...2009 GCE ‘A’ Level Solution Paper 1 (Contributed by Hwa Chong Institution) 1i) Let un = an2 + bn + c. u1 = a + b + c = 10 u2 = 4a + 2b + c = 6 u3 = 9a + 3b + c = 5 Using GC, a = 1.5, b = –8.5, c = 17. un = 1.5n2 – 8.5n + 17. (ii) Let y = 1.5n2 – 8.5n + 17 – 100 Teaching Point: The set of simultaneous equations can either be solved by using the application PlySmlt2 or finding rref of the augmented matrix formed by the 3 equations. Teaching Point: Please use ZoomFit on your GC to see the entire graph clearly. Besides finding the zero of the function y = 1.5n2 – 8.5n + 17 – 100, another method is to find the point of intersection of the curve y = 1.5n2 – 8.5n + 17 and the line y = 100. Hint to students: From GC, n > 10.79. Hence solution set = {n ℤ+ : n 11}. 1 1 0 4 – x2 dx 1 2+x 1 = [4 ln 2 – x ]0 1 = 4 ( ln 3 – ln 1 ) 1 = 4 ln 3 1 1/2p dx 0 1 – p2x2 1 1 = p 1/2p dx 0 1 2 p2 – x 1 1/2p = p [sin–1 px]0 1 1 = p (sin–1 2 ) 1 1 = p 6 = 4 ln 3 2 p = 3 ln 3 2) 3i) 1 2 1 –n+n+1 n–1 n(n + 1) – 2(n2 – 1) + n(n – 1) = n(n2 – 1) It is helpful to use the GC to do a quick check that the integration has been done correctly. Teaching point: Students sometimes leave out 1 the term p when integrating 1 . To safeguard this, 1 – p2x2 it is advisable to change the integrand into the form 1 before integrating. 2 a – x2 1 2 = n3 – n A = 2. Shown (ii) r=2 r3 – r n 1 1 n 2 = 2 r3 – r r=2 1 1 n 2 1 =2 (r–1–r+r+1) r=2 1 1 2 1 =2 [1–2+3 1 2 1 +2–3+4 1...
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...1 SOME IMPORTANT MATHEMATICAL FORMULAE Circle : Area = π r2; Circumference = 2 π r. Square : Area = x2 ; Perimeter = 4x. Rectangle: Area = xy ; Perimeter = 2(x+y). 1 Triangle : Area = (base)(height) ; Perimeter = a+b+c. 2 3 2 Area of equilateral triangle = a . 4 4 Sphere : Surface Area = 4 π r2 ; Volume = π r3. 3 2 3 Cube : Surface Area = 6a ; Volume = a . 1 Cone : Curved Surface Area = π rl ; Volume = π r2 h 3 π r l + π r2 Total surface area = . Cuboid : Total surface area = 2 (ab + bh + lh); Volume = lbh. Cylinder : Curved surface area = 2 π rh; Volume = π r2 h Total surface area (open) = 2 π rh; Total surface area (closed) = 2 π rh+2 π r2 . SOME BASIC ALGEBRAIC FORMULAE: 1.(a + b)2 = a2 + 2ab+ b2 . 2. (a - b)2 = a2 - 2ab+ b2 . 3.(a + b)3 = a3 + b3 + 3ab(a + b). 4. (a - b)3 = a3 - b3 - 3ab(a - b). 2 2 2 2 5.(a + b + c) = a + b + c +2ab+2bc +2ca. 6.(a + b + c)3 = a3 + b3 + c3+3a2b+3a2c + 3b2c +3b2a +3c2a +3c2a+6abc. 7.a2 - b2 = (a + b)(a – b ) . 8.a3 – b3 = (a – b) (a2 + ab + b2 ). 9.a3 + b3 = (a + b) (a2 - ab + b2 ). 10.(a + b)2 + (a - b)2 = 4ab. 11.(a + b)2 - (a - b)2 = 2(a2 + b2 ). 12.If a + b +c =0, then a3 + b3 + c3 = 3 abc . INDICES AND SURDS m n mn (ab)m = a m b m am 1. am an = am + n 2. = a m − n . 3. (a ) = a . 4. . an m am −m = 1 a 5. = . 6. a 0 = 1, a ≠ 0 . 7. a . 8. a x = a y ⇒ x = y m am b b 9. a x = b x ⇒ a = b 10. a ± 2 b = x ± y , where x + y = a and xy = b. S B SATHYANARAYANA ...
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...(1999). Effects of Peer-Assisted Learning Strategies in Reading with and without Training in Elaborated Help Giving. The Elementary School Journal, 99(3), 201-219. Mathes, P., Howard, J., Allen, S., & Fuchs, D. (1998). Peer-Assisted Learning Strategies for First-Grade Readers: Responding to the Needs of Diverse Learners. Reading Research Quarterly, 33(1), 62-94. Mathes, P., Torgesen, J., & Allor, J. (2001). The Effects of Peer-Assisted Literacy Strategies for First-Grade Readers with and without Additional Computer-Assisted Instruction in Phonological Awareness. American Educational Research Journal, 38(2), 371-410. Moats, L., & Tolman, C. (2017, December 11). Types of Reading Disability. Retrieved from http://www.readingrockets.org/article/types-reading-disability The IRIS Center. (2008). PALS: A reading strategy for grades 2-6.Retrieved from...
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...Land Use Control in Hydraulic Fracturing Prepared for Katherine Wears, Phd. Professor and Assistant Dean at Clarkson University Prepared by Martin Sable Student, Masters in Engineering Management at Clarkson University August 10, 2014 Executive Summary This paper will review the process of hydraulic fracturing, its effects on the environment, and the opposition against the practice. A chronological discussion of lobbying activities and regulatory actions will be discussed, with a particular focus on land use control. A discussion of some of the past and potential future litigation on land rights related to the subject will be covered. The paper will end with the author’s opinion on the subject and of the potential future of the industry. Background Hydraulic Fracturing is a method of simulating well production in both natural gas and oil wells. It was first introduced in 1947, and was adopted for commercial applications as early as 1949.15 The process involves drilling wells deep into ground rock formations, then injecting fluids at high pressure into the ground. The high pressure causes fracturing of the rocks that release gas or oil into the wells that may then be extracted. In 1968 high-volume hydraulic fracturing (HVHF) was introduced, in an effort to tap into the large shale basins containing deposits of natural gas. The main difference between this and conventional hydraulic fracturing is tremendous volume of fracturing fluids that are pumped...
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...There is argument against the benefit of exercise but it is not enough to treat and cure the rising instances of mental illness. Psychiatric treatment is necessary in combination with a healthy lifestyle. A study conducted in 2005 by Bjørnebekk , Mathé AA and Brené S. in Stockholm studied the impact running had on the strength of the connections within the brain. The result of this study was a connection made between the antidepressant effect of running with increased hippocampal cell proliferation. Subjects in a controlled environment were given access to running equipment while some were not, they found the depressed subjects to have lower rates of cell proliferation and were consistently those that did not have access to the running equipment. The study also found that the subjects who were depressed and given access to running equipment showed lowering levels of depression but not a absence. Cognitive behaviour therapy has begun to grow in recent years, it has proven to be effective...
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...\ \ Tribhuvan Unversity Faculty Of Management Oflice of the Dean C-,ourcClcle for Bachelor of Business Administration (BBA) (Four Years Program) First Semester ENG 201: 15 EngliS-I MGT 201: Principles of lu{magement ECO 201: Micro MTH Ecmmics 201 : Business lrl[demdir:s I ITC 201: Comprtr€r and Inffrmation Technologr Applications G *ro*"-oo ENG202: EngliS-tr Credit Hours 3 Credit Hours 3 Credit Hours 3 Credit Hours 3 Credit Hours 3 Credit Hours 15 Credit llours 3 Credit Hours MGT 202: Human Resource Management ECO 202: Macro Economics 3 Credit Hours MTH 202: Business Mathe,mdics tr 3 Credit Hours U C 202:. Introductory Database 3 Credit Hours Third Semester 15 ENG 203: Business Communication 3 Credit Hours STT 201: Statistics 3 Credit Hours ACC 201: Financial Accounting 3 Credit Hours FIN 201: Business Finance t"t 3 Credit Hours 3 Credit Hours ITC 203: Management Information System 3 Credit Hours Fourth Semester 15 MGT 204: Business Law. 3 Credit Hours MGT 206: Business Environment in Nepal 3 Credit Hours ACC 202: Cost and Management Accounting 3 Credit Hours PSY 201: Psychology 3 Credit Hours MTT 201: Fundamentals of Marketing 3 Credit Hours Credit Hours Credit Hours Fifth Semester MGT 207: International Business 3 Credit Hours MGT 205: Operations Management f 3 Credit Hours FIN 202: Basic Financial...
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...CHAPTER 1 INTRODUCTION This chapter describes the area of investigation, citing the objectives of the study as well as the justification of the study. It continues to discuss the theories which guide the research and the methods used to collect data. The researcher also identifies the gaps in the already existing literature. 1.1 AREA OF INVESTIGATION This study examines the significance of Arts and Cultural Commemorations at Tuli West areas, Gwanda South. It looks at how people at the selected areas benefit from the annual commemorations held on Arts and Cultural activities. The commemorations are organized by Matabeleland South Arts Council, local leaders, that is, the Chief and Councilors in conjunction with the Ministry of Education, Sports and Culture. This therefore enhances the involvement of the community at large with schools used as venues. The study seeks to identify the relevance of the activities to cultural beliefs of the people in the area with the majority being the Sotho speaking. The community participates in various artistic work including drama, poetry, dance, singing as well as craftwork. The fact that the venues used for the commemorations are schools, give school children the platform to learn about the artistic as well as cultural works which defines the Sotho community. Guetzkow (2002) highlight that children find learning through artistic and creative activity much more enjoyable, and so they will have an easier time engaging with the material. They...
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...20 Things Financial Institutions Should Do (But Don’t) Here are 20 priorities for retail financial institutions. This is what some are doing, but most others can’t, don’t or won’t. To some this might seem like a list of “duhs” — things that seem obvious, but nonetheless go ignored or unaddressed. What would you add to the list of marketing opportunities and low-hanging fruit for financial institutions? 1. Differentiate Any financial institution that looks like, acts like, or sounds like other banks and credit unions can’t complain when they are forced to compete on rates, fees and price. Differentiation is the key to a strong brand. 2. Personal communications You hear financial institutions bragging about how personal they are all the time, but Tim McAlpine, President of Currency, wonders how often they send handwritten thank you cards for loans, mortgages and renewals. How often do your employees make phone calls to customers thanking them for their business? Imagine how much love you could buy with a simple expression of appreciation. How many direct marketing messages do you send that start with “Dear Valued Customer…?” 3. Mobile solutions If your financial institution isn’t offering some form of mobile banking service currently, there had better be plans underway or you risk falling behind competitively. Demand for services like remote deposit, SMS, and apps for smart phones and iPads is growing rapidly, and are quickly becoming common consumer expectations. (See also...
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...increasing at accelerated pace. A lot of research areas had emerged for that purpose including one of the most fascinating and highly active areas at present, stem cells therapies. Due to self-renewal property and differentiation capability of stem cell, it becomes a new hope in modern treatment. The first successful case of stem cell therapy in human was reported in 1959. Bone marrow restorations were observed in leukemia patients who received total body irradiation subsequent by intravenous injection of their twins’ bone marrow (Thomas et al, 1957). Nevertheless, that effect was transient and the following bone marrow transplantation attempts in non-twin patients and donors can eventually lead to patient’s death from graft-versus-host disease (Mathé et al, 1965). During that time, the safety of hematopoietic cells transplantation was not guaranteed because of the limited knowledge in human histocompatibility and immunosuppression. However, the turning point came after the discovery of human leucocyte antigen (HLA) groups (Dausset, 1958; van Rood et al, 1958), HLA typing and compatibility testing were performed prior to the transplantation. In addition, the improvement of immunosuppressive protocol also helps bringing the bone marrow transplantation to become more and more successful (Donnall and Hutchinson, 1999). Although the success rate of hematopoietic stem cell therapy was great, patients’ mortality still happened as a result of some factors. Besides from graft-versus-host disease...
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...EFFECTIVENESS OF PEER TUTORING IN THE PERFORMANCE OF SELECTED GRADE 7 STUDENTS IN ELEMENTARY ALGEBRA IN SAINT MICHAEL’S COLLEGE OF LAGUNA S.Y. 2012-2013 CHAPTER 1 THE PROBLEM AND ITS BACKGROUND The teaching of Mathematics is enjoyable. This is true when the performance of the students is satisfactory or better. Otherwise, it is frustrating. Based from quizzes and examinations, it is observed that students have poor performance which may be due to weak foundation. Students have no mastery of on the basic skill needed in solving like integers, whole numbers, decimals and fractions. According to Smith (1989), some educators have proposed that an overhaul of the entire mathematics curriculum might be needed to improve skills. There are various techniques that are trying to improve those weak foundations. One good example of that is the peer tutoring. Peer tutoring offers a less intrusive solution also it is helping students to perform better in understanding and grasping concepts, develop computational skills and their moral and social values most especially to freely expresses their ideas. However, according to Lerner (1993), a well-designed peer tutoring program provides directed repetition, regular review, and functional practice to over learn skills, operations, and concepts. Each of these areas is important to the development of mathematical skills of students. Basically, peer tutoring is an instructional strategy that consists of pairing students...
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...at accelerated pace. A lot of research areas had emerged for that purpose including one of the most fascinating and highly active areas at present, stem cells therapies. Due to self-renewal property and differentiation capability of stem cell, it becomes a new hope in modern treatment. The first successful case of stem cell therapy in human was reported in 1959. Bone marrow restorations were observed in leukemia patients who received total body irradiation subsequent by intravenous injection of their twins’ bone marrow (Thomas et al, 1957). Nevertheless, that effect was transient and the following bone marrow transplantation attempts in non-twin patients and donors can eventually lead to patient’s death from graft-versus-host disease (Mathé et al, 1965). During that time, the safety of hematopoietic cells transplantation was not guaranteed because of the limited knowledge in human histocompatibility and immunosuppression. However, the turning point came after the discovery of human leucocyte antigen (HLA) groups (Dausset, 1958; van Rood et al, 1958), HLA typing and compatibility testing were performed prior to the transplantation. In addition, the improvement of immunosuppressive protocol also helps bringing the bone marrow transplantation to become more and more successful (Donnall and Hutchinson, 1999). Although the success rate of hematopoietic stem cell therapy was great, patients’ mortality still happened as a result of some factors. Besides from graft-versus-host disease...
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...All my life I have been nurtured in and exposed to the wonders of the world of mathematics. Because my father was the deputy director of the Institute o f Quantitative and Technical Economics at the Chinese Academy of Social Scie nces, during my childhood I was often surrounded by mathematical data, formu las and charts. As I grew older, I began to realize that by collecting and a nalyzing data and building mathematical models according to the data, my fat her had the power to forecast such grand concepts as the growth rate of the GDP (Gross Domestic Product). I was astonished by the power of mathematics a nd my curiosity drove me to read as many books as I could in the related fie ld. Gradually, I found that I had stepped into another world, a world of int elligence and aesthetics. I felt that it might be my destiny to probe this w orld. With self-confidence and my father's encouragement, I chose applied mathemat ics as my major in college. Thanks to the excellent faculty who guided me on my pilgrimage across the mathematical universe, my love for mathematics con tinued to bloom. In my analysis courses, I first met the continuous function under the definition of Cauchy. Then, my vision broadened to the Riemann in tegrable function space, which is composed of "almost" continuous functions. With the advent of the set theory, my vision again expanded to the measurab le function under the theory of the Lebesgue Integral. In my algebra courses , I was equipped...
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...Biological and Humanistic Approaches to Personality Paper By: LaTreena Alexander PSY/250 December 5, 2014 John Muench The biological approaches to personality are important elements needed in order to analyze each part of the process effectively. The information being presented uses Maslow’s hierarchy of needs to discuss the extent to which growth needs influence personality formation. The biological factors that influence the formation of personality are being described while the relationship of biological factors to Maslow’s theory of personality is being examined. The basic aspects of humanistic theory that are incompatible with biological explanations of personality are thoroughly explained within this informative paper. Through analyzing and researching Maslow’s hierarchy of needs one can get the full basic knowledge and understanding of how growth needs influence personality. Maslow made a pyramid known as the Maslow’s Hierarchy of Needs which was all based on two different groups made up of deficiency needs and growth needs. Within the deficiency needs there are lower needs that have to be attended to before moving on to higher needs, and once this happens a person can act to remove a deficiency in one is ever found in the future. The first four levels of needs are physiological such as hunger and thirst, safety and security, a sense of belongingness and love with others, and esteem to achieve specific goals or to gain approval for an achievement. According to...
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...Kyle Mathes Texas A&M Commerce MGT. 585 CDBG Case 1 Overview In early 2004 the Community Reinvestment Department of BOK Financial Corporation was no performing to BOK’s standards. The CRA Department is necessary for regulated banks to expand. This department was meeting the minimal standards, which resulted in “satisfactory”. BOK expected “outstanding“ performance ratings for all of its banking departments. The CRA Department had five locations with nineteen that were very unorganized. The head of the Department was located in Tulsa Oklahoma. A few of the major issues involved inside the CRA Department include issues with the CRA personnel reporting compliance issues, a lack of automation, and a bad reputation. Steven Bradshaw was assigned to turn the department around Discussion of the Decisions Two of Bradshaw’s major concerns were the department was not profitable and did not meet BOK’s standards. The first step he took to turn the department around was a change of leadership. Bradshaw hired Paula Ellis as the new leader. Ellis worked under Bradshaw in the past and was very well qualified for the position. The leadership of a department is extremely important and in this case Paula was a great decision. She has experience working with banks and in the community. Together, Ellis and Bradshaw helped create a good “tone at the top”. There were four key points the team wanted enact. They include establishing a new direction, building an effective group, automating...
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...After mathe me and chaz were walking down the hallway he was talking about himself as a pack of girls walked behind us giggling and and hiding every time we looked back one girl finally came up it was the katherinae soroka the most popular girl in middle school she...
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