# The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 72.

Size: px
Start display at page:

Download "The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 72."

Transcription

2 2 1 Two graphs A and B are shown below. (i) Write down an example of a cycle on graph A. [1] (ii) Why is U Y V Z Y X not a path on graph B? [1] (iii) How many arcs would there be in a spanning tree for graph A? [1] (iv) For each graph state whether it is Eulerian, semi-eulerian or neither. [2] (v) The graphs show designs to be etched on metal plates. The etching tool is positioned at a starting point and follows a route without repeating any arcs. It may be lifted off and positioned at a new starting point. What is the smallest number of times that the etching tool must be positioned, including the initial position, to draw each graph? [2] An arc is drawn connecting Q to U, so that the two graphs become one. The resulting graph is not Eulerian. (vi) Extra arcs are then added to make an Eulerian graph. What is the smallest number of extra arcs that need to be added? [2] OCR /01 Jun07

3 3 2 A landscape gardener is designing a garden. Part of the garden will be decking, part will be flowers and the rest will be grass. Let d be the area of decking, f be the area of flowers and g be the area of grass, all measured in m 2. The total area of the garden is 120 m 2 of which at least 40 m 2 must be grass. The area of decking must not be greater than the area of flowers. Also, the area of grass must not be more than four times the area of decking. Each square metre of grass will cost 5, each square metre of decking will cost 10 and each square metre of flowers will cost 20. These costs include labour. The landscape gardener has been instructed to come up with the design that will cost the least. (i) Write down a constraint in d, f and g from the total area of the garden. [1] (ii) Explain why the constraint g 4d is required. [1] (iii) Write down a constraint from the requirement that the area of decking must not be greater than the area of flowers. [1] (iv) Write down a constraint from the requirement that at least 40 m 2 of the garden must be grass and write down the minimum feasible values for each of d and f. [3] (v) Write down the objective function to be minimised. [1] (vi) Write down the resulting LP problem, using slack variables to express the constraints from parts (ii) and (iii) as equations. [3] (You are not required to solve the resulting LP problem.) 3 (i) Use shuttle sort to sort the five numbers 8, 6, 9, 7, 5 into increasing order. Write down the list that results at the end of each pass. Calculate and record the number of comparisons and the number of swaps that are made in each pass. [6] (ii) The algorithm below is part of another method for sorting a list into increasing order. Apply it to the list 8, 6, 9, 7, 5. Show the result of each step. [5] Step 1: Input the original list and call it list A. Step 2: Remove the first item in list A and call this item X. Step 3: If the first item remaining in list A is less than X move it to list B, otherwise move it to list C. Step 4: If the next item remaining in list A is less than X move it to become the next item in list B, otherwise move it to become the next item in list C. Step 5: If there are still items in list A, repeat Step 4. Step 6: Count the number of items in list B and call this N. Step 7: Put the items in list B at positions 1 to N of list A, item X at position N + 1 of list A and the items in list C at positions N + 2 onwards of list A. Step 8: Display list A. OCR /01 Jun07 [Turn over

4 4 4 Consider the linear programming problem: maximise P = 3x 5y, subject to x + 5y 12, x 5y 10, 3x + 10y 45, and x 0, y 0. (i) Represent the problem as an initial Simplex tableau. [3] (ii) Identify the entry on which to pivot for the first iteration of the Simplex algorithm. Explain how you made your choice of column and row. [2] (iii) Perform one iteration of the Simplex algorithm. Write down the values of x, y and P after this iteration. [6] (iv) Show that x = 11, y = 0.2 is a feasible solution and that it gives a bigger value of P than that in part (iii). [2] OCR /01 Jun07

5 5 5 Answer this question on the insert provided. The network below represents a simplified map of a building. The arcs represent corridors and the weights on the arcs represent the lengths of the corridors, in metres. The sum of the weights on the arcs is 765 metres. (i) Janice is the cleaning supervisor in the building. She is at the position marked as J when she is called to attend a cleaning emergency at B. On the network in the insert, use Dijkstra s algorithm, starting from vertex J and continuing until B is given a permanent label, to find the shortest path from J to B and the length of this path. [7] (ii) In her job Janice has to walk along each of the corridors represented on the network. This requires finding a route that covers every arc at least once, starting and ending at J. Showing all your working, find the shortest distance that Janice must walk to check all the corridors. [5] The labelled vertices represent cleaning stations. Janice wants to visit every cleaning station using the shortest possible route. She produces a simplified network with no repeated arcs and no arc that joins a vertex to itself. (iii) On the insert, complete Janice s simplified network. Which standard network problem does Janice need to solve to find the shortest distance that she must travel? [4] OCR /01 Jun07 [Turn over

6 6 6 Answer this question on the insert provided. The table shows the distances, in miles, along the direct roads between six villages, A to F. A dash ( ) indicates that there is no direct road linking the villages. A B C D E F A 6 3 B C D E 4 3 F (i) On the table in the insert, use Prim s algorithm to find a minimum spanning tree. Start by crossing out row A. Show which entries in the table are chosen and indicate the order in which the rows are deleted. Draw your minimum spanning tree and state its total weight. [6] (ii) By deleting vertex B and the arcs joined to vertex B, calculate a lower bound for the length of the shortest cycle through all the vertices. [3] (iii) Apply the nearest neighbour method to the table above, starting from F, to find a cycle that passes through every vertex and use this to write down an upper bound for the length of the shortest cycle through all the vertices. [4] OCR /01 Jun07

7 7 BLANK PAGE 4736/01 Jun07

8 8 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (OCR) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. OCR is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. OCR /01 Jun07

### Decision Mathematics 1 TUESDAY 22 JANUARY 2008

ADVANCED SUBSIDIARY GCE 4736/01 MATHEMATICS Decision Mathematics 1 TUESDAY 22 JANUARY 2008 Additional materials: Answer Booklet (8 pages) Graph paper Insert for Questions 3 and 4 List of Formulae (MF1)

### Decision Mathematics D1 Advanced/Advanced Subsidiary. Tuesday 5 June 2007 Afternoon Time: 1 hour 30 minutes

Paper Reference(s) 6689/01 Edexcel GCE Decision Mathematics D1 Advanced/Advanced Subsidiary Tuesday 5 June 2007 Afternoon Time: 1 hour 30 minutes Materials required for examination Nil Items included with

### MATHEMATICS Unit Decision 1

General Certificate of Education January 2008 Advanced Subsidiary Examination MATHEMATICS Unit Decision 1 MD01 Tuesday 15 January 2008 9.00 am to 10.30 am For this paper you must have: an 8-page answer

### MATHEMATICS Unit Decision 1

General Certificate of Education January 2007 Advanced Subsidiary Examination MATHEMATICS Unit Decision 1 MD01 Tuesday 16 January 2007 9.00 am to 10.30 am For this paper you must have: an 8-page answer

### Decision Mathematics D1. Advanced/Advanced Subsidiary. Friday 12 January 2007 Morning Time: 1 hour 30 minutes. D1 answer book

Paper Reference(s) 6689/01 Edexcel GCE Decision Mathematics D1 Advanced/Advanced Subsidiary Friday 12 January 2007 Morning Time: 1 hour 30 minutes Materials required for examination Nil Items included

### Monday 28 January 2013 Morning

Monday 28 January 2013 Morning AS GCE MATHEMATICS 4732/01 Probability and Statistics 1 QUESTION PAPER * 4 7 3 3 8 5 0 1 1 3 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education FIRST LANGUAGE ENGLISH 0500/03 Paper 3 Directed Writing and Composition For Examination from 2015

### MATHEMATICS Unit Decision 1

General Certificate of Education June 2007 Advanced Subsidiary Examination MATHEMATICS Unit Decision 1 MD01 Thursday 7 June 2007 9.00 am to 10.30 am For this paper you must have: an 8-page answer book

### Friday 24 May 2013 Morning

Friday 24 May 2013 Morning AS GCE MATHEMATICS 4732/01 Probability & Statistics 1 QUESTION PAPER * 4 7 1 5 5 2 0 6 1 3 * Candidates answer on the Printed Answer Book. OCR supplied materials: Printed Answer

### Cambridge International Examinations Cambridge Primary Checkpoint

Cambridge International Examinations Cambridge Primary Checkpoint MATHEMATICS 0845/02 Paper 2 For Examination from 2014 SPECIMEN PAPER 45 minutes Candidates answer on the Question Paper. Additional Materials:

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education FIRST LANGUAGE ENGLISH 0500/02 Paper 2 Reading Passages (Extended) For Examination from 2015 SPECIMEN

### Wednesday 13 June 2012 Morning

THIS IS A NEW SPECIFICATION F Wednesday 13 June 2012 Morning GCSE MATHEMATICS B J567/02 Paper 2 (Foundation Tier) *J517120612* Candidates answer on the Question Paper. OCR supplied materials: None Other

### UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level *4274470357* MATHEMATICS (SYLLABUS D) 4024/11 Paper 1 October/November 2012 2 hours Candidates answer

### UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

*8270368766* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/11 Paper 1 (Core) October/November 2012 Candidates answer on the

### THIS IS A NEW SPECIFICATION MODIFIED LANGUAGE

THIS IS A NEW SPECIFICATION GENERAL CERTIFICATE OF SECONDARY EDUCATION RELIGIOUS STUDIES B (PHILOSOPHY AND/OR APPLIED ETHICS) Ethics 1 (Relationships, Medical Ethics, Poverty and Wealth) B603 * OCE / 2

### Thursday 8 November 2012 Afternoon

H Thursday 8 November 2012 Afternoon GCSE MATHEMATICS B J567/04 Paper 4 (Higher Tier) *J517181112* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

### Monday 11 June 2012 Afternoon

THIS IS A NEW SPECIFICATION H Monday 11 June 2012 Afternoon GCSE MATHEMATICS A A502/02 Unit B (Higher Tier) *A517000612* Candidates answer on the Question Paper. OCR supplied materials: None Other materials

### egyptigstudentroom.com

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *5128615949* MATHEMATICS 0580/04, 0581/04 Paper 4 (Extended) May/June 2007 Additional Materials:

### Wednesday 6 November 2013 Morning

H Wednesday 6 November 2013 Morning GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) *J540550313* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

### Friday 20 January 2012 Morning

THIS IS A NEW SPECIFICATION H Friday 20 January 2012 Morning GCSE TWENTY FIRST CENTURY SCIENCE PHYSICS A A181/02 Modules P1 P2 P3 (Higher Tier) *A131500112* Candidates answer on the Question Paper. A calculator

### Tuesday 6 November 2012 Morning

H Tuesday 6 November 2012 Morning GCSE MATHEMATICS A A502/02 Unit B (Higher Tier) *A516821112* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

### Friday 18 January 2013 Afternoon

Friday 18 January 2013 Afternoon GCSE RELIGIOUS STUDIES B (PHILOSOPHY AND/OR APPLIED ETHICS) B603/01 Ethics 1 (Relationships, Medical Ethics, Poverty and Wealth) *B620060113* Candidates answer on the Answer

### Monday 11 June 2012 Afternoon

THIS IS A NEW SPECIFICATION F Monday 11 June 2012 Afternoon GCSE MATHEMATICS B J567/01 Paper 1 (Foundation Tier) *J517110612* Candidates answer on the Question Paper. OCR supplied materials: None Other

### Tuesday 6 November 2012 Morning

F Tuesday 6 November 2012 Morning GCSE MATHEMATICS B J567/01 Paper 1 (Foundation Tier) *J517151112* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

### MATHEMATICS A A502/01 Unit B (Foundation Tier)

THIS IS A NEW SPECIFICATION F GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS A A502/01 Unit B (Foundation Tier) *A533721112* Candidates answer on the question paper. OCR supplied materials: None

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level *0123456789* ACCOUNTING 9706/02 Paper 2 Structured Questions For Examination from 2016 SPECIMEN PAPER

### Thursday 28 February 2013 Afternoon

H Thursday 28 February 2013 Afternoon GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) *J533610313* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

Advanced Subsidiary GCE SOCIOLOGY Unit G671: Exploring socialisation, culture and identity Specimen Paper Additional Materials: Specimen Stimulus Material Book G671 (3 printed pages) Answer Booklet ( pages)

### Monday 12 May 2014 Morning

Monday 12 May 2014 Morning GCSE RELIGIOUS STUDIES B (PHILOSOPHY AND/OR APPLIED ETHICS) B603/01 Ethics 1 (Relationships, Medical Ethics, Poverty and Wealth) *1245022516* Candidates answer on the Answer

### Thursday 13 June 2013 Morning

THIS IS A NEW SPECIFICATION H Thursday 13 June 2013 Morning GCSE TWENTY FIRST CENTURY SCIENCE PHYSICS A A182/02 Modules P4 P5 P6 (Higher Tier) *A137290613* Candidates answer on the Question Paper. A calculator

### Wednesday 20 June 2012 Afternoon

Wednesday 20 June 2012 Afternoon A2 GCE PHYSICAL EDUCATION G453/01 Principles and Concepts Across Different areas of Physical Education *G430780612* Candidates answer on the Answer Booklet. OCR supplied

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education *0123456789* GEOGRAPHY 0460/02 Paper 2 Geographical skills For Examination from 2016 SPECIMEN PAPER

### Wednesday 5 November 2014 Morning

H Wednesday 5 November 2014 Morning GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) * 1 1 8 3 2 9 5 6 3 5 * Candidates answer on the Question Paper. OCR supplied materials: None Other materials required:

### Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education

Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education *3753884750* MATHEMATICS 0580/23 Paper 2 (Extended) May/June 2014 1 hour 30 minutes Candidates answer

### Wednesday 19 June 2013 Afternoon

Wednesday 19 June 2013 Afternoon A2 GCE PHYSICAL EDUCATION G453/01 Principles and Concepts Across Different Areas of Physical Education *G430780613* Candidates answer on the Answer Booklet. OCR supplied

### EdExcel Decision Mathematics 1

EdExcel Decision Mathematics 1 Linear Programming Section 1: Formulating and solving graphically Notes and Examples These notes contain subsections on: Formulating LP problems Solving LP problems Minimisation

### Tuesday 9 June 2015 Morning

Oxford Cambridge and RSA Tuesday 9 June 2015 Morning A2 GCE CLASSICS: CLASSICAL CIVILISATION F388/01 Art and Architecture in the Greek World *5050960752* Candidates answer on the Answer Booklet. OCR supplied

### Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Paper 1 May/June 2014 1 hour 15 minutes

*99598998* Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level APPLIED INFORMATION AND COMMUNICATION TECHNOLOGY 973/ Paper May/June 04 hour 5 minutes Candidates

### UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level ACCOUNTING 9706/04 Paper 4 Problem Solving (Supplementary Topics) For Examination from 2010 SPECIMEN PAPER

### Friday 8 November 2013 Morning

F Friday 8 November 2013 Morning GCSE MATHEMATICS B J567/02 Paper 2 (Foundation Tier) *J517160313* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

### Tuesday 20 May 2014 Morning

Tuesday 20 May 2014 Morning AS GCE PHYSICS B (ADVANCING PHYSICS) G491/01 Physics in Action *1203458796* Candidates answer on the Question Paper. OCR supplied materials: Data, Formulae and Relationships

### Friday 18 January 2013 Morning

Friday 18 January 2013 Morning AS GCE PHYSICS B (ADVANCING PHYSICS) G492/01 Understanding Processes / Experimentation and Data Handling *G411640113* Candidates answer on the Question Paper. OCR supplied

### UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *5473380703* INFORMATION AND COMMUNICATION TECHNOLOGY 0417/22 Paper 2 Practical

### Monday 4 March 2013 Morning

F Monday 4 March 2013 Morning GCSE MATHEMATICS B J567/02 Paper 2 (Foundation Tier) *J533600313* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education FIRST LANGUAGE ENGLISH 0522/01 Paper 1 Reading Passages (Core) For Examination from 2015 SPECIMEN

### Friday 13 June 2014 Morning

H Friday 13 June 2014 Morning GCSE MATHEMATICS B J567/04 Paper 4 (Higher Tier) * 3 0 5 9 4 6 2 0 7 5 * Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

### Chinese postman problem

PTR hinese postman problem Learning objectives fter studying this chapter, you should be able to: understand the hinese postman problem apply an algorithm to solve the problem understand the importance

### Thursday 23 May 2013 Morning

THIS IS A NEW SPECIFICATION H Thursday 23 May 2013 Morning GCSE TWENTY FIRST CENTURY SCIENCE PHYSICS A A181/02 Modules P1 P2 P3 (Higher Tier) *A137270613* Candidates answer on the Question Paper. A calculator

### How To Run Island Fly

*CUP/T47890* ADVANCED GCE APPLIED INFORMATION AND COMMUNICATION TECHNOLOGY Unit 15: Software Development INSTRUCTIONS FOR CANDIDATES JANUARY 2008 Pre-release Materials and Tasks Candidates Instructions

### Monday 11 June 2012 Morning

Monday 11 June 2012 Morning GCSE RELIGIOUS STUDIES B (PHILOSOPHY AND/OR APPLIED ETHICS) B602 Philosophy 2 (Good and Evil, Revelation, Science) *B620050611* Candidates answer on the Answer Booklet. OCR

### GATEWAY SCIENCE B651/01 PHYSICS B Unit 1 Modules P1 P2 P3 (Foundation Tier)

F GENERAL CERTIFICATE OF SECONDARY EDUCATION GATEWAY SCIENCE B651/01 PHYSICS B Unit 1 Modules P1 P2 P3 (Foundation Tier) *CUP/T63931* Candidates answer on the question paper A calculator may be used for

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education. Paper 1 May/June 2014 2 hours

*3483070646* Cambridge International Examinations Cambridge International General Certificate of Secondary Education INFORMATION AND COMMUNICATION TECHNOLOGY 047/ Paper May/June 04 hours Candidates answer

### Monday 11 June 2012 Afternoon

Monday 11 June 2012 Afternoon A2 GCE PHYSICS B (ADVANCING PHYSICS) G495 Field and Particle Pictures *G412090612* Candidates answer on the Question Paper. OCR supplied materials: Data, Formulae and Relationships

### Wednesday 16 January 2013 Afternoon

Wednesday 16 January 2013 Afternoon A2 GCE PHYSICS B (ADVANCING PHYSICS) G494/01 Rise and Fall of the Clockwork Universe *G411660113* Candidates answer on the Question Paper. OCR supplied materials: Data,

### www.xtremepapers.net

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *83455669* INFORMATION AND COMMUNICATION TECHNOLOGY 047/0 Paper May/June 2009 2 hours Candidates

### Data Structures and Algorithms Written Examination

Data Structures and Algorithms Written Examination 22 February 2013 FIRST NAME STUDENT NUMBER LAST NAME SIGNATURE Instructions for students: Write First Name, Last Name, Student Number and Signature where

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education *0123456789* ACCOUNTING 0452/01 Paper 1 For Examination from 2014 SPECIMEN PAPER 1 hour 45 minutes

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education MATHEMATICS 0580/02 Paper 2 (Extended) For Examination from 2015 SPECIMEN PAPER Candidates answer

### RELIGIOUS STUDIES B (PHILOSOPHY AND/OR APPLIED ETHICS) Philosophy 1 (Deity, Religious and Spiritual Experience, End of Life)

GENERAL CERTIFICATE OF SECONDARY EDUCATION RELIGIOUS STUDIES B (PHILOSOPHY AND/OR APPLIED ETHICS) Philosophy 1 (Deity, Religious and Spiritual Experience, End of Life) B601 *OCE/27375* Candidates answer

### Thursday 6 June 2013 Afternoon

Thursday 6 June 2013 Afternoon A2 GCE ENGLISH LITERATURE F663/01/QPI Drama and Poetry pre-1800 (Closed Text) QUESTION PAPER INSERT *F621220613* Duration: 2 hours This is a Closed Text examination. No textbooks

### 3. Evaluate the objective function at each vertex. Put the vertices into a table: Vertex P=3x+2y (0, 0) 0 min (0, 5) 10 (15, 0) 45 (12, 2) 40 Max

SOLUTION OF LINEAR PROGRAMMING PROBLEMS THEOREM 1 If a linear programming problem has a solution, then it must occur at a vertex, or corner point, of the feasible set, S, associated with the problem. Furthermore,

### www.xtremepapers.net

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *6585104589* INFORMATION AND COMMUNICATION TECHNOLOGY 0417/11 Paper 1 May/June 2011 2 hours Candidates

### Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education

Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education *4942783219* MATHEMATICS 0580/32 Paper 3 (Core) May/June 2014 Candidates answer on the Question

### UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level. Paper 3 October/November 2013 1 hour 15 minutes

*739084* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level APPLIED INFORMATION AND COMMUNICATION TECHNOLOGY 973/3 Paper 3 October/November 03 hour 5 minutes

### Monday 11 June 2012 Afternoon

THIS IS A NEW SPECIFICATION H Monday 11 June 2012 Afternoon GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) *J517130612* Candidates answer on the Question Paper. OCR supplied materials: None Other materials

### Thursday 24 January 2013 Morning

Thursday 24 January 2013 Morning A2 GCE ENGLISH LITERATURE F663/01/QPI Drama and Poetry pre-1800 (Closed Text) QUESTION PAPER INSERT *F621150113* Duration: 2 hours This is a Closed Text examination. No

### Wednesday 23 January 2013 Morning

Wednesday 23 January 2013 Morning GCSE HISTORY B (MODERN WORLD) A972/21 British Depth Study, 1890 1918 *A917940113* Candidates answer on the Answer Booklet. OCR supplied materials: 8 page Answer Booklet

### G055/IC. APPLIED INFORMATION AND COMMUNICATION TECHNOLOGY Networking Solutions ADVANCED GCE INSTRUCTIONS FOR CANDIDATES JUNE 2011

ADVANCED GCE APPLIED INFORMATION AND COMMUNICATION TECHNOLOGY Networking Solutions G055/IC *G031150611* INSTRUCTIONS FOR CANDIDATES Pre-release Material and Tasks To be opened on receipt JUNE 2011 INFORMATION

### Special Situations in the Simplex Algorithm

Special Situations in the Simplex Algorithm Degeneracy Consider the linear program: Maximize 2x 1 +x 2 Subject to: 4x 1 +3x 2 12 (1) 4x 1 +x 2 8 (2) 4x 1 +2x 2 8 (3) x 1, x 2 0. We will first apply the

### Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education

Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education *9994985227* MATHEMATICS 0580/33 Paper 3 (Core) May/June 2014 Candidates answer on the Question

### Friday 6 June 2014 Morning

Friday 6 June 2014 Morning A2 GCE ENGLISH LITERATURE F663/01 Drama and Poetry pre-1800 (Closed Text) *1274992149* Candidates answer on the Answer Booklet. OCR supplied materials: 12 page Answer Booklet

### Wednesday 11 June 2014 Afternoon

Wednesday 11 June 2014 Afternoon GCSE RELIGIOUS STUDIES B (PHILOSOPHY AND/OR APPLIED ETHICS) B601/01 Philosophy 1 (Deity, Religious and Spiritual Experience, End of Life) *1244417157* Candidates answer

### Friday 18 September 2015 1.00 PM 3.15 PM Time Allowed: 2 hours 15 minutes

Level 3 Certificate of Professional Competence for Transport Managers (Road Haulage) Unit R2 Case Study 05689 Friday 18 September 2015 1.00 PM 3.15 PM Time Allowed: 2 hours 15 minutes Case Study This document

### Maximum and minimum problems. Information sheet. Think about

Maximum and minimum problems This activity is about using graphs to solve some maximum and minimum problems which occur in industry and in working life. The graphs can be drawn using a graphic calculator

### Linear Programming Problems

Linear Programming Problems Linear programming problems come up in many applications. In a linear programming problem, we have a function, called the objective function, which depends linearly on a number

### SPECIMEN MATHEMATICS B J567/02 GENERAL CERTIFICATE OF SECONDARY EDUCATION. Paper 2 (Foundation Tier) Duration: 1 hour 30 minutes. Candidate Forename

F GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B J567/02 Paper 2 (Foundation Tier) Candidates answer on the Question Paper OCR Supplied Materials: None Other Materials Required: Geometrical instruments

### Monday 21 May 2012 Morning

THIS IS A NEW SPECIFICATION H Monday 21 May 2012 Morning GCSE TWENTY FIRST CENTURY SCIENCE PHYSICS A A182/02 Modules P4 P5 P6 (Higher Tier) *A135280612* Candidates answer on the Question Paper. A calculator

### UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

*1979877211* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education COMPUTER STUDIES 0420/31 Paper 3 Alternative to Coursework October/November 2012

### Approximation Algorithms

Approximation Algorithms or: How I Learned to Stop Worrying and Deal with NP-Completeness Ong Jit Sheng, Jonathan (A0073924B) March, 2012 Overview Key Results (I) General techniques: Greedy algorithms

### Social Media Mining. Graph Essentials

Graph Essentials Graph Basics Measures Graph and Essentials Metrics 2 2 Nodes and Edges A network is a graph nodes, actors, or vertices (plural of vertex) Connections, edges or ties Edge Node Measures

### UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

*9282687787* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education BIOLOGY 0610/21 Paper 2 Core October/November 2012 1 hour 15 minutes Candidates

### THIS IS A NEW SPECIFICATION

THIS IS A NEW SPECIFICATION GENERAL CERTIFICATE OF SECONDARY EDUCATION SOCIOLOGY Socialisation, Culture and Identity B672 * OCE / 117 2 3 * Candidates answer on the Answer Booklet OCR Supplied Materials:

### Cambridge International Examinations Cambridge Primary Checkpoint

Cambridge International Examinations Cambridge Primary Checkpoint ENGLISH 0844/02 Paper 2 For Examination from 2014 SPECIMEN PAPER 1 hour Candidates answer on the Question Paper. Additional Materials:

### G242 G G * * MEI STATISTICS Statistics 2 (Z2) ADVANCED SUBSIDIARY GCE. Wednesday 9 June 2010 Afternoon. Duration: 1 hour 30 minutes.

ADVANCED SUBSIDIARY GCE MEI STATISTICS Statistics 2 (Z2) G242 Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination Formulae and Tables (MF2)

### Study Guide 2 Solutions MATH 111

Study Guide 2 Solutions MATH 111 Having read through the sample test, I wanted to warn everyone, that I might consider asking questions involving inequalities, the absolute value function (as in the suggested

### Outline. NP-completeness. When is a problem easy? When is a problem hard? Today. Euler Circuits

Outline NP-completeness Examples of Easy vs. Hard problems Euler circuit vs. Hamiltonian circuit Shortest Path vs. Longest Path 2-pairs sum vs. general Subset Sum Reducing one problem to another Clique

### Monday 19 May 2014 Afternoon

Monday 19 May 2014 Afternoon AS GCE APPLIED BUSINESS F242/01/CS Understanding the Business Environment CASE STUDY *3230488360* Duration: 1 hour 30 minutes INFORMATION FOR CANDIDATES This is a clean copy

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level *0123456789* PHYSICS 9702/02 Paper 2 AS Level Structured Questions For Examination from 2016 SPECIMEN

### IE 680 Special Topics in Production Systems: Networks, Routing and Logistics*

IE 680 Special Topics in Production Systems: Networks, Routing and Logistics* Rakesh Nagi Department of Industrial Engineering University at Buffalo (SUNY) *Lecture notes from Network Flows by Ahuja, Magnanti

### UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Primary Checkpoint

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Primary Checkpoint SCIENCE 0846/02 Paper 2 Examination from 2012 SPECIMEN PAPER Candidates answer on the Question Paper. Additional Materials:

### THIS IS A NEW SPECIFICATION. This is a Closed Text examination. No textbooks or sources of information are allowed in the examination room.

THIS IS A NEW SPECIFICATION ADVANCED GCE ENGLISH LITERATURE Drama and Poetry pre-1800 (Closed Text) F663 * OCE / 1 9 2 98* Candidates answer on the Answer Booklet OCR Supplied Materials: 16 page Answer

### Cambridge International Examinations Cambridge Secondary 1 Checkpoint

Cambridge International Examinations Cambridge Secondary 1 Checkpoint SCIENCE 1113/02 Paper 2 For Examination from 2014 SPECIMEN PAPER Candidates answer on the Question Paper. Additional Materials: Pen

### GCSE Mathematics A. Mark Scheme for June 2014. Unit A501/02: Mathematics A (Higher Tier) General Certificate of Secondary Education

GCSE Mathematics A Unit A50/0: Mathematics A (Higher Tier) General Certificate of Secondary Education Mark Scheme for June 04 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading

### www.xtremepapers.net

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *6746873383* INFORMATION AND COMMUNICATION TECHNOLOGY 047/ Paper October/November 00 hours Candidates

### Chapter 10: Network Flow Programming

Chapter 10: Network Flow Programming Linear programming, that amazingly useful technique, is about to resurface: many network problems are actually just special forms of linear programs! This includes,

### CSE 326, Data Structures. Sample Final Exam. Problem Max Points Score 1 14 (2x7) 2 18 (3x6) 3 4 4 7 5 9 6 16 7 8 8 4 9 8 10 4 Total 92.

Name: Email ID: CSE 326, Data Structures Section: Sample Final Exam Instructions: The exam is closed book, closed notes. Unless otherwise stated, N denotes the number of elements in the data structure

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education *0123456789* INFORMATION AND COMMUNICATION TECHNOLOGY 0417/01 Paper 1 Theory For Examination from

### Practical Guide to the Simplex Method of Linear Programming

Practical Guide to the Simplex Method of Linear Programming Marcel Oliver Revised: April, 0 The basic steps of the simplex algorithm Step : Write the linear programming problem in standard form Linear