2/27/2024 0 Comments Circle geometry a level![]() For the student at school, this will be decided by the teacher for the student working alone, we would recommend an advance on a broad front through Chapters 1, 3, 6, 9, 10, 12 (the first two sections), 13, 17, 18. ![]() For convenience, the book has been prepared in the order algebra (Chapters 1-5), trigonometry (Chapters 6-8), calculus (Chapters 9-16), and co-ordinate geometry (Chapters 17-20), but this is not to imply that the chapters should be read in this order. This latter step comes at a later stage in their mathematical development. In this way, we hope that all students can progress quickly in the understanding and application of these techniques without the hindrance of having to justify everything they do. The emphasis throughout has been on technique, although we have tried to indicate where a particular result needs more rigorous justification than is given in this book. The teaching method adopted is for the most part that suggested by the various reports of the Mathematical Association. The book assumes a knowledge of mathematics up to Ordinary Level and covers all the pure mathematics necessary for the Advanced Level examination in mathematics (A26), of the Northern Universities Joint Matriculation Board, together with the great majority of the work required for the Advanced Level examinations of the Southern Universities Joint Board, the Welsh Joint Committee and London University. This is a textbook of pure mathematics written to meet the needs of the student studying for the General Certificate of Education at Advanced Level. The book is especially a didactical material for the mathematical students and instructors. One can navigate back and forth from the text of the problem to its solution using bookmarks. The solutions of the problems are at the end of each chapter. ![]() The degree of difficulties of the problems is from easy and medium to hard. After that, I have escaped in Turkey in September 1988 and lived in a political refugee camp in Istanbul and Ankara, and in March 1990 I immigrated to United States. This book is a translation from Romanian of "Probleme Compilate şi Rezolvate de Geometrie şi Trigonometrie" (University of Kishinev Press, Kishinev, 169 p., 1998), and includes problems of 2D and 3D Euclidean geometry plus trigonometry, compiled and solved from the Romanian Textbooks for 9th and 10th grade students, in the period 1981-1988, when I was a professor of mathematics at the "Petrache Poenaru" National College in Balcesti, Valcea (Romania), Lycée Sidi El Hassan Lyoussi in Sefrou (Morocco), then at the "Nicolae Balcescu" National College in Craiova and Dragotesti General School (Romania), but also I did intensive private tutoring for students preparing their university entrance examination. Answers are also provided for students to confirm their solutions. The exercises at the end are meant to challenge students to familiarize themselves with the application of the theorems treated earlier. These questions and their solutions are purposely targeted at WAEC, NECO and UTME as majority of them are pulled from past questions of these examinations. Chapter six treats a variety of questions cutting across all the ten theorems covered in this book. Chapter four deals with cyclic quadrilateral theorems while chapter five handles tangent theorems. Chapter one introduces circle geometry, chapter two treats theorems on chords, chapter three deals with segment theorems. To deal with this topic exhaustively, this book has been segmented into six chapters covering ten (10) fundamental theorems. Potential engineering students can lay hold on this material at their preliminary stage, as it prepares them for important engineering components like technical drawing. Preliminary and first year students at the University level can also find this book useful as it addresses some fundamental components of the curriculum. Importantly also, this book is written to prepare final year students who will write external examinations such as the West African Examination Council (WAEC), National Examination Council (NECO), Unified Tertiary Matriculation Examination (UTME) and Post UTME as circle geometry happens to be one of the subjects that dominate these examinations. I write this book to address these areas that pose a challenge to many a student who have eventually developed a phobia of the topic. Secondary, my teaching experience of over four years has taught me that several senior school students face similar challenges in the topic as I did during my days. The concept of circle geometry was completely a nightmare to me as I watched my teacher drew several circles and intersecting lines, within and without. My first motivation for writing this book came directly from a personal struggle faced during my secondary school days.
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