KISII SOUTH DISTRICT JOINT EVALUATION EXAMS-2014 Kenya certificate of secondary education (K.C.S.E)

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "KISII SOUTH DISTRICT JOINT EVALUATION EXAMS-2014 Kenya certificate of secondary education (K.C.S.E)"

Transcript

1 NAME:...INDEX NO:... SCHOOL:...CANDIDATES SIGNATURE: /1 CHEMISTRY PAPER 1 JUNE/JULY-2014 TIME: 2 HOURS DATE:... KISII SOUTH DISTRICT JOINT EVALUATION EXAMS-2014 Kenya certificate of secondary education (K.C.S.E) 233/1 CHEMISTRY PAPER 1 JUNE/JULY-2014 TIME: 2 HOURS INSTRUCTIONS TO CANDIDATES 1. Write your name and Index number in the spaces provided. 2. Answer ALL the questions. 3. Answers must be written in the spaces provided in the question paper. 4. Additional pages must not be inserted. 5. Candidates should check the question paper to ascertain that all the pages are printed. 6. This paper consists of 12 printed pages FOR EXAMINER S USE ONLY QUESTION MAXIMUM SCORE CANDIDATE S SCORE This paper consists of 12 printed pages. Candidates should check the question paper to ensure that all pages are printed as indicated and no questions are missing.

2 1. In a motoring magazine, a journalist wrote On a busy road the proportion of carbon (II) oxide has varied from 6 parts per million to 180 parts per million. a) Explain why the proportion of carbon (II) oxide varies as above. b) By what reaction is carbon (II) oxide above formed. c) What is the effect of carbon (II) oxide on blood and why does it make the gas poisonous. 2. Compound K reacts with sodium hydroxide as shown. H O H-C-O-C-C 17 H 35 H O H-C-OH H-C-O-C-C 17 H NaOH H-C-OH + 3C 17 H 35 COO - Na + (M) O H-C-O-C-C 17 H 35 H-C-OH H H a) What type of reaction is represented by the equation. b) To what class of organic compounds does K belong. c) How is M separated from aqueous mixture of L and M.

3 3. A mixture of ammonium chloride and sodium nitrite was heated as shown in the set up below. Heat a) Identify gas A. b) State and explain the precaution that should be taken before heating is stopped. (2mks) 4. Study the reaction below and answer the questions that follow. Reaction Equation J Ba (aq) + SO 3(aq) - K Br 2(g) + 2I (aq) BaSO 3(s) 2Br (aq) - + I 2(g) L 2Fe 2+ (aq) + Br 2(g) Fe (aq) + 2Br (aq) M HSO - - 4(aq) + OH (aq) SO 2-4(aq) + H 2 O N Fe (s) + S (s) heat FeS (s) a) Which of these reactions indicate; i) A precipitate reaction

4 ii) Displacement noction iii) Neutralisation reaction 5. Given the following half cells Pb 2+ (aq) / Pb (s) E θ = -0.13v Cu 2+ (aq) / Cu (s) E θ = +0.34v a) Write the ionic equations for the half-cell that undergoes (2mks) i) Oxidation ii) Reduction b) Calculate the e.m.f of the resulting electrochemical cell. 6. The formation of carbon (II) oxide and hydrogen from methane and steam at C, is represented by the equation below. CH 4(g) + H 2 O CO (g) + 3H 2(g) H = 206kJ a) Calculate the mass of methane that reacts to produce 556kJ of heat. (C=12 O=16 H=1) (2mks) b) What effect does increase in pressure have on the yield of carbon (II) oxide gas?

5 g of a salt of formula M 2 SO 4 was dissolved in water. The sulphate was precipitated by adding excess banum chloride solution. The mass of the precipitate formed was 4.66g. (Ba = 56, S = 32, O = 16) a) Determine the moles of sulphate ion present. b) Calculate the relative atomic mass of M in M 2 SO 4 (2mks) 8. Study the information in the table below and answer the questions that follow. A mixture contains three solids; aluminium sulphate sugar, and camphor. The solubility of these solids in different liquids is shown in the table below. Liquid Water Alcohol Ether Solid Al 2 (SO 4 ) 3 Soluble Insoluble Insoluble Sugar Soluble Soluble Insoluble Camphor Insoluble Soluble Very soluble Explain how you would obtain a solid sample of sugar from the mixture. (3mks) 9. The equation below represents changes in physical states of iron metal. Fe (s) Fe (s) H = +15.4kJ/mol Fe (l) Fe (g) H = +354 kj/mol Calculate the amount of heat required to change 11.2g of solid iron to gaseous iron. (Fe = 56.0)

6 (2mks) 10. The set up below was used to prepare a gas X. study it and answer the question that follow. Name; i) Gas X ii) Liquid P.

7 11. The following are standard electrode potential for some elements. E θ (Volts) A 2+ (aq) + 2e - A (s) B + (aq) + e - B (s) C 2+ (aq) + 2e - C (s) D 2+ (aq) + 2e - D (s) E 2+ (aq) + 2e - E (s) F + (aq) + e - F (s) a) An aqueous solution containing F + ions is placed in a container made of C. determine whether a reaction occurs or not, showing how you arrive at your answer. (2mks) b) Identify two half-cells which if combined give the highest e.m.f. 12. Complete the table to show how the factor given below affect the rate of reaction between acid and magnesium and give an explanation for each effect. Factor Effect on rate of reaction Explanation Using magnesium powder instead of ribbon (2mks) 13. The diagram below represent two iron nails with some parts wrapped tightly with zinc and copper stripes respectively.

8 State the observations that would be made at the exposed points A and B if the wrapped nails are left in the open for several months. Explain (3mks) g of a mixture of anhydrous sodium carbonate and sodium hydrogen carbonate when heated to a costant mass, gare 4.11g of residue. Calculate the percentage of anhydrous sodium carbonate in the mixture. (Na=23 O=16 H=1) (3mks) 15. State, giving reasons, the observations that would be made when concentrated sulphuric(vi) acid is added to powdered sulphur and the mixture heated. (3mks)

9 16. The curve below represent the changes in the concentrations of substance E and F with time in the reaction. E (g) F (g) a) Which curve represents the changes in the concentration of substance F? Give a reason (2mks) b) Give a reason for the shapes of the curves after time (t) minutes. 17. State and explain the change in mass that occur when the following substances are separately heated in open crumbles. (3mks) i) Copper metal ii) Copper (II) Nitrate iii) Anhydrous copper (II) sulphate

10 18. State Charles law for gases and explain it using kinetic theory of matter. (3mks) 19. Below is a diagram for the fountain experiment using ammonia gas. Red coloured water begins to rise up the tube from lower flask to upper flask and a fountain is observed in the upper flask. Red colour changes to blue. i) Why does the colour change to blue? ii) Explain why the fountain effect occurs. iii) Why is it necessary to have two tubes in the lower flask?

11 20. A student set-up the apparatus below in order to determine the percentage by volume of oxygen in air. AT BEGINING AT END a) Why did water rise when the reaction had stopped? b) The student wrote the expression for the percentage by volume of oxygen in air as y x y x100% Why was the volume of oxygen calculated using the above expression incorrect? c) What should have been done after the reaction had stopped in order to get a correct volume. 21. The table below shows the two allotropes of sulphur. Using the guidelines given, state the differences between the two allotropes. Property Rhombic Monoclinic (3mks)

12 Appearance Density Melting point ( 0 C) 22. An element X, forms an ion ion X 2- with the electronic configuration a) Write the electronic configuration of element X. b) An element Y is found in the 4 th group of the periodic table. Draw a dot (.) and (x) diagram to show bonding in compound formed when X and Y react. 23. State and explain two main factors considered in determining the position of an element in the periodic table. (2mks) 24. Explain what would be the ph of the final solution obtained after mixing equal volumes of 2M Sodium hydroxide and 2M Ethanol acid. (2mks) 25. The graph below shows the solubility curves for salt X and Y.

13 a) Which of the two salts is more soluble in water? Explain b) State and explain what happens when 100g of solution containing 20g of salt X and 20g of salt Y is cooled from 90 0 C to 20 0 C (2mks) 26. In an experiment to separate a mixture of two liquids A and B, a student set up the apparatus as shown below.

14 a) Name the apparatus b) Which liquid is denser c) Which other method can be used to separate the two liquids. 27. Study the information given below and use it to answer the questions that follow. Select Substance (oxide) Reaction with acids Melting point ( 0 C) J K L M No reaction Reacts explosively No reaction Reacts readily i) An oxide with giant atomic structure. ii) An oxide which dissolves in water to form an acidic solution. 28. When 94.5g of hydrated barium hydroxide Ba(OH) 2.nH 2 O were heated to constant mass, 51.3g of anhydrous barium hydroxide were obtained. Determine empirical formula of the hydrated barium hydroxide. (Ba = 137 O = 16 H = 1) (3mks)

15 29. Reagent bottles labelled H 2 SO 4, K 2 CO 3 and NaCl had labels accidentally removed. A packet of blue litmus paper is lying near a long with a rack of test-tubes, without using any other material explain how you would go about labeling the bottles correctly. (3mk)

16 ANSWERS: Order a copy of answers from NB> We charge Kshs. 100 ONLY to meet website, e-resource compilation and provision costs

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

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

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

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

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

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

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

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

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

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

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

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. (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

[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

, 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

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

(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

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

titanium laser beam volume to be heated joint titanium Fig. 5.1

titanium laser beam volume to be heated joint titanium Fig. 5.1 1 Lasers are often used to form precision-welded joints in titanium. To form one such joint it is first necessary to increase the temperature of the titanium to its melting point. Fig. 5.1 shows the joint

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

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

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

Conductivity Logging for Thermal Spring Well

Conductivity Logging for Thermal Spring Well /.,**. 25 +,1- **-- 0/2,,,1- **-- 0/2, +,, +/., +0 /,* Conductivity Logging for Thermal Spring Well Koji SATO +, Tadashi TAKAYA,, Tadashi CHIBA, + Nihon Chika Kenkyuusho Co. Ltd., 0/2,, Hongo, Funabashi,

Διαβάστε περισσότερα

2. Chemical Thermodynamics and Energetics - I

2. Chemical Thermodynamics and Energetics - I . Chemical Thermodynamics and Energetics - I 1. Given : Initial Volume ( = 5L dm 3 Final Volume (V = 10L dm 3 ext = 304 cm of Hg Work done W = ext V ext = 304 cm of Hg = 304 atm [... 76cm of Hg = 1 atm]

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

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

Enthalpy and Entropy

Enthalpy and Entropy F35 Equilibria, Energetics & Elements Enthalpy and Entropy 1. A Born Haber cycle for the formation of calcium sulphide is shown below. The cycle includes enthalpy changes for all Steps except Step F. (The

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

In your answer, you should make clear how evidence for the size of the nucleus follows from your description

In your answer, you should make clear how evidence for the size of the nucleus follows from your description 1. Describe briefly one scattering experiment to investigate the size of the nucleus of the atom. Include a description of the properties of the incident radiation which makes it suitable for this experiment.

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

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

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

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

CONCENTRATIVE PROPERTIES OF AQUEOUS SOLUTIONS: DENSITY, REFRACTIVE INDEX, FREEZING POINT DEPRESSION, AND VISCOSITY

CONCENTRATIVE PROPERTIES OF AQUEOUS SOLUTIONS: DENSITY, REFRACTIVE INDEX, FREEZING POINT DEPRESSION, AND VISCOSITY DENSITY, REFRACTIVE INDEX, FREEZING POINT DEPRESSION, AND VISCOSITY This table gives properties of aqueous solutions of 66 substances as a function of concentration. All data refer to a temperature of

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

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

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

REDOX (2) pe as a master variable. C. P. Huang University of Delaware CIEG 632

REDOX (2) pe as a master variable. C. P. Huang University of Delaware CIEG 632 REDOX (2) pe as a master variable C. P. Huang University of Delaware CIEG 632 1 8.0 pe as a Master Variable E O,R = E o O,R 2. 303RT log n R O E O, R = E o O, R + 2. 303RT n O log R E R, O = E o R, O 2.

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

*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 *4358398658* GREEK 0543/04 Paper 4 Writing May/June 2015 1 hour Candidates answer on the Question

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

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

Candidate Name. A.M. THURSDAY, 13 January hours

Candidate Name. A.M. THURSDAY, 13 January hours Candidate Name Centre Number Candidate Number 2 GCE AS/A level 1091/01 CHEMISTRY CH1 A.M. THURSDAY, 13 January 2011 1 1 2 hours FOR EXAMINER S USE ONLY Section A B Question 1-5 6 Mark ADDITIONAL MATERIALS

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

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

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

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

Tuesday 17 June 2014 Afternoon

Tuesday 17 June 2014 Afternoon Tuesday 17 June 2014 Afternoon A2 GCE CHEMISTRY A F325/01 Equilibria, Energetics and Elements *3175284854* Candidates answer on the Question Paper. OCR supplied materials: Data Sheet for Chemistry A (inserted)

Διαβάστε περισσότερα

Solutions to Exercise Sheet 5

Solutions to Exercise Sheet 5 Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X

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

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

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

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

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

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

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

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

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

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: 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

Τελική Εξέταση =1 = 0. a b c. Τµήµα Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών. HMY 626 Επεξεργασία Εικόνας

Τελική Εξέταση =1 = 0. a b c. Τµήµα Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών. HMY 626 Επεξεργασία Εικόνας Τελική Εξέταση. Logic Operations () In the grid areas provided below, draw the results of the following binary operations a. NOT(NOT() OR ) (4) b. ( OR ) XOR ( ND ) (4) c. (( ND ) XOR ) XOR (NOT()) (4)

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

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

Second Order RLC Filters

Second Order RLC Filters ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor

Διαβάστε περισσότερα

DuPont Suva. DuPont. Thermodynamic Properties of. Refrigerant (R-410A) Technical Information. refrigerants T-410A ENG

DuPont Suva. DuPont. Thermodynamic Properties of. Refrigerant (R-410A) Technical Information. refrigerants T-410A ENG Technical Information T-410A ENG DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 410A Refrigerant (R-410A) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered

Διαβάστε περισσότερα

PhysicsAndMathsTutor.com 1

PhysicsAndMathsTutor.com 1 PhysicsAndMathsTutor.com 1 Q1. The magnetic flux through a coil of N turns is increased uniformly from zero to a maximum value in a time t. An emf, E, is induced across the coil. What is the maximum value

Διαβάστε περισσότερα

Technical Information T-9100 SI. Suva. refrigerants. Thermodynamic Properties of. Suva Refrigerant [R-410A (50/50)]

Technical Information T-9100 SI. Suva. refrigerants. Thermodynamic Properties of. Suva Refrigerant [R-410A (50/50)] d Suva refrigerants Technical Information T-9100SI Thermodynamic Properties of Suva 9100 Refrigerant [R-410A (50/50)] Thermodynamic Properties of Suva 9100 Refrigerant SI Units New tables of the thermodynamic

Διαβάστε περισσότερα

Reaction of a Platinum Electrode for the Measurement of Redox Potential of Paddy Soil

Reaction of a Platinum Electrode for the Measurement of Redox Potential of Paddy Soil J. Jpn. Soc. Soil Phys. No. +*0, p.- +*,**1 Eh * ** Reaction of a Platinum Electrode for the Measurement of Redox Potential of Paddy Soil Daisuke MURAKAMI* and Tatsuaki KASUBUCHI** * The United Graduate

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

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

The Simply Typed Lambda Calculus

The Simply Typed Lambda Calculus Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and

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

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

Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1

Main source: Discrete-time systems and computer control by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 A Brief History of Sampling Research 1915 - Edmund Taylor Whittaker (1873-1956) devised a

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

Capacitors - Capacitance, Charge and Potential Difference

Capacitors - Capacitance, Charge and Potential Difference Capacitors - Capacitance, Charge and Potential Difference Capacitors store electric charge. This ability to store electric charge is known as capacitance. A simple capacitor consists of 2 parallel metal

Διαβάστε περισσότερα

Supporting information. An unusual bifunctional Tb-MOF for highly sensing of Ba 2+ ions and remarkable selectivities of CO 2 /N 2 and CO 2 /CH 4

Supporting information. An unusual bifunctional Tb-MOF for highly sensing of Ba 2+ ions and remarkable selectivities of CO 2 /N 2 and CO 2 /CH 4 Electronic Supplementary Material (ESI) for Journal of Materials Chemistry A. This journal is The Royal Society of Chemistry 2015 Supporting information An unusual bifunctional Tb-MOF for highly sensing

Διαβάστε περισσότερα

DuPont Suva 95 Refrigerant

DuPont Suva 95 Refrigerant Technical Information T-95 ENG DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 95 Refrigerant (R-508B) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered

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

Problem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ.

Problem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ. Chemistry 362 Dr Jean M Standard Problem Set 9 Solutions The ˆ L 2 operator is defined as Verify that the angular wavefunction Y θ,φ) Also verify that the eigenvalue is given by 2! 2 & L ˆ 2! 2 2 θ 2 +

Διαβάστε περισσότερα

Site-Selective Suzuki-Miyaura Cross-Coupling Reactions of 2,3,4,5-Tetrabromofuran

Site-Selective Suzuki-Miyaura Cross-Coupling Reactions of 2,3,4,5-Tetrabromofuran 1 Site-Selective Suzuki-Miyaura Cross-Coupling Reactions of 2,3,4,5-Tetrabromofuran Munawar Hussain, a Rasheed Ahmad Khera, a Nguyen Thai Hung, a Peter Langer* a,b a Institut für Chemie, Universität Rostock,

Διαβάστε περισσότερα

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ. Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action

Διαβάστε περισσότερα

1) Formulation of the Problem as a Linear Programming Model

1) Formulation of the Problem as a Linear Programming Model 1) Formulation of the Problem as a Linear Programming Model Let xi = the amount of money invested in each of the potential investments in, where (i=1,2, ) x1 = the amount of money invested in Savings Account

Διαβάστε περισσότερα

DuPont Suva 95 Refrigerant

DuPont Suva 95 Refrigerant Technical Information T-95 SI DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 95 Refrigerant (R-508B) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered

Διαβάστε περισσότερα

5.4 The Poisson Distribution.

5.4 The Poisson Distribution. The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable

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

Write a balanced equation for the thermal decomposition of calcium nitrate.

Write a balanced equation for the thermal decomposition of calcium nitrate. 1. (a) When solid calcium nitrate is heated, brown fumes of nitrogen dioxide, NO 2, are seen and the solid remaining after decomposition is calcium oxide. (i) Write a balanced equation for the thermal

Διαβάστε περισσότερα

What is meter P measuring?... What is meter Q measuring?...

What is meter P measuring?... What is meter Q measuring?... 1 The diagram shows an electrical circuit. (a) (b) Complete the two labels on the diagram. P and Q are meters. What is meter P measuring?... What is meter Q measuring?... (Total 4 marks) Page 1 of 24 2

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

14 Lesson 2: The Omega Verb - Present Tense

14 Lesson 2: The Omega Verb - Present Tense Lesson 2: The Omega Verb - Present Tense Day one I. Word Study and Grammar 1. Most Greek verbs end in in the first person singular. 2. The present tense is formed by adding endings to the present stem.

Διαβάστε περισσότερα

Wednesday 1 February 2012 Morning

Wednesday 1 February 2012 Morning Wednesday 1 February 2012 Morning A2 GCE CHEMISTRY A F325 Equilibria, Energetics and Elements *F314480112* Candidates answer on the Question Paper. OCR supplied materials: Data Sheet for Chemistry A (inserted)

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

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

Concrete Mathematics Exercises from 30 September 2016

Concrete Mathematics Exercises from 30 September 2016 Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

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

Wednesday 13 June 2012 Morning

Wednesday 13 June 2012 Morning Wednesday 13 June 2012 Morning A2 GCE CHEMISTRY A F325 Equilibria, Energetics and Elements *F314750612* Candidates answer on the Question Paper. OCR supplied materials: Data Sheet for Chemistry A (inserted)

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

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

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