GCSE: Number Stairs, Grids and Sequences
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 Level: GCSE
 Questions: 75

opposite corners
5 star(s)I predict that once again all answers will be the same. 3 X 3 Square 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 (3 x 21)  (1 x 23) = 40 (6 x 24)  (4 x 26) = 40 (10 x 28)  (8 x 30) = 40 I believe the answer will always be 40 for a 3 x 3 square on this grid.
 Word count: 1638

I am going to investigate the difference between the products of the numbers in the opposite corners of any rectangle that can be drawn on a 100 square (10x10) grid
4 star(s)65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 This is a 10x10 grid. On it (outlines in red) is a 2x2 square. Firstly, I?m going to see what the difference between the products of the corners is (D): 55x64=3520 54x65= 3510 35203510=10, D=10 Now: What if the same sized rectangle was placed in a different area of the grid?
 Word count: 1629

Number grids. In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid.
4 star(s)61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid. 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
 Word count: 941

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
4 star(s)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

Opposite Corners
4 star(s)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 11575=40 Difference = 40 6323=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

I am going to investigate by taking a square shape of numbers from a grid, and then I multiply the opposite corners to find the difference of these two results. Firstly I am going to start with a 10x10 grid
4 star(s)I predict if I move the 4x4 square up, I will get the same answer. 12 52x85=4420 55x82=4510 90 My prediction is right. I am going to use algebra to test my results. n n+3 n+30 n+33 (n+3)(n+30)=n�+90+33n n(n+33)=n�+33n Products difference is equal to (n�+90+33n)  (n�+33n) =90 In the same grid I will now work out a 5x5 square. number Left corner x right corner Right corner x left corner Products difference 13 6x50=300 10x46=460 160 14 16x60=960 20x56=1120 160 15 15x59=885 19x55=1045 160 I have noticed that the products difference of 5x5 squares in a 10x10 grid equal to 160.
 Word count: 3671

Maths coursework stair totals. I shall be investigating the total and difference in sets of stairs in different grid sizes. I will be investigating the relationship between stair totals on different grids.
3 star(s)Below is an example of just one of the three sets of stairs that I used to conduct my investigation: I have worked out the formula for the total inside the three step stairs in a 10 x 10 grid Key: x = corner number t = total inside stairs 1. I worked out the common relationship with the numbers inside the stairs and to be accurate here are two examples: x+x+1+x+2+x+10+x+11+x+20 = 6x+44 2. Noticing that this is the total I realised that it is not so hard to work out the formula for the total.
 Word count: 1525

Mathematics Coursework: problem solving tasks
3 star(s)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

Opposite Corners of a Square on a Number Grid
3 star(s)I think there will be a pattern, and an algebraic expression, which will work for all the box sizes. I think this investigation will be one in which you could branch off into many different sections. I think there will be a lot to explore and a lot to think about. Overall, I think this will be a challenging, but thoughtprovoking investigation and I think I will enjoy discovering the results. Data Example 1  2*2 Square: 12 * 23 = 276 13 * 22 = 286 Difference = 10 19 * 30 = 570 20 * 29 = 580
 Word count: 1196

Number Grid Aim: The aim of this investigation is to formulate an algebraic equation that works out the product of multiplying diagonally opposite corners of a particular shape and finding the difference between the results
3 star(s)Perhaps this means that because it is a 10 x 10 grid, that all the differences would be 10. I would still like to further investigate this theory. The grid below is once again a 2 x 2 box derived from the original 10 x 10 grid. 89 90 99 100 89 x 100 = 8900 90 x 99 = 8910 ? 8910  8900 = 10 This once again confirms what I stated; that the difference between the products of crossmultiplied boxes will always equal 10 in a 10 x 10 grid. I would like to determine if this is definitely correct, so I am going to do it again twice.
 Word count: 4565

In this coursework, I intend to investigate the differences of the products of the diagonally opposite corners of a rectangle, drawn on a 10x10 grid, with the squares numbered off 1 to 100
3 star(s)What is the same between the two alignments? What About Other Sizes of Rectangles? I will now try rectangles, all in the 2 x X series, with different lengths. I think I can now safely assume that the difference is always constant in relation to the size of the rectangle, therefore I only require one example of each difference. 2 x 4 2 x 5 Therefore, it can be seen that every time I increase the width by one, the difference increases by 10.
 Word count: 1516

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:
3 star(s)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

Opposite Corners
3 star(s)the opposite corners will have a difference of 10. 2x4 Rectangle 1 2 3 4 11 12 13 14 67 68 69 70 77 78 79 80 24 25 26 27 34 45 36 37 24x37=888 1x14=14 67x80=5360 34x27=918 11x4=44 77x70=5390 30 30 30 I have noticed a pattern occurring each time the width increases, the difference increases by 10, by 1. Prediction Using the theory I predict that when I multiply a 2x4 rectangle the opposite corners will have a difference of 30.
 Word count: 1956

In this piece course work I am going to investigate opposite corners in grids
3 star(s)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