数学课程描述
Mathematics Course Description
数学是所有高中生高中三年的必修课。高中数学可以提高空间想像、抽象概括、推理论证、运算求解、数据处理等基本能力。
本课程主要内容:包括必修课程和选修课程两部分。
(1)必修课程包含集合,函数概念与基本初等函数1、立体几何初步、平面解析几何初步、算法初步、统计、概率、基本初等函数2、平面上的向量、三角恒等变换、解三角形、数列、不等式。
(2)选修课程包含常用逻辑用语、圆锥曲线与方程、导数及其初步应用、统计案例、推理与证明、复数的引入、框图、常用逻辑用语、圆锥曲线与方程、空间中的向量与立体几何。Mathematics should be taken by all high school students during the three-year study. High school mathematics can improve the spatial imagination, abstraction, reasoning, argumentati-on, computing solving, data processing and other basic capabilities.
Main content of this course include: compulsory courses and elective courses.
(1) The compulsory courses include: a collection of concepts and the basic function of an element ary function, the initial three-dimensional geometry, initial
geometry of plane analysis, preliminary algorithms, statistics, probability, basic elementary functions 2, plane vectors, triangular identity
transformation, solution of triangles, series, and inequality.
(2) Elective courses include: common logic language, tapered curves and equations, derivatives a nd their preliminary application, statistical case, reasoning and proof and the introduction of compl ex numbers, block diagram, common logic language, tapered curves and equations, space.
单元内容Module
A.函数(基本函数指数函数幂函数对数函数)
Function(elementary function, exponential function, power function, logarithm function)
B.代数 Algebra
C.不等式 Inequality
(1)Unequal relationship and Inequality
(2)One-variable quadratic inequality and its solution
(3)Two-variable inequality and linear programming
(4)Fundamental inequality
D.平面几何 Plane analytic geometry
(1)Parametric representation
(2)Parallel and perpendicular lines
(3) Intersection of two lines
(4) Distance from a point to a line
(5) Angles between lines
(6)Reflections
(7) Polygon/polygon intersection
(8) Lighting
E.平面向量 Two dimensional vectors
(1) Linear combinations
(2) Vector representations
(3)Addition/ subtraction
(4)Scalar multiplication/ division
(5)The dot product
(6)Vector projection
(7)The cross product
F.圆锥曲线 Conics
(1)Curve and equation
(2)Oval
(3)Hyperbola
(4)Parabola
G.三角函数 Trigonometric function
(1)Common Angles
(2)The polar coordinate system
(3)Triangles properties
(4)Right triangles
(5)The trigonometric functions
(6)Applications of basic trigonometry
(7)Derivative trigonometric functions
(8)Inverse trig functions
(9)Identities
(10)Pythagorean identities
(11)Reduction identities
(12)Angle sum/Difference identities
(13)Double-angle identities
H.空间向量和立体几何 Space vector and solid geometry
(1)Ball, prism, pyramid, table surface area and volume of the formula
(2) Understand the application of vector method in the study of three - dimensional geometric problems.
(3) Using vector method to solve the problem of the calculation of the angle between straight line and straight line, straight line and plane, plane and plane.
(4)Can use axioms, theorems, and the conclusions that have been obtained to prove some simple propositions of spatial position relations.
(5)Space Cartesian Coordinate System
I.导数基础 Basic calculus
(1)Limit theory
(2)Derivative
(3)Differential
J.基础数列 Introduction to sequences and series
(1)Sequence of number
(2)Geometric sequence
(3)Arithmetic sequence and Equidistant sequence
K.复数初步 Complex number
(1)Algorithm
(2)Logical structure of flow chart and algorithm
(3)Output statement
(4)Input statement
(5)Assignment statement
L.概率统计初步 Introduction to probability and statistic
(1)Systematic sampling
(2)Group sampling
(3)Relationship between two variables
(4)Inter dependency of two variables
(5)Classical typology
(6)Random numbers and geometric profiles
M.数学逻辑用语 Logical Terms in Mathematics
(1)Statement and its relationship
(2)Necessary and sufficient conditions
(3)Basic logical conjunctions
(4)Existing quantifier and universal quantifier
N.推理与证明 Reasoning and proof
(1)Reasonable reasoning and deductive reasoning
(2)Direct proof and indirect proof
(3)Mathematical induction
O.技术原理 Counting principle
(1)Classification and counting principle, step multiplication counting principle
(2)Arrangement and combination
(3)Binomial theorem
上课时长Duration: September.2013 --- June.2016 540 hours lectures (4.6 hours/p.w)
参考书籍Literature: Teaching Materials Writing Group. Mathematics, People’s E ducation Press, 2007
