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...Syllabus Cambridge International A Level Further Mathematics Syllabus code 9231 For examination in June and November 2013 Contents Cambridge A Level Further Mathematics Syllabus code 9231 1. Introduction ..................................................................................... 2 1.1 1.2 1.3 1.4 Why choose Cambridge? Why choose Cambridge International A Level Further Mathematics? Cambridge Advanced International Certificate of Education (AICE) How can I find out more? 2. Assessment at a glance .................................................................. 5 3. Syllabus aims and objectives ........................................................... 7 4. Curriculum content .......................................................................... 8 4.1 Paper 1 4.2 Paper 2 5. Mathematical notation................................................................... 17 6. Resource list .................................................................................. 22 7 Additional information.................................................................... 26 . 7 .1 7 .2 7 .3 7 .4 7 .5 7 .6 Guided learning hours Recommended prior learning Progression Component codes Grading and reporting Resources Cambridge A Level Further Mathematics 9231. Examination in June and November 2013. © UCLES 2010 1. Introduction 1.1 Why choose Cambridge? University of Cambridge International Examinations (CIE) is the world’s largest provider of......

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...“The Final Report of the National Mathematics Advisory Panel” National policy must ensure the healthy development of a domestic technical workforce with adequate scale and top-level skill. But the concerns of national policy relating to mathematics education go well beyond those in our society who will become scientists or engineers. The national workforce of future years will surely have to handle quantitative concepts more fully and more deftly than at present. So will the citizens and policy leaders who deal with the public interest in positions of civic leadership. Sound education in mathematics across the population is a national interest. Mathematics literacy is a serious problem in the United States. According to Philips (2007), 78% of adults cannot explain how to compute the interest paid on a loan, 71% cannot calculate miles per gallon on a trip, and 58% cannot calculate a 10% tip for a lunch bill. Further, it is clear from the research that a broad range of students and adults also have difficulties with fractions (e.g., Hecht, Vagi, & Torgeson, 2007; Mazzocco & Devlin, in press), a foundational skill essential to success in algebra. The recent National Assessment of Educational Progress (NAEP, “the Nation’s Report Card”)shows that 27% of eighth-graders could not correctly shade 1/3 of a rectangle and 45% could not solve a word problem that required dividing fractions (U.S. Department of Education, 2004). Labor economists Richard J. Murnane and Frank...

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...Mathematics: An Integral Discipline Mathematics is one of the most foundational and elemental principles and disciplines to any educational institution. With the basic components of all mathematical disciplines and areas of studies being equal, there appears to be an inherent, social need to master this study of a seemingly complex nature, particularly since this subject is ingrained into so many important and relevant aspects of the world economy. Without the understanding and overall comprehension of at least some basic, elementary mathematical principles, it would go without saying that countless workforce employees and job seekers would fail to find the most meager of professions. It is also an unfortunate prospect to understand that mathematical principles and the study of such major applications is no longer a popular social trend. On the other hand of the social and professional spectrum, the vast majority of college students seeking future majors are leaning towards other convenient modes of study, including those in the healthcare industry and other related sciences and studies. Now understanding how modern culture had become so predisposed to ascertaining studies unrelated to heavy mathematical analytics, despite the obvious need to otherwise acquire, it will be important to frame this expose’s subject matter around the need to further explain and analyze how different regions of scholastic establishments have come to define mathematical disciplines in completely......

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...between language, symbols, pictures and real-life situations. This statement comes as a support for the idea that language effects the ability to solve mathematical problems. Further, Euclid (1956; 46) indicates that "Just as procedural mathematics courses tend to focus on plug and chug with an emphasis on symbolic manipulation, so conceptual mathematics courses focus on proof and argument with an emphasis on correct, clear, and concise expression of ideas. This is a difficult but crucial leap for students to make in transitioning from rudimentary to advanced mathematical thinking. At this stage, the classical tritium of grammar, logic, and rhetoric becomes an essential ally. It is shown in this statement how important language accuracy and constant development of language...

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... MTH 110 Rigoberto Martinez March 17, 2012 The Influence of Math on Economics The history of mathematics is an investigative study of the discoveries of mathematics methods and notations from the past. The study of mathematics began in the 6th century BC with the Pythagoreans who coined the ancient Greek term mathematics with the meaning subject of instruction. Before the spread of knowledge, mathematics was written expressions of the development of Babylonian, Egyptian, and Pythagorean Theorem, which demonstrate the basics of arithmetic and geometry. Arithmetic is one of the oldest forms of mathematics used by Antoine-Augustin Cournot and Joseph Louis Francois Bertrand for tasks of simple day-to-day counting to science and business activities. Arithmetic involves the study of quantity as it relates to addition, subtraction, multiplication, and division. Mathematicians refer to the more advanced term of number theory. Antoine-Augustin Cournot and Joseph Louis Francois Bertrand’s influence on mathematics lay the foundation of the economic effect of the application method on economic theory and analysis of how it will affect others. Each allows individuals to form a meaningful understanding of the complex expressions in various languages. Cournot and Bertrand have used the importance of mathematics to optimize the maximum values of economic functions. The development of Hindu and Arabic numerals devise place value concept as......

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...year. Graduation requirements include: 40 credits (4 years) English; 30 credits (3 years) Mathematics; 30 credits (3 years) Science; 30 credits (3 years) Social Science; 20 credits (2 years) of Language other than English; 10 credits (1 year) Visual and Performing Arts; 40 credits (4 years) Religion;20 credits (2 years) Physical Education/ Health and/or Sports Affiliation; 5 credits (1 semester) Speech Communication; 15 credits (1.5 years) of elective credit (may include core courses).Advanced Placement courses are offered in American Government; Art History; Biology; Calculus AB; Calculus BC; Chemistry; Economics; English Language; English Literature; Environmental Science; European History; Physics; Spanish; Statistics; Studio Art; United States History; World History. AP courses have prerequisites that students must meet in order to be enrolled. There is no limit of how many AP courses a student may enroll. In 2010-2011 462 students enrolled in AP courses; 462 students sat for 884 exams. Of the 884 exams taken, 583 received scores of 3,4 or 5. Honors courses are offered in most subject areas, specifically: Algebra 2/Trigonometry; Anatomy and Physiology; Asian Studies; English; French; Latin; Pre-Calculus. GRADING AND RANKING The Academy assigns letter grades using a 4.0 system. Letter grades are assigned as follows: A = 90-100%; B = 80-89%; C = 70-79%; D =60-69%. Advanced Placement and Honor courses are weighted by one point. All credit classes are......

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...Education College of Education West Visayas State University Luna St. La Paz, Iloilo 2012-2016 Secondary: Our Lady of the Snows Institute Poblacion, Ilaya, Dumarao, Capiz 2008-2012 Elementary Our Lady of the Snows Institute Poblacion, Ilaya, Dumarao, Capiz 2002-2008 Pre-profession Experience: Student Teacher, WVSU-Integrated Laboratory School, November- December 2015 Student Teacher, Jaro National Highschool, January- February 2016 Skills: * Highly skilled in planning effective classroom instructions. * Hands on experience in teaching mathematical concepts to students. * In depth knowledge of basic and advanced mathematics with a specialization in algebra. * Proficient in preparing effective and appropriate lesson plans. * Ensured adequate supervision to assure fitness, interests, and safety of all students. * Excellent grasp over advanced mathematical concepts. * Proven ability to effectively present educational materials. * Developed effective and efficient lesson plan and assessment tools inclined to k-12 curriculum. * Demonstrated competence in curriculum planning and teaching skills. Technical skills: Proficient in: Microsoft Office (Word, PowerPoint, Publisher), Internet, E-mail. Language: Fluent in Filipino, English and Hiligaynon Licenses/Awards: Passed the Licensure Examination for Teachers Membership/Activities: * Participated in the Best of Both Worlds Seminar with the theme: Academic and Curricular...

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...Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was an Indianmathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis,number theory, infinite series and continued fractions. Ramanujan was said to be a natural genius by the English mathematician G.H. Hardy, in the same league as mathematicians like Euler and Gauss.[1] Born in a poor Brahmin family, Ramanujan's introduction to formal mathematics began at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered by the age of 12; he even discovered theorems of his own, and re-discoveredEuler's identity independently.[2] He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan had conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant. Ramanujan received a scholarship to study at Government College in Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to pursue independent mathematical research, working as a clerk in the Accountant-General's office at the Madras Port Trust Office to support himself.[3] In 1912–1913, he sent samples of his theorems to three academics at the University of Cambridge. G. H. Hardy, recognizing the brilliance of his work, invited Ramanujan to visit and work with him at Cambridge. He became a Fellow of the......

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...Grade III pupils of Dona Pilar Learning Center Foundation, Inc. Mathematics is the foundation of learners to improve their reasoning and thinking skill. It is widely recognized not only as a core component of the curriculum but also as a critical contributor to many educational and career opportunities (Scriphai, S. & Damongpanit, S.,et al, 2011). In reality, mathematics encompasses a wide variety of skills and concepts. These skills and concept are related each other but there’s a chance that you can easily master to some and still struggles with others, (Nathan V. Lauren, Sarah Lee Adam 2000). Early academic skills appear to be the strongest predictor of subsequent scholastic success – early math skills more so than early reading skills. http://news.uci.edu/features/kids-skilled-early-in-math-do-better-in-school/ In its report on the 2006 PISA results, the OECD outlines the importance of math skills in today’s world: With the growing role of science, mathematics and technology in modern life, the objectives of personal fulfilment, employment and full participation in society increasingly require that all adults, not just those aspiring to a scientific career, should be mathematically, scientifically and technologically literate. The performance of a country’s best students in mathematics and related subjects may have implications for the role that that country will play in tomorrow’s advanced technology sector, and for its overall international......

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...statement circle a number 1-5 which indicates whether you strongly agree (5), agree (4), no opinion (3), disagree (2) or strongly disagree (1). 1. I usually have been at ease in math classes. 1 2 3 4 5 2. I see math as a subject I will rarely use. 1 2 3 4 5 3. I’m no good at math. 1 2 3 4 5 4. Generally, I have felt secure about attempting math. 1 2 3 4 5 5. I’ll need mathematics for my future work. 1 2 3 4 5 6. I’d be happy to get good grades in mathematics. 1 2 3 4 5 7. I don’t think that I could do advanced math. 1 2 3 4 5 8. It wouldn’t bother me at all to take more math courses. 1 2 3 4 5 9. For some reason, even though I study, math seems unusually hard for me. 1 2 3 4 5 10. My mind goes blank and I am unable to think clearly when working in mathematics. 1 2 3 4 5 11. Knowing mathematics will help me earn a living. 1 2 3 4 5 12. Math has been my worst subject. 1 2 3 4 5 13. I think I could handle more difficult mathematics. 1 2 3 4 5 14. I’m not the type to do well in mathematics. 1 2 3 4 5 15. Math doesn’t scare me at all. 1 2 3 4 5 Compute the mean for questions 1,4,5,6,8,11,and 15:_______________ Compute the mean for questions 2,3,7,9,10,12,and...

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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......

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...be a pastor. However, his love of mathematics directed him down another path. Regardless of intending to enter into ministry, his love of math reflected throughout his childhood, education, and he became an incredible mathematician. Riemann was born in Breselenz, Germany in 1826. He was one of the local Lutheran pastor’s six children. He was the second eldest, having one brother and four sisters. His mother, Charlotte, died when he was twenty. His father served as his teacher until he turned ten. He had already shown incredible mathematical abilities. However, like many great minds, he struggled with shyness and nerves. Additionally, he feared public speaking. Regardless of his shortcomings, his ability to calculate was exceptional and remained apparent throughout his life....

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...Running Head: CREATIVITY AND SCHOOL MATHEMATICS Mathematical Creativity Among School Children Gulsun KUGU Creativity Literature Review As a broad meaning, the concept of creativity has been expressed in not only social sciences such as literature, art and music, and but also physical sciences such as mathematics, computer sciences, biology and chemistry. Creativity catches scholars` attention so that they certainly define the notion of creativity and there are a variety of interpretations. Because of differences of definitions and characteristics of creativity, it is challenge to define creativity. According to Poincaré, creative acts occurred not in the process of doing unless combinations but in the period of useful combinations and small minority (Sriraman, 2004). Creativity also plays vital roles in mathematics. Lack of the definition of mathematical creativity has encouraged many of scholars in order to define it. To identify creative acts and creative potential is a challenge (Mann, 2009). Most of researches on the identification of creativity in mathematics focalize to make the development measuring creativity and to create instruments for such measurements. Current instruments made the measurement and exploring relationship between mathematical creativity and mathematical achievement, attitude towards mathematics, self-perception of creative ability, gender, and teacher perception of mathematical talent and creative ability. Because of that......

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...Today the use of applied mathematics to solve challenging problems in science and engineering or related fields by using numerical computation have reached to a new level. Computation is today considered as a very important tool needed for the advancement of scientific knowledge and engineering practice along with theory and experiment. In the modern world all sorts of calculations are done by sophisticated computer systems. Every company and research farms from small-scale to large-scale are getting more and more reliant on mathematical principles these days. Numerical simulation has enabled the study of complex systems and natural phenomena that would be too expensive or sometimes impossible, to study directly by experimentation. As a matter of fact, engineers and scientists now require solid knowledge of computer science and applied mathematics in order to get optimized output from a system. To make things easier in this matter, Scientific Computing is a discipline that conglomerates Mathematics, Computer Science and Engineering in a single degree program and utilizes mathematical models in computer simulations to solve complex problems for not only in science laboratories but also in business and engineering firms. I have always been fascinated by the application of mathematics and computer science in the real world problems. That is why...

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...Srīnivāsa Rāmānujan was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions. Ramanujan was said by the English mathematician G.H. Hardy to be in the same league as mathematicians like Euler and Gauss in terms of natural genius. He was born on 22na of December 1887 in a small village of Tanjore district, Madras. He failed in English in Intermediate, so his formal studies were stopped but his self-study of mathematics continued. .[9] His father, K. Srinivasa Iyengar, worked as a clerk in a sari shop and hailed from the district of Thanjavur.[10] His mother, Komalatammal, was a housewife and also sang at a local temple.[11] They lived in Sarangapani Street in a traditional home in the town of Kumbakonam. Born in Erode, Madras Presidency, to a poor Brahmin family, Ramanujan first encountered formal mathematics at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney.[2] He mastered them by age 12, and even discovered theorems of his own, including independently re-discovering Euler's identity.By 17, Ramanujan conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant. He received a scholarship to study at Government College in Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to......

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