Mathematics

Mathematics department’s major goal is to prepare our students for their future study at college, especially at Keio University where most of our students wish to enter. To achieve the goal, the department takes advantage of strengths of American education, Japanese education and other countries’ education by using textbooks and problem solving books published in the United States, in Japan and in Europe. Our major focus in each grade is as follows:

9th grade Algebra and Geometry, and 10th grade Algebra and Trigonometry: developing competence to deal with mathematical expressions. These are basic languages in mathematics.

Our education for 9th and 10th graders focuses on developing students’ competence in mathematical language.

11th grade Pre-calculus: developing competence in logical thinking and abstract thinking. This is where students fully utilize their mathematical language ability to mathematically express their ideas and to understand mathematically expressed abstract concepts. Training logical and abstract thinking through this process will be extremely valuable throughout their lives.

12th grade Calculus and Linear Algebra: introducing mathematics directly connecting to their study at Keio University, which is calculus and linear algebra. For elementary level students, who still have weaknesses in areas taught in previous grades, we try to strengthen their competence in such areas using materials in calculus.

As shown above, our core curriculum is structured based on mathematical content areas. This structure tends to have a weakness in developing students’ problem solving ability of utilizing knowledge of various content areas of mathematics. The two elective courses for 11th graders entitled “Mathematical Modeling” and “Advanced Problem Solving” are to help students develop problem solving ability of this kind. “Mathematical Modeling” course focuses on solving real world problems, such as social, economical, environmental while “Advanced Problem Solving” course focuses on mathematical problems.

Algebra and Geometry (Grade 9)
The goal of this course is to develop fluency in algebraic manipulations with polynomials and with irrational numbers and to develop ability to construct geometric proofs.
The course includes the following topics: Equations, Inequalities, Exponents and Polynomials, Polynomials and Factoring, Systems of Equations, Radical Expressions and Equations, Relations and Functions, Quadratic Equations, Introduction to Probability and Statistics; Congruent Triangle, Applying Congruent Triangles, Quadrilaterals, Similarity, Circles, Polygons and Areas, Surface Area and Volume.
Students will be placed either in an intermediate level class or in an honor level class by the results of the placement test.

Algebra and Trigonometry (Grade 10)
The goal of this course is to develop fluency in algebraic manipulations especially with rational and radical expressions and in solving quadratic equations.
The course includes the following topics: Equations and Inequalities, Systems of Equations and Problem Solving, Polynomials and Polynomial Equations, Equations of Second Degree, Rational Expressions and Equations, Polynomial Functions, Powers, Roots, and Complex Numbers, Quadratic Equations, Relations, Functions and Graphs, Quadratic Functions and Transformations, Exponential and Logarithmic Functions, Trigonometric Functions, Trigonometric Identities and Equations, Counting and Probability.
Students will be placed either in an elementary, intermediate or honor level class by the results of the placement test.

Pre-Calculus (Grade 11)
The goal of this course is to develop competence in logical and abstract thinking through the study of the following topics: Cartesian Coordinates, Second Degree Relations, Matrices, Circular Functions, Vectors, Sequence and Series, Rates and Tangents, Sums and Areas.
Students will be placed either in an elementary, intermediate or honor level class by grades of Algebra and Trigonometry.

Advanced Problem Solving (Grade 11)
This course is designed to increase the ability of our students to analyze and solve problems which are on the boundary between various mathematical topics. Those problems are often assigned at mathematical competitions. Examples of the topics are Combinatorics, Complex Numbers, Inversion in Plane, Mathematical Induction, Proofs by Contradiction.
For students to qualify for the course, they must be in an honor level Algebra and Trigonometry class at the end of the 10th grade.

Mathematical Modeling (Implementation of this course is currently under consideration.) (Grade 11)
This course is designed to develop the ability of our students to construct mathematical formulations of real world problems, such as social, economical, and environmental, and solve the problems by applying mathematical knowledge.

Calculus (for non-science majors) (Grade 12)
These courses fulfill a requirement for non-science major faculties.
These courses include the following topics: Limits of Functions, Derivatives (The Chain Rule, Implicit Differentiation, Parametric Representation, Differentiation of Exponential and Logarithmic Functions, Higher Derivatives), Applications of Differentiation (Maxima and Minima, Inflexion Points, Graph Sketching), Indefinite Integrals (Method of Substitution, Integration by Parts, Partial Fractions), Definite Integrals and Applications (Areas and Volumes).
Students will be placed either in an elementary, intermediate or honor level class by grades of Pre-Calculus. In addition, students must pass the placement test to be placed in the honor level class. For students to qualify for the placement test, they must either be in an honor level pre-calculus class at the time of the placement test or be in an intermediate level pre-calculus class with the combined grade of the first, second and the third quarter grade of a B or above.
Students who are placed in the honor level class are not allowed to change class to the intermediate class once they start the 12th grade.
If the number of students who have passed the placement test for the honor level class is too small, the honor level class will be cancelled. In that case, the students may take the placement test for the Advanced Calculus class.

Linear Algebra (Elective for Non-Science Majors. Strongly Recommended to Students Who Wish to Major in Economics or Commerce. ) (Grade 12)
This course is strongly recommended to students who wish to enter Faculty of Economics or Faculty of Commerce.
This course includes the following topics: Vectors, Systems of Linear Equations, Matrices, Eigenvalues and Eigenvectors, Orthogonality, Vector Space.

Advanced Calculus & Linear Algebra (for science majors) (Grade12)
This course is a requirement for students applying to faculty of science and technology, faculty of medicine and faculty of Pharmacy.
This course includes the following topics in addition to the topics included in the above Calculus Course and the above Linear Algebra course: Continuity of Functions, Polar Coordinates, and Differential Equations.
Students must pass the placement test to be placed in this class. For students to qualify for the placement test, they must be in an honor level pre-calculus class at the time of the placement test. Students who are placed in this class are not allowed to change class to the non-science major calculus class once they start the 12th grade.
Students must register as science majors to be placed in this class except for the case that the honor level calculus class for non-science majors is cancelled.