GCSE Maths Coursework Trouble Watch

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Mattitude
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#1
Report Thread starter 15 years ago
#1
I'm doing some maths coursework, and I've to put a formula in but i'm not sure what it is. Let me explain.

I have a number grid with 100 numbers in, i have to get 2 numbers next to each other, and the two directly udner it, for example:

1 - 2
11 - 12

Then I times the bottom left by the top right, and the bottom right by the top left. I then state the difference.

For a 2 by 2 grid, the difference is always 10. But I don't know how to put the forumla, so I can use it to predict the difference for any four of the numbers.

I hazard a guess at N times X minus 10, but a fellow student said she has N times 10 minus 10.

Anyone help? Or know what i'm on about?
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Eka
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#2
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#2
Have you been asked to multiply the top left and bottom right numbers or just add them together? if you are adding the rule would appear to be 2n +11 (top left to bottom right) and 2n + 9 (for top right to bottom left) Seems like we are doing the same cousre work. If you have to multiply the numbers I'll have to throw 12 pages of work in the bin!

Eka
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Mattitude
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#3
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#3
I have to times the bottom right, by the top left, and the bottom left by the top right.

If you add, you wont get a difference, it has to be times. @[email protected]

I believe it's X times 10 minus 10
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_GáMMá_
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(Original post by Mattitude)
I have to times the bottom right, by the top left, and the bottom left by the top right.

If you add, you wont get a difference, it has to be times. @[email protected]

I believe it's X times 10 minus 10
you'll have to explain it better than that for me to help you.... :confused:

(srry - don't know what you mean!)
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Mattitude
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#5
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#5
Right, I have a number grid, 1 to 100, 1 to 10 on the first line, 10 lines in total.

You pick two numbers from one line, for example, 2 3, then pick the two directly under those two which are 12 and 13

You need to times the bottom left number, which is 12, by the top right number which is 3 (3 x 12) then the bottom right (13) by the top left (2) which is 2 x 13.

2 x 13 = 26
2 X 12 = 36

Difference is 10. No matter where on the grid you choose the four numbers from (Same way as above) The difference will always be 10.

Using n, I need to show what the formula for this is.
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Eka
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#6
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#6
I Know if you add the two sets of numbers, as opposed to multiplying -(top left – bottom right and top right – bottom left) you’ll get the same result, but you will get a rule, 2n +11 (top left to bottom right) and 2n + 9 (for top right to bottom left) which will give you the result for any number with the grid.

My question shows a 10 x 10 grid with the number 12, 13, 22, and 23 boxed. It then asks:

• A box is drawn round four numbers
• Find the product of the top left number and the bottom right number in this box (I’m reading the product to mean add. Am I correct? I’ll have to check with my tutor!)
• Do the same with the top right and bottom left numbers
• Calculate the difference between these products (Might be a clue here that I should be multiplying! ) Albeit I’ve take the difference as 0.
• Investigate further

It may be that we have different questions! I’ll get back to you, but it’ll be few days.


Eka
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klugz
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#7
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#7
Hey, I just finished this coursework!!!

Right, you MUST use algebra to prove that the difference is the same for ALL squares of that sisze in that number grid...numerical exmaples will only get you as far as identifying there is a pattern. The working for a 2x2 square in a 10x10 number grid is as follows:

Let 'x' be the top left number of the square.

D = (x + 10)(x + 1) - x(x + 11)
D = x² + 11x + 10 - x² - 11x
D = 10

You should then extend your investigation to different sized squares within the same number grid, and come up with the equation D=10(n - 1)², where n is the length of one side of the square.

You should then continue the investigation to find an equation for any RECTANGLE inside any RECTANGULAR number grid. Th algebra is as follows.

let n and m be the sides of the rectangle
let r be the length of one row of the number grid
let x be the top left number of the rectangle (this eventually cancells, because it is irrelevant...this must be explained)

D = ((x + (n – 1))(x + r(m – 1))) – (x(x + r(m – 1) + (n – 1)))
D = (x + n – 1)( x + rm – r) – (x(x + rm – r +n – 1))
D = (x² + xrm – rx + nx + nrm – rn – x – rm + r) – (x² + xrm – rx + xn – x)
D = nrm – rn – rm + r
D = r(nm – n – m + 1)
D = r(n – 1)(m – 1)

You need to mention the limitations of the investigation (r must be greater or equal to n......q must be greater or equal to m (where q represents the vertical height of the number grid)

Also explain why there is no need for an algebraic variable for the height of the number grdi (because it is only the amount of numbers per row and height of the chosen rectangle, that affects the difference between numbers on the top row of the rectangle, and those on the bottom)

Hope I have been of help......Good Luck!!!
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Eka
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#8
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#8
Well it was back to the drawing board for me!! :mad: My first sweep with the 2 x 2 box of 4 number resulted in d = n2 (11n) – n2 (11n) + 10 = -10. Minus 10 because the course work asked for the product of the top left / bottom right first then to calculate the difference between that and the top right bottom left. Or have I got it wrong again!

I then went on to look at a 3 x 3 box of 9 numbers. The difference between the two products differs considerablely. Whilst my result to the 2 x 2 box is similar to klugz’s I afraid I don’t understand his, ‘D=10(n - 1)², where n is the length of one side of the square.’ This doesn’t appear to work. (Not for me anyway :rolleyes: )

A the moment I have n2 + 11n (n+22) for the product of a top left to bottom right 3 x 3 box, and I’m just resuming work on it!

See ya :cool:

Eka
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Eka
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#9
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#9
klugz I now get your, ‘D=10(n - 1)², I just need to prove it!
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Eka
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#10
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#10
I can get d = n(n+11)(n+22) to d = n^3 + 33n + 242

But how can I work out n+2(n+11)(n+20)? n^3 +33n + 440 does not appear to work.

Can anyone help?

Cheers
Eka
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Dayjo Aspen
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#11
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#11
I am also doing this Coursework and it need to be in tomorrow..lol..

I've pretty much finished but my teacher says I need to JUSTIFY my formulas using more algebra.. So i have something like this:

|__ a __|_ a+1 _|
|_a+10_|_a+11_|

and to show that it will work for any 2x2 sized box use a sum like this:

(a+10)(a+1) = a^2 + a + 10a + 10 which = a^2 + 11a + 10
and
a(a+11) = a^2 + 11a

so

(a^2 + 11a + 10) - (a^2 + 11a) = 10..and that would work for any 2x2 box.

Also for other sized boxes i need to do the same and then for different sized boxes on different sized grids (not just going up to 10 like this

| 1 | 2 | 3| 4| 5| 6 | 7 | 8 | 9 |10|
|11|12|13|14|15|16|17|18|19|20 |
ETC..

but like these aswell:

| 1 | 2 | 3| 4| 5| 6 |
| 7 | 8 | 9 |10|11|12|
|13 |14|15|16|17|18|
ETC..this is hard to do all of this i know...

But im just not sure how to write it all down showing those algebraic formula ^^

My opening statement for the justification part goes like this:

"I can justify the functionality of the formulas by using simple algebra to work out the ‘Opposite Corner Product Difference’ of any size box."

But now what do i write?...thanks..and if anyone still needs help please ask and i will try and help.. ..

~Dayjo (man! that 1st post was looong)
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Phil_C
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#12
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(Original post by Eka)
• A box is drawn round four numbers
• Find the product of the top left number and the bottom right number in this box (I’m reading the product to mean add. Am I correct? I’ll have to check with my tutor!)
Eka

No your wrong.
PRODUCT means multiply.
SUM means Add.
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Eka
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#13
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#13
I know ... I'm doing it all again! Klugz .. if you are about ... you mentioned d - 10(n-1)^2 ... this works for a 2 x 2 and 3 x 3 box .. but does not seem to work for a 4 x 4 box. When I look at the difference I get
3600 3800 4000 4200 4400 4600 1st level
-200 -200 -200 -200 -200 2nd level

and I can't work out a formula, the best I can get at the moment is

n(n+11)(n+22)(n+33) How do I get that to work!!!!

Well back to it!!

Eka
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Eka
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#14
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Dayjo ... if its not too late! For the 2 x 2 box I got n^2 + 11n for top left to bottom right and n^2 + 9n for top right to bottom left
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