D2 Pre-Exam Thread - Past Papers, Mark schemes etc
Maths exam discussion - share revision tips in preparation for GCSE, A Level and other maths exams and discuss how they went afterwards.
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etcOld spec papers adapted to new specthe answers are contained within the documents after the questions, I have also included bits from the mark schemes you may need
Last edited by Arsey; 30-05-2012 at 18:18. -
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etcPast boundaries and Model Solutions
June 11 solutions are Gibbo's
Code:Unit Module Session 100' 90' 80' 70' 60' 50' 40' 6690 D2 Jun-11 75 70 64 55 46 38 30 6690 D2 Jun-10 75 68 61 52 44 36 28 6690 D2 Jun-09 73 65 57 49 41 34 27
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etcDefinitions and other stuff to learn
Transportation
unbalanced when supply > demand
dummy column needed if unbalanced
degenerate when occupied cells is less than columns + rows - 1
(if this happens you need to smack a zero into your solution)
Salesman
walk - finite sequence of edges such that the end vertex of one edge is the start vertex of the next
tour - a walk which visits every vertex and returns to the starting vertex
classical solution - tour visiting each vertex once
practical solution - tour visiting each vertex at least once
Game theory
Zero sum game - total gain for all players in the game is zero
No stable solution if column minimax is not equal to row maximin
Saddle point - the location of a stable solution where row maximin = column minimax
In a pay-off matrix for player A...
if every element in row A is greater than the corresponding value in row B, then row A dominates row B. Row B can now be deleted from the game as Player A should never play row B.
if every element in column A is smaller than the corresponding value in column B, then column A dominates column B. Column B can now be deleted from the game as Player B should never play column B.
If the pay-off for player A is X then the pay-off for player B is -X
Flows
A series of arcs whose removal splits the network into two separate halves one containing the sink node(s), the other containing the source node(s)
When calculating the capacity of a cut add in the CAPACITIES (not flows) of arcs flowing into the cut
A minimum cut is one which passes only through saturated arcs and/or empty arcs flowing back through the cut
minimum cut = max flow by the maximum flow - minimum cut theorem
Dynamic Programming
in a Minimax problem put max( , ) in your value column then star the minimum of those
in a Maximin problem put min( , ) in your value column then star the maximum of those
Bellman’s principle of optimality - any part of an optimal path is itself optimal
Minimax route - the route chosen such that the maximum arc is as small as possible
Maximin route - the route chosen such that the minimum arc is as large as possibleLast edited by Arsey; 30-05-2012 at 22:37. -
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etcGeneral tips and advice
there are only 3 types of forming lnear programming problems
Transportation
Game Theory
Allocation
LEARN THEM ALL
Given the theme of the current papers (summer 2012) I think it would be sensible to learn how to form a simplex tableau from a game theory problem 3x3 that cannot be reduced say.Last edited by Arsey; 26-05-2012 at 23:00. -
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etcNeed this to be very high, the content isn't hard just a bit too long, plus I have a bad teacher who is very boring and we only have had 1 D2 lesson a week all year so much of it is forgotten :/ here is hope for 90ums+ atm I averaging at 70 :/ and there aren't many past papers ¬¬ I am screwed FML
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etcI have just put about 14 up - that will keep you going until Thu(Original post by JordanS94)
Need this to be very high, the content isn't hard just a bit too long, plus I have a bad teacher who is very boring and we only have had 1 D2 lesson a week all year so much of it is forgotten :/ here is hope for 90ums+ atm I averaging at 70 :/ and there aren't many past papers ¬¬ I am screwed FML -
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etccan you think of anymore?(Original post by Gibbo81)
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(Original post by Arsey)
Definitions and other stuff to learn
Transportation
unbalanced when supply > demand
dummy column needed if unbalanced
degenerate when occupied cells is less than columns + rows - 1
(if this happens you need to smack a zero into your solution)
Salesman
walk - finite sequence of edges such that the end vertex of one edge is the start vertex of the next
tour - a walk which visits every vertex and returns to the starting vertex
classical solution - tour visiting each vertex once
practical solution - tour visiting each vertex at least once
Game theory
Zero sum game - total gain for all players in the game is zero
No stable solution if column minimax is not equal to row maximin
Saddle point - the location of a stable solution where row maximin = column minimax
In a pay-off matrix for player A...
if every element in row A is greater than the corresponding value in row B, then row A dominates row B. Row B can now be deleted from the game as Player A should never play row B.
if every element in column A is greater than the corresponding value in column B, then column A dominates column B. Column A can now be deleted from the game as Player B should never play column A.
If the pay-off for player A is X then the pay-off for player B is -X
Flows
When calculating the capacity of a cut add in the CAPACITIES (not flows) of arcs flowing into the cut
A minimum cut is one which passes only through saturated arcs and/or empty arcs flowing back through the cut
minimum cut = max flow by the maximum flow - minimum cut theorem
Dynamic Programming
in a Minimax problem put max( , ) in your value column then star the minimum of those
in a Maximin problem put min( , ) in your value column then star the maximum of those
Bellman’s principle of optimality - any part of an optimal path is itself optimal
Minimax route - the route chosen such that the maximum arc is as small as possible
Maximin route - the route chosen such that the minimum arc is as large as possible -
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etcGood luck with that, it took me about four/five weeks to self teach the module, but then again I was only doing 2 exercises a day. Why would you leave it so late?!(Original post by anuradha_d)
AHA im attempting to relearn the whole of D2 by Monday evening...
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etcWell, we started learning it in Feb, after we finished D1, and I kinda needed to focus on my AS exams... :/(Original post by WaNaBe)
Good luck with that, it took me about four/five weeks to self teach the module, but then again I was only doing 2 exercises a day. Why would you leave it so late?!
I finished the first 3 chapters yday LOL. -
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Re: D2 Pre-Exam Thread - Past Papers, Mark schemes etcOhh right fair enough. Yeah the first 3 chapters are fairly straightforward. The last part of the last chapter can be tough to get your head around - dynamic programming from a table.(Original post by anuradha_d)
Well, we started learning it in Feb, after we finished D1, and I kinda needed to focus on my AS exams... :/
I finished the first 3 chapters yday LOL.
