high-school-mathematical-course-description-高中數(shù)學(xué)課程描述

1、Mathematics Course DescriptionMathematics 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 choo

2、sen by students which is accrodding their interests.Compulsory Courses:Set TheoryCourse 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 perpared

3、 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 functio

4、ns and sets to set the stage for the next stepKey Topics:Ø The language of set theoryØ Set membershipØ Subsets, supersets, and equalityØ Set theory and functionsFunctionsCourse content:This lesson begin with talking about the role of functions and look at the concept of mapping v

5、alues between domain and range. From there student spend a good deal of time looking at how to visualize various kinds of functions using grahs. this course will begin with the absolute value function and then move on to discuss both exponential and logarithmic functions. Students get an opportunity

6、 to see how these functions can be used to model various kinds of phenomena.Key Topics:Ø Single-variable functionsØ Two variable functionsØ Exponential function Ø Logarithmic function Ø Power- functionCalculusCourse content:In the first step, the course introduces the concep

7、tion 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:Ø Limit theoryØ Derivative&

8、#216; Differential AlgorithmCourse content:Introduce the conception of algorithm and the method to design algorithm. Then the figures of flow charts and the conception of logcial structure, like sequential structure, constructure of condition and cycle structure are introduced to studnets. Next step

9、 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:Ø Algorithm Ø Logical structure of flow chart and algorithmØ Output state

10、mentØ Input statement Ø Assingnment statement StatisticsCourse content:The course starts with basic knowledge of statistics, such as systematic sampling and group sampling. During the lesson students acquire the knowlegde like how to estimate collectivity distribution accroding frequency d

11、istribution 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 r

12、egression line,and what is Method of Square. Key Topics:Ø Systematic samplingØ Group samplingØ Relationship between two variablesØ Interdependency of two variablesBasic Trigonometry ICourse content:This course talks about the properties of triangles and looks at the relationship

13、that exist between their internal angles and lenghs 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 properites and functions to sol

14、ve a number of issues. Key Topics:Ø Common AnglesØ The polar coordinate systemØ Triangles propertiesØ Right trianglesØ The trigonometric functionsØ Applications of basic trigonometryBasic Trigonometry IICourse content:This course will look at the very important inverse

15、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:Ø Derivative trigonometric functionsØ

16、 Inverse trig functionsØ Identitiesl Pythagorean identitiesl Reduction identitiesl Angle sum/Difference identitiesl Double-angle identitiesAnalytic Geometry ICourse content:This course introduces analytic geometry as the means for using functions and polynomials to mathematically represent poin

17、ts, lines, planes and ellipses. All of these concepts are vital in students 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,

18、planes and also briefly talk about ellipsoidal intersections.Key Topics:Ø Parametric representationØ Parallel and perpendicular linesØ Intersection of two linesØ Distance from a point to a lineØ Angles between linesAnalytic Geometry IICourse content:Students look at how anal

19、ytic 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

20、 dot products can be used to determine the lighting and shading of points across a surface.Key Topics:Ø ReflectionsØ Polygon/polygon intersectionØ Lighting Sequence of Number Course content:This course begin with introducing serveral conceptions of sequence of number, such as, term, f

21、inite 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, stuendents gradually understand and utilize the knowldege of s

22、equence of number, eventually students are able to sovle mathematical questions. Key Topics:Ø Sequence of numberØ Geomertic sequenceØ Arithmetic sequenceInequality This course introduces conception of inequality as well as its properties. In the following lessons students learn the so

23、lutions and arithmetics of one-variable quadratic inequality, two variables inequality, fundamental inequality as well how to solve simple linear programming problems.Key Topics:Ø Inequal relationship and Inequality Ø One-variable quadratic inequality and its solutionØ Two-variable in

24、equality and linear programming Ø Fundamental inequalityVector MathematicsCourse 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

25、-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 mes

26、h vertices.Key Topics:Ø Linear combinationsØ Vector representationsØ Addition/ subtractionØ Scalar multiplication/ divisionØ The dot productØ Vector projectionØ The cross productOptional CoursesMatrix ICourse content:In this course, students are introduced to the c

27、oncept 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.

28、 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:Ø Matrix relationsØ Matrix operation

29、sl Addition/subtractionl Scalar multiplicationl Matrix Multiplicationl Transposel Determinantl InversePolynomialsCourse 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 wit

30、h 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 f

31、unction 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:Ø Polynomial algebra ( single varible)l addition/subtractionl multiplication/divisionØ Quadratic equationsØ Graphing polynomialsLogical Terms in MathematicsCourse content:This course introduces the relationshiop of four kinds of statements, necessary and sufficient conditions, basic logical conjunctions,existing quantifier and universal quant