高中数学课程描述(英文)

Mathematics Course Description
Mathematics course in middle school has two parts: compulsory courses and optional courses.
Compulsory courses content lots of modern mathematical knowledge and conceptions, such as
calculus,statistics, analytic geometry, algorithm and vector. Optional courses are chosen by
students which is according their interests.

Compulsory Courses:

Set Theory
Course content:
This course introduces a new vocabulary and set of rules that is foundational to the mathematical
discussions. Learning the basics of this all- important branch of mathematics so that students are
prepared to tackle and understand the concept of mathematical functions. Students learn about
how entities are grouped into sets and how to conduct various operations of sets such as unions
and intersections(i.e. the algebra of sets). We conclude with a brief introduction to the
relationship between functions and sets to set the stage for the next step

Key Topics:
? The language of set theory
? Set membership
? Subsets, supersets, and equality
? Set theory and functions

Functions
Course content:
This lesson begins with talking about the role of functions and look at the concept of mapping
values between domain and range. From there student spend a good deal of time looking at how
to visualize various kinds of functions using graphs. This course will begin with the absolute
value function and then move on to discuss both exponential and logarithmic functions. Students
get an opportunity to see how these functions can be used to model various kinds of phenomena.

Key Topics:
? Single-variable functions
? Two –variable functions
? Exponential function
? Logarithmic function
? Power- function

Calculus
Course content:
In the first step, the course introduces the conception of limit, derivative and differential. Then
students can fully understand what is limit of number sequence and what is limit of function
through some specific practices. Moreover, the method to calculate derivative is also introduced
to students.

Key Topics:
? Limit theory
? Derivative
? Differential

Algorithm
Course content:
Introduce the conception of algorithm and the method to design algorithm. Then the figures of
flow charts and the conception of logical structure, like sequential structure, contracture of
condition and cycle structure are introduced to students. Next step students can use the
knowledge of algorithm to make simple programming language, during this procedure, student
also approach to grammatical rules and statements which is as similar as BASIC language.

Key Topics:
? Algorithm
? Logical structure of flow chart and algorithm
? Output statement
? Input statement
? Assignment statement

Statistics
Course content:
The course starts with basic knowledge of statistics, such as systematic sampling and group
sampling. During the lesson students acquire the knowledge like how to estimate collectivity
distribution according frequency distribution of samples, and how to compute numerical
characteristics of collectivity by looking at numerical characteristics of samples. Finally, the
relationship and the interdependency of two variables is introduced to make sure that students
mastered in how to make scatterplot, how to calculate regression line, and what is Method of
Square.
Key Topics:
? Systematic sampling
? Group sampling
? Relationship between two variables
? Interdependency of two variables

Basic Trigonometry I
Course content:
This course talks about the properties of triangles and looks at the relationship that exists between
their internal angles and lengths of their sides. This leads to discussion of the most commonly
used trigonometric functions that relate triangle properties to unit circles. This includes the sine,
cosine and tangent functions. Students can use these properties and functions to solve a number of
issues.

Key Topics:
? Common Angles
? The polar coordinate system
? Triangles properties
? Right triangles
? The trigonometric functions
? Applications of basic trigonometry

Basic Trigonometry II
Course content:

This course will look at the very important inverse trig functions such as arcsin, arcos, and arctan,
and see how they can be used to determine angle values. Students also learn core trig identities
such as the reduction and double angle identities and use them as a means for deriving proofs.

Key Topics:
? Derivative trigonometric functions
? Inverse trig functions
? Identities
? Pythagorean identities
? Reduction identities
? Angle sumDifference identities
? Double-angle identities


Analytic Geometry I
Course content:
This course introduces analytic geometry as the means for using functions and polynomials to
mathematically represent points, lines, planes and ellipses. All of these concepts are vital in
student’s mathematical development since they are used in rendering and optimization, collision
detection, response and other critical areas. Students look at intersection formulas and distance
formulas with respect to lines, points, planes and also briefly talk about ellipsoidal intersections.

Key Topics:
? Parametric representation
? Parallel and perpendicular lines
? Intersection of two lines
? Distance from a point to a line
? Angles between lines

Analytic Geometry II
Course content:
Students look at how analytic geometry plays an important role in a number of different areas of
class design. Students continue intersection discussion by looking at a way to detect collision
between two convex polygons. Then students can wrap things up with a look at the Lambertian
Diffuse Lighting model to see how vector dot products can be used to determine the lighting and
shading of points across a surface.

Key Topics:
? Reflections
? Polygonpolygon intersection
? Lighting

Sequence of Number
Course content:
This course begin with introducing several conceptions of sequence of number, such as, term,
finite sequence of number, infinite sequence of number, formula of general term and recurrence
, the conception of geometric sequence and arithmetic sequence is introduced to
students. Through practices and mathematical games, students gradually understand and utilize

the knowledge of sequence of number, eventually students are able to solve mathematical
questions.

Key Topics:
? Sequence of number
? Geometric sequence
? Arithmetic sequence

Inequality
This course introduces conception of inequality as well as its properties. In the following lessons
students learn the solutions and arithmetic of one-variable quadratic inequality, two variables
inequality, fundamental inequality as well how to solve simple linear programming problems.

Key Topics:
? Unequal relationship and Inequality
? One-variable quadratic inequality and its solution
? Two-variable inequality and linear programming
? Fundamental inequality

Vector Mathematics
Course content:
After an introduction to the concept of vectors, students look at how to perform various important
mathematical operations on them. This includes addition and subtraction, scalar multiplication,
and the all-important dot and cross products. After laying this computational foundation, students
engage in games and talk about their relationship with planes and the plane representation, revisit
distance calculations using vectors and see how to rotate and scale geometry using vector
representations of mesh vertices.

Key Topics:
? Linear combinations
? Vector representations
? Addition subtraction
? Scalar multiplication division
? The dot product
? Vector projection
? The cross product

Optional Courses
Matrix I
Course content:
In this course, students are introduced to the concept of a matrix like vectors, matrices and so on.
In the first two lessons, student look at matrices from a purely mathematical perspective. The
course talks about what matrices are and what problems they are intended to solve and then looks
at various operations that can be performed using them. This includes topics like matrix addition
and subtraction and multiplication by scalars or by other matrices. At the end, students can
conclude this course with an overview of the concept of using matrices to solve system of linear
equations.

Key Topics:

? Matrix relations
? Matrix operations
? Additionsubtraction
? Scalar multiplication
? Matrix Multiplication
? Transpose
? Determinant
? Inverse

Polynomials
Course content:
This course begins with an examination of the algebra of polynomials and then move on to look
at the graphs for various kinds of polynomial functions. The course starts with linear interpolation
using polynomials that is commonly used to draw polygons on display. From there students are
asked to look at how to take complex functions that would be too costly to compute in a relatively
relaxed studying environment and use polynomials to approximate the behavior of the function to
produce similar results. Students can wrap things up by looking at how polynomials can be used
as means for predicting the future values of variables.

Key Topics:
? Polynomial algebra ( single variable)
? additionsubtraction
? multiplicationdivision
? Quadratic equations
? Graphing polynomials

Logical Terms in Mathematics
Course content:
This course introduces the relationships of four kinds of statements, necessary and sufficient
conditions, basic logical conjunctions, existing quantifier and universal quantifier. By learning
mathematical logic terms, students can be mastered in the usage of common logical terms and
can self-correct logical mistakes. At the end of this course, students can deeply understand the
mathematical expression is not only accurate but also concise.

Key Topics:
? Statement and its relationship
? Necessary and sufficient conditions
? Basic logical conjunctions
? Existing quantifier and universal quantifier

Conic Sections and Equation
Course content:
By using the knowledge of coordinate method which have been taught in the lesson of
linear and circle, in this lesson students learn how to set an equation according the character
of conic sections. Students is able to find out the property of conic sections during
establishing equations. The aim of this course is to make students understand the idea of
combination of number and shape by using the method of coordinate to solve simple
geometrical problems which are related to conic sections.

Key Topics:
? Curve and equation
? Oval
? Hyperbola
? Parabola