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Mathematics 2: Japanese Grade 11 (Mathematical World)

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This Japanese textbook provides a challenging general mathematics course. It is designed for an elective course taken by eleventh grade Japanese students who do not wish to prepare for rigorous courses in calculus and probability and statistics. It covers a variety of topics, including exponential, logarithmic, and trigonometric functions, vectors, sequences and series, differential and integral calculus, probability and statistics, and computer flowcharts. The coverage of each topic is necessarily narrow, but it is deep enough to provide the reader with numerous challenging problems.

The treatment of exponential, logarithmic, and trigonometric functions is cursory. These functions are explored in considerably greater depth in American pre-calculus texts. Still, there is some interesting material relating base 10 logarithms to the decimal representation of numbers.

Vectors are covered in greater depth. In addition to discussing operations on vectors, the text delves into conditions for parallelism and perpendicularity, parametric equations of lines, the distance between a point and a line, and applications to figures.

The following chapter on progressions addresses arithmetic and geometric sequences and series, summation notation, and recursive definition. The latter topic is a source for some challenging problems.

Topics from differential and integral calculus are introduced. Attention is restricted to polynomial functions. While this limits the scope of what can be covered, the text does address velocity, linear motion, the tangent line problem, computing areas and volumes, increasing and decreasing functions, and local extrema.

Probability and statistics are introduced through a discussion of basic combinatorics, including permutations and combinations. This leads to a discussion of basic probabilistic principles, including sample spaces, complementary events, mutually exclusive events, conditional probability, and independent events. The succeeding discussion of random distributions, expected value, variance, standard deviation, and the normal distribution leads to a discussion of statistics. There are some notational problems at the end of the chapter of probability that are clarified in the chapter on statistics, in which sampling is discussed.

The final chapter, which is somewhat dated, discusses how simple calculators and computer programs work. The problems in this chapter entail writing computer programs or flowcharts to solve mathematical problems.

There are problems embedded within the text to test your understanding of the material. There are also exercise sets at the end of each section and the end of each chapter. Answers are only provided to the chapter exercises. While there are routine problems, many of the problems are challenging. Some of the problems require some ingenuity to solve.

Some of the topics in this book are covered in more depth in the texts Algebra and Geometry: Japanese Grade 11 and Basic Analysis: Japanese Grade 11. However, other topics including probability, statistics, and computer flowcharts are not addressed in those texts since students who take the simultaneous courses based on those texts have the option of taking both a rigorous course on calculus and a rigorous course on probability and statistics in twelfth grade.

If you are a student planning to study mathematics or a related field in college, this text is somewhat superfluous. After studying pre-calculus, you could work through the through the text Mathematics 1: Japanese Grade 10 (Mathematical World, V. 8), and then study the texts Algebra and Geometry: Japanese Grade 11 (Mathematical World, V. 10) and Basic Analysis: Japanese Grade 11 (Mathematical World, V. 11). That will provide you with a strong foundation for studying mathematics in college. Teachers of high school mathematics would benefit from using this text as a source of enrichment problems for their honors pre-calculus students.