Mathematics Theory Tests and Solutions for Grades 9-12 -
800 Problems and Sulutions
Theory and Tests - By Liliana Usvat
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This book is designed primarily to assist students in acquiring a more thorough knowledge and proficiency in the high school mathematics. It includes a thorough coverage of algebra, plane trigonometry, plane analytic geometry together with selected topics in solid analytic geometry and a brief introduction to the calculus.
Major users of this work
" In addition to the use of the book by high school students taking formal high school courses, it should also be of considerable value to:
" Those who wish to review the fundamental principles and application in anticipation of further work in mathematics.
" Teachers will find the organization and coverage of this work will provide essential tools to be used in addition to the text books
" Home schooling students and parents would have an excellent aid using this book, in understanding and comprehension of mathematics
Organization of this work
The book has 3 major chapters: "Theory", "Tests" and complete "Solutions" to the tests.
The first chapter is structured in 4 subchapters. Theory for Grade 9, Theory for Grade 10, Theory for Grade 11, and Theory for Grade 12 which presents the essentials of mathematics thought in each grade. In a sense the book can be used as a reference for the basic mathematical concepts learned in high school.
The second chapter has groups of problems for each grade organizes in tests. There are 20 tests for each grade from grade 9 to grade 12. Each test having 10 problems.
" The third chapter there are solution to the problems from the second chapter. In the solution chapter each problem has a detailed solution. There are in total 800 problems with solutions, 200 problems for each grade structured in tests of 10 problems each.
Subjects of the book
The book treats subjects such as: polygons, analytic geometry, array syntax and limits, simple and compound interest, polar coordinates, regular solids, equations of a line, sequences, proof of the law of cosines, median bisector of an angle, hyperbolic definitions, two and three dimensional coordinate system, base 2,4,8 and 16 and converting to base 10, quadratic functions and equations, arithmetic and geometric progressions and means, factorials, permutations, combinations, similar triangles, Exceptional sections, complex numbers, complex plane, analytic trigonometry, conic sections, compound interest, probability theory, medians of a triangle, ellipse, vectors, the derivative, limit definition of the derivative, integral, composition of functions, chain rule.
The tests serve to illustrate and amplify the theory, provide the repetition of basic principles so vital to effective teaching, and bringing into sharp focus those fine points without which the student continually feels on unsafe ground. Derivation of formulas and proofs are included among the solved problems.
The reader will find that the material is a useful supplement to all current standard texts.
Material that has been included in the book will stimulate further interest in the topics.
An attempt has been made to make the explanations and discussions clear and complete so that the book can also be used for home study or in courses where greater reliance that usual is placed upon the student's reading.
All examples are worked out in full so that the student can see in operation the theory principles has a clear procedure after which to pattern his own work.
Much of the material contained in this book was developed and used by the author in tutoring session with her students, and published in the "Mathematics Magazine for Grades 9-12" journal. The author is also the Editor and Publisher of the "Mathematics Magazine" website.
This book will help students become proficient with mathematics.