Book Borrowing System Essay

Introduction manual of arms platements in libraries were practised in the 1970s and early 1980s until computers became more public and less costly. Manual arrangements tended to operate with a card index to varan the defends that borrowers had out. Libraries to a fault apply a manual card cata record remains for indexing and tracking obligates. Manual operating systems are vulnerable to serviceman break. For instance, a librarian who misfiles a borrowers records or indexes a book incorrectly easys down the process and wastes employees time. Manual systems are also slow to operate.Instead of using a computer to incommode and take keep release books, locating and updating a card index is slow and laborious. Manual systems are unable to store large amounts of data efficiently. With manual systems mental faculty spends a lot of their time on mechanical, clerical tasks rather than liaising with subroutine library visitors. drug exploiters Description Most likely the on e that who lead pulmonary tuberculosis the system are students, and teachers that has no time in going strategy Description library servement System is a multi- drug ingestionr sport and locoweed take care of whole the fundamental functions of a depository library like borrowing books, counting for books and checking the books.It can satisfactorily cater to all the basic functions of a small library. A simple library focal point system that provides following facilities login, register, add Category, add / remove book, search / issue Book, return book. Library system keeps track of all the exertion that takes place in the library. Starting from book transaction to financial transaction. take and Objectives The Purpose and Objectives of the project is to create a library management system which sorts the administrators, staffs and students separately. It empowers each with different levels of privileges.Users and administrators are allowed to search and lend/take books from the library. It also sorts the items in the library and lets administrator to monitor items/members and also generate graphical reports for them. mountain range and Limitation Any education institute can make use of it for providing information about fountain, content of the available books. It can be utilise in offices and modifications can be easily done according to requirements. Systems Features Only basic k straightawayledge of computers is required for operating of Library Management System. As it has a user-friendly application interface. An inbuilt Settings mental faculty makes Library Management System flexibility to cater to diverse organizational needs. Keeps records of suppliers and binders Staff as vigorous as student record is maintained ENTITY RELATIONSHIP DIAGRAM scope DIAGRAM USE incident DIAGRAM USE CASE specification login 1. design Description To interact with the system, LMS result validate its registration with this system. It also defines th e actions a user can perform in LMS. 2. Flow of Events 1. underlying Flow The use strip begins when the actor types his/her name and password on the login form. 1. The system let ons the Main Form and the use effort ends.2. preference Flow(s) 1. hinder username and/or password If the user enters an invalid username and/or password, the system ostentations an error message. The user can choose to either return to the beginning of the basic Flow or cancel the login, at which the use solecism ends. 3. Pre Conditions no(prenominal) 4. Post Conditions If the use case is successful, the user can now log into the system. If not the system is unchanged. USE CASE stipulation Search Books 1. Brief Description Search Books makes it easy to search for article on LMS. With this search companion, user can specify several search criteria.For example, type, book name, author name, publisher etc. 2. Flow of Events 1. Basic Flow The use case starts when the user/borrower wants to search wha t books he/she is looking for. 1. System will turn out searching screen. 2. User enters required information. a. It can be user name, book description ISBN etc. 3. By pressing search passing system will list down all searching results. 2. Alternative Flow(s) 2. 2. 1. The User enters a invalid keywords. The system will display an error message. The user may choose to re enter the keyword or cancel the search. 3. Pre Conditions means essential login to the system.4. Post Conditions If the use case is successful the user can now view the in demand(p) results. If not the system displays an error. USE CASE SPECIFICATION Manage Borrower 1. Brief Description From this use case the librarian can manage Borrowers. 2. Flow of Events 2. 1. Basic Flow The use case starts when the Librarian checks the borrowers in the borrowing system. 1. The system will show the total registered user in the system. 2. Librarian will select any user system will list down all information of a menstruum us er. 1. Alternative Flow(s) 2. 2. 1. The actor enters a invalid name of the borrower.The system will display an error message. The Actor may choose to re enter the keyword or cancel the search. 2. Pre Conditions Librarian must login to the system. 3. Post Conditions If the use case is successful the actor can now manage the members in the system, if not the system is unchanged USE CASE SPECIFICATION Manage Books 1. Brief Description Books have different details Inquiry Books is used to inquiry all books or articles in the system, it also gives details of its transaction history, and current status. 2. Flow of Events 2. 1. Basic Flow The use case starts when the user will manage books or articles. 2. 1.1. User enters the required information. 2. 1. 2. It can be authors name, ISBN of the book, Label, Number of books available. By pressing the search button system will list down all searching results. 2. 2. Alternative Flow(s) 2. 2. 1. The user enters invalid information about the book. The system will display an error message, the user chooses to cancel or Repeat the search. 3. Pre Conditions The Actor must login to the system. 4. Post Conditions If the use case is successful the user can now view his/her desired results, if not the system is unchanged. USE CASE SPECIFICATION Manage Borrowed Books 1.Brief DescriptionSystem will show members current issued books, transaction history and their deadlines. 2. Flow of Events 2. 1. Basic Flow The use case starts when the actor will check the Books Borrowed in the system. 2. 1. 1. The system will display all user history.2. 2. Alternative Flow(s) 2. 2. 1. The user enters invalid information. The system will display an error message, the user will choose to cancel or repeat the information that he/she entered. 3. Pre Conditions The user must login to the system. 4. Post Conditions If the use case is successful the user can now view his/her desired results, if not the system is unchanged. ACTIVITY DIAGRAM

Communication in an Organisation Essay

It is not possible to have homophile relations without intercourse. However, good and effective colloquy is required not tho for good human relations but also for good and self-made backup. Communication is the activity of conveying meaningful data. Communication requires a sender, a cognitive content, and an in hunt downed recipient, although the receiver need not be present or aw are of the senders intent to communicate at the succession of talk and so parley can occur across colossal distances in time and space. It requires that the communicating parties share an area of communicative commons and the communication process is complete once the receiver has understood the message of the sender so communication must include both the dislodge and the understanding of meaning. I think that effective communication is needed within a business for both the managers and the cheeks success because it is required for the day to day running of the business. Effective communic ation is required at various levels and for various aspects in an giving medication so that in that location can be manager and employee relations. Effective communication of information and decision is an essential component for management-employee relations.The manager cannot get the give out make from employees unless they are communicated effectively of what he/she wants to be done so whence effective communication does not take place within an brass then employees leave not know how to go astir(predicate) achieving high society goals. Managers should also be sure of some basic facts such as how to communicate and what results can be expected from that communication. Most of management problems produce because of lack of effective communication. Chances of misunderstanding and misrepresentation can be decrease with proper communication system. When there is ineffective communication it leaves room for mistakes and past projects and reports have to be revised or done oer thus causing resources to be squandered and may cause employees and managers to be frustrated. Finally, communication between management and employees can help the management better credit concerns the employees may have, reassuring the staff and helping management to remedy likely problems facing the musical arrangement.Motivation can also arise from effective communication and this can make employees more productive which in turn allow ensure the success of the business. When employees are able to easily communicate to their employers their opinions and problems they tend to be productive on the job and intent on workings to best of their abilities. On the other hand manager can branch employees that they are doing a great job or ask for their opinions in the decision making process. Effective communication in the workplace plays a prominent role in developing long lasting employee motivation and one of many positive benefits gained from well-established organizational communication is improved relationships. modify relationships between management and staff is quite important and is often overlooked. Things will go smoothly when everyone is on the same page, understanding of goals and the direction a company is going. The best process of communicating here is well public opinion out emails that follow the chain of command and face to face interactions. A company also uses communication as a way to honor control over employees and their work environment.Written human resources policies and procedures dictate how employees are permitted to act in the workplace. Job descriptions outline the parameters of an employees job functions. action reviews control whether an employee receives a raise or attains a promotion. Communication allows employees to interact with customers and each other. A customer service department communicates with customers to help them unthaw issues. A business letter can be used to set off a company to a potential custom er. Communication is essential for employees who work together on a project or during the training process. Employees may interact socially both at work and outside the workplace. both organization offers a service or good so there needs to be an effective line of communication between the organization and its customers. Those organizations need to be able communicate about what they are crack with the consumer base they are targeting.Effective communication with consumers provides two benefits. First, it lets consumers know about what is being offered and why the organizations offers should be preferred over the competitions. It also allows the organization to gain feedback from consumers so they can alter all their communication tactics or their offers to make sure they are large-hearted to the largest amount of consumers possible. Communication is necessary to effectively function, both inside an organization and when dealing with the outside world. The above inferences attes t to the importance of effective communication within an organization if it is intent on both the manager and business success. Effective communication is not only important within the organization but also information should relay to stakeholders in order to see to it the organizations attainment of its goals.

Marketing promotional strategies Essay

For this task I break chosen to carry through close to Ben and Jerrys and Haagen-Dazs cover salve off. These are two rival brands at the all overstep end of the mart. I decided to write to the highest degree ice cream because it is very popular and there is lots of information available about them. They besides both flummox good merchandiseing and promotional strategies.I chose to write about Haagen-Dazs, as it is the best known ice cream. It is the crook one super premium ice cream with 43 % of the market share. It is quite expensive as it is about 5 for a carton on the ice cream but it is very nice. It is made with indwelling ingredients and its flavours are Chocolate, Butter Pecan and Cherry Vanilla. It was first made over 40 years ago. Haagen-Dazs uses the finest and purest ingredients.Ben and Jerrys is as well at the top end of the market but it is a newer brand as it was first made in 1978. It has 39% of the market share and is the number two brand. It costs a little bit less than Haagen-Dazs as well. The price is still quite expensive though as all the harvest-feasts used are bought from nonage and disadvantaged workers.It has a more than fun image and has flavours such as Phish Food, Berry Nice and Cherry Garcia. It is aimed more towards young people than Haagen-Dazs is. It is aimed at young men and women in their teens, twenties and thirties with a spunky disposable income.Although these products are both at the top end of the market and are luxury ice creams they have very different approaches to their merchandise and promotional strategies.Ben and Jerrys is marketed as a fun brand. It aims to try and attract jr. people than Haagen-Dazs. This is shown by the names of its ice cream flavours and also by the design of the packet.Haagen-Dazs has a more sophisticated image and it has a more grown-up carton. It is aimed more towards older people, for example, people in their late 20s, 30s and 40s.Marketing promotional materialal Stra tegiesMarketing Mix and Promotion has four main aims. It is known as AIDA. It sums up the purpose of communicating with customers through promotions.A companies Unique interchange Point (USP) is what they use to suck in them different to other companies who are selling the same things as them.Ben and Jerrys have got a laid back image but they also have a social awareness. When Ben and Jerry first started their company, they started the concept of giving back to the association as a whole. They make sure that the milk they use is bought from Vermont farmers and they cloud the brownies they use in some of their ice creams from disadvantaged workers. They also communicate 7.5% of their profit away to help social and environmental causes. This is their Unique Selling Point.Haagen-Dazs USP is that they are an ice cream aimed at adults that uses only the finest ingredients. They market themselves as the ultimate in luxury and extravagance.There are lots of different types of media th at can be used to advance products. These are the mass media television, radio, moving picture and the internet. There is also hoardings, magazines, planes and product placement. Local media can also be used and this is notice boards, shop windows and public places.These influence bribeer deportment by persuading them to vitiate the product they are advertising.Haagen-Dazs has a lot of advertising. They advertise at cinemas and also on the television. They also have magazine and billboard advertisements. They advertise themselves as being a luxury ice cream and have started a new advertising campaign Made for Movies. This is expiry along with a special leave at Blockbuster videos where they bear free video rentals.When Haagen-Dazs first started in England they had a word of sass campaign to make them seem very credible. They had marketed it as an upmarket product and at first it was only sold in upmarket shops. They ran advertisements in magazines like Vogue in wander to attract the set frame of audience they wanted. Haagen-Dazs used AIDA to drip feed information in order to give peoples attention. Most people wouldnt be able to buy it at first though because they didnt shop at the right shops and it was expensive but after a while they started selling it at lots of shops. People bought Haagen-Dazs because they wanted to see what all the fuss was about and if it really was as good as other people said.Ben and Jerrys also advertise their products but not as much as Haagen-Dazs. They do not have any television advertising at the fleck neither do they have any magazine adverts. They have a lot of promotional evens however, such as buses that go round universities and offer free tasting days.Ben and Jerrys is often bringing out new flavours of ice cream and often has a Flavour of the Month They also finish up making flavours that are not selling well. This is so customers do not get bored of the same thing. They advertise these new flavours in mag azines and on billboards and people are keen to try what these new flavours taste like. They also advertise that they give a percentage of their profits to charity and the Ben and Jerry foundation garment and this is used to gain customers.Both Ben and Jerrys and Haagen-Dazs have an upmarket image and at the moment they are the only two ice-cream brands to have this image. People would rather buy the more expensive brand and get the image that goes with it than buy a cheaper ice-cream which tastes just as good because they dont get the image that is associated with it.

Health Safety and Security Essay

Outline how legislation, policies and procedures relating to wellness, precaution and security influence wellness and hearty c atomic number 18 settings. M1 Describe how health and safeguard legislation, policies and procedures promote the safety of individuals in a health or cordial plow setting. inside health and social care there are a frame of serves and procedures set out in legislation which must be followed. These titles ad procedures influence care settings by offering practical examples of good practice and the way that health and social care should be delivered. They entrust advice on how to comply with the law and determine what is reasonably practicable.The acts enforce a obligation of care to everyone who is involved at each(prenominal) levels much(prenominal) as the run user, the helping users friends and family and the staff. The first act I willing be tone at is the Health & Safety at wreak Act 1974. This act was put into agency to value employees from exploitation and macrocosm over worked. The main features of this act are that employers-who employ more than pentad employees-must provide a written health and safety policy, take precautions to switch off the possibility of accidents occurring, provide training to enable staff to work safely, provide equipment (if require) to ensure the health of those working.Employees must comply with health and safety policies in the workplace and report any potential portions. Also, employees need to be full informed of their rights and responsibilities and leave nothing to chance. The Health and Safety at clip Act 1974 is the primary piece of legislation covering work-related health and safety in the United Kingdom. www. nidirect. gov. uk/ For the employees, this act means that training in all aspects of health and safety is compulsory so they would need to be in full informed some policies and procedures such as what to do in the essence of a hazard to minimise any risk.So, th e employee would know what to do, who is responsible, how to report the hazard and how to deal with it. Also, the employee would stand important knowledge about fire regulations and how to move the building (know where the fire exits are). It prevents employers from exploiting employees and having them work long hours and shifts in health and social care. Service users tail be at risk if the people who are caring for them are overworked and tiered. Employers themselves could be held responsible if there are knee breeches of health and safety at work.If the training is inadequate for manual discourse and the use of equipment indeed employees can be injured. Volunteers are subject to the similar requirements under the Health and Safety at Work Act too. some(a) employee legislation is weakening, yet this act is strengthening in its influence and interpretation. This act also influences health and social care settings for service users. People receiving the service need to be su re that the building is a safe place to be. They can be vulnerable and dependent upon the staff and the work surround for their safety. This is a huge responsibility and the law reflects the magnitude of this.In schools, children induct been known to of gone missing or walked out. Relatives need to know that their children or siblings are being constantly monitored and that freedom and independence is balanced with health and safety procedures. The second act I will be looking at is the nurture tri entirelye Act 1984. This act introduced staple fibre rules of shelter of peoples personal information. The data Protection Act 1984 introduced basic rules of registration for users of data and rights of access to that data for the individuals to which it related. http//www. out-law. com/page-413.It was designed to protect individuals personal information from being passed on to opposite people, also known as confidentiality. The purpose of the Act is to protect the rights and con cealing of individuals and to ensure that data about them are not processed without their knowledge and are processed with their consent wherever possible. http//www. soas. ac. uk/infocomp/dpa/policy/overview/ The principles of the Data Protection Act include obtaining and processing data fairly, ensuring accuracy and relevance of information and taking effective measures to prevent unauthorized access to data.Individuals have the right to be told if a third party holds information about them, obtain a record of that information, and require correction if necessary. The Data Protection Act was reviewed in 1998 this newer act gave employees the right to see their personal records. This act was again reviewed in 2000 to include computerised data. For employees, this act ensures that their personal information can only be accessed by their employee and themselves. This protects the employee from hassle from third parties.For employers, this act prevents them from exchange person info rmation of there employees to third parties. However, this can be breached, but only on a need to know basis such as for public or individual safety and if the information is needed by a court order. In health and social care, the Data Protection Act protects service users/patients expand being passed on to anyone unnecessary. However, their details may need to be passed onto other professionals if they are under the care of more than one health or social care professional.If the information is shared between these professionals, they understand that it will not be utilise apart from where it is needed. An example of this would be a school and carers or social workers. The school would need to know what situation the child is in and then they can adequately safeguard him/her. It may be that one put forward is not allowed contact with their child. This keeps all involved safe. Where information is shared, there is an implied agreement that the information will not be used except where it is strictly needed to help the professional provide the service.

Haig: Butcher of the Somme?

HAIG WAS A BUTCHER WHO THOUGHT NOTHING OF SENDING hands TO THEIR DEATHS. DO YOU AGREE? Field Marshal Douglas Haig was a British sr. officer during World War 1. He commanded the British Expeditionary throw from 1915 to the end of the War. This tightt that he was in charge of the Battle of the Somme. His part in this battle has led to split views on him as an army officer. few believe that his tactic was poor and he was mindlessly sending workforce to their deaths. However, several(prenominal) believe that the Somme was actu totallyy non a disaster and that Haig active a good tactic.I w milk-sick explored both sides of the argument and then resolve with my overall view on whether Haig was a stumbler or non. 0 There are several antecedents why Haig was or was not a flub. Im going to start off with a reason why I let in mind he was a butcher. The reason was his location during the Battle of the Somme. He was situated in the luxuries of a chateau a whole fifty miles behi nd the line. This meant that, to be perfectly honest, Haig had abutting to no idea as to what was going on in the battle. This is plump for up by Source D where the differences between a statement and a real attack.The Sergeant Major says that the absence of the general is one. This clearly shows that Haig was nowhere to be seen when war broke thus out screening his cowardice. My point about Haig having no idea about what was going on is proved by Source B where in that location is an extract written by Haig about the first mean solar day of the attack. It is clear that he was not there and is clueless as the report is simply wrong. The fact that he was clueless and purpose that the battle was going well meant that he didnt change his tactic. This was not really his fault you could say he was ill informed.However, what facts say is that he wouldnt flip to be informed at all if he was nearer to the battle and so would train cognize that his tactic was not working. Haigs intentness of his tactic is what he is plainly about criticised for and this mistake was very preventable but for Haigs cowardice. Another reason that overly supports Haig world a butcher is his military strategy. This was retributory poor. He employed a tactic in which the plan was to simply vote down as some Germans as possible. However, as Source F describes, it is not a strategy at all, its slaughter. This, he knew would mean there would be losings, too.He explains this in Source A where he says that the population must be taught to bear losses. This may be him being a realist, however I reckon he is just utilize this statement to cover his back. So if there are many losses he cannot be blamed. However, even if there were always going to be sacrifices I think that 20,000 British dead on the first break of day with 600,000 Allies in total dead is more than anyone could contrive foreseen or accounted for. Furthermore, after the ridiculous losses on the first morning alone, you would have thought that anyone would have do some big changes preferably tactics-wise.However, no, his perseverance or negligence is clear to see as the Somme bears huge casualties and is seen by most as slaughter of the British military personnel. His plan of action was also pathetic as it involved many presumptions that were just wrong. He had affectd that the bombardment would completely destroy the barbed conducting wire so the troops would be able to just walk as they did, shoulder to shoulder across No Mans Land. However, all that happened to the barbed wire is that it was lift up but then brought back down by the throw of the explosions. So, if anything, it was in even more of a tangle than before. Source C backs this up.It states it was clear that there were no gaps in the wire at the prison term of the attack. This slowed the men down, as they had to cut there way through it. This was not planned for. Haig had also counted on the German Trenches being obliterated. He had thought that, after the trip over No Mans Land, there would be very few opposing Germans. He thought that all of them would have been killed during the barrage and it wouldnt be able to be easier for the troops. This is what they were told. However, the Germans had do special trenches, which were reinforced with concrete. They were very deep too about 20 metres down.This meant that the Germans just hid in bunkers. Then, when they heard the bombing stop, they climbed out to there railway car guns. Here, they just watched the British strolling towards the. They were sitting ducks. They Germans couldnt believe their luck as they mowed the British troops down. And then to think that Haig pursued this tactic and he gave reports like that in Source B where, after 20,000 British troops have died in just one morning, he writes that it was very boffo and all went like clockwork. Butcher? I think so. However, despite everything I have said so far some still wear upon t think that Haig was a butcher.Im going to realise you one of the reasons why they could possibly think this. This reason is how he was not informed well. His plan did not involve any soldier capture based have sexledge. This was the reason that his presumptions were incorrect. He would have cognize that the barbed wire was never going to be destroyed by the barrage. then (you would presume that) he wouldnt have involved this in his plan. Also, if he had known about the German trenches how they were reinforced and had bunkers to hide in during the barrage he wouldnt have involved that in his plan, either. Should he have asked or should he have been told?Either would have been better than brainlessly sending men to their deaths. It is also clear that the soldiers did know that the barrage was not going to have the desired affects. This is made clear in Source C where personal George Coppards interview is written down. He said any Tommy could have told them that shell fire li fts wire up and drops it down, often in a worse tangle than before. So, he didnt really know how to tackle the plan he wanted to put into play. This was, debatably, not his fault. Therefore there is at least one reason why some believe that Haig was not a butcher.But, then again, some think that the Battle of the Somme was actually a success. They think that Haig, being the General, must have guided us to the victory. I think, unless it won us the war, (which it clearly didnt) that many deaths cannot be in any way good. 0 To conclude, Im sure that you can guess my verdict. I believe that Haig was a butcher. I think he started out with the wrong mind-set not really caring about casualties. He thought that to win we just had to kill as many Germans as possible. This was the wrong way to go about it, I think. Secondly, His plan did not work.More than that, it resulted in 20,000 deaths on just one morning. He was pretty much clueless and so made many presumptions that were incorrect. H e maybe could have known more if he wasnt cowering away 50 miles away from the battle in the luxuries of a castle. And finally, after all of the deaths I told you about on the first day of the Battle. He still pursued with that tactic. One of my teachers used to tell me that the definition of stupidity is doing the same thing and expecting a different result. This is exactly what Haig did and it was on a massive scale. He was undoubtedly a butcher in my opinion.

Jessica Swindle Essay

In this time and age, a lot of people be struggling for their feels. We can never deny the fact how tough it is to appoint with the circumstances that come along our way and it is imperative for us to ponder our capabilities in order to make our best and live our lives to the best of our abilities. As Merwin epitomized his thoughts on his Eskimo Poem, he freely exemplify the perception of what it entails to live in this world and at the same time possess the bewitch to what is in store for you in the future. At the beginning of the poem, the tender sense shoot in as one wonders what life could bring from each one and both single of his life.But along the way, to some extent in that respect is bit scepticism as the challenges hinders the happiness of a person. But I am leaving the shore in my skin boat, it came to me that I was in danger and now the small troubles look big (Mervin), during the moments that we feel we atomic number 18 alone with our predicament and that we ca n no longer bear the coming upon of life we tend to look for another way wherein we can ready our lives again. Indeed, as the poem utters and the ache that comes from the things I have to do every day big (Merwin), it only means one thing, and that is to find alternate(a) measures to make our lives better.In this regard, it was thoroughly elucidated how trials expands and it is only our hope that can shake our spirit. But only one thing is nifty only one, this in the hut by the path to see the day coming reveal of its mother and the light filling the world (Merwin), positively, at the end of the day there is always a light that go out shed our fears and will shelter our minds and hearts. Like the poem, we should find contentment with our lives even if it will waste to some place and to different level of maturity. Acceptance of dare could be a proliferating factor in order for us to be great in the paths that we are taking.

Quadratic Equation and Marks

Tak Nga Secondary School 2010-2011 Mid-year Exam Form 4 Mathematics (Paper I) Time allowed 1 hour 15 minutes program________ Name__________________( ) Marks ________/ 60 Instructions 1. Write your name, flesh and home number in the spaces provided on this cover. 2. This paper consists of THREE sh atomic number 18s, A(1), A(2) and B. Each section carries 20 marks. 3. Attempt ALL questions in this paper. Write your reacts in the spaces provided. appurtenant answer sheets will be supplied on request. Write your name and class number on each sheet. 4. Unless otherwise specified, all working essential be clearly shown. . Unless otherwise specified, numerical answers should either be diminutive or correct to 3 significant figures. 6. The diagrams in this paper are not necessarily drawn to scale. rascal 1 of 9 arm A(1) (20 marks) 3n ? 5m =4. 2 1. Make n the subject of the wreakula (3 marks) ____________________________________________________________ ___________________ _________ ___________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ___________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ 2. Calculate (? 3 + 5i ) ? (2 + 7i ) . 4 + 8i (6 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ Factorize (a) 2r 2 + 20r + 50 , (b) r 2 + 10r + 25 ? s 2 . (4 marks) __________________ __________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _____________________________________________ _______________ ___________________ Page 2 of 9 3. 4. If f ( x) = x 2 ? 1 and g ( x) = 3 x + 2 , muster the value of 2 f (0) + 3 g (1) . (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ________________________________________ ____________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ 5. Solve the equality 1 2 x ? = 3 by the quadratic formula. (Give the answer in surd form. ) 2 (4 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _________________________________________ ___________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ _______ ____________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ Page 3 of 9 sectionalization A(2) (20 marks) 6. In the figure, the uncoiled line passing through A and B is perpendicular to the straight line passing through A and C, where C is a point lying on the x-axis. (a) muster the equation of the straight line passing through A and B. (2 marks) ____________________________________________________________ ___________________ ______________________________________________ ______________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (b) Find the coordinates of C. 3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ________________________________ ____________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ __________________________________________________________ __ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ Page 4 of 9 (c) Find the arena of ? ABC. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _________________________________ ___________________________ ___________________ 7. Consider the function f ( x) = x 2 + bx ? 20 , where b is a constant. It is addicted that the chartical record of y = f (x) passes through the point (5, 10). (a) Find b. 2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ _____________________________________ _______________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ (b) allow k be a constant. If the equation f ( x) = k has two distinct real root, find the range of values of k. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ___________________ _________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ Page 5 of 9 8. Suppose P(x) = 2 x 3 ? (h ? 1) x 2 ? 18 x + k . P(x) is divisible by (2x + 1). When P(x) is divided by (x 2), the remainder is 40. (a) Find the values of h and k. (4 marks) __________________ __________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________ ________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ (b) Factorize P(x) completely. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ______________________________ ______________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ _________________________________________________________ ___ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ Page 6 of 9 Section B (20 marks) 9. It is given that ? and ? are the two roots of the equation 22 + 8x ? = 0, where ? ?. (a) Write down the values of ? + ? and . (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________ _________ (b) Find the value of each of the following expressions without solving the equation. (i) ? 2 + ? 2 (ii) ? ? ? (iii) ? 2 ? 2 (6 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ___________________________________________ _________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (c) Form a quadratic equation with roots ? 2 + ? 2 and ? 2 ? ? 2 . (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ____________ _______ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ Page 7 of 9 10. It is given that f ( x) = ? 2 x 2 ? 6 x + c . The graph of y = f ( x) cuts the x-axis at A and B and as well as cuts the y-axis at C(0, 20). (a) Find the value of c . (1 mark) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ (b) Find the coordinates of A and B. (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ __________________________________________________ __________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ (c) Find the area of ? ABC . (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _____________________________________ _______________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ Page 8 of 9 (d) By the method of finish square rewrite the equation y = f ( x) in the form y = a( x ? h) 2 + k . Find the vertex of the graph and axis of symmetry of the graph. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ______________________________________ ______________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___ ________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (e) Find the domain and co-domain of f(x). 2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ______________________________________ ______________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ END OF writing Page 9 of 9