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

Romanesque Architecture and Renaissance Architecture Compared Essay

Romanesque Architecture and Renaissance Architecture Compared - Essay Example This paper evaluates historic movements such as Romanesque, Gothic, Renaissance, Islamic and mannerism, and seeks further to compare and contrast some architectural designs and artworks of these movements. Answer to Question one Romanesque architecture The term Romanesque architecture describes the building style adopted between 800AD to 1100 AD. One of the finest Romanesque architecture buildings in England is the Durham Cathedral and is often regarded as the leading Romanesque building in the world (Kimball & Edgell 251). The composite piers, of the cathedral, are alternated with drum columns, flying buttresses or lateral abutments all concealed within the triforium over the isles. These characteristics were highly inspired by the religious fervor of the Romanesque architecture period. Therefore, the design shows the Christian values which were highly valued by the people of the time. Gothic architecture Gothic architecture is an architectural style that was most common during the early and late medieval period from 12th century through 16th century. An example of a Gothic architecture is the Cologne cathedral, which dates back in the early 19th century (Kimball & Edgell 260). The geometrical and mathematical nature of the construction is indicative of the orderly universe, which is laid logically and with rationality. The statue, the sculptural decoration, stained glass and murals incorporate the creative genius as portrayed by the old and new testaments. The building and its style emphasize the religious nature of the people and the way they valued God’s power and creative works of logic. Renaissance architecture Renaissance architecture started in the fifteenth century through the early seventeenth century and replaced Gothic architecture. An example of renaissance architecture is the Palladio's Basilica in Vicenza, Italy (Kimball & Edgell 258). The church has orderly arrangement of columns, pilasters and lintels. There is the use of hemispherical d omes, which are all characteristics of the renaissance architecture (Kimball & Edgell 252). All these details were used to emphasize solid and spatial relationship where the idea of harmony leads to free and imaginative rhythms. The details of the style especially in the church building were more civic than spiritual. This feeling, therefore, emphasizes the blending of religious and secular values of the people of the time. Answer to Question two Islamic architecture incorporates both secular and religious styles from the time when Islam was founded to date and is extensively used in the shrines of Mecca and Medina (Bloom & Blair 152). Comparing the Fatimid’s architecture used in Bab al-Futuh gate and the Gothic architecture at the entrance of Carmo Church in Lisbon, Portugal, there are notable differences. Bab al-Futuh gate has a hemispherical dome while the main entrance of Carmo church has a pointed arch. In content, the Gothic architecture is created to give less democrac y in the religious sense, while the mosque architecture emphasizes freedom and secularism (Bloom & Blair 159). Therefore, the sense of holiness elicited by the two gates varies from the outside details depending on the gate architectural style. The form and content of the two are seen in the materials used, the color designs, murals employed and the emphasized details with regards to logical arrangements, balance and creativity. Answer to Question three These two works of art represent the two periods; the early Northern Renaissance and the early Italian Renaissance respectively. These two artworks are different in form. The first element that differentiates their form is the painting details, which are emphasized by

BHE 314 Mod 5 SLP Environmental Health and Safety Essay

BHE 314 Mod 5 SLP Environmental Health and Safety - Essay Example In this regard, this paper will describe and discuss some of the health effects associated with exposure of ultraviolet radiation. It is indicated by physicians that humans can have beneficial effects from small amounts of ultraviolet radiation, such as production of vitamin D in skin pores. However, frequent and serious short-term, as well as, long term effects are caused by overexposure to such ultraviolet radiation. In severe cases, individuals confront skin peeling and swelling after reddening of skin that occurs after the sunburn caused by ultraviolet radiation. (Hanslmeier, 2006) Physicians have indicated that UV-B is one of the most destructive ultraviolet bands that cause the abovementioned sunburn in humans. Moreover, they have indicated that more sensitivity is expressed by people that have skin of lighter tone, and thus, they confront more health issues. Some of the health related organizations have specified that cornea and conjunctiva confront aching irritation due to UV radiation, which is referred as Welders’ flash. (Hessen, 2002) In Welders’ flash, eye does not confront any permanent damages; however, protective pigment and outer layer of human eye is adversely affected on temporary basis. Some other researches have noted that people gone through any eye related operations are found to be more sensitive with ultraviolet radiation, and thus, confront greater risks of having a retinal injury. In this regard, a number of companies offer eyeglasses and lens implants that can absorb ultraviolet rays. On the other hand, crystalline in normal eye plays the role of filtering ultraviolet radiation; however, prolong radiation may result in adverse effect on normal eye as well. A number of clinical studies have associated risks of skin cancer with overexposure of ultraviolet radiation for a prolonged period. Some of the

Code-switching Among Students in the UK Essay Example | Topics and Well Written Essays - 3750 words

Code-switching Among Students in the UK - Essay Example This paper has been a pilot study to investigate the code-switching between English and Arabic among the Kuwaiti students in the utterances and construction level in the speech.The respondents of this study were undergraduate and postgraduate Kuwaiti students, studying in one of the UK universities programmes of both genders in different ages. The target population were from different universities, majors, and social status. The graph shows the results of the analysis. Most of the respondents do not find it a reason to code switch from Arabic to English because they want to raise audience and interest of what they are talking about with about 40 per cent said they slightly agree. There was about 25 per cent of those who disagree slightly with this fact while about 15 per cent strongly disagree. The first language of the target and sample population is Arabic, and second language is English where most of them have learned it as a compulsory subject at the age of six in the state schoo ls or earlier if they were in private schools. The quantitative method was used in this research. This was aimed at providing data for meeting the objectives of the study. This report makes a conclusion that this was a pilot study and it was aimed at finding out how the actual research will be conducted. The main aim was to find out the structure of the questions and how well they were understood by the respondents. Based on the results analyzed, most of the research questions were well understood. This is because there was no missing question that the respondents did not answer.

Managing information systems Essay Example | Topics and Well Written Essays - 3000 words

Managing information systems - Essay Example This report is aimed at assessing the need of information for the better management and handling of the huge event of the London Olympics 2012. This report will offer a great assistance in managing, controlling and handling the event viewers and public approaching the city. Management information systems have turned out to be significant component of every business that allows extensive management of the organizational data and information processing, storage, handling and management. It is really difficult for an organization to handle the organizational management tasks without having management information systems facility. The introduction of basic terms is essential before defining management information system. Data are combination of unrefined facts representing events taking place in organizations or the physical environment prior to they have been structured and managed into a structure that people can recognize and utilize. Data can include text, numbers, images and videos. On the other hand, information refers to data that have been transformed into a structure that is important and functional to human beings (Shelly, Cashman, & Vermaat, 2005, p. 6; Norton, 2001, p. 4; Laudon & Laudon, 1999, p. 7). According to (Turban, Leidner, McLean, & Wetherbe, 2005, p. 18), an information system gathers, stores, operates, evaluates, and distributes information for a particular function. Similar to any other system, an information system consists of inputs (such as instructions and data) and outputs (reports, calculations). It performs operations on the inputs by using technology like PCs and develops outputs that are delivered to users or to other systems by means of electronic networks (Turban, Leidner, McLean, & Wetherbe, 2005, p. 18). â€Å"The term information system can be described technically as a collection of interrelated components that bring together, process,

Read instructions Essay Example | Topics and Well Written Essays - 750 words - 1

Read instructions - Essay Example Through caste system, everybody who is born in the society knows what is expected of him or her and this in turn ensures distribution of human capital in all important professions. There are 4 major castes, namely Brahmans, Kshatriyaas, Vaishayas, and Shudras. These castes included religious scholars, rulers and soldiers, farmers and traders, and common unskilled workers respectively (Jaffrelot, 174). The purpose of each caste was fixed and, therefore, a proper balance of all professionals existed in the society. This is one of the major advantages of caste system. Caste system also ends power struggle and violence in the society as everyone is aware of his or her job. No farmer or trader will have an ambition to become a soldier or ruler, and no similarly religious scholar will want to become rule. This puts an end to power struggle in the society and decreases violence related to power to a certain extent. Disregarding the demerits of caste system on individuals, one of its main advantages of caste system is that it creates a society where there is political stability. This can be termed, in a way, as an advantage of the caste system. The caste system has many disadvantages for common man. There is no chance for social mobility in a society with caste system and this can create significant disparity between rich and poor. A poor and socially downgraded person will never have a chance to improve the situation of his or her family. There is monotony in the lives of people who live under a caste system and this monotony is not easy to get rid of. A person has to live all his life with the label with which he was born. There is no chance to break away from the identity one is given at the time of birth. Another disadvantage of caste system is that it destroys principles of merit and skill. The intellectual ability of a person is determined from the caste in which he or she is born, and not by characteristics of his

Ir Essay Example | Topics and Well Written Essays - 750 words

Ir - Essay Example Mr Johnson has admitted that the people have a just point when they complain. The claim that the rebels represent Islam, but Muslim theologians say they do not follow the teachings of Islam. An Islamic theological institute, Al-Azhar in Egypt, has strongly denounced the abductions, saying it â€Å"completely contradicts the teachings of Islam and its tolerant principles.† President Johnson has admitted the country is struggling, but his wife has told the group they are just playing games. The report states that the government is corrupt. Boko Haran only has a few hundred men, yet the Nigerian army seem powerless. The kidnappings have taken place just before the World Economic Forum on Africa, with 6,000 troops deployed for security, so this is an embarrassment for the president. The delegates may be kept secure, but the army cannot protect its own vulnerable people safe, so how can it hope to attract investment. This is written from a very personal viewpoint of the ‘It could have been me’ as the reporter had travelled as a student on the very same ferry route to that where tragedy recently struck. He describes how there was no thought of possible danger and that the ship was just a giant playground for the school children. The incident is described as a preventable accident, and from this the writer sees lessons which can be learnt. The ship was very overloaded and the cargo was not properly secured so it moved about, affecting the stability of the ship. The captain had left the ship in the charge of a very inexperienced mate, and this resulted in only two life boats being used and many lives lost. He describes the fury of the Korean public that the captain was among the first to leave the ship. This isn’t the only image of Korea he insists, and gives the example of a Korean crash in San Francisco where stewardesses carried injured passengers to safety. The difference