C2 Paper

Paper Reference(s) 6664 Edexcel GCE Core Mathematics C2 Advanced Subsidiary Tuesday 10 January 2006 ? Afternoon Time: 1 hour 30 minutes Materials required for examination Mathematical Formulae (Green) 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, candidate number, the unit title (Core Mathematics C2), the paper reference (6664), your surname, other name 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. The marks for individual questions and the parts of questions are shown in round brackets: e. g. (2). There are 9 questions on this paper. The total mark for this paper is 75. 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. N23552A This publication may only be reproduced in accordance with Edexcel Limited copyright policy.  ©2006 Edexcel Limited. 1. Given that f(1) = 0, (x) = 2Ãâ€"3 + x2 – 5x + c, where c is a constant. (a) find the value of c, (2) (b) factorise f(x) completely, (4) (c) find the remainder when f(x) is divided by (2x – 3). (2) 2. (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of (1 + px)9, where p is a constant. (2) The first 3 terms are 1, 36x and qx2, where q is a constant. (b) Find the value of p and the value of q. (4) N23552A 2 3. y B Figure 1 C P O A x In Figure 1, A(4, 0) and B(3, 5) are the end points of a diameter of the circle C. Find (a) the exact length of AB, (2) (b) the coordinates of the midpoint P of AB, (2) (c) an equation for the circle C. (3) 4. The first term of a geometric series is 120. The sum to infinity of the series is 480. (a) Show that the common ration, r, is 3 . 4 (3) (b) Find, to 2 decimal places, the difference between the 5th and 6th terms. (2) (c) Calculate the sum of the first 7 terms. (2) The sum of the first n terms of the series is greater than 300. (d) Calculate the smallest possible value of n. (4) N23552A 3 5. Figure 2 A 6m 5m 5m B O In Figure 2 OAB is a sector of a circle, radius 5 m. The chord AB is 6 m long. 7 ? . (a) Show that cos AOB = 25 (2) ? (b) Hence find the angle AOB in radians, giving your answer to 3 decimal places. (1) (c) Calculate the area of the sector OAB. (2) (d) Hence calculate the shaded area. (3) 6. The speed, v m s–1, of a train at time t seconds is given by v = ? (1. 2t – 1), 0 ? t ? 30. The following table shows the speed of the train at 5 second intervals. t v 0 0 5 1. 22 10 2. 28 15 20 6. 11 25 30 (a) Complete the table, giving the values of v to 2 decimal places. 3) The distance, s metres, travelled by the train in 30 seconds is given by ? s = ? ? (1. 2 t ? 1) dt . ?0 (b) Use the trapezium rule, with all the values from your table, to estimate the value of s. (3) 30 N23552A 4 7. The curve C has equation y = 2Ãâ€"3 – 5Ãâ€"2 – 4x + 2. (a) Find dy . dx (2) (b) Using the result from part (a), find the coordinates of the turning points of C. (4) d2 y (c) Find . dx 2 (2) (d) Hence, or otherwise, determine the nature of the turning points of C. (2) 8. (a) Find all the values of ? to 1 decimal place, in the interval 0? ? ? < 360? for which 5 sin (? + 30? ) = 3. (4) (b) Find all the values of ? , to 1 decimal place, in the interval 0? ? ? < 360? for which tan2 ? = 4. (5) N23552A 5 9. y Figure 3 3 2 A R B O x Figure 3 shows the shaded region R which is bounded by the curve y = –2Ãâ€"2 + 4x and the 3 line y = . The points A and B are the points of intersection of the line and the curve. 2 Find (a) the x-coordinates of the points A and B, (4) (b) the exact area of R. (6) TOTAL FOR PAPER: 75 MARKS END N23552A 6

Crito Questions Essay Example | Topics and Well Written Essays - 500 words

Crito Questions - Essay Example He also feel that it would be a shameful thing for Socrates to be publicly executed because he is no criminal. His other premise is that it is Socrates right to escape, in fact his duty since he has clearly been unjustly accused and imprisoned. Ans 2)Socrates had been imprisoned by the very people whom he was trying to help and educate. Although Socrates never believed that he was wise(one of his most famous quotes reflects this modesty) he had a method of cross questioning which became very famous because it destroyed the arguments that men gave in response to the questions he put to them. Although Socrates became very popular amongst a very powerful segment of Athenian society his tendency to question every thing including Athenian democracy won him the displeasure of many at the helm. According to an article written by Megan Worley three figures were specifically important in bringing the charges against Socrates, these were Anytus, Meletus, and Lycon. Ans 3) Winston Churchill was head of state for Great Britain at a very painful time in Europe’s history and he had to make a series of tough decisions. He is known for his inspirational leadership, and courageous decision making. I am of the opinion that both these men valued truth, dignity, awareness and justice, however Winston Churchill’s position as leader puts him in a decision where perhaps safety and victory for Britain is more important than truth and dignity. Although Socrates has developed a powerful following in Athens he does not have any nor does he apparently seek any political power. He does not feel responsible for leading Athens and this in a way leaves him free to make what he believes to be the morally right decision something that perhaps Winston Churchill did not have. Logos-‘Then, my friend, we must not regard what the many say of us: but what he, the one man who has

Security Management Research Paper Example | Topics and Well Written Essays - 4250 words - 1

Security Management - Research Paper Example This evaluation is often referred to as Return on Investment (ROI) in finance. The Return on Investment is calculated by: The concept of Return on Investment is applicable to all investments in an organization. Security sector of an organization is never an exception. The executive decision makers of organizations often have the interest to know the impact of security on the bottom-line operations of the firm. It is imperative to know how much the lack of security in an organization costs the firm before deciding on the amounts of capital to invest on security. The firm thereafter decides on the most cost effective solutions to its security woes. When applied to the security sector of the firm, a Return on Security Investment (ROSI) calculation provides quantitative answers to a firm’s essential financial questions. The Return on Security Investment aids the organization to determine if it spends too much on its security bids. It informs the organization on the financial impact on productivity that the lack of security could cause. Additionally, Return on Security Investment calculation aids the firm’s management to know the extent to which the security investment is enough (Bruce, 2008). Finally, ROSI gives the firm an overview on the benefits of the security product or system. This task looks at security management issues, dissecting aspects of ROSI with reference to Blackberry Company. Blackberry Company is a Canadian wireless equipment and telecommunication company with a reputation of developing Blackberry brands of tablets and hand-held phones. The company was originally known as Research in Motion (RIM). The company’s dominance in the United States market once stood at 43% of the market share. This dominance has precipitously declined in the recent past due to intense competition from Google’s Android and Apple’s iPhone brands. By 2013, the company’s US

Business law Essay Example | Topics and Well Written Essays - 1000 words

Business law - Essay Example There are three main approaches to statutory interpretation, also known as canons. The first is the textual canon which gives rules for interpreting legislation as written. For example, one of the textual canons suggests that anything not mentioned on a list given in a statute is not included in the law. The second is the substantive category, which includes canons that promote the judge to favour specific results or judgements. For example, this includes the Charming Betsy canon, stating that decisions made should not conflict with international law, based upon Murray v. The Charming Betsy (Steele, 2007). Finally, there are a group of deference canons, which allow the court to defer to another authority when using interpretation (Steele, 2007), such as the UK Supreme Court. Question 3 Prior to the Human Rights Act 1998, European Convention was not a source of rights (Steele, 2007), and was not allowed to be used for statutory interpretation in many cases (Steele, 2007). The Human Ri ghts Act 1998 has now made it obligatory for courts to interpret the UK legislation in a way that fits in with European Convention rights (as in the substantive category of canons). This effect can be seen in cases such as Venables and Thompson v. News Group Newspapers [2001] 1 All ER 908 (Clarkson et al, 2008). ... This is also applicable in areas where case law is the source of law because there are no legislative pieces that adequately allow the judge to come to a decision (Gruner, 2004). The strength of binding judicial precedent is that it allows decisions to be made based on previous cases without excessive need for interpretation. However, it does take the focus away from the facts of the case in hand which may cause a wrong decision to be made. Task Two Question 1 The exception to the general rule that a corporation is criminally liable occurs in cases where either the crime or the punishment cannot be committed by or served by a company. For example, in the case of R v ICR Haulage Co Ltd [1944] KB 551 (Gruner, 2004), the company was convicted of a common law conspiracy to defraud. However, it was decided that the company as an entity cannot ‘conspire’ as it does not possess mens rea (Gruner, 2004). Additionally, as the punishment for murder is life imprisonment, a company c annot be convicted as it would not be applicable to an organization. Question 2 Using the principle of identification is difficult in some cases when dealing with business law. For example, a company cannot be convicted of manslaughter without some proof that a directing or leading mind behind the company is the reason for this gross negligence, then the prosecution will fail. The main issue with this is that the directing mind has proven to be extremely difficult to identify in many companies (Laufer, 2008), and only 7 of the 34 work-related manslaughter cases brought since 1997 have succeeded (Select Committee on Home Affairs and Work and Pensions First Report, 2004). To illustrate this, in the case

Organisational Behaviour Essay Example | Topics and Well Written Essays - 1000 words - 1

Organisational Behaviour - Essay Example The field of organizational behavior is concerned with the study of what people do in an organization and how that behavior affects the performance of the organization. Organizational behavior is derived by incorporating various behavioral sciences like psychology, sociology, anthropology, political science and social psychology to ascertain the expectation level. (Foundations of human behavior, 2006) (i) Interpersonal Roles: which derives from the manager's position and the formal authority like leadership, liaison etc. (ii) Informational role: this is a direct result of the interpersonal roles ending up in information exchange, e.g., spokesperson, a monitor (iii)Decisional role: managers role as problem-solver, negotiator, resource allocator etc which is a derivation from the above two roles. (GRI Report, 2001:6) All these roles are important in a manager's job and are interrelated, even though some roles may be more influential than others depending upon the managerial position. For instance, sales managers may give more importance to interpersonal roles, while the production managers give more importance to decisional roles. The above facts lead to a clear picture that the organizational behavior is necessarily concatenated with the behavioral sciences. ... udying the interrelated behavioral processes, their disparity at specific situations and their interaction in the decision and communication performance within and among the organizational elements themselves. (Behavioral Science, 2006) Behavioral sciences like psychology, sociology, anthropology etc, help to focus in deriving organizational behavior theories. The current study focuses on three main topics (i) Personality, (ii) Stereotypes and (iii) Group Dynamics I. Personality and the "Trait Theory" Individuals are different in their mental and physical traits. People who form the main components of an organization thus differ both physically (age, sex, height, weight, etc), and also psychologically (intelligence, attitude, motivational level, perceptions, etc.) This belief that each human being is totally different from each other is known as "Law of individual differences". This points out to a crucial fact that the management has to treat them uniquely to get the best out of each and every one. (Robbins & Judge, 2006) A theory on personality aspect, The Trait theory suggests that people have some traits in common with each other and are also different from others in certain other aspects. The main five personality traits emerged from this theory related to job performance could be summarized as extroversion, agreeableness, conscientiousness, emotional stability and openness to experience. In an organizational setup the personality factors which affect its performance are the Need pattern, introversion or extroversion, tolerance for ambiguity, self esteem and self concept, Type A and Type B personalities etc. These aspects will differ from person to person and as per the managers are concerned; they need to master the tolerance for ambiguity with other

There is an ongoing debate on the use of capital punishment. Discuss Essay - 1

There is an ongoing debate on the use of capital punishment. Discuss the social, moral and historical aspects of this controversial topic - Essay Example religious leaders, and foreign press make quite a spectacle of how the Throughout the world legal systems regularly sentences people to die for the crimes they have committed. As such, many nations around the globe view the death penalty as something of a novelty (Debrevnik, 2004). From a purely economic standpoint, capital punishment is an extraordinarily expensive form of punishment. As compared with life in prison, the average cost of execution is approximately the same cost to keep a prisoner housed and fed for over 100 years (Petersen & Lynch, 2012). Currently, the average cost of execution in California exceeds 4 million dollars per criminal executed. Comparatively, the average cost to keep a prisoner housed and fed as well as ensuring proper health care and medicine usually does not exceed $35,000 per year (Semeshenko et al, 2012). At such an exorbitantly high expense, it is clear that choosing capital punishment on the grounds that killing the criminal will somehow save the state money over time is entirely illogical. As such, the argument for execution does not hinge on economic savings; instead, it hinges upon the Judeo-Christian belief of â€Å"an eye for an eye and a tooth for a tooth†. In this way, the major supporters of the death penalty believe that certain crimes are so heinous that rehabilitation is not possible. As such, one’s life is forfeit for certain crimes if convicted. This further raises the tangential issue of the purpose of prison; whether it is it to rehabilitate or to punish. According to death penalty activists, prison’s primary objective is to punish with rehabilitation being a very distant second. A secondary issue with the death penalty in its current form is that they death penalty has been proven not to be a significant deterrent against the crimes it punishes. It is obvious that murder rates throughout the world are comparably higher than almost any other nation that currently does not have the death penalty as

Philosophy (Theory of knowledge) Essay Example | Topics and Well Written Essays - 1250 words - 1

Philosophy (Theory of knowledge) - Essay Example First, reason is an objective and powerful decision tool for any body in any areas of life. As written by several authors, I believe that reason is a way of knowing what is right and wrong; what is true and not true; what is valid and not valid; and what is good and bad. As such, anybody could be guided in what to do by reasoning. For example, the decision to help others in need might be both good and bad. Taking for instance the giving of help to a sick person who is hungry. Giving the food asked is good because it will fill his hunger but this could be bad if the kind of food, the time of giving, and the way the food is to be taken are not in accordance with the doctor’s prescription. The reason(s) to help will assist the person in appropriately deciding whether to give or not the food, and if the person should give, what kind of food; when should the food be given; and in what manner should the food be taken. Likewise, in rearing a child, the decision whether to punish or n ot is based on the parents’ motives and manners of discipline which consist of reasons. Further, the decision of going to school and performing best is arrived if a person desires to prepare for the future. Hence, one can manage a better life by advantageously using reason as a guide in decision making. Second, reason is a clear or open inference to support claims and this is so because it is based on facts. Koukl says â€Å"we draw inferences based on cause and effect, or we draw conclusions by employing the laws of rationality.†1 Along this notion, Koukl cited the example that â€Å"square circles can not exist† to emphasize the law of non-contradiction. Consequently, genuine fact is tantamount to certainty which leads to a conclusion that can not be contradicted. For example, in claiming for