21
X+22
X+23
47
48
49
50
X+30
X+31
X+32
X+33
[image003.gif] [image011.gif] 17 x 50 = 850
x (x + 33) x2 + 33x
[image012.gif] 47 x 20 = 940 (x + 3) (x +
30) x2 + 30x + 3x + 90
=(x2 + 33x + 90) - (x2
+ 33x) = 90
940 - 850 = 90
The difference between the two numbers is 90
Box 2
1
2
3
4
11
12
13
14
21
22
23
24
31
32
33
34
[image013.gif] 1 x 34 = 34
31 x 4 = 124
124 - 34 = 90
The difference between the two numbers is 90
Box 3
64
65
66
67
74
75
76
77
84
85
86
87
94
95
96
97
[image014.gif] 64 x 97 = 6208
94 x 67 = 6298
6298 - 6208 = 90
The difference between the two numbers is 90
ü 5 x 5 Boxes (Prediction)
I am now going to predict the outcome of a 5 x 5 box. From doing
these boxes I have discovered that each of the differences i.e. 10, 40
and 90 are square numbers that are multiplied by 10. For every box