Tivo 2002 Essay Example

Tivo 2002 Essay nbsp; CONTENTS 1. Point of View 2. Marketing Objectives and Relevant Case Facts 3. Problem/Opportunity Statement 4. Alternative Courses of Action 5. Evaluation of Alternatives 6. Decision 7. Implementation Plan 8. Contingency Plan / Risk Analysis 1. POINT OF VIEW Taking the marketing manager perspective the main issue is centered on the department’s inability to classify the recently collected customer experience data to clearly explain consumer behavior; more specifically, purchasing behavior. The department is unable to connect customer experience to consumer behavior, and customer behavior into sales. In addition, the current product message is not reaching customers adequately. 2. MARKETING OBJECTIVES AND RELEVANT CASE FACTS (RENIER) The current situation can be analyzed using the relavant finance and marketing facts. The finance facts are: †¢ Steady, but less than expected sales; †¢ Steady market growth at approx. 20% per quarter; †¢ Heavy marketing investments lead to significant net losses; †¢ Gross margins turned positive for first time in last half year. We will write a custom essay sample on Tivo 2002 specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Tivo 2002 specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Tivo 2002 specifically for you FOR ONLY $16.38 $13.9/page Hire Writer The marketing facts are: †¢ Market research yielding customer experience; customer satisfaction and equipment usability; †¢ Two customer segments identified; †¢ Marketing department has decided more emphasis should be put into the message of convenience; †¢ Marketing research has focused on current client base, without investigating consumer behavior of other consumers. Marketing objectives Focusing on these facts the marketing objectives should be to increase understanding of consumer behavior. Key areas of focus for the marketing department will be to identify the reasons for the purchase, the purchase drivers and their sources. At this point, the cultural, social and individual forces, specifically motivation and perception, and the psychological processes need to be determined. Finally, the buying process needs to be examined. The increased understanding of the consumer behavior should lead to opportunities to improve the product message and thus influence consumer behavior more effectively. In summary, the plan is to understand our current customer’s behavior to understand buying patterns. Then, adjust our processes and message as needed. And, develop a plan to stimulate identified drivers through the product message. 3. PROBLEM/OPPORTUNITY STATEMENT The main problem TiVo faced was not achieving the desired sales level, leading to significant financial losses. In order to better address this issue the company’s approach was to prepare a series of surveys with its current clients in order to better understand their level of satisfaction with the product, reason to buy, most important product features, and demographics. These surveys revealed a very high general customer satisfaction, but gave limited insight in the consumer behavior in the buying process. The problem statement for this situation is therefore: In order to answer the problem statement presented above and to set up an effective action plan to increase sales, TiVo has to overcome three critical obstacles: 1. The company needs to shift focus from understanding current clients to understanding consumers in general (that is: potential clients). This implies a shift in marketing research focus. 2. The company needs to find a way to stimulate recognition of a problem in watching television. This implies focus on the first step of the buying process. 3. The company needs to leverage the satisfaction of current clients. This implies using the social factor of family influence in consumer behavior. 1. Shift marketing research focus TiVo’s market research efforts were put on understanding current clients while it was not clear the total number of still available clients in the market as well as other important factors regarding buying behavior were not being considered. We cannot assume that everyone with a TV enjoys it as much as current clients do and feel the necessity to record their TV shows. The focus in current clients’ behavior and the lack of information about the rest of the market considering client’s cultural, social and personal factors does not allow us to clearly see the potential for this product and more effort must be put on that rather than simple sales effort. Furthermore, it should be noticed that the results of the marketing research carried out by TiVo could be influenced by a set of other biases: non-response bias; web users bias; reward bias; questionnaire length bias and formulation-bias (the bi-annual survey asks directly about â€Å"satisfaction†, which makes respondents typically score high). 2. Influence problem recognition From these learnings we can see that there was an important element in promoting the product which is referral and trial. This demonstrates that many clients would only recognize a need once they were shown the benefits of using TiVo. . Leverage satisfaction as a social factor Basically, new clients relied a lot on current clients before making a decision (70. 1% knew someone who had the product) and more than half of the clients who bought it either read an article, tried the product in a store or had a reference (data from exhibit 3). We also realize from surveys that people who had Tivo were heavy TV users since from case exhibit 7 more than seventy percent of the clients affirm that their lives were better with Tivo and before acquisition TV schedules would affect their personal schedules not to miss their favorite shows. As so many people were socially influenced by friends and family to buy TiVo, the company should find a way to further leverage the very high customer satisfaction to increase sales. 4. ALTERNATIVE COURSES OF ACTION TiVO can take action in each of the 4 P’s of marketing trying to stimulate sales. In this chapter these courses of action are set out, the following chapter will evaluate all of the actions proposed in order to arrive at a recommended approach. Action 0 Prior to exploring the opportunities for changes to Product, Price, Placement and Promotion, we need to point out the opportunity TiVo has to change nothing. Although the financial situation of the company is not promising, gross margin has recently turned positive and the number of new subscriptions is increasing each quarter. Product Customizing TV consumption has proven to be a market opportunity. TiVo’s reputation among their customers leads to conclude that this is an appreciated product, with high rates on consumers’ satisfaction in relation to the service provided. However, since 1999, the year when TiVo was created, the trend on TV consumption, with the invasion of the Internet as an entertainment provider has drastically changed the picture. As competitors withdraw providing the service to the market, this leads to the assumption that DVR innovation is not being properly transmitted to consumers. This situation leads to the following potential actions in the area of product changes: †¢ Explore completely different platforms, combining Internet and TV; †¢ Add features to the device in order to further improve the customer experience. Price Pricing is well defined taking into account TiVo out sources via Direct TV the customer’s acquisition costs being the latter financially responsible. Difference in prices, whether the service is provided through TiVo alone, or through Direct TV customers brings options to customers and we consider it a positive fact. The case does not provide much detail on the pricing strategy of the company and does not offer clues that lead to the idea that the product is priced wrongly. The company might benefit from offering discounts to increase sales. Potential actions in the area of price are: †¢ Investigate the price-elasticity of the service in order to see if prices could be increased; †¢ Offer cheap or free trials to trigger new consumers to try the product; †¢ Offer discounts to customers that are effective in referencing the product to others (buzzing). Placement TiVo is currently using Best Buy as the exclusive retailer. Coverage of Best Buy can be read as a huge success, with more than 1. 400 stores in the US, plus its subsidiaries such as â€Å"Geek Squad†. Furthermore, the placement in cooperation with the cable providers should bring in additional revenues. Potential changes to this strategy are: †¢ Widen the scope to other retailers not so technologically oriented. This could open a new segment for final purchasers acquiring TiVo at stores (Sears, Macys); †¢ Build more partnerships and joint ventures with cable companies; †¢ Build partnerships with TV hardware companies to sell the TiVo with the TV; †¢ Sell the Company to cable or satellite TV suppliers. Promotion The detailed surveys carried out by TiVo’s marketing team do not provide a onvincing reason for the lower than expected sales. The high rate of buyers that have had recommendations from friends and that have seen demos of the product seem to indicate that TiVo needs to convey the message of how TiVo can change the customer’s life (â€Å"problem recognition†) more effectively. New marketing campaigns and promotions could be driven to either swap to other targets (other than young men or busy families) or stimulate the existing ones by further exploring the â€Å"deep emotional response† TiVo can be proud of obtaining from its final customers. Potential promotion actions are: †¢ Carry out consumer surveys in the mainstream market, not only targeting current customers; †¢ Target the mainstream market without first carrying out more marketing research in this segment; †¢ Strengthen the problem recognition-message in all marketing campaigns; †¢ Incentivize current customers to carry out more Word of Mouth marketing to friends and family. 5. EVALUATION OF ALTERNATIVES The potential actions set out above will need to bring TiVo the required sales increase in order to become profitable in the long run. Furthermore, all the company should urgently improve its short term financial position. Interest income has stopped and interest expenses are skyrocketing, indicating increasing debt and lack of cash. Sales Marketing account for 60% of the overall expenses over the last year. These expenses result in a significant net loss for the company. The actions taken should therefore be beneficial for both short term and long term financial performance. Other criteria to be considered when evaluating the alternatives are the ease of implementation and the risk level associated with the action. The criteria defined for evaluation are: 1. Cost of implementation (short term) 2. Ease of implementation 3. Market size share impact 4. Profitability/margin impact (long term) 5. Risk level â€Å"Table 1 Evaluation of alternatives† gives the detailed evaluation on these alternatives based on these criteria. Obviously, changes to the product will be time consuming, expensive and carry a high risk. Pricing and discount alternatives are attractive due to relatively low risk and good options to leverage the high customer satisfaction in both trials and buzz-marketing. Placement changes will involve high levels of negotiation and might involve legal issues as Best Buy is currently the exclusive retailer and existing partnerships with cable companies might have exclusivity-clauses. For all promotion changes considered in the table the amount of funds available for marketing is considered fixed. Naturally, sales will increase further if more funds are made available. However, marketing ROI appears to be low in the short term, considering the enormous amounts of money spent on marketing in the past years. Tuning the marketing message appears to be most promising. Table 1 Evaluation of alternatives [pic] 6. DECISION After analyzing the survey results, consumer behavior and evaluating the potential actions, we propose the marketing team the following strategies, combining the promising actions defined in the previous chapter: 1. Redefine campaign message (Corresponds to action nr. 12 in table above) The company has to redesign the marketing campaign to increase the sales level very fast in order to solve the cash problem it has. We believe the best way of doing this is to have a clear tailored message focused on problem recognition, thus influencing the buying process. The message should be tailored for specific audiences (e. g. single women; families with teenagers, etc. ), as the benefits of the product are specific to segments. Changing the message to make the positive impact of TiVo on the life of customers clearer is a low risk, low cost strategy that could have very high sales impact. 2. Incentivize Word of Mouth (Corresponds to action nr. 13) By the surveys it is known that the subscribers are mostly single men and families and also that the majority of the people that buys TiVo do it after a recommendation, so it can be inferred that the product is selling as a consequence of a mouth to mouth campaign. We recommend launching a marketing campaign to our customers incentivizing them to bring new clients to the company. We recommend sending all customers online information, and printed catalogues annou ncing that for each new subscriber they refer they will get determined prizes; some of them will be for children in order to get all the family members involved. . Offer Trials (Corresponds to action nr. 4) Another important factor to use in the new campaign will be to show real cases of customers? satisfaction. As the surveys showed, the clients who have the product are in majority very happy with it so this feeling has to be transmitted to the possible customers in order to transform them into clients. A good way to convince potential clients about the benefits of TiVo is to offer them cheap or free product trials (price to be determined based on project costs) for a limited period (e. g. 14 days). 4. Survey whole market (corresponds to action nr. 0) The company will need to improve understanding of the needs of the whole market. All the surveys the company has done until now have been only to its clients, not to the non-clients. We believe it is essential to make surveys to the w hole market to understand why people are not buying the product. Because of lack of awareness about the product? s benefits, too high price, sale points, among others. 7. IMPLEMENTATION PLAN The actions defined above should all be started as soon as possible, but will have different time paths, as shown in Figure 1. 1. Redefine campaign message The potential customers are all TV-owners who wish to gain more control over their agendas or that want to â€Å"capture† the TV-moment or â€Å"re-watch† scenes from the main program to commercials. In order to achieve this campaigns should focus on â€Å"showing the end game†: interview or show ads of real people with real experiences; connecting with the rest of TV watchers (potential customers) who were either looking the same experience or triggered an interest to get the same experience. The message changes from â€Å"buy it because we believe is good† to â€Å"buy it because we have proof from real consumers just like you! The redesign of the marketing campaigns will take approximately 4 months, so that the new message can be launched long before the Christmas shopping season. 2. Incentivize Word of Mouth Word of Mouth (WoM) is one of the most powerful marketing tools that should give result that can alter the current situation. TiVo needs to give incentives (e. g. free month of use or presents) to customers who persuade others to try or buy the product. This program should be run for a number of months and then be evaluated. [pic] Figure 1 Implementation plan 3. Offer trials In order to show how confident TiVo is about the product and to give our customers a chance to â€Å"check-out† the product, the company should offer customers a â€Å"pay after 14 days† policy. The customer can try the product for free for 14 days and if they want to keep it, they pay for the product in full; otherwise they have to return the product â€Å"in the same condition† as they have purchased it. This will allow many more customers’ attention and interest about the product which we believe will lead to increase in sales. This campaign can be launched within months and evaluated while running the campaign. Risk of the campaign will be the cost of returned devices that will have to be sold at a discount. 4. Survey whole market Although TiVo did survey consumers (which provided valuable information if we wanted to implement our current product), TiVo’s purpose is to attract potential customers and it’s important to know the current trend and what the mainstream markets are. Most of the customers have answered positively about the product once they’ve purchased it. It is a matter of letting the product be known Knowing about the mainstream market and preferences of ustomers in these markets will enable the company to better understanding of the market and how to promote it to be attractive. The survey results will help redesigning the campaign, as defined in the first action. 8. CONTINGENCY PLAN / RISK ANALYSIS Risk profile of the actions explored above is very low. In the first place costs will be low in relation to the Marketing Sales budget. Secondly the brand ima ge is not likely to suffer from the â€Å"customer friendly† actions. In case the change of marketing message would work counter-productive, it would be easy to shift to the current message again. Sales forecasts will need to be adjusted in both scenarios. Key risk for the company seems to be to run out of cash required for marketing in the short term. As gross margin recently turned positive, the contingency plan in this case would be to cut marketing costs and focus on Word of Mouth, while at the same time trying to attract more capital. [pic][pic][pic] What actions should TiVo take in order to convince the public to buy its product, in that way increasing sales in order to become profitable?

Media Focus more on the personality than the politician. essays

Media Focus more on the personality than the politician. essays Pay no attention to that man behind the curtain is a line taken from the Wizard of Oz and is spoken by the wizard to symbolize that it is not the person pulling the strings and levers who is of importance, but rather the effect that one experiences in front of that curtain. A useful quote to illustrate that which confronts political audiences everyday. What we see and hear with respect to politicians, what we understand by policy or party affiliation is such that we need to question what it is that is actually being conveyed and for what reason? More importantly, as the audience or enquiring social scientist, is it not of consequence to know who the wizard actually is, whether he be the media or the politician? In the last fifty years, the media, in its numerous forms, has become a central social institution. Whether it be through television, newspapers or the internet, the media is the principle means by which information is communicated to us. The media is by no means a definitive source of knowledge, but it certainly is a valuable and practical source by which information, that would otherwise have gone unknown, be communicated to the general public. Political awareness today, for the majority of us, is brought directly to us as a result of the media. In the U.S., for example, television is the main method by which Americans find out about news politics etc, and therefore candidates not only try to obtain as much airtime as possible but also spend a large proportion of their budget on television advertising. With the advent of new technology enabling information to be conveyed to the masses, politicians were quick to reap the benefits that the media had to offer. Although the need to campaign door-to-door has some benefits, they are benefits for of a politician of a past generation. Today, such campaigning, is only of viable when it is mediated to the...

MIH512-Demography and Health (Module 2-CBT) Essay

MIH512-Demography and Health (Module 2-CBT) - Essay Example The reliability of the data presented is excellent because the U.S. census bureau administers the site. Another good site is found at the University of Virginia. The URL for the site is http://fisher.lib.virginia.edu/collections/stats/histcensus/. The name is referred to as the Historical Census Browser. Data for each census from 1790 to 1960 is available. This resource is outstanding because the data is organized neatly in charts and graphs. There also is a function called â€Å"MapIt† that will create a chloropleth map for any data set. The data would be very accurate because the University of Virginia is a well-respected institution of higher education. Poor information would lessen their academic standing. A third site with census data is the Tiger mapping service of the U.S. census bureau. The URL is http://tiger.census.gov/. This information is excellent but the maps are difficult to produce. The service is slow and the maps do not offer much flexibility as far as manipulating data and copying. The information is dependable because it comes from the U.S. census bureau. A great site for gathering census data on the country of Brazil is found at URL http://www.ibge.gov.br/english/. The IBGE is the Brazilian equivalent of the U.S. census bureau. It differs in that this agency seems much more concerned with gathering statistical data on agricultural and geographical data and not just population data. The site has an official feel to it and it is obviously administered by a governmental agency. The major drawback is some of the reports and statistics are not presented in English. The home page has an English option, but other parts of the site are not yet translated. A second site that gives census statistics for foreign trade is the U.S. census bureau at URL http://www.census.gov/foreign-trade/balance/c3510.html. Though this census information is specific to foreign trade with the U.S. it still is a good,

Irish revolution Essay Example | Topics and Well Written Essays - 1250 words

Irish revolution - Essay Example A clash of opinions and perspectives results into conflicts. ‘Revolutionary changes’ ultimately refer to the outcomes of a revolution i.e. the resulting reforms and alterations that progress after a revolution. Most changes begin with a single major conflict but it is not until later that we realize whether it is revolutionary or not. On the other hand, when a nation faces the problem of sovereignty, a revolutionary outcome is guaranteed. When various major parties arise in a nation, with various ideologies, that condition is known as multiple sovereignty. Yet the result i.e. victory and defeat, in any condition can never be predicted with certainty. Dual sovereignty is when a nation has two major parties, mainly the ruling party and the opposition party, with two different point of views. Irish revolution was a rebellion against the British rule by the ‘united Irishmen’ of Ireland (The 1798 Irish rebellion 2013). ‘United society of Irishmen’ wa s a combination of various protesting parties into a single society. They demanded the separation of Ireland from Britain. The causes for this demand were deep rooted. The main conflict between the British and the Irish was due to religion. For many years Ireland had been ruled by the Anglican minority as they were a member of ‘established church that was loyal to the British crown’. ... he fact that Ireland was given lesser rights than other British colonies are some of the reasons which led to numerous disagreements between the government and the public. The United society of Irishmen mainly relied on the intervention of the French military. Their assistance came as promised in fleets however adverse weather conditions scattered them leaving the Irish support less. The French fleets were an open declaration of rebellion thus the British, acting from the Dublin castle, suppressed the society to almost non-existence. Contrary to further plans, the Dublin rebels retreated at the last second of rebellion and brought the minor resistances up front creating confusion, chaos and terror. All the rebellions were suppressed with the exception of Wexford. However the rebels again faced defeat New Ross, Arklow, Newtownbarry. The northern rebellions in Ballymena, Antrim and Ballynahinch were brutally crushed by the military. The United Irishmen suffered much causality and the n orthern revolt was suppressed. The army then progressed towards the Vinegar Hill where the rebels had camped. The army made a surprise attack upon them. They were slaughtered and hanged mercilessly. The British regained control over the country. The last blow on behalf of the Irish rebels was made by the French when 1000 troops attacked and won at Castlebar. However it was an empty victory as the French soon ran out of steam and surrendered to the British. The chief outcome of the rebellious activities was the abolishment of Irish parliament. Their failed freedom and independence movement led the British to take even more severe measures against them. This resulted in even lesser freedom, equality and liberty to the citizens of Ireland. The numerous amounts of causalities due to this

History And Evolution Of Sitcoms

History And Evolution Of Sitcoms In the field of entertainment, everybody could use a good laugh and this is where the comedy genre comes in. As the name states, its purpose is to bring humor and laughter to the audience. Comedies come in many formats in movies and television. In television, one of the most common genre is the situation comedy or sitcom, for short. As the name states the plot is centered on a particular situation set in a typical setting such as a home or workplace. A situation comedy features a regular cast of characters plus recurring ones who would appear in subsequent episodes as well as special guest stars. There are sitcoms that are aired performed before a live studio audience, making it similar to a theatrical play. One can tell it is live whenever a special guest star would appear as the audience would cheer enthusiastically. Another distinctive feature of the sitcom is the laugh track or what is called canned laughter which is played every time a hilarious scene unfolds. What makes sitcoms different from stand up comedy and sketch comedy is that they have a storyline and this essentially makes it a comedic drama; and as mentioned before, the setting is usually centered on family, workplace, or a group of friends as the principal characters or mainstays. Sitcoms came about when the television was introduced and this enabled audiences to return to a certain program if they like it. As a result of this (initial) trend, the performers who have key roles would become mainstays and the situations would remain the same to enable audiences to be familiar with them. Even animated shows, also adapt the sitcom format to cater to a specific audience as well, not merely children. Another feature of the sitcom is that it is often character driven and naturally, running gags often develop during a series or season. The plot of a sitcom episode is typical: It starts with the status quo where everything is normal among the characters and then, a disruption will occur, thereby affecting the usual situation and the relationships of the characters, but by the end of the episode, these issues will be settled, the situation will revert to the status quo and it is alls well that ends well until the next episode where the it will happen all over again but in a different plot. History and Evolution: Throughout its history, sitcoms over the years have evolved not only in the performers but also in the plot as well as how humor is delivered. In the early years of sitcom, the most common method of delivery is the slapstick approach of the 1950s and well into the 1960s. The slapstick is characterized by exaggerated violence where the characters appear to be hitting one another with exaggerated sound effects without getting hurt. This is common is earlier comedies such as The Three Stooges. Slapstick also features characters doing unthinkable or crazy stunts or acts or silly things in the scene to the point of making complete fools of themselves. One of the most popular sitcoms of the period was I Love Lucy starring the real-life couple of Lucille Ball and Desi Arnaz. This sitcom is one of those that features the slapstick delivery. One example is a scene in one episode where Lucy works in a chocolate factory. The chocolates are being churned out so fast that Lucy had to eat those that could not be packaged. In another episode, Lucy was mashing grapes in a winery and wrestled with another worker in the vat, making a mess out of themselves (Oppenheimer, 4-5). As for the setting, it centers on a typical couple, Lucy and Ricky (Arnaz) Ricardo. What makes the story interesting is that Lucy is not content in being a plain housewife while her husband works as a bandmaster in a club. Lucy aspires to have a career and this is the source of the humor. Besides these madcap adventures and misadventures, there is also the relationship with their neighbors Fred and Ethel who play the straight couple to their seemingly dysfunctional one to provide balance. Essentially, women would be portrayed as scatterbrained but extremely clever, men would be indignant (like Ricky), and friends or neighbors would be unwitting pawns, accomplices or villians (such as Fred and Ethel). Besides the typical family setting, early sitcoms offer different settings but with similar plots such as Sergeant Bilko, which looks at the humorous side of the military; Car 54 Where Are You? for the police officers and McHales Navy in the US Navy set during World War II to boot. The 1960s added a fantasy touch with sitcoms like I Dream of Jeannie and Bewitched. This was made possible with advancements in the realm of special effects which enabled these magic tricks to be performed. In addition, 1960s sitcoms deviated from the earlier ones in the sense that they were not filmed before live audiences but were filmed instead where the sessions are called tapings. The 1970s and 1980s saw a change in the character makeup of the sitcoms as evidenced by such shows as The Jeffersons, Different Strokes, Barney Miller and Chico and the Man where nonwhites began to share top billing as well yet the plot remains the same. This underscored by the real-world events happening the changes America has been going through by way of racial integration and that nonwhites were not regarded as equals to whites. This is what these shows intend to convey besides providing laughter (Dalton and Linder 125-126; Hamamoto 87, 90-91). In terms of delivery, studio audiences became the norm again on shows that were not filmed in several locations and several factors have to be taken into consideration such budget (Dalton and Linder 49-50). There were also changes in the composition of the characters or how they are shown in the show. It is no longer the typical family. The show would center on the kids or teens such as Facts of Life and Charles in Charge which deals prima rily with issues teenagers usually face. Besides race, feminism got into the act with shows such as Rhoda and The Mary Tyler Moore Show as women took lead roles in sitcoms as well. The 1990s saw a continued surge of similar shows such as Murphy Brown and Just Shoot Me. There were even instances when some shows would challenge morals at the time such as MarriedWith Children which features a dysfunctional family, an introduction to the genre commonly known as transgression comedy. One other noticeable feature of sitcoms starting in the 1970s was the evolution of the delivery. Slapstick was no longer used at this point in time. Rather, the producers and the performers make use of the current situations they are in, whether they are personal, affecting only them or the social situation that affects them entirely. In other words, they poke fun at their problems without having to do crazy stunts or exaggerated violence reminiscent of The Three Stooges. The 1990s saw the emergence of sitcoms in animation followed the lead of live shows such as The Simpsons which is still enjoying a following to this day, and later South Park (Dalton and Linder 270-271). This trend would go on well into the 21st century with similar shows coming out such as The Office and 30 Rock which still follow the same trend. Furthermore, sitcoms have also broken down into categories according to age groups. Disney Channel offers sitcoms for children and teenagers such as Thats so Raven, Hannah Montana and Corey in the House. Naturally, the shows centers on the younger characters with the adults in the supporting role but the plot is nonetheless similar to the mainstream sitcoms (Dalton and Linder 44-45). Analysis: By the 21st century, the trend in the entertainment industry is leaning toward reality-TV shows which feature non-actors and single-camera recordings. The reason for this increasing popularity is that the participants are not actors and the audience can easily relate to them as the cameras capture every moment of their life and they are seen in their best and their worst and there are no cuts and takes, the camera continues rolling. It is as real as it gets and all the elements or genres are there from action, drama and even comedy without the canned laughter. It is said that these shows will replace mainstream programming which would affect soap operas and sitcoms. But this does not mean sitcoms will fade into oblivion or give up without a fight. In the latter shows, for instance, The Office, 30 Rock and even The Drew Carey Show make use of an element called the pathos. Where the shows make the viewers sympathize with the characters, and relate to them on a level unlike any other show (Graham 1). Old sitcoms never had this pathos. The problems facing the characters in the show are similar problems the audience faces on a regular basis in real life (Graham 1). In addition, this pathos need not be exaggerated like in slapstick. It is shown in a plain simple way similar to what real people go through every day. The characters, especially the main ones, are depicted as the everyman or average Joe. In the case of the three sitcoms, they reflect the joys, trials and tribulations the average (American) employee goes through in their daily routine. Nothing is exaggerated and the issues they face are real since real people experience them too. Matthew G ilbert puts it nicely At their best these single hand held sitcoms are an uplifting art form, one that has come of age in the past 20 years. They can invent a unique comic lexicon, invite us to laugh at our failings, capture the brilliance of our imaginations, and satirize our culture, they can reflect, clarify, and normalize human nature(Gilbert 1). Even animated sitcoms like The Simpsons and South Park show that as well this is why such animated series also appeal to adults, breaking the notion that they are only for children. Shows like Arrested Development and The Office are amongst some of a growing number of sitcoms that look different and are produced differently from sitcoms in the past. Eric Berlin states on the changing sitcom This new genre combines oddball characters, stress on improv acting, cinematic look, expert single-camera production work, and inventive use of flashbacks, private one on one confessions with the camera and quick cut-aways. The writing is daring, smart, and resembles the everyday awkward encounters that humans experience(Berlin 3). Shows like The Office and Arrested Development have been appropriately termed by author Brett Mills as the televisual style called comedy verite(Thompson 63). What comedy verità © is doing through its distinctive televisual style is shift the source of humor in the television comedy from the constructed joke, as seen in prior sitcoms, to the observation of a comic event (Thompson 67). Thompson states The observational component of these sitcoms, w hich includes not just what they look like but also the timing of shots and the sense that at times we observe events in real time, creates a different type of engagement with the narrative. The sitcom is thus reinvigorated by a shift from the tired realm of the staged sitcom, with its three cameras, studio audience, or one-camera, coverage shooting, to an experience of observation or witness(Thompson 67). A big part of these new comedy verite style sitcoms is how they convey the observational mode that the viewer is caught in, primarily through handheld shooting and a pacing that suggests particular segments unfold in real time as if their viewer were there (Thompson 68). However these segments and scenes are increasingly taking place in intimate settings, including shots conveying a particular characters subjectivity and vulnerability, and are less marked by characters performing for the camera, a fly on the wall type of perspective (Thompson 68). This production style that is new to the Sitcom tries to convey to the viewer that they are not watching comedy but are observing the comedic acts that unfold before the ever present handheld camera. Whether the acting is improvised or carefully scripted, it looks like it just happened and thats the whole point (Thompson 71). As a mode of production, this new developed sub genre of the sitcom is addressing comedy like never before and is effective in the use of presenting what is truly funny to viewers. Furthermore, what makes sitcoms better than reality TV is, as mentioned earlier, these shows do not only try to make the audience relate to the character as far as pathos is concerned, but being a comedy, it encourages the audience to laugh off their problems as well. Furthermore, unlike reality shows, it is the characters that are laughed at, not the people themselves. Because of this, this is what will make sitcoms last longer and keep on entertaining people.

Edexcel Maths Fp2 Paper

Paper Reference(s) 6667 Edexcel GCE Further Pure Mathematics FP1 Advanced Level Specimen Paper Time: 1 hour 30 minutes Materials required for examination Answer Book (AB16) Graph Paper (ASG2) Mathematical Formulae (Lilac) Items included with question papers Nil Candidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Thus candidates may NOT use calculators such as the Texas Instruments TI-89, TI-92, Casio CFX-9970G, Hewlett Packard HP 48G.Instructions to Candidates In the boxes on the answer book, write the name of the examining body (Edexcel), your centre number, com/geo-sba-cxc/" class="ilgen">candidate number, the unit title (Further Pure Mathematics FP1), the paper reference (6667), your surname, initials and signature. When a calculator is used, the answer should be given to an appropriate degree of accuracy. Information for Candidates A booklet ‘Mathematical Formulae and Statistical Tables’ is provid ed. Full marks may be obtained for answers to ALL questions. This paper has eight questions. Advice to Candidates You must ensure that your answers to parts of questions are clearly labelled.You must show sufficient working to make your methods clear to the Examiner. Answers without working may gain no credit. This publication may only be reproduced in accordance with London Qualifications Limited copyright policy. Edexcel Foundation is a registered charity.  ©2003 London Qualifications Limited 1. Prove that a (r r =1 n 2 – r -1 = ) 1 (n – 2)n(n + 2) . 3 (5) 2. 1 f ( x ) = ln x – 1 – . x (a) Show that the root a of the equation f(x) = 0 lies in the interval 3 < a < 4 . (2) (b) Taking 3. 6 as your starting value, apply the Newton-Raphson procedure once to f(x) to obtain a second approximation to a.Give your answer to 4 decimal places. (5) 3. Find the set of values of x for which 1 x > . x -3 x -2 (7) 4. f ( x ) ? 2 x 3 – 5 x 2 + px – 5, p I ?. The equation f (x) = 0 has (1 – 2i) as a root. Solve the equation and determine the value of p. (7) 5. (a) Obtain the general solution of the differential equation dS – 0. 1S = t. dt (6) (b) The differential equation in part (a) is used to model the assets, ? S million, of a bank t years after it was set up. Given that the initial assets of the bank were ? 200 million, use your answer to part (a) to estimate, to the nearest ? illion, the assets of the bank 10 years after it was set up. (4) 2 6. The curve C has polar equation r 2 = a 2 cos 2q , -p p ? q ? . 4 4 (a) Sketch the curve C. (2) (b)Find the polar coordinates of the points where tangents to C are parallel to the initial line. (6) (c) Find the area of the region bounded by C. (4) 7. Given that z = -3 + 4i and zw = -14 + 2i, find (a) w in the form p + iq where p and q are real, (4) (b) the modulus of z and the argument of z in radians to 2 decimal places (4) (c) the values of the real con stants m and n such that mz + nzw = -10 – 20i . (5) 3 Turn over 8. (a) Given that x = e t , show that (i) y dy = e -t , dx dt 2 dy o d2 y – 2t ? d y c 2 – ?. =e c 2 dt ? dx o e dt (ii) (5) (b) Use you answers to part (a) to show that the substitution x = e t transforms the differential equation d2 y dy x 2 2 – 2x + 2y = x3 dx dx into d2 y dy – 3 + 2 y = e 3t . 2 dt dt (3) (c) Hence find the general solution of x2 d2 y dy – 2x + 2y = x3. 2 dx dx (6) END 4 Paper Reference(s) 6668 Edexcel GCE Further Pure Mathematics FP2 Advanced Level Specimen Paper Time: 1 hour 30 minutes Materials required for examination Answer Book (AB16) Graph Paper (ASG2) Mathematical Formulae (Lilac) Items included with question papers NilCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Thus candidates may NOT use calculators such as the Texas Instruments TI 89, TI 92, Casio CFX-9970G, Hewlett Pac kard HP 48G. Instructions to Candidates In the boxes on the answer book, write the name of the examining body (Edexcel), your centre number, candidate number, the unit title (Further Pure Mathematics FP2), the paper reference (6668), your surname, initials and signature. When a calculator is used, the answer should be given to an appropriate degree of accuracy.Information for Candidates A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. Full marks may be obtained for answers to ALL questions. This paper has eight questions. Advice to Candidates You must ensure that your answers to parts of questions are clearly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers without working may gain no credit. This publication may only be reproduced in accordance with London Qualifications Limited copyright policy. Edexcel Foundation is a registered charity.  ©2003 London Qualifications Limited 1.The displacement x of a particle from a fixed point O at time t is given by x = sinh t. 4 At time T the displacement x = . 3 (a) Find cosh T . (2) (b) Hence find e T and T. (3) 2. Given that y = arcsin x prove that (a) dy = dx (1 – x ) 2 1 , (3) (b) (1 – x 2 ) d2 y dy -x = 0. 2 dx dx (4) Figure 1 3. y P(x, y) s A y O x Figure 1 shows the curve C with equation y = cosh x. The tangent at P makes an angle y with the x-axis and the arc length from A(0, 1) to P(x, y) is s. (a) Show that s = sinh x. (3) (a) By considering the gradient of the tangent at P show that the intrinsic equation of C is s = tan y. 2) (c) Find the radius of curvature r at the point where y = p . 4 (3) S 4. I n = o x n sin x dx. p 2 0 (a) Show that for n ? 2 ?p o I n = nc ? e 2o n -1 – n(n – 1)I n – 2 . (4) (4) (b) Hence obtain I 3 , giving your answers in terms of p. 5. (a) Find ? v(x2 + 4) dx. (7) The curve C has equation y 2 – x 2 = 4. (b) Use your answer to part (a) to find the area of the fin ite region bounded by C, the positive x-axis, the positive y-axis and the line x = 2, giving your answer in the form p + ln q where p and q are constants to be found. (4) Figure 2 6. y O 2pa x The parametric equations of the curve C shown in Fig. are x = a(t – sin t ), y = a(1 – cos t ), 0 ? t ? 2p . (a) Find, by using integration, the length of C. (6) The curve C is rotated through 2p about Ox. (b) Find the surface area of the solid generated. (5) 7 7. (a) Using the definitions of sinh x and cosh x in terms of exponential functions, express tanh x in terms of e x and e – x . (1) (b) Sketch the graph of y = tanh x. (2) 1 ? 1 + x o lnc ?. 2 e1 – x o (c) Prove that artanh x = (4) (d) Hence obtain d (artanh x) and use integration by parts to show that dx o artanh x dx = x artanh x + 1 ln 1 – x 2 + constant. 2 ( ) (5) 8.The hyperbola C has equation x2 y2 = 1. a2 b2 (a) Show that an equation of the normal to C at P(a sec q , b tan q ) is by + ax sin q = a 2 + b 2 tan q . (6) ( ) The normal at P cuts the coordinate axes at A and B. The mid-point of AB is M. (b) Find, in cartesian form, an equation of the locus of M as q varies. (7) END U Paper Reference(s) 6669 Edexcel GCE Further Pure Mathematics FP3 Advanced Level Specimen Paper Time: 1 hour 30 minutes Materials required for examination Answer Book (AB16) Graph Paper (ASG2) Mathematical Formulae (Lilac) Items included with question papers NilCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Thus candidates may NOT use calculators such as the Texas Instruments TI 89, TI 92, Casio CFX 9970G, Hewlett Packard HP 48G. Instructions to Candidates In the boxes on the answer book, write the name of the examining body (Edexcel), your centre number, candidate number, the unit title (Further Pure Mathematics FP3), the paper reference (6669), your surname, initials and signature. When a calculator is used, the answer sho uld be given to an appropriate degree of accuracy.Information for Candidates A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. Full marks may be obtained for answers to ALL questions. This paper has eight questions. Advice to Candidates You must ensure that your answers to parts of questions are clearly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers without working may gain no credit. This publication may only be reproduced in accordance with London Qualifications Limited copyright policy. Edexcel Foundation is a registered charity.  ©2003 London Qualifications Limited 1. y = x 2 – y, y = 1 at x = 0 . dx y – y0 ? dy o Use the approximation c ?  » 1 with a step length of 0. 1 to estimate the values of y h e dx o 0 at x = 0. 1 and x = 0. 2, giving your answers to 2 significant figures. (6) 2. (a) Show that the transformation w= z -i z +1 maps the circle z = 1 in the z-plane to the line w – 1 = w + i in the w-plane. (4) The region z ? 1 in the z-plane is mapped to the region R in the w-plane. (b) Shade the region R on an Argand diagram. (2) 3. Prove by induction that, all integers n, n ? 1 , ar > 2 n r =1 n 1 2 . (7) 4. dy d2 y dy +y = x, y = 0, = 2 at x = 1. 2 dx dx dxFind a series solution of the differential equation in ascending powers of (x – 1) up to and including the term in (x – 1)3. (7) 5. ? 7 6o A=c c 6 2? . ? e o (a) Find the eigenvalues of A. (4) (a) Obtain the corresponding normalised eigenvectors. (6) NM 6. The points A, B, C, and D have position vectors a = 2i + k , b = i + 3j, c = i + 3 j + 2k , d = 4 j + k respectively. (a) Find AB ? AC and hence find the area of triangle ABC. (7) (b) Find the volume of the tetrahedron ABCD. (2) (c) Find the perpendicular distance of D from the plane containing A, B and C. (3) 7. ? 1 x – 1o c ? 5 A( x) = c 3 0 2 ? , x ? 2 c1 1 0 ? e o (a) Calculate the inverse of A(x). (8) ? 1 3 â €“ 1o c ? B = c3 0 2 ? . c1 1 0 ? e o ? po c ? The image of the vector c q ? when transformed by B is cr? e o (b) Find the values of p, q and r. (4) ? 2o c ? c 3? . c 4? e o 11 8. (a) Given that z = e iq , show that zp + 1 = 2 cos pq , zp where p is a positive integer. (2) (b) Given that cos 4 q = A cos 4q + B cos 2q + C , find the values of the constants A, B and C. (7) The region R bounded by the curve with equation y = cos 2 x, rotated through 2p about the x-axis. (c) Find the volume of the solid generated. (6) p p ? x ? , and the x-axis is 2 2END NO EDEXCEL FURTHER PURE MATHEMATICS FP1 (6667) SPECIMEN PAPER MARK SCHEME Question number 1. Scheme Marks M1 B1 a (r r =1 n 2 – r -1 = a r2 – a r – a1 r =1 r =1 r =1 ) n n n ? n o c a1 = n ? e r =1 o = = = n (n + 1)(2n + 1) – ? 1 on(n + 1) – n c ? 6 e 2o n 2n 2 – 8 6 [ ] M1 A1 A1 (5) (5 marks) 1 n(n – 2 )(n + 2 ) 3 2. (a) f ( x) = ln x – 1 – 1 x f (3) = ln 3 – 1 à ¢â‚¬â€œ 1 = -0. 2347 3 f (4) = ln 4 – 1 – 1 = 0. 1363 4 f (3) and f (4) are of opposite sign and so f ( x ) has root in (3, 4) (b) x 0 = 3. 6 f ? (x ) = 1 1 + x x2 M1 A1 (2) M1 A1 f ? (3. 6 ) = 0. 354 381 f (3. 6) = 0. 003 156 04 Root  » 3. – f (3. 6) f ? (3. 6) M1 A1 ft A1 (5) (7 marks)  » 3. 5911 13 EDEXCEL FURTHER PURE MATHEMATICS FP1 (6667) SPECIMEN PAPER MARK SCHEME Question number 3. Scheme x x x 2 – 3x + 3 1 1 > ? >0 ? >0 x-3 x-2 x-3 x-2 (x – 3)(x – 2 ) Marks M1 A1 B1 B1 Numerator always positive Critical points of denominator x = 2, x = 3 x < 2 : den = (- ve)(- ve) = + ve 2 < x < 3 : den = (- ve)(+ ve) = – ve 3 < x : den = (+ ve)(+ ve) = + ve M1 A1 A1 (7) (7 marks) Set of values x < 2 and x > 3 {x : x < 2} E {x : x > 3} 4. If 1 – 2i is a root, then so is 1 + 2i B1 M1 A1 M1 A1 ft A1 A1 (7) x – 1 + 2i )(x – 1 – 2i ) are f actors of f(x) so x 2 – 2 x + 5 is a factor of f (x) f ( x ) = x 2 – 2 x + 5 (2 x – 1) Third root is 1 2 ( ) and p = 12 (7 marks) 5. (a) dS – (0. 1)S = t dt – ( 0. 1)dt Integrating factor e o = e -(0. 1)t M1 d Se – (0. 1)t = te – (0. 1)t dt Se – (0. 1)t = o te – (0. 1)t dt = -10te – (0. 1)t – 100e – (0. 1)t + C [ ] A1 A1 M1 A1 A1 (6) S = Ce (0. 1)t – 10t – 100 (b) S = 200 at t = 0 ? 200 = C – 100 i. e. C = 300 S = 300e (0. 1)t – 10t – 100 M1 A1 At t = 10, S = 300e – 100 – 100 = 615. 484 55 M1 A1 ft (4) (10 marks) Assets ? 615 million NQ EDEXCEL FURTHER PURE MATHEMATICS FP1 (6667)SPECIMEN PAPER MARK SCHEME Question number 6. (a) l Scheme Marks q B1 (Shape) B1 (Labels) (2) (b) Tangent parallel to initial line when y = r sin q is stationary Consider therefore d 2 a cos 2q sin 2 q dq ( ) M1 A1 = -2 sin 2q sin 2 q + cos 2q (2 sin q cos q ) =0 2 sin q [cos 2 q cos q – sin 2q sin q ] = 0 sin q ? 0 ? cos 3q = 0 ? q = p -p or 6 6 M1 A1 o ? ? o ? 1 p o? 1 -p Coordinates of the points c c a, ? c a, ? c 6 6 oe 2 e 2 A1 A1 (6) 1 o4 2 1 2o4 (c) Area = o r dq = a o cos 2q dq 2 o -p 2 o -p 4 4 p p M1 A1 a2 a2 1 2 e sin 2q u = a e = [1 – (- 1)] = 2 e 2 u -4p 4 2 u p 4 M1 A1 (4) (12 marks) 15EDEXCEL FURTHER PURE MATHEMATICS FP1 (6667) SPECIMEN PAPER MARK SCHEME Question number 7. (a) z = -3 + 4i, zw = -14 + 2i Scheme Marks w= = = – 14 + 2i (- 14 + 2i )(- 3 – 4i ) = (- 3 + 4i )(- 3 – 4i ) – 3 + 4i M1 A1 A1 A1 M1 A1 M1 A1 M1 A1 A1 M1 A1 (5) (13 marks) (4) (42 + 8) + i(- 6 + 56) 9 + 16 50 + 50i = 2 + 2i 25 (4) (b) z = (3 2 + 42 = 5 4 = 2. 21 3 ) arg z = p – arctan (c) Equating real and imaginary parts 3m + 14n = 10, 4m + 2n = -20 Solving to obtain m = -6, n = 2 NS EDEXCEL FURTHER PURE MATHEMATICS FP1 (6667) SPECIMEN PAPER MARK SCHEME Question number 8. (a)(i) x = et , dy dy dy dt = = e -t dt dx dt dxSch eme Marks M1 A1 ? dx t o c =e ? e dt o (ii) d 2 y dt d e – t dy u e = dt u dx 2 dx dt e u e M1 e dy d2 yu = e – t e – e -t + e -t 2 u dt dt u e e d 2 y dy u = e – 2t e 2 – u dt u e dt (b) x2 2t A1 A1 (5) d2 y dy – 2x + 2y = x3 2 dx dx – 2t e e e d 2 y dy u t – t dy + 2 y = e 3t e 2 – u, – 2e e dt u dt e dt M1 A1, A1 (3) d2 y dy – 3 + 2 y = e 3t 2 dt dt (c) Auxiliary equation m 2 – 3m + 2 = 0 (m – 1)(m – 2) = 0 Complementary function y = Ae t + Be 2t e 3t 1 Particular integral = 2 = e 3t 3 – (3 ? 3) + 2 2 General solution y = Ae t + Be 2t + 1 e 3t 2 = Ax + Bx 2 + 1 x 3 2 M1 A1 M1 A1 M1 A1 ft 6) (14 marks) 17 EDEXCEL FURTHER PURE MATHEMATICS FP2 (6668) SPECIMEN PAPER MARK SCHEME Question Number 1. cosh 2 T = 1 + sinh 2 T = 1 + 16 25 = 9 9 Scheme Marks M1 A1 (2) M1 A1 A1 ft (3) cosh T =  ± 5 5 = since cosh T > 1 3 3 4 5 + =3 3 3 e T = cosh T + sinh T = Hence T = ln 3 2. (5 marks) (a) y = arcsin x ? sin y = x M1 cos y dy =1 dx dy 1 1 = = dx cos y 1- x2 M1 A1 (3) (b) d2 y dx 2 = – 1 1- x2 2 ( ) -3 2 (- 2 x ) M1 A1 = x 1- x2 ( ) -3 2 (1 – x ) 2 d2 y dy -x = 1 – x2 x 1 – x2 2 dx dx ( )( ) -3 2 – x 1- ( 1 2 -2 x ) =0 M1 A1 (4) (7 marks) NU EDEXCEL FURTHER PURE MATHEMATICS FP2 (6668)SPECIMEN PAPER MARK SCHEME Question Number 3. Scheme x 0 Marks (a) s=o e ? dy o 2 u 2 e1 + c ? u dx e e dx o u u e dy = sinh x dx 1 y = cosh x, x B1 s = o 1 + sinh 2 x 2 dx 0 [ ] 1 = o cosh x dx = sinh x 0 x M1 A1 (3) (b) Gradient of tangent dy = tan y = sinh x = s dx s = tan y M1 A1 M1 A1 A1 (2) (c) r= ds = sec2 y dy At y = p , r = sec2 p = 2 4 4 (3) (8 marks) 19 EDEXCEL FURTHER PURE MATHEMATICS FP2 (6668) SPECIMEN PAPER MARK SCHEME Question Number 4. Scheme I n = o x n sin x dx = x n (- cos x ) p 2 0 Marks (a) [ ] p 2 0 – o 2 nx n -1 (- cos x )dx 0 p M1 A1 i i = 0 + ni x n -1 sin x i i [ -o 0 p 2 p 2 0 = n (p ) 2 [ n -1 – (n â⠂¬â€œ 1)I n -2 n -1 ] u i (n – 1)x n- 2 sin x dxy i ? A1 So I n = n(p ) 2 2 – n(n – 1)I n -2 A1 (4) (b) ?p o I 3 = 3c ? – 3. 2 I 1 e2o I 1 = o x sin x dx = [x(- cos x )] + o cos x dx 0 p 2 0 p 2 p 2 0 M1 = [sin x ] = 1 0 p 2 A1 3p ? p o I 3 = (3)c ? – 6 = -6 4 e 2o 2 2 M1 A1 (4) (8 marks) OM EDEXCEL FURTHER PURE MATHEMATICS FP2 (6668) SPECIMEN PAPER MARK SCHEME Question Number 5. Scheme x = 2 sinh t Marks B1 (a) (x 2 + 4 = 4 sinh 2 t + 4 ) ( 2 ) 1 2 = 2 cosh t dx = 2 cosh t dt I =o (x + 4 dx = 4 o cosh 2 t dt ) M1 A1 = 2 o (cosh 2t + 1) dt = sinh 2t + 2t + cM1 A1 M1 A1 ft (7) = 1 x 2 (x 2 2 ? xo + 4 + 2arsinh c ? + c e 2o 2 0 ) (b) Area = o y dx = o 0 (x ) 2 + 4 dx 2 ) M1 e1 =e x e2 = 2 ( xu u e x + 4 u + e 2arsinh u 2u0 u0 e 2 2 1 2 2 8 + 2arsinh (1) 2] = 2 2 + ln 3 + 2 A1 2 + 2 ln[1 + ( 2 ) M1 A1 (4) (11 marks) 21 EDEXCEL FURTHER PURE MATHEMATICS FP2 (6668) SPECIMEN PAPER MARK SCHEME Question Number 6. Scheme 2p 0 Marks (a) s=o e e x + y u dt e u e u  · 2 1  · u2 2 dy  · dx  · = x = a (1 – cos t ); = y = a sin t dt dt s=o 2p 0 M1 A1; A1 2p 0 a (1 – cos t ) + sin 2 t 2 dt = a o 2 p ? 2 sin c 0 2p [ ] 1 [2 – 2 cos t ]2 dt M1 A1, A1 ft (6) 1 = 2a o e ? t ou to ? t , = -4a ecosc ? u = 8a e 2o e e 2 ou 0 1 o2 (b) s = 2p o = 2p o 2p 0 ? yc x + y ? dt c ? e o 1 22 2p  · 2  · 2 2p 0 a 2 (1 – cos t ) 2 dt M1 A1 M1 3 = 8pa 2 o 0 2p 0 ?to sin 3 c ? dt e 2o = 8pa 2 o 2 e t 2 ? t ou e1 – cos c 2 ? u sin 2 dt e ou e 2p 64pa 2 t 2 e 3 t u = 8pa e – 2 cos + cos u = 2 3 2u0 3 e A1 A1 ft (5) (11 marks) OO EDEXCEL FURTHER PURE MATHEMATICS FP2 (6668) SPECIMEN PAPER MARK SCHEME Question Number 7. Scheme tanh x = sinh x e x – e – x = cosh x e x + e – x B1 Marks (1) (a) (b) 1 y 0 x -1 B1 B1 (2) (c) artanhx = z ? tanh z = x e z – e-z e z + e -z =x M1 A1 e z – e-z = x e z + e-z ( ) 1 – x )e z = (1 + x )e – z e2z = z= 1+ x 1- x 1 ? 1 + x o lnc ? = artanh x 2 e1- x o M1 A1 M1 A1 1 x dx (4) (d) dz 1 ? 1 1 o 1 = c + ? = dx 2 e 1 + x 1 – x o 1 – x 2 o artanh x dx = (x artanh x ) – o 1 – x = (x artanh x ) + 2 M1 A1 A1 (5) 1 ln 1 – x 2 + constant 2 ( ) (10 marks) 23 EDEXCEL FURTHER PURE MATHEMATICS FP2 (6668) SPECIMEN PAPER MARK SCHEME Question Number 8. Scheme x2 y2 =1 a2 b2 2 x 2 y dy =0 a 2 b 2 dx Marks (a) M1 A1 M1 A1 dy 2 x b 2 b 2 a sec q b = 2 = 2 = dx a 2 y a b tan q a sin q Gradient of normal is then a sin q b a Equation of normal: ( y – b tan q ) = – sin q (x – a sec q ) b x sin q + by = a 2 + b 2 tan q (b) M: A normal cuts x = 0 at y = B normal cuts y = 0 at x = ( ) M1 A1 (6) (a 2 + b2 tan q b ) M1 A1 (a = ( ) a2 + b2 tan q a sin q + b2 a cos q 2 ) A1 e a2 + b2 u a2 + b2 sec q , tan q u Hence M is e 2b e 2a u Eliminating q sec 2 q = 1 + tan 2 q 2 2 ( ) M1 M1 e 2aX u e 2bY u =1+ e 2 e u u ea2 + b2 u ea + b2 u A1 2 4a 2 X 2 – 4b 2Y 2 = a 2 + b 2 [ ] A1 (7) (15 marks) OQ EDEXCEL FURTHER MATHEMATICS FP3 (6669) SPECIMEN PAPER MARK SCHEME Question Number 1. Scheme Marks ? dy o x 0 = 0, y 0 = 1, c ? = 0 – 1 = -1 e dx o 0 ? dy o y1 – y 0 = hc ? ? y1 = 1 + (0. 1)(- 1) = 0. e dx o 0 ? dy o x1 = 0. 1, y1 = 0. 9, c ? e dx o 1 ? dy o y 2 = y1 + hc ? e dx o 1 = (0. 1) – 0. 9 2 B1 M1 A1 ft A1 = -0. 89 = 0. 9 + (0. 1)(- 0. 89) = 0. 811  » 0. 81 z -i ? w( z + 1) = ( z – i ) z +1 M1 A1 (6) (6 marks) 2. (a) w= z (w – 1) = -i – w z= -i-w w -1 -i-w =1 w -1 M1 A1 z =1? i. e. w – 1 = w + i (b) z ? 1? w + i ? w -1 M1 A1 (4) B1 (line) B1 (shading) (2) (6 marks) OR qiea=liEe EDEXCEL FURTHER PURE MATHEMATICS FP3 (6669) SPECIMEN PAPER MARK SCHEME Question Number 3. Scheme For n = 1, LHS =1, RHS = So result is true for n = 1 Assume true for n = k. Then k +1 r =1 Marks 1 2 M1 A1 r > 2 k2 + k +1 = = 1 2 1 k + 2k + 1 + 2 2 1 (k + 1)2 + 1 2 2 1 M1 A1 ( ) M1 A1 A1 (7) (7 marks) If true for k, true for k+1 So true for all positive integral n d2 y dy dy +y = x, y = 0, = 2 at x = 1 2 dx dx dx d2 y = 0 +1=1 dx 2 Differentiating with respect to x d 3 y ? dy o d2 y + c ? + y 2 =1 dx 3 e dx o dx 2 4. B1 M1 A1 d3 y dx 3 = -(2) + 0 + 1 = -3 2 A1 x =1 By Taylor’s Theorem y = 0 + 2(x – 1) + = 2(x – 1) + 1 1 2 3 1( x – 1) + (- 3)(x – 1) 3! 2! M1 A1 A1 (7) (7 marks) 1 (x – 1)2 – 1 (x – 1)3 2 2 OS EDEXCEL FURTHER MATHEMATICS FP3 (6669) SPECIMEN PAPER MARK SCHEME Question Number 5.Scheme A – lI = 0 Marks (a) (7 – l ) 6 6 =0 (2 – l ) M1 A1 (7 – l )(2 – l ) – 36 = 0 l2 – 9l + 14 – 36 = 0 l2 – 9l – 22 = 0 (l – 11)(l + 2) = 0 ? l1 = -2, l2 = 11 (b) l = -2 Eigenvector obtained from M1 A1 (4) 6 o ? x1 o ? 0 o ? 7 – (- 2) c ? c ? =c ? c 6 2 – (- 2)? c y 1 ? c 0 ? e oe o e o 3×1 + 2 y1 = 0 ? 2o 1 ? 2o c ? e. g. c ? normalised c – 3? c ? 13 e – 3o e o M1 A1 M1 A1 ft ? – 4 6 o ? x2 o ? 0o c ? c ? =c ? l = 11 c ? c ? c ? e 6 – 9o e y2 o e 0o – 2 x2 + 3 y 2 = 0 ? 3o 1 ? 3o c ? e. g. c ? normalised c 2? c ? 13 e 2 o e o A1 A1 ft (6) (10 marks) 27 EDEXCEL FURTHER PURE MATHEMATICS FP3 (6669)SPECIMEN PAPER MARK SCHEME Question Number 6. (a) AB = (- 1, 3, – 1) ; AC = (- 1, 3, 1) . i j k Scheme Marks M1 A1 AB ? AC = – 1 3 – 1 -1 3 1 = i (3 + 3) + j (1 + 1) + k (- 3 + 3) = 6i + 2 j M1 A1 A1 Area of D ABC = = 1 AB ? AC 2 1 36 + 4 = 10 square units 2 = = = 1 AD . AB ? AC 6 M1 A1 ft (7) (b) Volume of tetrahedron ( ) M1 A1 (2) 1 – 12 + 8 6 2 cubic units 3 ? ?  ® ? ? ® (c) Unit vector in direction AB ? AC i. e. perpendicular to plane containing A, B, and C is 1 n= (6i + 2 j) = 1 (3i + j) 10 40 M1 p = n ? AD = 1 10 (3i + j) ? (- 2i + 4 j) = 1 2 -6+4 = units. 10 10 M1 A1 (3) (12 marks) OUEDEXCEL FURTHER MATHEMATICS FP3 (6669) SPECIMEN PAPER MARK SCHEME Question Number Scheme ? 1 x – 1o c ? A( x ) = c 3 0 2 ? c1 1 0 ? e o 3 o ? – 2 2 c ? Cofactors c – 1 1 x – 1? c 2 x – 5 – 3x ? e o Determinant = 2 x – 3 – 2 = 2 x – 5 ? – 2 1 c A (x ) = c 2 2x – 5 c e 3 -1 Marks 7. (a) M1 A1 A1 A1 M1 A1 M1 A1 (8) -1 1 (x – 1) 2x o ? -5 ? – 3x ? o (b) ? 2o ? po ? – 2 – 1 6 o ? 2o c ? 1c c ? ?c ? -1 1 – 5? c 3? c q ? = B c 3? = c 2 c 4? 1 c 3 cr? 2 – 9? c 4? e o e o e oe o M1 A1 ft M1 A1 = (17, – 13, – 24 ) (4) (12 marks) 29 EDEXCEL FURTHER PURE MATHEMATICS FP3 (6669) SPECIMEN PAPER MARK SCHEME Question NumberScheme zp + Marks 8. (a) 1 1 = e ipq + ipq p z e = e ipq + e -ipq = 2 cos pq ( ) M1 A1 (2) (b) By De Moivre if z = e iq zp + 1 = 2 cos pq zp 4 1o ? 4 p = 1 : (2 cos q ) = c z + ? zo e M1 A1 M1 A1 1 1 1 1 = z 4 + 4 z 3 . + 6 z 2 2 + 4 z. 3 + 4 z z z z 1 o ? 1 o ? = c z 4 + 4 ? + 4c z 2 + 2 ? + 6 z o e z o e = 2 cos 4q + 8 cos 2q + 6 M1 A1 3 8 cos 4 q = 1 c os 4q + 1 cos 2q + 8 2 A1 ft (7) (c) V =p o p 2 p 2 p 2 p 2 y dx = p o 2 p 2 p 2 cos 4 x dx =p o 3o 1 ? 1 c cos 4q + cos 2q + ? dq 8o 2 e8 p M1 A1 ft 1 3 u 2 e1 = p e sin 4q + sin 2q + q u 4 8 u-p e 32 2 M1 A1 ft 3 = p2 8 M1 A1 (6) (15 marks) PM

Computer Motherboard (Descriptive)

Computer Motherboard Motherboard acts like the arteries of a human taking the blood all over allowing the blood to travel. It has many line-like structures that are like the veins and the arteries. These lines are the wires mounted on the motherboard that keep thousandths or even millions of connection. Motherboard is a small yet powerful device inside the computer system. The motherboard has three cards on it. First, the graphics card, it is like the eyes of the computer, it acts like the eye that saw and reflects images to the screen.Second, the sound card it is the mouth of the computer, it sends sound to the speaker, it shouts what the computer says. And the third, the modem, the nose of the computer. It sniffs messages from the wires coming from the telephone lines. If there’s a blood, there’s also the heart. The processor of the computer acts as the heart of the computer. It has a square-shaped chip that has many pins. It sits on the motherboard controlling all th e cards including the motherboard.It controls, allows, and restricts information that is being disseminated into the system like the heart. It also has a heat sink and a fan keeping the processor cool. To be able to complete the system, it also has the brain. Hard disk serves as the brain of the computer. It is rectangular in shape. Inside it, there’s a mirror-like disk where all the information are stored. The disk spin at greater speed, depending on the information /data is being written into the disk.Motherboard is also consists of chips, transistors, and capacitors. It is the other component of the motherboard that acts like the organs of the system. These chips may be small as a grain of rice and bigger as a coin. Transistor is a small, black in color and rectangular in shape. It is sometimes recognizable because of its three metal legs attached on it. Transistors is consists of thousand or even million of IC (Integrated Circuit) packed in one part. And the capacitors ar e like tanks attached in the motherboard.It varies in size; it may be small, medium or large depending on the voltage and its capacitance. Motherboard is consists of millions of chips, transistors and IC’s. It acts like the body of the computer. Without it, the computer will not work. It is like the trunk of a tree. It is an amazing thing that has millions of wires attached in a small board. It is powerful and fundamental part that the computer will not work without it. Reference: * Motherboard. Retrieved from http://www. en. wikipedia. org/wiki/motherboard