IBDP数学课程简介

1、旧DP数学课程简介1. Introduction of IBDP Mathematics旧DP数学课程介绍Introduction:The nature of mathematics can be summarized in a number of ways: for example, it can be seen as a well-defined body of knowledge, as an abstract system of ideas, or as a useful tool. For many people it is probably a combination of the

2、se, but there is no doubt that mathematical knowledge provides an important key to understanding the world in which we live. This prevalence of mathematics in our lives, with all its interdisciplinary connections, provides a clear and sufficient rationale for making this subject compulsory for stude

3、nts studying for the full diploma.介绍：数学的本质可以用多种方式来归纳： 例如，它可以被看作个被良好定 义的知识体，是一个抽象的思想系 统，或作个有用的工具。 对于很 多人来说它可能是它们的组合，但毫 无疑问的是数学知识是让我们了解 所生活的世界的一个重要的关键。 数 学在我们的生活中的普遍性，其所拥 有的跨学科的联系，使得这一学课拥 有充分理由成为每个学生的必修科 目。Aim:enjoy mathematics, and develop an appreciation of the elegance and power of mathematicsdevel

4、op an understanding of the principles and nature of mathematicsdevelop logical, critical and creative thinking, and patience and persistence in problem-solving目标：.享受数学，发现并欣赏数学的优 雅和力量。.理解数学的原理和本质.培养逻辑，批判性和创造性思维， 和在解决问题上的耐心和毅力Belonging to:Group 5 Mathematics所属类别： 第五组数学Syllabus-Core and Options:CoreTop

5、ic1: AlgebraTopic2： Functions and equationsTopic3: Circular functions and trigonometryTopic4： VectorsTopic5: Statistics and probabilityTopic6: CalculusOption (Choose one from four)Topic7： statistics and probabilityTopic8: Sets, relations and groupsTopic9: Series and differential equationsTopic10: Di

6、screte mathematics学习范围-必修和选修：必修主题1:代数主题2:函数与方程主题3:三角函数主题4:向量主题5:统计与概率主题6:微积分选修（四所）主题7:概率和统计主题8:集合，关系和群主题9:级数和微分方程主题10:离散数学How to assess:Internal Assessment and External Assessment考试形式：内部测试+外部考试。.学习准备与方法。在整个DP数学学习中，都鼓励学生要掌握学习数学的方法并加以结合实践。数学研究，数学模型 和应用，还有现代技术在数学中的应用都应该适当了解。这些都会贯穿在整个过程中，不应被当成分离的部分。数学研究

7、旧的理念是通过实验，质疑和探索来学习。在 旧 课堂上，学生应作为学习的积极参与者， 而不是 指令的接受者。数学模型和应用学生应能运用数学解决现实世界中的问题。 让学生参加数学建模可以提供这样的机会。 学生应学会 开发，应用，批判和分析模型。现代技术在数学中的使用现代技术是数学教学和学习的强有力的工具。现代技术可以让数学概念可视化并增强学生的理解。它可以协助收集， 记录，组织和分析数据。学生也要学会运用计算机等高级计算工具去反思原因， 解决问题和做出决策。. SL/HL在教学大纲及考纲方面的区别。附一,教学大纲区别SyllabusTeaching hours教学大纲教学时长SLHLSLHLCor

8、e Topic 1: AlgebraArithmetic sequences and series;Exponents and logarithms.Counting principles, including permutations and combinations. (HL only)The binomial theoremProof by mathematical induction (HL only)Complex numbers (HL only)Powersof complex numbers (HL only)Conjugate roots of polynomial equa

9、tions with real coefficients (HL only)Solutions of systems of linear equations (HL only)930主题一：代数等差数列和级数；指数和对数。计数原理，包括排列和组合（仅限HL）二项式定理数学归纳法证明（仅限HL）复数（仅限HL）高幕次复数（仅限HL）实系数多项式方程（仅限HL）解线性方程组（仅限HL）930Core Topic 2: Functions and EquationConcept of functionThe graph of a functionTransformations of graphsTh

10、e rational function and its GraphPolynomial functions and their graphs. The factor and remainde theorems (HL only)Solving quadratic and polynomial equationsExponential and Logarithmic functions and their graphsSolutions of f(x)g(x)5 24r22主题二：函数与方程概念函数的曲线图变换图形有理函数及其图象多项式函数及其图形，余数定理（仅限HL）解二次和多项式方程指数函数

11、与对数函数及其图像解 f（x）g（x）2422Core Topic 3: Circular functions and trigonometryThe circle: radian measure of angles; length of an arc; area of a sector.Definition of cos 0 /sin 0 /tanin 8 terms of the unit circle .Compound and Double angle identities.The circular functions. Composite functions of the form

12、of trigonometry and transformation.The inverse functions (HL Only)Solving trigonometric equations, both graphically and analytically.Solution of triangles.1622主题二：二角函数圆：角弧度；圆弧的长度COS , SIN 9和tan 9在单位圆 表小的定义。复合和双角的定理。三角复合函数的变形。反函数（仅限HD以图形和分析求解一个有限区 问三角方程，。解三角形。1622Core Topic 4: VectorsVectors as displ

13、acements in the plane and in three dimensions.The scalar product of two vectorsVector equation of a line in two and three dimensionsCoincident, parallel, intersecting a and distinguishing between these casesThe definition of the vector product of two vectors (HL Only)Vector equation of a plane (HL O

14、nly)Intersections of: a line with a plane; two planes; three planes (HL Only)16*24主题四：向量向量作为在平向上和在三维空 问中的位移。两个向里的标重积在二维和三维的矢量方程重合，平行，相交和这些情况之 间的区别两个向量的向量积的定义（仅限HD一个平间的矢量方程（仅限HD交叉：一个平卸和直线，两个平 面，三个平间（仅限HD1624Core Topic 5:Statistics andprobabilityConcepts and statistical measuresandtheirinterpretations

15、.Cumulative frequency and frequency graphs; use to find median, quartiles, percentiles (SL only)Linear correlation of bivariate data (SL only)Concepts of trial, outcome, equally likely outcomes, sample space ( U) and event.CombinedeventsandConditional probabilityConcept of discrete random variables

16、and their probability distributionsBinomial distributionNormal distributions and curvesPoisson distribution (HL only3536主题九：统计与概率概念和统计的计算及其诠释。累积频率；累计频率曲线图，用 来查找中位数，四分位数，百分位 数（仅限SL）双变量数据的线性相关性（仅 限SL）试验，结果，相同概率的结果， 样本空间（U）和事件。联合事件和条件概率离散型随机艾量及其概率分布二项分布止态分布和曲线泊松分布（仅限HD3536Core Topic 6 : CalculusLimitDi

17、fferentiation and higher derivativesLocal maximum and minimum points and graph behaviorIndefiniteintegrationasanti-differentiationDefinite integralsKinematic problems4048主题六：微积分极限微分及高阶导数局部最大值，最小值和曲线走势不定积分定积分运动学问题4048Options HL Only048选修部分仅限HL048Total teaching hours140230140230Assessment componentWei

18、ghting考试组成比重External assessment (3 hours)80%外部考试，3个小时80%Paper 1-1 hour and half (90 marks)40%1.5小时，90分：40%Section AA部分一必修内容简答题。Compulsory short-response questions based on the whole syllabusB部分一必修内容拓展题。Section BCompulsoryextended-responsequestions based on the whole syllabusPaper 2 - 1 hour and half

19、 (90 marks)40%卷二,1.5小时，90分:A部分一必修内容简答题。40%Section ACompulsory short-response questions based on the whole syllabusB部分一必修内容拓展题。Section BCompulsoryextended-responsequestions based on the whole syllabusInternal assessment20%内部测评20%This component is internally assessedby the teacher and externally moder

20、ated y the IB at the end of the course.1.此部分由内部老师来评分， IB会在课程结束时进行外部评 分。Internal assessment in mathematics SL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics2.学生需要完成1篇评论文 章，文章是对某一数学领域进 行分析。附二考试大纲SL部分Assessment componentWeighting考试组成比重External assessment (5 hours)80%外部考试5小时80%Paper 1- 2 hours (120 marks)30%2小时，120分A部分一必修内容简答题。B部分一必修内容拓展题。30%Section ACompulsory short-response questions based on the whole syllabusSection BCompulsoryextended-responsequestions based on the whole syllabusPape