Underage Drinking Essay Example | Topics and Well Written Essays - 1500 words

Underage Drinking - Essay Example Lacks of legal framework coupled by moral decay in the society are the two main barriers to mitigating the problem of underage drinking. The number of young people engaging in underage drinking has been increasing with time. Everyday there are more than 5,000 kids in the US who are aged 16 and below who have the first full alcoholic drink. Statistics have shown that alcohol is the most abused substance compared to other like tobacco, marijuana, or other hard drugs by the young people. The average age of drinking has been set ad 12 to 17 years although the average age at which kids are introduced to alcoholic drinks is at 13 years. The episode of binge dirking has also been increasing with time. It is shown that the level of binge drinking by young people has increased by more that a half compared to the level in 1990s. Between 1993 and 2001 studies have found out that more than 56% of the kids aged between 13 and 20 had at least one binge drinking occasion in the past 30 days. A recent study has show that more than 10.8 million persons between the age of 12 and 20 reported to have been drinking alcohol in the past on e month. Almost 7.2 million of them were binge drinkers. (The Center for Alcohol Marketing, 2008) There are many reasons that have given by the young drinkers as to why they find it easy to abuse alcohol compared to other substances. They have given a variety of reasons but the availability of alcohol and lack of restrictive laws on the use of alcohol has been given as the most prevalent factor why they abuse alcohol than other drugs It has been shown that alcohol is readily available and can be purchased without restrictions unlike other substances. But a good number of them also showed that there is little apparently control. Even when they go to their home drunk, they are not reprimanded by their parents. This is perhaps the greatest factor that has contributed to increased number of underage drinking as compared to other reasons that can be given. It shows an intricate moral decay and lack of parental control on underage drinking. On the issue of availably of the drinks, the convenient suitor have been criticized for promoting under age drinking they have been providing drinks to the kids even without need of identification. While there are strict government laws regulation the sale of alcohol in other areas, these rules have not been well enforced in convenience stores. The fact that there are not official to look at what kids are drinking makes it more complicated to control underage drinking. However it may be difficult for the convenience stores to put in place control measures that will ensure that underage drinkers don't purchase drinks since it has been shown that some of them come in company of their parents and purchase the drinks. The issue of underage drinking has been tackled using a variety of tactics. The state security machinery including the police force has been directed to deal firmly with the problem. But the underage

Strategic Management Essay Example | Topics and Well Written Essays - 2000 words - 38

Strategic Management - Essay Example According McKienan and Carter, planning enables the company or organization to set priorities focus energies and resources, strengthen operations and ensures employees and stakeholders are working towards a common goal (2000). It helps managers to establish the objectives they want to achieve and the intended outcome from their activities and assess and adjust the organization direction in response to the changing market structure. To achieve all these management needs to come up with a strategic plan that will guide them in management. A strategic plan is a document used to communicate the organizational objectives and goals that focuses on the actions that needed to be taken to realize these goals. Strategic management is guided by that written document. Clark maintains that strategic management transforms the static plan into a structure that provides strategic performance response to decision-making process and enables it to grow and adjust to changes (2004). Execution of the plan is synonymous with management, and it results in a systematic implementation of the plan. A good strategy tends to answer three critical questions that are; where is the organization at the moment? Where does it want to go? And, how will it get there? It should consider the end always. It is not about predicting the future it is about preparing for it with the exact steps the company has to follow in mind in order to gain a competitive advantage. Competitive advantage is what keeps a company ahead of others in the same industry. According to Lowendahl and Revang, a company with a competitive advantage will perform fairly better than the rest in terms of revenue development and customers’ satisfaction (2004). Planning is not guarantee that companies will achieve more competitive advantage over the rest, but it is an essential process that can enhance sustainability of the company in the business. Strategy

Teaching The Electrocardiography Procedure

Teaching The Electrocardiography Procedure The teaching session commenced with identification of the goals and expectations for clinical learning and continued through assessing students, planning electrocardiography procedure activities, guiding students, and evaluating ECG procedure learning and performance. The goals and expectations provided areas of assessment, teaching guidelines, and the basis of evaluating learning. They were often expressed in the form of clinical objectives established for the entire teaching session for specific teaching activities. The ECG procedure teaching objectives specified knowledge acquisition, nurturing of values, and performance of psychomotor and technological skills (Braunwald, 1997). The use of constructivist model as an essential approach in the teaching actively interacted students with the material system and concepts in electrocardiography procedure domain. Through effective supervision, students were able to discuss their developing understanding and competences in carrying out electrocardiography procedure (Gaberson, 1999). This paper is based on: teaching session conducted with peers in week seven. It reflects on my effectiveness as a teacher; the creativity and efforts applied to engage and teach learners; and broadly linking all these to the teaching philosophy, learning theories, and teaching strategies. The paper also analyzes the literature related to teaching electrocardiography procedure; teaching strategies used and details recommendations on how to improve future teaching sessions in the clinical environment (Tanner, 2009). Relevant Literature Review Including Pedagogies used in Clinical Education Learning involves the process through which knowledge, is achieved and provided meaning; and comes from experience, reading, and living life. The result of learning is growth, that is, transformation in thinking, feeling or behaving. Many studies that endeavor to explain how learning occurs have been done through the years; and they been done through the lenses of disciplines such as psychology, physiology, and sociology (Vandeveer, 2005). Findings of these studies have led in the evolution of theories that try to explain how individuals learn. A theory is developed from fact analysis in relation to one another and is then applied to explain a phenomenon. The knowledge achieved from such studies has contributed to the theoretical underpinnings for entire theoretical structures or frameworks for education (Roberta, 2003). Behavioral Theories of Learning Education has been influenced more by behaviorism than any other single theory. Currently, behavioral principles continue to be used appropriately and successfully whereas others have been rejected. Behaviorism foundational principles were developed by psychologists Pavlov, Thorndike, and Skinner; these principles were derived from observations of learning in animals (Braungart, 2003). There were also other behavioral theorists who presented a variety of principles. However, all shared a common element that all behavior is learned, and that learning is influenced through environmental manipulation in which it happens and the rewards given to encourage it (Vandeveer, 2005). Behaviorism was carried into a classroom where learning experiences were structured in a manner that would assist educators attain goals through the development of objectives. Tyler (1979) stated that the most useful form for stating objectives is to express them in terms which identify both the kind of behavior to be developed in the student and the content or area of life in which this behavior is to operate; and this was the foundation of behavioral objectives. Bloom et al (1956) continued to make a classification of educational objectives that addressed the cognitive domain, the recall or recognition of knowledge or development of intellectual abilities and skills through the application of observable actions. Krathwohl (1956) led efforts in the affective domain of knowledge with a behavioral inclination. The objectives here were mainly emphasizing on an emotion, a feeling tone or a degree of acceptance or rejection; also attitudes, values, appreciations, and emotional sets or pr ejudices (Krathwohl, 1956). Achievement of the objectives continued to be through highly structured, clearly delineated, and visible behaviors. Behavioral theories enabled teachers and students alike to learn to construct behavioral objectives to guide teaching and identify measurable outcomes as the basis for evaluating learning. Behavioral theoretical learning aspects are common and continue to be applied in clinical educational settings, particularly in gaining of technical skills. Commonly, at the start of clinical nursing education, what is important to known, experienced and demonstrated is determined by the faculty. Even today, faculty still retains primary influence and authority despite increase in students involvement in their own learning. Knowledge grows, that is, prior knowledge forms a reference point for both the assimilation of new knowledge and the application transfer of knowledge from one learning experience to another. Understanding prior knowledge available allows the teacher to help students connect new knowledge to old and hence, improve overall understanding. Classically, technical skills are learnt as procedures, following a designed approach. The behavioral objectives, designed keenly to identify the expected learning outcomes, prescribes both exposure of students to learning experien ces and for their evaluation. The sequential procedural format of the nursing process, and the resulting nursing care plans are a direct outgrowth of behaviorism. Any activity learners participate in that follows this procedure, for instance, development of teaching plans, reflects behavioral learning theories. Written and verbal positive reinforcement provides a strong extrinsic learning reward; and rewarding the achievement of intended outcomes is a key behavioral aspect. Cognitive Theories of Learning Behavioral theorists emphasize that which is external to the learner. On the other hand, cognitive theories emphasize on what occurs within the learner. According to cognitive theorists, mental processes involved in acquiring, processing, and structuring information are important aspects of learning (Braungart, 2003). They particularly identified six classes of cognitive learning; presented from simple to complex. These classes were; knowledge, comprehension, application, analysis, synthesis, and evaluation. Each class was broken down further into varying numbers of components. For instance, knowledge class may be broken into knowledge of specifics, then of ways and means to deal with those specifics, and the knowledge of the universals and abstractions associated with a given field of study. Each level is associated with specific learning behavior, also verbs descriptive of those behaviors, which are to be used when writing objectives (Bloom et al., 1956). Faculty formulates the app ropriate objectives based on whether learning is new or constructed depending on prior learning, and the desired end point level of cognitive learning. Used verbs also give guidance for how the learning will be evaluated (Roberta, 2003). Models of Clinical Nursing Education Knowledge and understanding of models available in clinical practice empowers clinical education to work in a manner that suits teachers, students, and patients. Models have been defined as tools for generating ideas, guiding conceptualization, and generating explanations (Young, 2002). Clinical teachers can apply models in teaching to the procedure being experienced. Two approaches were used during the teaching session; traditional and constructivism models. Traditional Model Teaching electrocardiography procedure requires careful design of an environment in which students get opportunities to build mutual respect and support for each other while they are achieving identified learning outcomes, that is, recording electrocardiography procedures. Teachers in clinical teaching form a crucial bridge to successful experience for students (Braunwald, 1997). Research in nursing education shows that effective medical teachers are clinically competent; are able to teach; have collegial relationships with learners and agency staff; and are friendly, supportive, and patient (Halstead, 1996). Its essential for the teacher to be knowledgeable and able to share the knowledge with students in clinical setting. Such knowledge includes an understanding of the theories and concepts related to the practice of nursing, such as; recording electrocardiography procedure. Karuhije (1997) contends that attention to three teaching domains; instructional, evaluative and interpretat ional, facilitates achievement of teaching skills required to enhance success in clinical settings. Instructional infers those approaches or strategies adopted to facilitate knowledge transfer from didactic to practicum (Norton, 1998). Evaluative approach relates to making determinatives about performance and achievements as goals. Interpersonal approaches relate to relationships and interactions (Knox, 1985). Competence in clinical practice of nursing has been documented as being necessary for effective clinical teaching. Gaberson (1999) revealed that best clinical teachers exhibit expert clinical skills and judgment. Expert skills have particularly been described by students to be important. They tend to describe effective clinical teaching as those who demonstrate nursing competence in a real situation (Horst, 1988). Knowing how to teach is also a prerequisite for effective clinical teaching. Wong (1988) adds that effective clinical teachers are expected to have expertise in the art of teaching. Equally important are teacher behaviors that facilitate learning and support students in their acquisition of nursing skills (McCarbe, 1985). Brophy (1998) reveals that empirical evidence exists that correlates specific teaching methods with enhanced student learning; examples of such methods are use of objectives, effective questioning, and responding to questions. A study conducted by Pugh (19 88) revealed that preparation and the ability to explain concepts clearly and stimulate learning are also important. Other effective behaviors include being fair in evaluation, communicating expectations clearly, and providing positively timed and specific feedback (Nehring, 1990). Constructivism Model Adoption of constructivism approach to teaching in nursing gives nurse teachers with a new vision of teaching. It also parallels a paradigm shift in nursing practice from nurse centered to patient centered nursing practice (Bevis, 1989). In constructivist teaching, the teacher commences with the experience of the student and together they develop knowledge, skills and competencies for professional practice (Bergum, 2003). Teachers who embrace constructivist teaching not only prepare student nurses with the substantive knowledge necessary for competent practice, but also create an environment in students learn to think critically, practice reflectively, work effectively in groups, and access and use new information to support their practice, while modeling respect for meanings of lived experiences, learning and collaborative processes (Bevis, 2001). Bergum (2003) envisions nursing as a dynamic, interpersonal, generative and caring practice. To be consistent with this view of nursing, teaching nursing should be a relational, generative practice that occurs formally and informally; between the student and the teacher; the student and the patient; the student and colleagues; the student and peers; and the student and professionals from other courses (Young, 2002). Such learning needs to occur in diverse settings including the classroom, lab, and clinical areas; hospitals as well as community sites. Teaching nursing requires facilitating a thoughtful engagement between the learners and learning materials to ensure that students gain skills and knowledge for rotational (Bergum, 2003). Constructivism is a philosophy that applies well in clinical teaching. It bodes well in clinical teaching and learning since its central focus is the idea that students construct knowledge for themselves (Young, 2002). Students construct meaning individual as they learn. They attain this by reflecting on experiences. Under constructivist theory, students make their own rules and mental models which they apply to make sense of their experiences. Miranda (2005) provides guiding principles of constructivism, which includes: learning as an active process, searching for meaning. Therefore, it must commence with issues around which learners are trying to construct meaning actively; learning as a social activity associated with link to other people, such as, the teachers and peers; constructivist learning that concentrates on primary concepts, not isolated facts; understanding mental models in order to teach well (Wong, 1987). Learners use mental models to perceive the world and the assumpt ions they make to support those models; the learning purpose for individuals to construct their own meaning. Assessment requires being part of the learning process and gives learners information on the quality of their learning; time taken to learn. Students need to revisit ideas, think over them, try them out, and use them for significant learning to occur; and finally motivation as an essential tool for learning (Miranda, 2005). Models, Theories and Principles of Teaching and Learning In teaching ECG procedure, five steps followed in clinical teaching process; identifying the goals and learning outcomes of ECG procedure, assessing the learning needs of students, planning ECG learning activities, guiding learners, and evaluating ECG learning and performance. However, this process was not linear; instead each of these steps influenced the others. For instance, ECG procedure evaluation revealed data on further learning needs of the learners, which suggested fresh learning activities. Similarly, working with students, resulted to observations on performance that altered assessment, thus, suggesting different learning activities. First, the session commenced by identifying the goals and outcomes of the ECG clinical experience. Teaching at this stage was formed by behavioral theories which contemplated learning as influenced through environmental manipulation. This theory was carried into classroom in a way that assisted in making learners understand: the different aspects of ECG; reasons of using ECG; emergencies which require ECG for diagnosis; how ECG is conducted in an emergency: and ECG recordings generally considered as normal and abnormal. These learning goals and outcomes provided clearly areas of assessment, teaching guidelines, and the basis for evaluating learning. They were often expressed the form of clinical objectives and established for the entire teaching session, and specific clinical activities. Gaberson (1997) stated that learning objectives may specify knowledge acquisition, development of values, and performance of psychomotor and technological skills. ECG teaching objectives addressed eight key areas of learning; knowledge, concepts, and theories applicable to perform an ECG procedure; assessment, diagnoses, planning, and evaluation; psychomotor and technological skills; values related to patient care, families and communities; communication skills, ability to build interpersonal relationships, and skill in collaboration with others; leadership abilities, role behavior, and management care; accountability and responsibility on the part of the student; and finally, self development and continued learning. Guided by the traditional approach in clinical teaching, a learning environment was designed in a way that provided students with opportunities to build mutual respect and support one another while they achieved competence in performing ECG procedure (Braunwauld, 1997). The teaching strategy specified learning outcomes in terms of students competencies in demonstrating ECG procedure in full. They were able to have basic knowledge on carrying electrocardiography procedure in an emergency situation. As postulated by Lippincott (2008), electrocardiography is one of the essential and commonly used procedures to evaluate a cardiac arrest patient in an emergency circumstance (Braunwald, 1997). Through electrocardiography, the hearts electrical functions as a wave form can be displayed. Electrocardiogram is able to monitor impulses moving through the conduction system of the heart producing electric currents that can be monitored on the bodys surface. Normally, the electrodes attached to the skin can sense these electric currents and send them to an electrocardiogram; an instrument that produces a record of cardiac activity (Lippincott, 2008). Braunwald (2008) states that electrocardiography can be used effectively in diagnosing several conditions of the heart. Nurses who encounter patients in emergency wards must have knowledge on the importance of electrocardiography procedure in a life saving situation. The responsibility of caring patients with cardiovascular disorders cuts across every area of nursing practice. As a result, cardiovascular care is a rapidly growing area in nursing. Lippincott (2003) mentions cardiovascular care to be a dynamic field, with continued inventions of new diagnostic tests, new drugs and other treatments, and sophisticated monitoring equipment. Consequently, nurses need to keep up with these changing developments through relevant clinical education (Lippincott, 2008). The students were able to demonstrate their specific abilities; and often reflected their proficiencies required to perform specific tasks on ECG procedure that assigned to them. Performance criteria were established to determine the level of learner achievement of competency in carrying out necessary ECG procedure. For instance, gauging performance criteria for competency of; understanding the value of ECG in an emergency situation, assessing potential cases that require ECG attention, interpreting the electrical activity of the heart and its recordings by using skin electrodes (Lippincott, 2008). Constructivism model provided a new vision of teaching. Students were allowed to participate in the clinical objectives and competences established for carrying out ECG procedure from simple to complex. This approach made it possible for learners to be prepared with substantive knowledge necessary for performing ECG procedure. It also created an environment where students were able to think critically, practice ECG procedure reflectively, collaborate in groups, and others. Some of the outcomes were achieved by learners and had to add others to meet individual learning needs and goals. Student objectives were made flexible to the extent that they met essential ECG procedure objectives. Learning activities were directed by asking questions that provoked thought without interrogating them. Asking open ended questions about their thoughts and the rationale they applied for reaching at clinical decisions, enhanced their growth of their critical thinking skills. Queries were asked to asses s students grasp of relevant concepts and theories and how they were used in clinical practice (Bergum, 2003). The key principles of constructivism were applied to create sessions which assisted students to graduate with their own ideas. For instance, they were assisted in openly sharing their ideas through discussion strategy during and after each learning session. They were free to vary their concepts whenever possible. This enabled them remember the key concepts of electrocardiography. Frequent assessments on the students enabled to evaluate their strengths and weaknesses. conveniently asked and valued their interpretations of what they learnt. Teaching plans were also varied effectively at some points to cope with the intelligence and cognitive abilities of students. What students provided as feedback, was not considered in a prejudiced manner; neither were judgmental comments (Brooks, 1993). Secondly, an assessment was conducted on the learning needs of students. The assessment was guided by cognitive theory which assisted in formulation of appropriate objectives on what the students had learnt. Teaching started at the level of the student. Therefore, assessed was done on; the present level of knowledge and skill of the students, and other factors that may had influenced their achievement of objectives. Data was collected to determine whether the students had necessary knowledge and skills to carry out ECG procedure and complete the learning activities. The teachers assessment was important as it engaged learners in learning activities that developed on their current knowledge and skills in ECG procedure competencies (Young, 2002). Third, instruction planned and delivered following the assessment of students learning needs. The plan for learning activities catered for clinical objectives and individual learner needs. Selected ECG learning activities met objectives of carrying out ECG procedure effectively. The learning activities included patient assignments where learners engaged in practical setting. Miranda (2005) contends that constructivism advocates for a curriculum that is related to learners prior knowledge and puts more emphasis on problem solving. Therefore, concentration focused on connecting between facts and fostering new understanding among learners. They heavily depended on questions that are open-ended and were encouraged dialogue among them. Constructivist model had direct application in ECG procedural setting, based on these facts. It centered in providing an overall approach that involved other theories and approaches, such as; experiential learning, reflection and problem based learning. It enabled teacher and faculty to direct educational experiences to suit their clinical setting and provide learners opportunity to integrate their learning (Bradshaw, 2006). More so, it accorded learners responsibility to make sense of what goes on in ECG clinical setting and motivates them grow and nurture a deeper understanding of ECG procedure (Cobb, 1999). Fourth, they were guided in achieving essential knowledge, skills and values for ECG practice through problem solving strategy. Facilitation and support of the process enabled students to achieve the intended outcomes; guiding them with their learning activities. Demonstrations were made to learners and they were questioned to enhance their levels of understanding ECG procedure. As a skilled person in this practice, the teacher was able to: observe learners clinical performance, make sound judgment about their performance, and planned for extra learning activities in instances necessary; and questioned students without interrogation. Observing learners as they performed the ECG learning activities enabled teacher to identify continued areas of learning and establish when help was needed (Gaberman, 1999). The third session was conducted in a training class in the ECG room where learners were taught on how ECG procedure is taken. They were provided enough opportunities to perform electrocardiography procedure themselves. In collaboration with the technician on duty, learners were guided throughout the clinical practice. At the end of the session, the students were able to: examine the patient in the emergency room and understand the significance of ECG procedure in a life-saving scenario; perform an ECG as an initial step with patients who arrive with cardiovascular complications, chest pains or after an accident; interpret the electrical activity of the heart and externally by using skin electrodes; and perform non invasive procedure in patients (Lippincott, 2008). Fifth, effective evaluation of clinical learning and performance was done on learners. The evaluation served two important purposes; formative and summative. Learners progress was monitored towards achieving clinical objectives through formative evaluation; through written examination. Demonstration strategy was also used to ascertain their competency in clinical practice. Through formative evaluation strategy, diagnoses for extra learning requirements of students and where additional clinical instruction was required for further instruction was realized. Recommendations for Improving Teaching Strategies Based on Feedback from Peer and Analysis of Literature Based on the feedback received from peers and analysis of the literature, the following recommendations to improve future teaching sessions in the clinical environment were suggested; one, identification of challenges learners are faced with. Commends made by peers indicated that teaching did not take into account the challenges the students faced. It was noted that initiation process of probing to understand students well was lacking. For instance, they may have been overburdened with family issues, language problems, fee problems, and many others. These factors impede effective clinical teaching as it heightens the fear of nurses to make mistakes that could injure patients or even fail a program (OConnor, 2001). Two, recommend extension of the possibilities of evaluation showing learners performance in relation to teaching and learning objectives. Ghazi (1988) noted that motivation for learners was sustained through strategies such as individualized learning, formative evaluations, and others. Teaching did not quite offer feedback on the areas of strengths and potential areas of development for students. Students were not given opportunities to evaluate their learning (OConnor, 2001). Three, recommend further research on effective characteristics of clinical teachers. The analysis of related literature reveals that students judged effective teachers as those having characteristics such as being clinically competent, knowledgeable, good interpersonal relationship, and enthusiastic (Gaberman, 1999). Laurent (2001) contends that teachers, who learners viewed as helpful, modeled competent behavior consistently and demonstrated a positive attitude and humanistic orientation. This will enhance responsiveness to the needs of students. Four, recommend collaborative planning of learning activities. It was felt that the teaching lacked a bit of this element. Learners are usually receptive to selecting among a variety of learning activities and contribute suggestions. Five, recommend different methods of assessing clinical performance. Teaching strategies were limited to only a few methods of assessing clinical performance, such as, discussions, lecture, question and answer, and rounds. Other important approaches involve role plays, case studies, group activities, and many others. More emphasis must have been made on case management also. Conclusion In sum, minimum requirements for an effective teaching and learning; these included the environment, dialogue and the closure. Provision was accorded for sufficient lighting, ample sitting arrangements and adequate audio-visual aids that enhanced an environment that was conducive for teaching and learning. Dialogue in a formal, clear, and logical way; therefore, students did not miss any part of it. At the end of the teaching session, sufficient time for discussion and clarifying doubts was allocated. Teaching summery was submitted at the end of the session. McTaggart (1997) contends that teaching must end by educators being in a position to submit a summery. Young (2002) also insisted that a teacher must be able to use proper teaching and learning principles in the three domains of cognitive, affective, and psychomotor. References List Bergum, V. (2003). Relational Pedagogy. Nursing Philosophy, 4, 121-128. Bloom, B., Engelhart, M., Furst, E., Hill, W., Krathwohl, R. (1956). Taxonomy of Educational Objectives. New York: David McKay Company. Bradshaw, M., Lowenstein, A. (2006). Innovative Teaching Strategies in Nursing and Related Health Profession. London: Jones and Bartlett Publishers. Brooks, M., Brooks, J. (1993). In Search of Understanding. The Case of the Constructivist Classroom. New York: Sunny. Braunwald, E., Lowenstein, A. (2006). Innovative Teaching Strategies in Nursing and Related Health Profession. London: Jones and Bartlett Publishers. Cobb, T. (1999). Applying constructivism: A test for the learner as scientist. Educational Technology Research Development, 47 (3), 15-31. Gaberson, K., Oerman, M. (1999). Clinical Teaching Strategies in Nursing. London: Springer Publishing Company. Ghazi, F. Henshaw, L. (1998). How to Keep Student Nurses Motivated . Nursing standard, 13 (8), 43-49. Halstead, A. (1996). The Significance of Student Faculty Interactions: Review of Research in Nursing. New York: National League of Nursing Press. Horst, M. (1988). Students Rank Characteristics of the Clinical Teacher. Nurse Education, 13 (6), 3. Karuhije, E. (1997). Classroom and Clinical Teaching in Nursing: Delineating Differences. Nursing Forum, 32 (2): 5-12 Knox, J. Morgan. (1985). Important Clinical Teacher Behaviors as perceived by University Nursing Foculty Students and Graduates. Journal of Advanced Nursing, 10, 25-30. Krathwohl, R., Bloom, B., Masia, B. (1956). Taxonomy of Educational Objectives. New York: David McKay Company. Laurent, T., Weidner, T. (2001). Clinical Instructors and Student Athletic Trainers Perceptions of Helpful Clinical Instructor Characteristics. Journal of Athletic Training, 36 (1), 58-61. Lippincott, W. (2008). Lippincotts Nursing Procedures. Sydney: Wolters Kluwer Health McCabe, B. (1985). The Improvement of Instruction in the Clinical Area. Journal of Nursing Education, 24, 255-257. McTaggart, R. (1997). Participatory Action Research. New York: Sunny Press. Miranda, Best, D. (2005). Transforming Practice through Clinical Education, Professional Supervision. Sydney: Elsevier Health sciences. Nehring, V. (1990). Nursing and Clinical Teacher Effectiveness Inventory. Journals of Advenced Nursing, 15, 934-940. Norton, B. (1998). From Teaching to Learning: Theoretical Foundations. Philadelphia: Saunders. OConnor, A. (2001). Clinical Instruction and Evaluation. London: Jones and Bartlett. Tanner, C. Chesla, C. (2009). Expertise in Nursing Practice. New York: Springer Publishing. Tyler, W. (1979). Basic Principles of Curriculum and Instruction. Chicago: University of Chicago Press. Pugh, E. (1988). Soliciting Student Input to Improve Clinical Teaching. Nurse Education, 13 (3), 28-33. Roberta, E. (2003). Nursing Education in Clinical Teaching. Sydney: Elsevier Health Sciences. Vandeveer, M. Norton, B. (2005). From Teachings to Learning. Philadelphia: Saunders. Wong, J. Wong, S. (1987). Towards Effective Clinical Teaching in Nursing. Journal of Advanced Nursing, 12, 505-513. Young, L., Paterson, B. (2007). Teaching Nursing: Developing A Student Centered Learning Environment. Philadelphia: Lippincott, Williams Wilkins.

Abortion Legalized leads to Assault :: essays research papers

This article â€Å"Pro-Life Laws Lead to Assault† by Steven Ereit is intrusive, and completely opinionated. This article noticeably mentions that many incidents of killings and assaults that have gone on between young teenagers are the direct result of legalized abortion. It is stated in the article by Ereit that having abortion legalized shows teens that killing is one of the solutions to life’s problems. Also that if the soon to be mother doesn’t comply with having the abortion the soon to be father has the right to assault or even kill their wives/girlfriends. The law making abortion legal doesn’t insist on anyone killing to solve the problems in their life. The contemplation of killing for peace comes from that persons own mental state or family background. Ereit’s conclusion is based on his own personal opinions, and is completely invalid.   Ã‚  Ã‚  Ã‚  Ã‚  It’s clearly stated in the article that legalized abortion is stating that killing is the solution to life’s problems. That instead of abortion these teens need help in making good decisions about sex, relationships, and responsibility. Ereit made the point that since abortion was legalized and teens have been notified about this fact they have no need for important information about sex, and relationships.   Ã‚  Ã‚  Ã‚  Ã‚  Teenagers being taught about safe sex, and making smart decisions when it comes towards relationships is based on their environment while growing up. The fact that abortion was made legal has nothing to do with teenagers not making good decisions when it comes to matters of the opposite sex. Parents, Guardians, or important people in that child life are supposed to teach them what’s right and what’s wrong.   Ã‚  Ã‚  Ã‚  Ã‚   Ereit also mentioned that since abortion was made legal, soon to be fathers feel that they have the right to take matters into their own hands and give the mother an abortion. The law making abortion legal in no way gives or states that the father has any rights to abort the baby himself. The decision on what will be done with the child is left strictly up to the mother. The father has no right to that baby until it is out of its mother’s womb.   Ã‚  Ã‚  Ã‚  Ã‚  The article Ereit wrote was totally invalid and a bunch of opinions. There was no valid information to back up what he was saying. Abortion doesn’t teach teens that killing is the solution to all life’s problems.

Chapter 20 The First Task

Harry got up on Sunday morning and dressed so inattentively that it was a while before he realized he was trying to pull his hat onto his foot instead of his sock. When he'd finally got all his clothes on the right parts of his body, he hurried off to find Hermione, locating her at the Gryffindor table in the Great Hall, where she was eating breakfast with Ginny. Feeling too queasy to eat, Harry waited until Hermione had swallowed her last spoonful of porridge, then dragged her out onto the grounds. There, he told her all about the dragons, and about everything Sirius had said, while they took another long walk around the lake. Alarmed as she was by Sirius's warnings about Karkaroff, Hermione still thought that the dragons were the more pressing problem. â€Å"Let's just try and keep you alive until Tuesday evening,† she said desperately, â€Å"and then we can worry about Karkaroff.† They walked three times around the lake, trying all the way to think of a simple spell that would subdue a dragon. Nothing whatsoever occurred to them, so they retired to the library instead. Here, Harry pulled down every book he could find on dragons, and both of them set to work searching through the large pile. â€Å"Talon-clipping by charms†¦treating scale-rot†¦' This is no good, this is for nutters like Hagrid who want to keep them healthy†¦Ã¢â‚¬  â€Å"Dragons are extremely difficult to slay, owing to the ancient magic that imbues their thick hides, which none but the most powerful spells can penetrate†¦' But Sirius said a simple one would do it†¦Ã¢â‚¬  â€Å"Let's try some simple spellbooks, then,† said Harry, throwing aside Men Who Love Dragons Too Much. He returned to the table with a pile of spellbooks, set them down, and began to flick through each in turn, Hermione whispering nonstop at his elbow. â€Å"Well, there are Switching Spells†¦but what's the point of Switching it? Unless you swapped its fangs for wine-gums or something that would make it less dangerous†¦.The trouble is, like that book said, not much is going to get through a dragon's hide†¦.I'd say Transfigure it, but something that big, you really haven't got a hope, I doubt even Professor McGonagall†¦unless you're supposed to put the spell on yourself? Maybe to give yourself extra powers? But they're not simple spells, I mean, we haven't done any of those in class, I only know about them because I've been doing O.W.L. practice papers†¦.† â€Å"Hermione,† Harry said, through gritted teeth, â€Å"will you shut up for a bit, please? I m trying to concentrate.† But all that happened, when Hermione fell silent, was that Harry's brain filled with a sort of blank buzzing, which didn't seem to allow room for concentration. He stared hopelessly down the index of Basic Hexes for the Busy and Vexed. Instant scalping†¦but dragons had no hair†¦pepper breath†¦that would probably increase a dragon's firepower†¦horn tongue†¦just what he needed, to give it an extra weapon†¦ â€Å"Oh no, he's back again, why can't he read on his stupid ship?† said Hermione irritably as Viktor Krum slouched in, cast a surly look over at the pair of them, and settled himself in a distant corner with a pile of books. â€Å"Come on, Harry, we'll go back to the common room†¦his fan club'll be here in a moment, twittering away†¦.† And sure enough, as they left the library, a gang of girls tiptoed past them, one of them wearing a Bulgaria scarf tied around her waist. Harry barely slept that night. When he awoke on Monday morning, he seriously considered for the first time ever just running away from Hogwarts. But as he looked around the Great Hall at breakfast time, and thought about what leaving the castle would mean, he knew he couldn't do it. It was the only place he had ever been happy†¦well, he supposed he must have been happy with his parents too, but he couldn't remember that. Somehow, the knowledge that he would rather be here and facing a dragon than back on Privet Drive with Dudley was good to know; it made him feel slightly calmer. He finished his bacon with difficulty (his throat wasn't working too well), and as he and Hermione got up, he saw Cedric Diggory leaving the Hufflepuff table. Cedric still didn't know about the dragons†¦the only champion who didn't, if Harry was right in thinking that Maxime and Karkaroff would have told Fleur and Krum†¦. â€Å"Hermione, I'll see you in the greenhouses,† Harry said, coming to his decision as he watched Cedric leaving the Hall. â€Å"Go on, I'll catch you up.† â€Å"Harry, you'll be late, the bell's about to ring -â€Å" â€Å"I'll catch you up, okay?† By the time Harry reached the bottom of the marble staircase, Cedric was at the top. He was with a load of sixth-year friends. Harry didn't want to talk to Cedric in front of them; they were among those who had been quoting Rita Skeeter's article at him every time he went near them. He followed Cedric at a distance and saw that he was heading toward the Charms corridor. This gave Harry an idea. Pausing at a distance from them, he pulled out his wand, and took careful aim. â€Å"Diffindo!† Cedric's bag split. Parchment, quills, and books spilled out of it onto the floor. Several bottles of ink smashed. â€Å"Don't bother,† said Cedric in an exasperated voice as his friends bent down to help him. â€Å"Tell Flitwick I'm coming, go on†¦Ã¢â‚¬  This was exactly what Harry had been hoping for. He slipped his wand back into his robes, waited until Cedric's friends had disappeared into their classroom, and hurried up the corridor, which was now empty of everyone but himself and Cedric. â€Å"Hi,† said Cedric, picking up a copy of A Guide to Advanced Transfiguration that was now splattered with ink. â€Å"My bag just split†¦brand-new and all†¦Ã¢â‚¬  â€Å"Cedric,† said Harry, â€Å"the first task is dragons.† â€Å"What?† said Cedric, looking up. â€Å"Dragons,† said Harry, speaking quickly, in case Professor Flitwick came out to see where Cedric had got to. â€Å"They've got four, one for each of us, and we've got to get past them.† Cedric stared at him. Harry saw some of the panic he'd been feeling since Saturday night flickering in Cedric's gray eyes. â€Å"Are you sure?† Cedric said in a hushed voice. â€Å"Dead sure,† said Harry. â€Å"I've seen them.† â€Å"But how did you find out? We're not supposed to know†¦.† â€Å"Never mind,† said Harry quickly – he knew Hagrid would be in trouble if he told the truth. â€Å"But I'm not the only one who knows. Fleur and Krum will know by now – Maxime and Karkaroff both saw the dragons too.† Cedric straightened up, his arms full of inky quills, parchment, and books, his ripped bag dangling off one shoulder. He stared at Harry, and there was a puzzled, almost suspicious look in his eyes. â€Å"Why are you telling me?† he asked. Harry looked at him in disbelief. He was sure Cedric wouldn't have asked that if he had seen the dragons himself. Harry wouldn't have let his worst enemy face those monsters unprepared – well, perhaps Malfoy or Snape†¦. â€Å"It's just†¦fair, isn't it?† he said to Cedric. â€Å"We all know now†¦we're on an even footing, aren't we?† Cedric was still hooking at him in a slightly suspicious way when Harry heard a familiar clunking noise behind him. He turned around and saw Mad-Eye Moody emerging from a nearby classroom. â€Å"Come with me, Potter,† he growled. â€Å"Diggory, off you go.† Harry stared apprehensively at Moody. Had he overheard them? â€Å"Er – Professor, I'm supposed to be in Herbology -â€Å" â€Å"Never mind that, Potter. In my office, please†¦Ã¢â‚¬  Harry followed him, wondering what was going to happen to him now. What if Moody wanted to know how he'd found out about the dragons? Would Moody go to Dumbledore and tell on Hagrid, or just turn Harry into a ferret? Well, it might be easier to get past a dragon if he were a ferret, Harry thought dully, he'd be smaller, much less easy to see from a height of fifty feet†¦. He followed Moody into his office. Moody closed the door behind them and turned to look at Harry, his magical eye fixed upon him as well as the normal one. â€Å"That was a very decent thing you just did, Potter,† Moody said quietly. Harry didn't know what to say; this wasn't the reaction he had expected at all. â€Å"Sit down,† said Moody, and Harry sat, looking around. He had visited this office under two of its previous occupants. In Professor Lockhart's day, the walls had been plastered with beaming, winking pictures of Professor Lockhart himself. When Lupin had lived here, you were more likely to come across a specimen of some fascinating new Dark creature he had procured for them to study in class. Now, however, the office was full of a number of exceptionally odd objects that Harry supposed Moody had used in the days when he had been an Auror. On his desk stood what looked hike a large, cracked, glass spinning top; Harry recognized it at once as a Sneakoscope, because he owned one himself, though it was much smaller than Moody's. In the corner on a small table stood an object that looked something like an extra-squiggly, golden television aerial. It was humming slightly. What appeared to be a mirror hung opposite Harry on the wall, but it was not reflecting the room. Shadowy figures were moving around inside it, none of them clearly in focus. â€Å"Like my Dark Detectors, do you?† said Moody, who was watching Harry closely. â€Å"What's that?† Harry asked, pointing at the squiggly golden aerial. â€Å"Secrecy Sensor. Vibrates when it detects concealment and lies†¦no use here, of course, too much interference – students in every direction lying about why they haven't done their homework. Been humming ever since I got here. I had to disable my Sneakoscope because it wouldn't stop whistling. It's extra-sensitive, picks up stuff about a mile around. Of course, it could be picking up more than kid stuff,† he added in a growl. â€Å"And what's the mirror for?† â€Å"Oh that's my Foe-Glass. See them out there, skulking around? I'm not really in trouble until I see the whites of their eyes. That's when I open my trunk.† He let out a short, harsh laugh, and pointed to the large trunk under the window. It had seven keyholes in a row. Harry wondered what was in there, until Moody's next question brought him sharply back to earth. â€Å"So†¦found out about the dragons, have you?† Harry hesitated. He'd been afraid of this – but he hadn't told Cedric, and he certainly wasn't going to tell Moody, that Hagrid had broken the rules. â€Å"It's all right,† said Moody, sitting down and stretching out his wooden leg with a groan. â€Å"Cheating's a traditional part of the Triwizard Tournament and always has been.† â€Å"I didn't cheat,† said Harry sharply. â€Å"It was – a sort of accident that I found out.† Moody grinned. â€Å"I wasn't accusing you, laddie. I've been telling Dumbledore from the start, he can be as high-minded as he likes, but you can bet old Karkaroff and Maxime won't be. They'll have told their champions everything they can. They want to win. They want to beat Dumbledore. They'd like to prove he's only human.† Moody gave another harsh laugh, and his magical eye swiveled around so fast it made Harry feel queasy to watch it. â€Å"So†¦got any ideas how you're going to get past your dragon yet?† said Moody. â€Å"No,† said Harry. â€Å"Well, I'm not going to tell you,† said Moody gruffly. â€Å"I don't show favoritism, me. I'm just going to give you some good, general advice. And the first bit is – play to your strengths.† â€Å"I haven't got any,† said Harry, before he could stop himself. â€Å"Excuse me,† growled Moody, â€Å"you've got strengths if I say you've got them. Think now. What are you best at?† Harry tried to concentrate. What was he best at? Well, that was easy, really – â€Å"Quidditch,† he said dully, â€Å"and a fat lot of help -â€Å" â€Å"That's right,† said Moody, staring at him very hard, his magical eye barely moving at all. â€Å"You're a damn good flier from what I've heard.† â€Å"Yeah, but†¦Ã¢â‚¬  Harry stared at him. â€Å"I'm not allowed a broom, I've only got my wand†¦Ã¢â‚¬  â€Å"My second piece of general advice,† said Moody loudly, interrupting him, â€Å"is to use a nice, simple spell that will enable you to get what you need.† Harry looked at him blankly. What did he need? â€Å"Come on, boy†¦Ã¢â‚¬  whispered Moody. â€Å"Put them together†¦it's not that difficult†¦Ã¢â‚¬  And it clicked. He was best at flying. He needed to pass the dragon in the air. For that, he needed his Firebolt. And for his Fire-bolt, he needed – â€Å"Hermione,† Harry whispered, when he had sped into greenhouse three minutes later, uttering a hurried apology to Professor Sprout as he passed her. â€Å"Hermione – I need you to help me.† â€Å"What d'you think I've been trying to do, Harry?† she whispered back, her eyes round with anxiety over the top of the quivering Flutterby Bush she was pruning. â€Å"Hermione, I need to learn how to do a Summoning Charm properly by tomorrow afternoon.† And so they practiced. They didn't have lunch, but headed for a free classroom, where Harry tried with all his might to make various objects fly across the room toward him. He was still having problems. The books and quills kept losing heart halfway across the room and dropping hike stones to the floor. â€Å"Concentrate, Harry, concentrate†¦.† â€Å"What d'you think I'm trying to do?† said Harry angrily. â€Å"A great big dragon keeps popping up in my head for some reason†¦Okay, try again†¦Ã¢â‚¬  He wanted to skip Divination to keep practicing, but Hermione refused point-blank to skive off Arithmancy, and there was no point in staying without her. He therefore had to endure over an hour of Professor Trelawney, who spent half the lesson telling everyone that the position of Mars with relation to Saturn at that moment meant that people born in July were in great danger of sudden, violent deaths. â€Å"Well, that's good,† said Harry loudly, his temper getting the better of him, â€Å"just as long as it's not drawn-out. I don't want to suffer.† Ron looked for a moment as though he was going to laugh; he certainly caught Harry's eye for the first time in days, but Harry was still feeling too resentful toward Ron to care. He spent the rest of the lesson trying to attract small objects toward him under the table with his wand. He managed to make a fly zoom straight into his hand, though he wasn't entirely sure that was his prowess at Summoning Charms – perhaps the fly was just stupid. He forced down some dinner after Divination, then returned to the empty classroom with Hermione, using the Invisibility Cloak to avoid the teachers. They kept practicing until past midnight. They would have stayed longer, but Peeves turned up and, pretending to think that Harry wanted things thrown at him, started chucking chairs across the room. Harry and Hermione left in a hurry before the noise attracted Filch, and went back to the Gryffindor common room, which was now mercifully empty. At two o'clock in the morning, Harry stood near the fireplace, surrounded by heaps of objects: books, quills, several upturned chairs, an old set of Gobstones, and Neville's toad, Trevor. Only in the last hour had Harry really got the hang of the Summoning Charm. â€Å"That's better, Harry, that's loads better,† Hermione said, looking exhausted but very pleased. â€Å"Well, now we know what to do next time I can't manage a spell,† Harry said, throwing a rune dictionary back to Hermione, so he could try again, â€Å"threaten me with a dragon. Right†¦Ã¢â‚¬  He raised his wand once more. â€Å"Accio Dictionary!† The heavy book soared out of Hermione's hand, flew across the room, and Harry caught it. â€Å"Harry, I really think you've got it!† said Hermione delightedly. â€Å"Just as long as it works tomorrow,† Harry said. â€Å"The Firebolt's going to be much farther away than the stuff in here, it's going to be in the castle, and I'm going to be out there on the grounds†¦Ã¢â‚¬  â€Å"That doesn't matter,† said Hermione firmly.† Just as long as you're concentrating really, really hard on it, it'll come. Harry, we'd better get some sleep†¦you're going to need it.† Harry had been focusing so hard on learning the Summoning Charm that evening that some of his blind panic had heft him. It returned in full measure, however, on the following morning. The atmosphere in the school was one of great tension and excitement. Lessons were to stop at midday, giving all the students time to get down to the dragons' enclosure – though of course, they didn't yet know what they would find there. Harry felt oddly separate from everyone around him, whether they were wishing him good luck or hissing â€Å"We'll have a box of tissues ready, Potter† as he passed. It was a state of nervousness so advanced that he wondered whether he mightn't just lose his head when they tried to lead him out to his dragon, and start trying to curse everyone in sight. Time was behaving in a more peculiar fashion than ever, rushing past in great dollops, so that one moment he seemed to be sitting down in his first lesson, History of Magic, and the next, walking into lunch†¦and then (where had the morning gone? the last of the dragon-free hours?), Professor McGonagall was hurrying over to him in the Great Hall. Lots of people were watching. â€Å"Potter, the champions have to come down onto the grounds now†¦.You have to get ready for your first task.† â€Å"Okay,† said Harry, standing up, his fork falling onto his plate with a clatter. â€Å"Good luck, Harry,† Hermione whispered. â€Å"You'll be fine!† â€Å"Yeah,† said Harry in a voice that was most unlike his own. He heft the Great Hall with Professor McGonagall. She didn't seem herself either; in fact, she looked nearly as anxious as Hermione. As she walked him down the stone steps and out into the cold November afternoon, she put her hand on his shoulder. â€Å"Now, don't panic,† she said, â€Å"just keep a cool head†¦.We've got wizards standing by to control the situation if it gets out of hand†¦.The main thing is just to do your best, and nobody will think any the worse of you†¦.Are you all right?† â€Å"Yes,† Harry heard himself say. â€Å"Yes, I'm fine.† She was leading him toward the place where the dragons were, around the edge of the forest, but when they approached the clump of trees behind which the enclosure would be clearly visible, Harry saw that a tent had been erected, its entrance facing them, screening the dragons from view. â€Å"You're to go in here with the other champions,† said Professor McGonagall, in a rather shaky sort of voice, â€Å"and wait for your turn, Potter. Mr. Bagman is in there†¦he'll be telling you the – the procedure†¦. Good luck.† â€Å"Thanks,† said Harry, in a flat, distant voice. She left him at the entrance of the tent. Harry went inside. Fleur Delacour was sitting in a corner on a how wooden stool. She didn't look nearly as composed as usual, but rather pale and clammy. Viktor Krum looked even surlier than usual, which Harry supposed was his way of showing nerves. Cedric was pacing up and down. When Harry entered, Cedric gave him a small smile, which Harry returned, feeling the muscles in his face working rather hard, as though they had forgotten how to do it. â€Å"Harry! Good-o!† said Bagman happily, looking around at him. â€Å"Come in, come in, make yourself at home!† Bagman looked somehow like a slightly overblown cartoon figure, standing amid all the pale-faced champions. He was wearing his old Wasp robes again. â€Å"Well, now we're all here – time to fill you in!† said Bagman brightly. â€Å"When the audience has assembled, I'm going to be offering each of you this bag† – he held up a small sack of purple silk and shook it at them – â€Å"from which you will each select a small model of the thing you are about to face! There are different – er – varieties, you see. And I have to tell you something else too†¦ah, yes†¦your task is to collect the golden egg!† Harry glanced around. Cedric had nodded once, to show that he understood Bagman's words, and then started pacing around the tent again; he looked slightly green. Fleur Delacour and Krum hadn't reacted at all. Perhaps they thought they might be sick if they opened their mouths; that was certainly how Harry felt. But they, at least, had volunteered for this†¦ And in no time at all, hundreds upon hundreds of pairs of feet could be heard passing the tent, their owners talking excitedly, laughing, joking†¦.Harry felt as separate from the crowd as though they were a different species. And then – it seemed like about a second later to Harry – Bagman was opening the neck of the purple silk sack. â€Å"Ladies first,† he said, offering it to Fleur Delacour. She put a shaking hand inside the bag and drew out a tiny, perfect model of a dragon – a Welsh Green. It had the number two around its neck And Harry knew, by the fact that Fleur showed no sign of surprise, but rather a determined resignation, that he had been right: Madame Maxime had told her what was coming. The same held true for Krum. He pulled out the scarlet Chinese Fireball. It had a number three around its neck. He didn't even blink, just sat back down and stared at the ground. Cedric put his hand into the bag, and out came the blueish-gray Swedish Short-Snout, the number one tied around its neck. Knowing what was left, Harry put his hand into the silk bag and pulled out the Hungarian Horntail, and the number four. It stretched its wings as he looked down at it, and bared its minuscule fangs. â€Å"Well, there you are!† said Bagman. â€Å"You have each pulled out the dragon you will face, and the numbers refer to the order in which you are to take on the dragons, do you see? Now, I'm going to have to leave you in a moment, because I'm commentating. Mr. Diggory, you're first, just go out into the enclosure when you hear a whistle, all right? Now†¦Harry†¦could I have a quick word? Outside?† â€Å"Er†¦yes,† said Harry blankly, and he got up and went out of the tent with Bagman, who walked him a short distance away, into the trees, and then turned to him with a fatherly expression on his face. â€Å"Feeling all right, Harry? Anything I can get you?† â€Å"What?† said Harry. â€Å"I – no, nothing.† â€Å"Got a plan?† said Bagman, lowering his voice conspiratorially. â€Å"Because I don't mind sharing a few pointers, if you'd like them, you know. I mean,† Bagman continued, lowering his voice still further, â€Å"you're the underdog here, Harry†¦.Anything I can do to help†¦Ã¢â‚¬  â€Å"No,† said Harry so quickly he knew he had sounded rude, â€Å"no – I – I know what I'm going to do, thanks.† â€Å"Nobody would know, Harry,† said Bagman, winking at him. â€Å"No, I'm fine,† said Harry, wondering why he kept telling people this, and wondering whether he had ever been less fine. â€Å"I've got a plan worked out, I -â€Å" A whistle had blown somewhere. â€Å"Good lord, I've got to run!† said Bagman in alarm, and he hurried off. Harry walked back to the tent and saw Cedric emerging from it, greener than ever. Harry tried to wish him luck as he walked past, but all that came out of his mouth was a sort of hoarse grunt. Harry went back inside to Fleur and Krum. Seconds hater, they heard the roar of the crowd, which meant Cedric had entered the enclosure and was now face-to-face with the living counterpart of his model†¦. It was worse than Harry could ever have imagined, sitting there and listening. The crowd screamed†¦yelled†¦gasped like a single many-headed entity, as Cedric did whatever he was doing to get past the Swedish Short-Snout. Krum was still staring at the ground. Fleur had now taken to retracing Cedric's steps, around and around the tent. And Bagman's commentary made everything much, much worse†¦.Horrible pictures formed in Harry's mind as he heard: â€Å"Oooh, narrow miss there, very narrow†Ã¢â‚¬ ¦ â€Å"He's taking risks, this one!†Ã¢â‚¬ ¦Ã¢â‚¬ Clever move – pity it didn't work!† And then, after about fifteen minutes, Harry heard the deafening roar that could mean only one thing: Cedric had gotten past his dragon and captured the golden egg. â€Å"Very good indeed!† Bagman was shouting. â€Å"And now the marks from the judges!† But he didn't shout out the marks; Harry supposed the judges were holding them up and showing them to the crowd. â€Å"One down, three to go!† Bagman yelled as the whistle blew again. â€Å"Miss Delacour, if you please!† Fleur was trembling from head to foot; Harry felt more warmly toward her than he had done so far as she heft the tent with her head held high and her hand clutching her wand. He and Krum were left alone, at opposite sides of the tent, avoiding each other's gaze. The same process started again†¦.†Oh I'm not sure that was wise!† they could hear Bagman shouting gleefully. â€Å"Oh†¦nearly! Careful now†¦good lord, I thought she'd had it then!† Ten minutes later, Harry heard the crowd erupt into applause once more†¦.Fleur must have been successful too. A pause, while Fleur's marks were being shown†¦more clapping†¦then, for the third time, the whistle. â€Å"And here comes Mr. Krum!† cried Bagman, and Krum slouched out, leaving Harry quite alone. He felt much more aware of his body than usual; very aware of the way his heart was pumping fast, and his fingers tingling with fear†¦yet at the same time, he seemed to be outside himself, seeing the walls of the tent, and hearing the crowd, as though from far away. â€Å"Very daring!† Bagman was yelling, and Harry heard the Chinese Fireball emit a horrible, roaring shriek, while the crowd drew its collective breath. â€Å"That's some nerve he's showing – and – yes, he's got the egg!† Applause shattered the wintery air like breaking glass; Krum had finished – it would be Harry's turn any moment. He stood up, noticing dimly that his legs seemed to be made of marshmallow. He waited. And then he heard the whistle blow. He walked out through the entrance of the tent, the panic rising into a crescendo inside him. And now he was walking past the trees, through a gap in the enclosure fence. He saw everything in front of him as though it was a very highly colored dream. There were hundreds and hundreds of faces staring down at him from stands that had been magicked there since he'd last stood on this spot. And there was the Horntail, at the other end of the enclosure, crouched low over her clutch of eggs, her wings half-furled, her evil, yellow eyes upon him, a monstrous, scaly, black lizard, thrashing her spiked tail, heaving yard-long gouge marks in the hard ground. The crowd was making a great deal of noise, but whether friendly or not, Harry didn't know or care. It was time to do what he had to do†¦to focus his mind, entirely and absolutely, upon the thing that was his only chance. He raised his wand. â€Å"Accio Firebolt!† he shouted. Harry waited, every fiber of him hoping, praying†¦.If it hadn't worked†¦if it wasn't coming†¦He seemed to be looking at everything around him through some sort of shimmering, transparent barrier, like a heat haze, which made the enclosure and the hundreds of faces around him swim strangely†¦. And then he heard it, speeding through the air behind him; he turned and saw his Firebolt hurtling toward him around the edge of the woods, soaring into the enclosure, and stopping dead in midair beside him, waiting for him to mount. The crowd was making even more noise†¦.Bagman was shouting something†¦but Harry's ears were not working properly anymore†¦listening wasn't important†¦. He swung his leg over the broom and kicked off from the ground. And a second later, something miraculous happened†¦. As he soared upward, as the wind rushed through his hair, as the crowd's faces became mere flesh-colored pinpnicks below, and the Horntail shrank to the size of a dog, he realized that he had left not only the ground behind, but also his fear†¦.He was back where he belonged†¦. This was just another Quidditch match, that was all†¦just another Quidditch match, and that Horntail was just another ugly opposing team†¦. He looked down at the clutch of eggs and spotted the gold one, gleaming against its cement-colored fellows, residing safely between the dragon's front legs. â€Å"Okay,† Harry told himself, â€Å"diversionary tactics†¦let's go†¦Ã¢â‚¬  He dived. The Horntail's head followed him; he knew what it was going to do and pulled out of the dive just in time; a jet of fire had been released exactly where he would have been had he not swerved away†¦but Harry didn't care†¦that was no more than dodging a Bludger†¦. â€Å"Great Scott, he can fly!† yelled Bagman as the crowd shrieked and gasped. â€Å"Are you watching this, Mr. Krum?† Harry soared higher in a circle; the Horntail was still following his progress; its head revolving on its long neck – if he kept this up, it would be nicely dizzy – but better not push it too long, or it would be breathing fire again – Harry plummeted just as the Horntail opened its mouth, but this time he was less lucky – he missed the flames, but the tail came whipping up to meet him instead, and as he swerved to the left, one of the long spikes grazed his shoulder, ripping his robes – He could feel it stinging, he could hear screaming and groans from the crowd, but the cut didn't seem to be deep†¦.Now he zoomed around the back of the Horntail, and a possibility occurred to him†¦. The Horntail didn't seem to want to take off, she was too protective of her eggs. Though she writhed and twisted, furling and unfurling her wings and keeping those fearsome yellow eyes on Harry, she was afraid to move too far from them†¦but he had to persuade her to do it, or he'd never get near them†¦.The trick was to do it carefully, gradually†¦. He began to fly, first this way, then the other, not near enough to make her breathe fire to stave him off, but still posing a sufficient threat to ensure she kept her eyes on him. Her head swayed this way and that, watching him out of those vertical pupils, her fangs bared†¦. He flew higher. The Horntail's head rose with him, her neck now stretched to its fullest extent, still swaying, hike a snake before its charmer†¦. Harry rose a few more feet, and she let out a roar of exasperation. He was like a fly to her, a fly she was longing to swat; her tail thrashed again, but he was too high to reach now†¦.She shot fire into the air, which he dodged†¦.Her jaws opened wide†¦. â€Å"Come on,† Harry hissed, swerving tantalizingly above her, â€Å"come on, come and get me†¦up you get now†¦Ã¢â‚¬  And then she reared, spreading her great, black, leathery wings at last, as wide as those of a small airplane – and Harry dived. Before the dragon knew what he had done, or where he had disappeared to, he was speeding toward the ground as fast as he could go, toward the eggs now unprotected by her clawed front legs – he had taken his hands off his Firebolt – he had seized the golden egg – And with a huge spurt of speed, he was off, he was soaring out over the stands, the heavy egg safely under his uninjured arm, and it was as though somebody had just turned the volume back up – for the first time, he became properly aware of the noise of the crowd, which was screaming and applauding as loudly as the Irish supporters at the World Cup – â€Å"Look at that!† Bagman was yelling. â€Å"Will you look at that! Our youngest champion is quickest to get his egg! Well, this is going to shorten the odds on Mr. Potter!† Harry saw the dragon keepers rushing forward to subdue the Horntail, and, over at the entrance to the enclosure, Professor McGonagall, Professor Moody, and Hagrid hurrying to meet him, all of them waving him toward them, their smiles evident even from this distance. He flew back over the stands, the noise of the crowd pounding his eardrums, and came in smoothly to land, his heart lighter than it had been in weeks†¦.He had got through the first task, he had survived†¦. â€Å"That was excellent, Potter!† cried Professor McGonagall as he got off the Firebolt – which from her was extravagant praise. He noticed that her hand shook as she pointed at his shoulder. â€Å"You'll need to see Madam Pomfrey before the judges give out your score†¦.Over there, she's had to mop up Diggory already†¦.† â€Å"Yeh did it, Harry!† said Hagrid hoarsely. â€Å"Yeh did it! An' agains' the Horntail an' all, an' yeh know Charlie said that was the wors' -â€Å" â€Å"Thanks, Hagrid,† said Harry loudly, so that Hagrid wouldn't blunder on and reveal that he had shown Harry the dragons beforehand. Professor Moody looked very pleased too; his magical eye was dancing in its socket. â€Å"Nice and easy does the trick, Potter,† he growled. â€Å"Right then, Potter, the first aid tent, please†¦Ã¢â‚¬  said Professor McGonagall. Harry walked out of the enclosure, still panting, and saw Madam Pomfrey standing at the mouth of a second tent, looking worried. â€Å"Dragons!† she said, in a disgusted tone, pulling Harry inside. The tent was divided into cubicles; he could make out Cedric's shadow through the canvas, but Cedric didn't seem to be badly injured; he was sitting up, at least. Madam Pomfrey examined Harry's shoulder, talking furiously all the while. â€Å"Last year dementors, this year dragons, what are they going to bring into this school next? You're very lucky†¦this is quite shallow†¦it'll need cleaning before I heal it up, though†¦.† She cleaned the cut with a dab of some purple liquid that smoked and stung, but then poked his shoulder with her wand, and he felt it heal instantly. â€Å"Now, just sit quietly for a minute – sit! And then you can go and get your score.† She bustled out of the tent and he heard her go next door and say, â€Å"How does it feel now, Diggory?† Harry didn't want to sit still. He was too full of adrenaline. He got to his feet, wanting to see what was going on outside, but before he'd reached the mouth of the tent, two people had come darting inside – Hermione, followed closely by Ron. â€Å"Harry, you were brilliant!† Hermione said squeakily. There were fingernail marks on her face where she had been clutching it in fear. â€Å"You were amazing! You really were!† But Harry was looking at Ron, who was very white and staring at Harry as though he were a ghost. â€Å"Harry,† he said, very seriously, â€Å"whoever put your name in that goblet – I – I reckon they're trying to do you in!† It was as though the last few weeks had never happened – as though Harry were meeting Ron for the first time, right after he'd been made champion. â€Å"Caught on, have you?† said Harry coldly. â€Å"Took you long enough.† Hermione stood nervously between them, looking from one to the other. Ron opened his mouth uncertainly. Harry knew Ron was about to apologize and suddenly he found he didn't need to hear it. â€Å"It's okay,† he said, before Ron could get the words out. â€Å"Forget it.† â€Å"No,† said Ron, â€Å"I shouldn't've -â€Å" â€Å"Forget it, â€Å"Harry said. Ron grinned nervously at him, and Harry grinned back. Hermione burst into tears. â€Å"There's nothing to cry about!† Harry told her, bewildered. â€Å"You two are so stupid!† she shouted, stamping her foot on the ground, tears splashing down her front. Then, before either of them could stop her, she had given both of them a hug and dashed away, now positively howling. â€Å"Barking mad,† said Ron, shaking his head. â€Å"Harry, c'mon, they'll be putting up your scores†¦.† Picking up the golden egg and his Firebolt, feeling more elated than he would have believed possible an hour ago, Harry ducked out of the tent, Ron by his side, talking fast. â€Å"You were the best, you know, no competition. Cedric did this weird thing where he Transfigured a rock on the ground†¦turned it into a dog†¦he was trying to make the dragon go for the dog instead of him. Well, it was a pretty cool bit of Transfiguration, and it sort of worked, because he did get the egg, but he got burned as well – the dragon changed its mind halfway through and decided it would rather have him than the Labrador; he only just got away. And that Fleur girl tried this sort of charm, I think she was trying to put it into a trance – well, that kind of worked too, it went all sleepy, but then it snored, and this great jet of flame shot out, and her skirt caught fire – she put it out with a bit of water out of her wand. And Krum – you won't believe this, but he didn't even think of flying! He was probably the best after you, though. Hit it with some sort of spell right in the eye. Only thing is, it went trampling around in agony and squashed half the real eggs – they took marks off for that, he wasn't supposed to do any damage to them.† Ron drew breath as he and Harry reached the edge of the enclosure. Now that the Horntail had been taken away, Harry could see where the five judges were sitting – right at the other end, in raised seats draped in gold. â€Å"It's marks out of ten from each one,† Ron said, and Harry squinting up the field, saw the first judge – Madame Maxime – raise her wand in the air. What hooked like a long silver ribbon shot out of it, which twisted itself into a large figure eight. â€Å"Not bad!† said Ron as the crowd applauded. â€Å"I suppose she took marks off for your shoulder†¦Ã¢â‚¬  Mr. Crouch came next. He shot a number nine into the air. â€Å"Looking good!† Ron yelled, thumping Harry on the back. Next, Dumbledore. He too put up a nine. The crowd was cheering harder than ever. Ludo Bagman – ten. â€Å"Ten?† said Harry in disbelief. â€Å"But†¦I got hurt†¦.What's he playing at?† â€Å"Harry, don't complain!† Ron yelled excitedly. And now Karkaroff raised his wand. He paused for a moment, and then a number shot out of his wand too – four. â€Å"What?† Ron bellowed furiously. â€Å"Four? You lousy, biased scum-bag, you gave Krum ten!† But Harry didn't care, he wouldn't have cared if Karkaroff had given him zero; Ron's indignation on his behalf was worth about a hundred points to him. He didn't tell Ron this, of course, but his heart felt lighter than air as he turned to leave the enclosure. And it wasn't just Ron†¦those weren't only Gryffindors cheering in the crowd. When it had come to it, when they had seen what he was facing, most of the school had been on his side as well as Cedric's†¦.He didn't care about the Slytherins, he could stand whatever they threw at him now. â€Å"You're tied in first place, Harry! You and Krum!† said Charlie Weasley, hurrying to meet them as they set off back toward the school. â€Å"Listen, I've got to run, I've got to go and send Mum an owl, I swore I'd tell her what happened – but that was unbelievable! Oh yeah – and they told me to tell you you've got to hang around for a few more minutes†¦.Bagman wants a word, back in the champions' tent.† Ron said he would wait, so Harry reentered the tent, which somehow looked quite different now: friendly and welcoming. He thought back to how he'd felt while dodging the Horntail, and compared it to the long wait before he'd walked out to face it†¦.There was no comparison; the wait had been immeasurably worse. Fleur, Cedric, and Krum all came in together. One side of Cedric's face was covered in a thick orange paste, which was presumably mending his burn. He grinned at Harry when he saw him. â€Å"Good one, Harry.† â€Å"And you,† said Harry, grinning back. â€Å"Well done, all of you!† said Ludo Bagman, bouncing into the tent and looking as pleased as though he personally had just got past a dragon. â€Å"Now, just a quick few words. You've got a nice long break before the second task, which will take place at half past nine on the morning of February the twenty-fourth – but we're giving you something to think about in the meantime! If you look down at those golden eggs you're all holding, you will see that they open†¦see the hinges there? You need to solve the clue inside the egg – because it will tell you what the second task is, and enable you to prepare for it! All clear? Sure? Well, off you go, then!† Harry left the tent, rejoined Ron, and they started to walk back around the edge of the forest, talking hard; Harry wanted to hear what the other champions had done in more detail. Then, as they rounded the clump of trees behind which Harry had first heard the dragons roar, a witch leapt out from behind them. It was Rita Skeeter. She was wearing acid-green robes today; the Quick-Quotes Quill in her hand blended perfectly against them. â€Å"Congratulations, Harry!† she said, beaming at him. â€Å"I wonder if you could give me a quick word? How you felt facing that dragon? How you feel now, about the fairness of the scoring?† â€Å"Yeah, you can have a word,† said Harry savagely. â€Å"Good-bye.† And he set off back to the castle with Ron.

Quadratic Equation and Marks

Tak Nga Secondary School 2010-2011 Mid-year Exam Form 4 Mathematics (Paper I) Time allowed: 1 hour 15 minutes Class:________ Name:__________________( ) Marks: ________/ 60 Instructions: 1. Write your name, class and class number in the spaces provided on this cover. 2. This paper consists of THREE sections, A(1), A(2) and B. Each section carries 20 marks. 3. Attempt ALL questions in this paper. Write your answers in the spaces provided. Supplementary answer sheets will be supplied on request. Write your name and class number on each sheet. 4. Unless otherwise specified, all working must be clearly shown. . Unless otherwise specified, numerical answers should either be exact or correct to 3 significant figures. 6. The diagrams in this paper are not necessarily drawn to scale. Page 1 of 9 Section A(1) (20 marks) 3n ? 5m =4. 2 1. Make n the subject of the formula (3 marks) ____________________________________________________________ ___________________ __________________________________ __________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ___________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ 2. Calculate (? 3 + 5i ) ? (2 + 7i ) . 4 + 8i (6 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _____ _______________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ Factorize (a) 2r 2 + 20r + 50 , (b) r 2 + 10r + 25 ? s 2 . (4 marks) ___________________________________________ _________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ _________ __________ Page 2 of 9 3. 4. If f ( x) = x 2 ? 1 and g ( x) = 3 x + 2 , find the value of 2 f (0) + 3 g (1) . (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ _______ ___________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ 5. Solve the equation 1 2 x ? = 3 by the quadratic formula. (Give the answer in surd form. ) 2 (4 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ _________ __________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ________________ ____________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ Page 3 of 9 Section A(2) (20 marks) 6. In the figure, the straight line passing through A and B is perpendicular to the straight line passing through A and C, where C is a point lying on the x-axis. (a) Find the equation of the straight line passing through A and B. (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ________ ____________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (b) Find the coordinates of C. 3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ______________ _____ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ _____________________ _______________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ Page 4 of 9 (c) Find the area of ? ABC. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ _________________ __ 7. Consider the function f ( x) = x 2 + bx ? 20 , where b is a constant. It is given that the graph of y = f (x) passes through the point (5, 10). (a) Find b. 2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _________________ ___________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ (b) Let k be a constant. If the equation f ( x) = k has two distinct real roots, find the range of values of k. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ __ __________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ Page 5 of 9 8. Suppose P(x) = 2 x 3 ? (h ? 1) x 2 ? 18 x + k . P(x) is divisible by (2x + 1). When P(x) is divided by (x – 2), the remainder is – 40. (a) Find the values of h and k. (4 marks) ____________________________________________________________ _____ ______________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________ ________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ (b) Factorize P(x) completely. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ _________________ __ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ________________________ ____________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ Page 6 of 9 Section B (20 marks) 9. It is given that ? and ? are the two roots of the equation 2Ãâ€"2 + 8x ? = 0, where ? > ?. (a) Write down the values of ? + ? and . (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (b) Find the value of each of th e following expressions without solving the equation. (i) ? 2 + ? 2 (ii) ? ? ? (iii) ? 2 ? 2 (6 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____ ________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (c) Form a quadratic equation with roots ? 2 + ? 2 and ? 2 ? ? 2 . (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ __________________________________ __________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ Page 7 of 9 10. It is given that f ( x) = ? 2 x 2 ? 6 x + c . The graph of y = f ( x) cuts the x-axis at A and B and also cuts the y-axis at C(0, 20). (a) Find the value of c. (1 mark) ______________________________________ ______________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ (b) Find the coordinates of A and B. (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ __________________ __________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ (c) Find the area of ? ABC . (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _____ _______________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ Page 8 of 9 (d) By the method of completing square rewrite the equation y = f ( x) in the form y = a( x ? h) 2 + k . Find the vertex of the graph and axis of symmetry of the graph. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ___ _________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _____________________________ _______________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (e) Find the domain and co-domain of f(x). 2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ___ _________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ END OF PAPER Page 9 of 9