高中数学课程描述(英文)

2024年1月25日发(作者：瑞安教师编制小学数学试卷)

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 sum/Difference 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

➢ Polygon/polygon 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

formula. Then, 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

 Addition/subtraction

 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)

 addition/subtraction

 multiplication/division

➢ 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