CHEM4. General Certificate of Education Advanced Level Examination January Unit 4 Kinetics, Equilibria and Organic Chemistry

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "CHEM4. General Certificate of Education Advanced Level Examination January 2010. Unit 4 Kinetics, Equilibria and Organic Chemistry"

Transcript

1 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination January 2010 Question 1 2 Mark Chemistry Unit 4 Kinetics, Equilibria and Organic Chemistry Wednesday 27 January am to am For this paper you must have: the Periodic Table/Data Sheet provided as an insert (enclosed) a calculator. Time allowed 1 hour 45 minutes CEM TOTAL Instructions Use black ink or black ball-point pen. Fill in the boxes at the top of this page. Answer all questions. You must answer the questions in the spaces provided. Answers written in margins or on blank pages will not be marked. All working must be shown. Do all rough work in this book. Cross through any work you do not want to be marked. Information The marks for questions are shown in brackets. The maximum mark for this paper is 100. The Periodic Table/Data Sheet is provided as an insert. Your answers to the questions in Section B should be written in continuous prose, where appropriate. You will be marked on your ability to: use good English organise information clearly use accurate scientific terminology. Advice You are advised to spend about 70 minutes on Section A and about 35 minutes on Section B. (JAN10CEM401) CEM4

2 2 SECTION A Answer all questions in the spaces provided. 1 A mixture was prepared using 1.00 mol of propanoic acid, 2.00 mol of ethanol and 5.00 mol of water. At a given temperature, the mixture was left to reach equilibrium according to the following equation. C 3 C 2 COO + C 3 C 2 O C 3 C 2 COOC 2 C O = 22 kj mol 1 The equilibrium mixture contained 0.54 mol of the ester ethyl propanoate. 1 (a) (i) Calculate the amounts, in moles, of propanoic acid, of ethanol and of water in this equilibrium mixture. Moles of propanoic acid... Moles of ethanol... Moles of water... (3 marks) 1 (a) (ii) Write an expression for the equilibrium constant, K c, for this equilibrium. 1 (a) (iii) Calculate a value for K c for this equilibrium at this temperature. Explain why this K c value has no units. Calculation... Explanation... (3 marks) (Extra space)... (02)

3 3 1 (b) For this equilibrium, predict the effect of an increase in temperature on each of the following. 1 (b) (i) the amount, in moles, of ester at equilibrium 1 (b) (ii) the time taken to reach equilibrium 1 (b) (iii) the value of K c 10 Turn over for the next question Turn over (03)

4 2 In this question, give all values of p to 2 decimal places. 2 (a) (i) Write an expression for the term p. 4 2 (a) (ii) Calculate the concentration, in mol dm 3, of an aqueous solution of sulfuric acid that has a p of (b) A student carried out a titration by adding an aqueous solution of sodium hydroxide from a burette to an aqueous solution of ethanoic acid. The end-point was reached when cm 3 of the sodium hydroxide solution had been added to cm 3 of mol dm 3 ethanoic acid. 2 (b) (i) Write an equation for the reaction between sodium hydroxide and ethanoic acid. 2 (b) (ii) Calculate the concentration, in mol dm 3, of the sodium hydroxide solution used. (04)

5 2 (b) (iii) A list of indicators is shown below. 5 Indicator p range thymol blue bromophenol blue litmus cresol purple Select from the list the most suitable indicator for the end-point of this titration. 2 (b) (iv) Suggest why the concentration of sodium hydroxide in a solution slowly decreases when left open to air. 2 (c) At 298 K, the value of the acid dissociation constant, K a, for ethanoic acid in aqueous solution is mol dm 3 2 (c) (i) Write an expression for the acid dissociation constant, K a, for ethanoic acid. 2 (c) (ii) Calculate the p of mol dm 3 ethanoic acid at this temperature. (3 marks) (Extra space)... Question 2 continues on the next page Turn over (05)

6 6 2 (c) (iii) Calculate the p of the buffer solution formed when cm 3 of mol dm 3 potassium hydroxide are added to cm 3 of mol dm 3 ethanoic acid. (6 marks) (Extra space) (06)

7 7 There are no questions printed on this page DO NOT WRITE ON TIS PAGE ANSWER IN TE SPACES PROVIDED Turn over (07)

8 8 3 Propanone and iodine react in acidic conditions according to the following equation. C 3 COC 3 + I 2 IC 2 COC 3 + I A student studied the kinetics of this reaction using hydrochloric acid and a solution containing propanone and iodine. From the results the following rate equation was deduced. rate = k[c 3 COC 3 ][ + ] 3 (a) Give the overall order for this reaction (b) When the initial concentrations of the reactants were as shown in the table below, the initial rate of reaction was found to be mol dm 3 s 1. initial concentration / mol dm 3 C 3 COC I Use these data to calculate a value for the rate constant, k, for the reaction and give its units. Calculation Units (3 marks) 3 (c) Deduce how the initial rate of reaction changes when the concentration of iodine is doubled but the concentrations of propanone and of hydrochloric acid are unchanged.... (08)

9 9 3 (d) The following mechanism for the overall reaction has been proposed. Step 1 C 3 COC C + C O C 3 Step 2 C + C O C 3 C C C O C 3 Step 3 C C C 3 + I 2 IC 2 C + I O O + Step 4 IC 2 C O O + C 3 IC 2 C C Use the rate equation to suggest which of the four steps could be the rate-determining step. Explain your answer. Rate-determining step... Explanation (e) Use your understanding of reaction mechanisms to predict a mechanism for Step 2 by adding one or more curly arrows as necessary to the structure of the carbocation below. Step 2 C + C O C 3 C C C O 8 Turn over (09)

10 10 4 Two isomeric ketones are shown below. C 3 C C 2 C 2 C 3 C 3 C 2 C C 2 C 3 O O Q R 4 (a) Name and outline a mechanism for the reaction of compound Q with CN and name the product formed. Name of mechanism... Mechanism Name of product... (6 marks) (10)

11 11 4 (b) Some students were asked to suggest methods to distinguish between isomers Q and R. One student suggested testing the optical activity of the products formed when Q and R were reacted separately with CN. By considering the optical activity of these products formed from Q and R, explain why this method would not distinguish between Q and R (3 marks) (Extra space) (c) Other students suggested using mass spectrometry and the fragmentation patterns of the molecular ions of the two isomers to distinguish between them. They predicted that only one of the isomers would have a major peak at m/z = 57 in its mass spectrum so that this method would distinguish between Q and R. 4 (c) (i) Identify the isomer that has a major peak at m/z = 57 in its mass spectrum. 4 (c) (ii) Write an equation for the fragmentation of the molecular ion of this isomer to form the species that produces the peak at m/z = (c) (iii) Predict the m/z value of a major peak in the mass spectrum of the other isomer. 13 Turn over (11)

12 12 5 The triester, T, shown below is found in palm oil. When T is heated with an excess of sodium hydroxide solution, the alcohol glycerol is formed together with a mixture of three other products as shown in the following equation. C 2 OOC(C 2 ) 14 C 3 C 2 O COOC(C 2 ) 7 C=C(C 2 ) 7 C 3 + 3NaO CO + C 2 OOC(C 2 ) 12 C 3 C 2 O T glycerol C 3 (C 2 ) 14 COONa + C 3 (C 2 ) 7 C=C(C 2 ) 7 COONa + C 3 (C 2 ) 12 COONa 5 (a) (i) Give the IUPAC name for glycerol. 5 (a) (ii) Give a use for the mixture of sodium salts formed in this reaction. 5 (b) When T is heated with an excess of methanol, glycerol is formed together with a mixture of methyl esters. 5 (b) (i) Give a use for this mixture of methyl esters. 5 (b) (ii) One of the methyl esters in the mixture has the IUPAC name methyl (Z)-octadec-9-enoate. Draw two hydrogen atoms on the diagram below to illustrate the meaning of the letter Z in the name of this ester. C C (12)

13 13 5 (b) (iii) One of the other methyl esters in the mixture has the formula C 3 (C 2 ) 12 COOC 3 Write an equation for the complete combustion of one molecule of this ester. 5 Turn over for the next question Turn over (13)

14 14 6 The three amino acids shown below were obtained by hydrolysis of a protein. 2 N C COO 2 N C COO 2 N C COO C 3 alanine C(C 3 ) 2 valine C 2 (C 2 ) 3 N 2 lysine 6 (a) (i) Draw the zwitterion of alanine. 6 (a) (ii) Draw the species formed when valine is dissolved in an alkaline solution. 6 (a) (iii) Draw the species formed by lysine at low p. (14)

15 15 6 (b) Draw the two dipeptides formed by the reaction of alanine with valine. 6 (c) Name a suitable method by which the mixture of amino acids formed by hydrolysis of the protein can be separated Turn over for the next question Turn over (15)

16 16 7 Organic chemists use a variety of methods to identify unknown compounds. When the molecular formula of a compound is known, spectroscopic and other analytical techniques are used to distinguish between possible structural isomers. Use your knowledge of such techniques to identify the compounds described below. Use the three tables of spectral data on the Data Sheet where appropriate. Each part below concerns a different pair of structural isomers. Draw one possible structure for each of the compounds A to J, described below. 7 (a) Compounds A and B have the molecular formula C 3 6 O A has an absorption at 1715 cm 1 in its infrared spectrum and has only one peak in its n.m.r. spectrum. B has absorptions at 3300 cm 1 and at 1645 cm 1 in its infrared spectrum and does not show E Z isomerism. A B 7 (b) Compounds C and D have the molecular formula C 5 12 In their 1 n.m.r. spectra, C has three peaks and D has only one. C D (16)

17 17 7 (c) Compounds E and F are both esters with the molecular formula C 4 8 O 2 In their 1 n.m.r. spectra, E has a quartet at δ = 2.3 ppm and F has a quartet at δ = 4.1 ppm. E F 7 (d) Compounds G and have the molecular formula C 6 12 O Each exists as a pair of optical isomers and each has an absorption at about 1700 cm 1 in its infrared spectrum. G forms a silver mirror with Tollens reagent but does not. G 7 (e) Compounds I and J have the molecular formula C 4 11 N and both are secondary amines. In their 13 C n.m.r. spectra, I has two peaks and J has three. I J 10 Turn over (17)

18 18 SECTION B Answer all questions in the spaces provided. 8 Three isomers of C 6 4 (NO 2 ) 2 are shown below. NO 2 NO 2 NO 2 NO 2 NO 2 W X NO 2 Y 8 (a) (i) Give the number of peaks in the 13 C n.m.r. spectrum of each isomer. (3 marks) 8 (a) (ii) Draw the displayed formula of the compound used as a standard in recording these spectra. (18)

19 19 8 (b) Isomer X is prepared from nitrobenzene by reaction with a mixture of concentrated nitric acid and concentrated sulfuric acid. The two acids react to form an inorganic species that reacts with nitrobenzene to form X. 8 (b) (i) Give the formula of this inorganic species formed from the two acids and write an equation to show its formation. 8 (b) (ii) Name and outline a mechanism for the reaction of this inorganic species with nitrobenzene to form X. (4 marks) Question 8 continues on the next page Turn over (19)

20 8 (c) Isomer Y is used in the production of the polymer Kevlar. Y is first reduced to the diamine shown below N N 2 8 (c) (i) Identify a suitable reagent or mixture of reagents for the reduction of Y to form this diamine. Write an equation for this reaction using [] to represent the reducing agent. 8 (c) (ii) This diamine is then reacted with benzene-l,4-dicarboxylic acid to form Kevlar. Draw the repeating unit of Kevlar. (20)

21 21 8 (c) (iii) Kevlar can be used as the inner lining of bicycle tyres. The rubber used for the outer part of the tyre is made of polymerised alkenes. State the difference in the biodegradability of Kevlar compared to that of rubber made of polymerised alkenes. Use your knowledge of the bonding in these polymer molecules to explain this difference. (4 marks) (Extra space) Turn over for the next question Turn over (21)

22 22 9 (a) Name and outline a mechanism for the reaction of C 3 C 2 N 2 with C 3 C 2 COCl Name the amide formed. (6 marks) (22)

23 9 (b) aloalkanes such as C 3 Cl are used in organic synthesis. 23 Outline a three-step synthesis of C 3 C 2 N 2 starting from methane. Your first step should involve the formation of C 3 Cl In your answer, identify the product of the second step and give the reagents and conditions for each step. Equations and mechanisms are not required (6 marks) (Extra space) END OF QUESTIONS (23)

24 24 There are no questions printed on this page DO NOT WRITE ON TIS PAGE ANSWER IN TE SPACES PROVIDED Copyright 2010 AQA and its licensors. All rights reserved. (24)

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.

Διαβάστε περισσότερα

Unit 4 Further Physical and Organic Chemistry

Unit 4 Further Physical and Organic Chemistry Surname Other Names Leave blank Centre Number Candidate Number Candidate Signature General Certificate of Education January 2002 Advanced Level Examination CHEMISTRY Unit 4 Further Physical and Organic

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: Understanding and Written Response

Advanced Subsidiary Unit 1: Understanding and Written Response Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes

Διαβάστε περισσότερα

CHEM5. General Certificate of Education Advanced Level Examination June 2011. Unit 5 Energetics, Redox and Inorganic Chemistry

CHEM5. General Certificate of Education Advanced Level Examination June 2011. Unit 5 Energetics, Redox and Inorganic Chemistry Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination June 2011 Question 1 2 Mark Chemistry

Διαβάστε περισσότερα

CH 3 CH 2 COOCH 2 CH 2 CH 3 + H 2 O

CH 3 CH 2 COOCH 2 CH 2 CH 3 + H 2 O Q1.An experiment was carried out to determine the equilibrium constant, K c, for the following reaction. CH 3 CH 2 COOH + CH 3 CH 2 CH 2 OH CH 3 CH 2 COOCH 2 CH 2 CH 3 + H 2 O A student added measured

Διαβάστε περισσότερα

PHYA1. General Certificate of Education Advanced Subsidiary Examination June 2012. Particles, Quantum Phenomena and Electricity

PHYA1. General Certificate of Education Advanced Subsidiary Examination June 2012. Particles, Quantum Phenomena and Electricity Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Centre No. Candidate No. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Materials required for examination Nil Paper Reference

Διαβάστε περισσότερα

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *2517291414* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2013 1 hour 30 minutes

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes

Paper Reference. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced Thursday 11 June 2009 Morning Time: 1 hour 30 minutes Materials required for examination Mathematical Formulae

Διαβάστε περισσότερα

CHEM5 (JUN15CHEM501) General Certificate of Education Advanced Level Examination June 2015. Energetics, Redox and Inorganic Chemistry

CHEM5 (JUN15CHEM501) General Certificate of Education Advanced Level Examination June 2015. Energetics, Redox and Inorganic Chemistry Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination June 2015 Question 1 2 Mark Chemistry

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

CH3HP. (Jun13CH3HP01) General Certificate of Secondary Education Higher Tier June 2013. Unit Chemistry C3. Written Paper TOTAL. Time allowed 1 hour

CH3HP. (Jun13CH3HP01) General Certificate of Secondary Education Higher Tier June 2013. Unit Chemistry C3. Written Paper TOTAL. Time allowed 1 hour Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Chemistry General Certificate of Secondary Education igher Tier June 2013 C3P Question 1 2

Διαβάστε περισσότερα

PHYA1 (JAN12PHYA101) General Certificate of Education Advanced Subsidiary Examination January 2012. Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JAN12PHYA101) General Certificate of Education Advanced Subsidiary Examination January 2012. Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

Figure 1 T / K Explain, in terms of molecules, why the first part of the graph in Figure 1 is a line that slopes up from the origin.

Figure 1 T / K Explain, in terms of molecules, why the first part of the graph in Figure 1 is a line that slopes up from the origin. Q1.(a) Figure 1 shows how the entropy of a molecular substance X varies with temperature. Figure 1 T / K (i) Explain, in terms of molecules, why the entropy is zero when the temperature is zero Kelvin.

Διαβάστε περισσότερα

Br, is used in the production of polymers.

Br, is used in the production of polymers. 1 Allyl bromide, =CH Br, is used in the production of polymers. (a) Part of the C=C double bond in allyl bromide is called a π-bond. Draw a labelled diagram to show the formation of the π-bond. [2] (b)

Διαβάστε περισσότερα

Modern Greek Extension

Modern Greek Extension Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write

Διαβάστε περισσότερα

*2354431106* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2009

*2354431106* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2009 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *2354431106* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2009 1 hour 30 minutes

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education GREEK 0543/04 Paper 4 Writing For Examination from 2015 SPECIMEN PAPER Candidates answer on the Question

Διαβάστε περισσότερα

Nuclear Physics 5. Name: Date: 8 (1)

Nuclear Physics 5. Name: Date: 8 (1) Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly

Διαβάστε περισσότερα

CHEM5. (JUN13CHEM501) WMP/Jun13/CHEM5. General Certificate of Education Advanced Level Examination June 2013

CHEM5. (JUN13CHEM501) WMP/Jun13/CHEM5. General Certificate of Education Advanced Level Examination June 2013 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination June 2013 Question 1 2 Mark Chemistry

Διαβάστε περισσότερα

Enthalpy data for the reacting species are given in the table below. The activation energy decreases when the temperature is increased.

Enthalpy data for the reacting species are given in the table below. The activation energy decreases when the temperature is increased. Q1.This question is about the reaction given below. O(g) + H 2O(g) O 2(g) + H 2(g) Enthalpy data for the reacting species are given in the table below. Substance O(g) H 2O(g) O 2(g) H 2(g) ΔH / kj mol

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education *4358398658* GREEK 0543/04 Paper 4 Writing May/June 2015 1 hour Candidates answer on the Question

Διαβάστε περισσότερα

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level * 6 3 1 7 7 7 6 4 0 6 * MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 October/November 2013 Candidates answer

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education *8175930111* GREEK 0543/04 Paper 4 Writing May/June 2017 1 hour Candidates answer on the Question

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education *1880009435* GREEK 0543/04 Paper 4 Writing May/June 2018 1 hour Candidates answer on the Question

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding

Paper Reference. Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Centre No. Candidate No. Paper Reference 1 7 7 6 0 1 Surname Signature Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Thursday 24 May 2007 Morning Time: 45 minutes

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education *3148288373* GREEK 0543/04 Paper 4 Writing May/June 2016 1 hour Candidates answer on the Question

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

PHYA1 (JUN13PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2013. Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JUN13PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2013. Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level * 0 5 1 0 3 4 8 7 8 5 * MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 May/June 2013 Candidates answer on the

Διαβάστε περισσότερα

Tuesday 13 June 2017 Afternoon

Tuesday 13 June 2017 Afternoon Oxford Cambridge and RSA Tuesday 13 June 2017 Afternoon A2 GCE CHEMISTRY A F324/01 Rings, Polymers and Analysis *6765314342* Candidates answer on the Question Paper. OCR supplied materials: Data Sheet

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding

Paper Reference. Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Centre No. Candidate No. Paper Reference 1 7 7 6 0 1 Surname Signature Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Friday 18 June 2010 Morning Time: 45 minutes

Διαβάστε περισσότερα

Paper Reference. Modern Greek Paper 1 Listening and Responding. Friday 15 May 2009 Afternoon Time: 45 minutes (+5 minutes reading time)

Paper Reference. Modern Greek Paper 1 Listening and Responding. Friday 15 May 2009 Afternoon Time: 45 minutes (+5 minutes reading time) Centre No. Candidate No. Paper Reference 1 7 7 6 0 1 Surname Signature Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Friday 15 May 2009 Afternoon Time: 45 minutes

Διαβάστε περισσότερα

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

The table shows some standard enthalpy of formation data.

The table shows some standard enthalpy of formation data. Q1.Vanadium is an important metal. Ferrovanadium, an alloy of iron and vanadium, is used to make a strong type of vanadium-steel. Pure vanadium is used in nuclear reactors. (a) The table shows some standard

Διαβάστε περισσότερα

PHYA1 (JAN13PHYA101) General Certificate of Education Advanced Subsidiary Examination January Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JAN13PHYA101) General Certificate of Education Advanced Subsidiary Examination January Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Section 1: Listening and Responding/ Aκουστική εξέταση Στο πρώτο μέρος της

Διαβάστε περισσότερα

43603H. (NOV1243603H01) WMP/Nov12/43603H. General Certificate of Secondary Education Higher Tier November 2012. Unit 3 10 11 H

43603H. (NOV1243603H01) WMP/Nov12/43603H. General Certificate of Secondary Education Higher Tier November 2012. Unit 3 10 11 H Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier November 2012 Pages 3 4 5 Mark Mathematics

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3) Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)

Διαβάστε περισσότερα

Advanced Unit 2: Understanding, Written Response and Research

Advanced Unit 2: Understanding, Written Response and Research Write your name here Surname Other names Edexcel GCE Centre Number Candidate Number Greek Advanced Unit 2: Understanding, Written Response and Research Thursday 9 June 2011 Morning Time: 3 hours Paper

Διαβάστε περισσότερα

Monday 14 January 2013 Afternoon

Monday 14 January 2013 Afternoon Monday 14 January 2013 Afternoon A2 GE EMISTRY A F324/01 Rings, Polymers and Analysis *F314460113* andidates answer on the Question Paper. R supplied materials: Data Sheet for hemistry A (inserted) ther

Διαβάστε περισσότερα

CHEM2. (JAN13CHEM201) WMP/Jan13/CHEM2. General Certificate of Education Advanced Subsidiary Examination January Unit 2 Chemistry in Action PMT

CHEM2. (JAN13CHEM201) WMP/Jan13/CHEM2. General Certificate of Education Advanced Subsidiary Examination January Unit 2 Chemistry in Action PMT Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Subsidiary Examination January 2013 Question 1 2

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

PHYA4/2. (JUN14PHYA4201) WMP/Jun14/PHYA4/2/E4. General Certificate of Education Advanced Level Examination June 2014

PHYA4/2. (JUN14PHYA4201) WMP/Jun14/PHYA4/2/E4. General Certificate of Education Advanced Level Examination June 2014 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A General Certificate of Education Advanced Level Examination June 2014 PHYA4/2 Question

Διαβάστε περισσότερα

Candidate Number. In addition to this paper you will require: a calculator. Number

Candidate Number. In addition to this paper you will require: a calculator. Number Surname Other Names Leave blank Centre Number Candidate Number Candidate Signature General Certificate of Education January 2005 Advanced Level Examination CHEMISTRY Unit 4 Further Physical and Organic

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

F324. CHEMISTRY A Rings, Polymers and Analysis ADVANCED GCE. Friday 24 June 2011 Morning. Duration: 1 hour

F324. CHEMISTRY A Rings, Polymers and Analysis ADVANCED GCE. Friday 24 June 2011 Morning. Duration: 1 hour ADVANCED GCE CHEMISTRY A Rings, Polymers and Analysis F324 *F318640611* Candidates answer on the question paper. OCR supplied materials: Data Sheet for Chemistry A (inserted) Other materials required:

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 7615/01 London Examinations GCE Modern Greek Ordinary Level. Friday 14 May 2010 Afternoon Time: 3 hours

Paper Reference. Paper Reference(s) 7615/01 London Examinations GCE Modern Greek Ordinary Level. Friday 14 May 2010 Afternoon Time: 3 hours Centre No. Candidate No. Paper Reference 7 6 1 5 0 1 Surname Signature Paper Reference(s) 7615/01 London Examinations GCE Modern Greek Ordinary Level Friday 14 May 2010 Afternoon Time: 3 hours Initial(s)

Διαβάστε περισσότερα

Candidate Number. General Certificate of Secondary Education Higher Tier November 2013

Candidate Number. General Certificate of Secondary Education Higher Tier November 2013 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Pages Mark General Certificate of Secondary Education Higher Tier November 2013 3 4 5 Mathematics

Διαβάστε περισσότερα

physicsandmathstutor.com Paper Reference Core Mathematics C4 Advanced Level Tuesday 23 January 2007 Afternoon Time: 1 hour 30 minutes

physicsandmathstutor.com Paper Reference Core Mathematics C4 Advanced Level Tuesday 23 January 2007 Afternoon Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference(s) 6666/01 Edexcel GCE Core Mathematics C4 Advanced Level Tuesday 23 January 2007 Afternoon Time: 1 hour 30 minutes Materials required for examination Mathematical

Διαβάστε περισσότερα

Code Breaker. TEACHER s NOTES

Code Breaker. TEACHER s NOTES TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,

Διαβάστε περισσότερα

1999 MODERN GREEK 2 UNIT Z

1999 MODERN GREEK 2 UNIT Z STUDENT NUMBER CENTRE NUMBER HIGHER SCHOOL CERTIFICATE EXAMINATION 1999 MODERN GREEK 2 UNIT Z (55 Marks) Time allowed Two hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Write your Student

Διαβάστε περισσότερα

Paper Reference R. Statistics S1 Advanced/Advanced Subsidiary. Tuesday 10 June 2014 Morning Time: 1 hour 30 minutes

Paper Reference R. Statistics S1 Advanced/Advanced Subsidiary. Tuesday 10 June 2014 Morning Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference(s) 6683/01R Edexcel GCE Statistics S1 Advanced/Advanced Subsidiary Tuesday 10 June 2014 Morning Time: 1 hour 30 minutes Materials required for examination Mathematical

Διαβάστε περισσότερα

Physics (Specification A & B) PHY6T/Q11/test

Physics (Specification A & B) PHY6T/Q11/test Centre Number Surname Candidate Signature Candidate Number Other Names Notice to Candidate. The work you submit for assessment must be your own. If you copy from someone else or allow another candidate

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

Wednesday 19 June 2013 Morning

Wednesday 19 June 2013 Morning Wednesday 19 June 2013 Morning A2 GE EMISTRY A F324/01 Rings, Polymers and Analysis *F314730613* andidates answer on the Question Paper. R supplied materials: Data Sheet for hemistry A (inserted) ther

Διαβάστε περισσότερα

Advanced Unit 2: Understanding, Written Response and Research

Advanced Unit 2: Understanding, Written Response and Research Write your name here Surname Other names Edexcel GCE Centre Number Candidate Number Greek Advanced Unit 2: Understanding, Written Response and Research Tuesday 18 June 2013 Afternoon Time: 3 hours Paper

Διαβάστε περισσότερα

Core Mathematics C34

Core Mathematics C34 Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C34 Advanced Tuesday 21 June 2016 Morning Time: 2 hours 30 minutes

Διαβάστε περισσότερα

THIS IS A NEW SPECIFICATION

THIS IS A NEW SPECIFICATION TIS IS A EW SPEIFIATI ADVAED GE EMISTRY A Rings, Polymers and Analysis F324 * E / 1 5371* andidates answer on the Question Paper R Supplied Materials: Data Sheet for hemistry A (inserted) ther Materials

Διαβάστε περισσότερα

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0. DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec

Διαβάστε περισσότερα

Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) sin - 11π 1 1) + - + - - ) sin 11π 1 ) ( -

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011 Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

Wednesday 12 June 2013 Afternoon

Wednesday 12 June 2013 Afternoon Wednesday 12 June 2013 Afternoon A2 GCE CHEMISTRY A F325/01 Equilibria, Energetics and Elements *F314750613* Candidates answer on the Question Paper. OCR supplied materials: Data Sheet for Chemistry A

Διαβάστε περισσότερα

Correction Table for an Alcoholometer Calibrated at 20 o C

Correction Table for an Alcoholometer Calibrated at 20 o C An alcoholometer is a device that measures the concentration of ethanol in a water-ethanol mixture (often in units of %abv percent alcohol by volume). The depth to which an alcoholometer sinks in a water-ethanol

Διαβάστε περισσότερα

Candidate Number. General Certificate of Education Advanced Level Examination June 2010

Candidate Number. General Certificate of Education Advanced Level Examination June 2010 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination June 2010 Question 1 2 Mark Physics

Διαβάστε περισσότερα

Advanced Unit 2: Understanding, Written Response and Research

Advanced Unit 2: Understanding, Written Response and Research Write your name here Surname Other names Pearson Edexcel GCE Centre Number Candidate Number Greek Advanced Unit 2: Understanding, Written Response and Research Thursday 11 June 2015 Afternoon Time: 3 hours

Διαβάστε περισσότερα

F324. CHEMISTRY A Rings, Polymers and Analysis ADVANCED GCE. Wednesday 26 January 2011 Morning. Duration: 1 hour

F324. CHEMISTRY A Rings, Polymers and Analysis ADVANCED GCE. Wednesday 26 January 2011 Morning. Duration: 1 hour ADVANCED GCE CHEMISTRY A Rings, Polymers and Analysis F324 *CE/25761* Candidates answer on the question paper. CR supplied materials: Data Sheet for Chemistry A (inserted) ther materials required: Scientific

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8  questions or comments to Dan Fetter 1 Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test

Διαβάστε περισσότερα

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού)

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Προσδοκώμενα αποτελέσματα Περιεχόμενο Ενδεικτικές δραστηριότητες

Διαβάστε περισσότερα

2 Answer all the questions.

2 Answer all the questions. 2 Answer all the questions. 1 Lattice enthalpy can be used as a measure of ionic bond strength. Lattice enthalpies are determined indirectly using an enthalpy cycle called a Born Haber cycle. The table

Διαβάστε περισσότερα

, are amongst the easiest enthalpy changes to determine directly.... [2]

, are amongst the easiest enthalpy changes to determine directly.... [2] 1 Enthalpy changes of combustion, Δ c, are amongst the easiest enthalpy changes to determine directly. (a) Define the term enthalpy change of combustion.. [2] (b) A student carried out an experiment to

Διαβάστε περισσότερα

Unit 4 Further Physical and Organic Chemistry

Unit 4 Further Physical and Organic Chemistry Surname Other Names Leave blank Centre Number Candidate Number Candidate Signature General Certificate of Education January 2003 Advanced Level Examination CHEMISTRY Unit 4 Further Physical and Organic

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3

Διαβάστε περισσότερα

Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is

Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is Volume of a Cuboid The formula for the volume of a cuboid is Volume = length x breadth x height V = l x b x h Example Work out the volume of this cuboid 10 cm 15 cm V = l x b x h V = 15 x 6 x 10 V = 900cm³

Διαβάστε περισσότερα

Copper-catalyzed formal O-H insertion reaction of α-diazo-1,3-dicarb- onyl compounds to carboxylic acids with the assistance of isocyanide

Copper-catalyzed formal O-H insertion reaction of α-diazo-1,3-dicarb- onyl compounds to carboxylic acids with the assistance of isocyanide Electronic Supplementary Material (ESI) for ChemComm. This journal is The Royal Society of Chemistry 2014 Copper-catalyzed formal O-H insertion reaction of α-diazo-1,3-dicarb- onyl compounds to carboxylic

Διαβάστε περισσότερα

( ) 2 and compare to M.

( ) 2 and compare to M. Problems and Solutions for Section 4.2 4.9 through 4.33) 4.9 Calculate the square root of the matrix 3!0 M!0 8 Hint: Let M / 2 a!b ; calculate M / 2!b c ) 2 and compare to M. Solution: Given: 3!0 M!0 8

Διαβάστε περισσότερα

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1. Exercises 0 More exercises are available in Elementary Differential Equations. If you have a problem to solve any of them, feel free to come to office hour. Problem Find a fundamental matrix of the given

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: The Core Principles of Chemistry

Advanced Subsidiary Unit 1: The Core Principles of Chemistry Write your name here Surname Other names Edexcel GCE Centre Number Chemistry Advanced Subsidiary Unit 1: The Core Principles of Chemistry Candidate Number Wednesday 3 June 2009 Morning Time: 1 hour 15

Διαβάστε περισσότερα

Advanced Subsidiary Paper 1: Understanding and Written Response. Wednesday 24 January 2018 Morning Time: 2 hours 30 minutes

Advanced Subsidiary Paper 1: Understanding and Written Response. Wednesday 24 January 2018 Morning Time: 2 hours 30 minutes Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Greek Advanced Subsidiary Paper 1: Understanding and Written Response Wednesday 24 January

Διαβάστε περισσότερα

UNIVERSITY OF CALIFORNIA. EECS 150 Fall ) You are implementing an 4:1 Multiplexer that has the following specifications:

UNIVERSITY OF CALIFORNIA. EECS 150 Fall ) You are implementing an 4:1 Multiplexer that has the following specifications: UNIVERSITY OF CALIFORNIA Department of Electrical Engineering and Computer Sciences EECS 150 Fall 2001 Prof. Subramanian Midterm II 1) You are implementing an 4:1 Multiplexer that has the following specifications:

Διαβάστε περισσότερα

C.S. 430 Assignment 6, Sample Solutions

C.S. 430 Assignment 6, Sample Solutions C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order

Διαβάστε περισσότερα

Η ΕΠΙΔΡΑΣΗ ΤΗΣ ΑΙΘΑΝΟΛΗΣ,ΤΗΣ ΜΕΘΑΝΟΛΗΣ ΚΑΙ ΤΟΥ ΑΙΘΥΛΟΤΡΙΤΟΤΑΓΗ ΒΟΥΤΥΛΑΙΘΕΡΑ ΣΤΙΣ ΙΔΙΟΤΗΤΕΣ ΤΗΣ ΒΕΝΖΙΝΗΣ

Η ΕΠΙΔΡΑΣΗ ΤΗΣ ΑΙΘΑΝΟΛΗΣ,ΤΗΣ ΜΕΘΑΝΟΛΗΣ ΚΑΙ ΤΟΥ ΑΙΘΥΛΟΤΡΙΤΟΤΑΓΗ ΒΟΥΤΥΛΑΙΘΕΡΑ ΣΤΙΣ ΙΔΙΟΤΗΤΕΣ ΤΗΣ ΒΕΝΖΙΝΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΑΒΑΛΑΣ ΣΧΟΛΗ ΤΕΧΝΟΛΟΓΙΚΩΝ ΕΦΑΡΜΟΓΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Η ΕΠΙΔΡΑΣΗ ΤΗΣ ΑΙΘΑΝΟΛΗΣ,ΤΗΣ ΜΕΘΑΝΟΛΗΣ ΚΑΙ ΤΟΥ ΑΙΘΥΛΟΤΡΙΤΟΤΑΓΗ ΒΟΥΤΥΛΑΙΘΕΡΑ ΣΤΙΣ ΙΔΙΟΤΗΤΕΣ ΤΗΣ ΒΕΝΖΙΝΗΣ ΟΝΟΜΑΤΕΠΩΝΥΜΟ

Διαβάστε περισσότερα

Tuesday 3 June 2014 Afternoon

Tuesday 3 June 2014 Afternoon Tuesday 3 June 2014 Afternoon AS GCE CHEMISTRY A F322/01 Chains, Energy and Resources *1393437837* Candidates answer on the Question Paper. OCR supplied materials: Data Sheet for Chemistry A (inserted)

Διαβάστε περισσότερα

Core Mathematics C12

Core Mathematics C12 Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C12 Advanced Subsidiary Wednesday 25 May 2016 Morning Time: 2 hours

Διαβάστε περισσότερα

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education GREEK 0543/03 Paper 3 Speaking and Listening Role Play Booklet One For Examination from 2011

Διαβάστε περισσότερα

PHYA1 (JUN14PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2014. Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JUN14PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2014. Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

Modern Greek *P40074A0112* P40074A. Edexcel International GCSE. Thursday 31 May 2012 Morning Time: 3 hours. Instructions. Information.

Modern Greek *P40074A0112* P40074A. Edexcel International GCSE. Thursday 31 May 2012 Morning Time: 3 hours. Instructions. Information. Write your name here Surname Other names Edexcel International GCSE Centre Number Modern Greek Candidate Number Thursday 31 May 2012 Morning Time: 3 hours You do not need any other materials. Paper Reference

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Όλοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα μικρότεροι του 10000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Αν κάπου κάνετε κάποιες υποθέσεις

Διαβάστε περισσότερα

Paper Reference. Advanced/Advanced Subsidiary. Thursday 9 June 2005 Morning Time: 1 hour 30 minutes

Paper Reference. Advanced/Advanced Subsidiary. Thursday 9 June 2005 Morning Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference 6 6 8 3 0 1 Paper Reference(s) 6683/01 Edexcel GCE Statistics S1 Advanced/Advanced Subsidiary Thursday 9 June 2005 Morning Time: 1 hour 30 minutes Surname Signature

Διαβάστε περισσότερα

THIS IS A NEW SPECIFICATION

THIS IS A NEW SPECIFICATION THIS IS A NEW SPECIFICATIN ADVANCED GCE CHEMISTRY A Rings, Polymers and Analysis F324 * CE / 1 5373* Candidates answer on the Question Paper CR Supplied Materials: Data Sheet for Chemistry A (inserted)

Διαβάστε περισσότερα