改革后IB数学考纲介绍 这些内含考点的新考纲错过就要失分了

同学们看了最近IBO官方发布的有关IB大考消息了吗？马上就是大考了，为了让大家对考点有一个更好的把握，我们给大家带来了一些改革后IB数学考纲介绍，以及一些常规问题的解答。

改革后IB数学考纲介绍

数学分析与方法（SL)考纲

from patterns to generalizations: sequences and series模式和概括：序列和极数

1.1: Number patterns and sigma notation 数字模式和∑求和

1.2: Arithmetic and geometric sequences算数和几何序列

1.3: Arithmetic and geometric series算数和几何极数

1.4: Modelling using arithmetic and geometric series用算数和几何极数模型化

1.5: The binomial theorem 二项式定理

1.6: Proofs 证明题

Representing relationships: introducing functions表达关系：函数介绍

2.1: What is a function? 什么是函数？

2.2: Functional notation 函数符号

2.3: Drawing graphs of functions 函数的绘制

2.4: The domain and range of a function域值

2.5: Composition of functions组合函数

2.6: Inverse functions反函数

Modelling relationships: linear and quadratic functions关系模型化：线性函数和二次方函数

3.1: Parameters of a linear function线性函数的参数

3.2: Linear functions线性函数

3.3: Transformations of functions函数变化

3.4: Graphing quadratic functions二阶函数的绘制

3.5: Solving quadratic equations by factorization and completing the square因式分解和完全平方公式求根

3.6: The quadratic formula and the discriminant二阶公式的判别

3.7: Applications of quadratics二次方应用

Equivalent representations: rational functions等效呈现：有理数

4.1: The reciprocal function倒数函数

4.2: Transforming the reciprocal function反倒数函数

4.3: Rational functions of the form ax+b/cx+d ax+b/cx+d 有理函数的形式

Measuring change: differentiation测量变化：微分

5.1: Limits and convergence 极限和收敛

5.2: The derivative function导数函数

5.3: Differentiation rules微分法规则

5.4: Graphical interpretation of first and second derivatives第一和第二导数的图形解释

5.5: Application of differential calculus: optimization and kinematics微积分应用：最优化和运动学

Representing data: statistics for univariate data呈现数据：多因素方差统计

6.1: Sampling取样

6.2: Presentation of data数据呈现

6.3: Measures of central tendency集中趋势

6.4: Measures of dispersion离差测量

Modelling relationships between two data sets: statistics for bivariate data两套数据的关系模型化：双变量数据统计

7.1: Scatter diagrams点聚图

7.2: Measuring correlation测量相关性

7.3: The line of best fit 最佳拟合直线

7.4: Least squares regression最小平方回归法

Quantifying randomness: probability量化随机性：可能性

8.1: Theoretical and experimental probability理论和实验可能性

8.2: Representing probabilities: Venn diagrams and sample spaces表达可能性：韦恩图和样本空间

8.3: Independent and dependent events and conditional probability独立事件和相关事件，以及条件概率

8.4: Probability tree diagrams可能性树形图

Representing equivalent quantities: exponentials and logarithms呈现相等数量：指数曲线和对数

9.1: Exponents指数

9.2: Logarithms对数

9.3: Derivatives of exponential functions and the natural logarithmic function指数函数和导数和自然对数函数

From approximation to generalization: integration从近似值到归纳：积分

10.1: Antiderivatives and the indefinite integral反导数和不定积分

10.2: More on indefinite integrals不定积分更多内容

10.3: Area and definite integrals区间和定分

10.4: Fundamental theorem of calculus微积分基本定理

10.5: Area between two curves两个曲线之间的面积

Relationships in space: geometry and trigonometry in 2D and 3D空间关系：2D和3D中的几何学和三角学

11.1: The geometry of 3D shapes 3D图形几何学

11.2: Right-angles triangle trigonometry 直角几何学

11.3: The sine rule 正弦规则

11.4: The cosine rule 余弦规则

11.5: Applications of right and non-right angled trigonometry 直角三角和非直角三角的应用

Periodic relationships: trigonometric functions周期关系：三角函数

12.1: Radian measure, arcs, sectors and segments 弧度测量，弧，节面和弓形

12.2: Trigonometric ratios in the unit circle 单位圆中的三角比例

12.3: Trigonometric identities and equations 三角恒定式和方程式

12.4: Trigonometric functions 三角函数

Modelling change: more calculus关系模型化：微积分更多内容

13.1: Derivatives with sine and cosine正弦和余弦的导数

13.2: Applications of derivatives导数运用

13.3: Integration with sine, cosine and substitution正弦，余弦和取代法的解释

13.4: Kinematics and accumulating change运动学和累加变化

Valid comparisons and informed decisions: probability distributions有效比较和信息明确下的决策：可能性分布

14.1: Random variables随机变化

14.2: The binomial distribution二项式分布

14.3: The normal distribution 正态分布

Exploration数学分析与方法（HL)考纲

From patterns to generalizations: sequences and series模式和概括：序列和极数

1.1: Sequences, series and sigma notation 序列，极数和∑求和

1.2: Arithmetic and geometric sequences and series 算数和几何序列和极数

1.3: Proof 证据

1.4: Counting principles and the binomial theorem 计算原则和二项式定理

Representing relationships: introducing functions表达关系：函数介绍

2.1: Functional relationships 函数关系

2.2: Special functions and their graphs 特殊函数和图像

2.3: Classification of functions 函数分类

2.4: Operations with functions函数运算

2.5: Function transformations函数转化

Expanding the number system: complex numbers扩展数字体系：复数

3.1: Quadratic equations and inequalities 二次方相等和不等

3.2: Complex numbers 复数

3.3: Polynomial equations and inequalities 多项式相等和不等

3.4: The fundamental theorem of algebra代数的基本理论

3.5: Solving equations and inequalities解决方程式和不等

3.6: Solving systems of linear equations线性方程式的解决体系

Measuring change: differentiation测量变化：微分

4.1: Limits, continuity and convergence极限，连续性和收敛

4.2: The derivative of a function 一个函数的导数

4.3: Differentiation rules微分法规则

4.4: Graphical interpretation of the derivatives 导数的图形解释

4.5: Applications of differential calculus 微积分应用

4.6: Implicit differentiation and related rates 隐微分法和相关比率

Analysing data and quantifying randomness: statistics and probability分析数据和量化随机性：统计和可能性

5.1: Sampling取样

5.2: Descriptive statistics描述统计学

5.3: The justification of statistical techniques统计技术的辩护

5.4: Correlation, causation and linear regression相关性，原因和线性回归

Relationships in space: geometry and trigonometry空间关系：几何学和三角学

6.1: The properties of 3D space 3D图形的属性

6.2: Angles of measure 角的测量

6.3: Ratios and identities 比率和相等

6.4: Trigonometric functions 三角函数

6.5: Trigonometric equations 三角相等

Generalizing relationships: exponents, logarithms and integration概括关系：指数幂，对数和积分

7.1: Integration as antidifferentiation and definite integrals 反导函数和定分的整合

7.2: Exponents and logarithms 幂和对数

7.3: Derivatives of exponential and logarithmic functions; tangents and normal指数和对数函数的导数；切线和常态

7.4: Integration techniques整合技巧

Modelling changes: more calculus变化模型化：微积分更多内容

8.1: Areas and volumes 面积与体积

8.2: Kinematics运动学

8.3: Ordinary differential equations (ODEs) 常规微方方程

8.4: Limits revisited函数极限再讨论

Modelling 3D space: vectors3D空间模型化：矢量

9.1: Geometrical representation of vectors矢量的几何学呈现

9.2: Introduction to vector algebra矢量代数介绍

9.3: Scalar product and its properties数积和它的属性

9.4: Vector equations of a line 一条直线的矢量方程式

9.5: Vector product and properties矢量积和属性

9.6: Vector equation of a plane平面的矢量方程式

9.7: Lines, planes and angles直线，平面和角

9.8: Application of vectors矢量的应用

Equivalent systems of representation: more complex numbers呈现的等效系统：复数更多内容

10.1: Forms of a complex number复数的组成

10.2: Operations with complex numbers in polar form极坐标形式中复数的操作

10.3: Powers and roots of complex numbers in polar form功率和极坐标形式中复数的根

Valid comparisons and informed decisions: probability distributions有效比较和信息明确下的决策：可能性分布

11.1: Axiomatic probability systems自明可能性系统

11.2: Probability distributions可能性分布

11.3: Continuous random variables连续随机变量

11.4: Binomial distribution二项式分布

11.5: The normal distribution正态分布Exploration

数学应用与解析（HL)考纲

Measuring space: accuracy and geometry测量空间:精度和几何尺寸

1.1: Representing numbers exactly and approximately准确、近似地表示数字

1.2: Angles and triangles角度和三角形

1.3: three-dimensional geometry三维几何

Representing and describing data: descriptive statistics表示和描述数据:描述性统计

2.1: Collecting and organizing data收集和整理数据

2.2: Statistical measures统计测量方式

2.3: Ways in which we can present data展示数据的方式

2.4: Bivariate data二元数据

Dividing up space: coordinate geometry, lines, Voronoi diagrams, vectors划分空间:坐标几何，线，Voronoi图，向量

3.1: Coordinate geometry in 2 and 3 dimensions二维和三维坐标几何

3.2: The equation of a straight line in 2 dimensions二维直线方程

3.3: Voronoi diagrams Voronoi图

3.4: Displacement vectors位移向量

3.5: The scalar and vector product标量与向量的乘积

3.6: Vector equations of lines线的向量方程

Modelling constant rates of change: linear functions and regressions建模恒定变化率:线性函数和回归

4.1: Functions功能

4.2: Linear models线性模型

4.3: Inverse functions逆函数

4.4: Arithmetic sequences and series等差数列和级数

4.5: Linear regression线性回归

Quantifying uncertainty: probability量化不确定性:概率

5.1: Theoretical and experimental probability理论概率和实验概率

5.2: Representing combined probabilities with diagrams用图表表示组合概率

5.3: Representing combined probabilities with diagrams and formulae用图表和公式表示组合概率

5.4: Complete, concise and consistent representations完整、简洁、一致的表达

Modelling relationships with functions: power and polynomial functions与函数的建模关系:幂函数和多项式函数

6.1: Quadratic models二次模型

6.2: Quadratic modelling二次造型

6.3: Cubic functions and models三次函数与模型

6.4: Power functions, inverse variation and models幂函数、逆变分及模型

Modelling rates of change: exponential and logarithmic functions与函数的建模关系:幂函数和多项式函数

7.1: Geometric sequences and series几何序列和级数

7.2: Financial applications of geometric sequences and series几何序列和级数在金融中的运用

7.3: Exponential functions and models指数函数与模型

7.4: Laws of exponents - laws of logarithms指数和对数函数的运算法则

7.5: Logistic models对数模型

Modelling periodic phenomena: trigonometric functions and complex numbers周期现象建模:三角函数和复数

8.1: Measuring angles测量角度

8.2: Sinusoidal models: f(x) = asin(b(x-c))+d

正弦模型:f(x) = asin(b(x-c))+d

8.3: Completing our number system成我们的数字系统

8.4: A geometrical interpretation of complex numbers复数的几何解释

8.5: Using complex numbers to understand periodic models使用复数来理解周期模型

Modelling with matrices: storing and analyzing data用矩阵建模:存储和分析数据

9.1: Introduction to matrices and matrix operations矩阵和矩阵运算导论

9.2: Matrix multiplication and properties矩阵乘法及其性质

9.3: Solving systems of equations using matrices使用矩阵解方程组

9.4: Transformations of the plane平面的变换

9.5: Representing systems代表系统

9.6: Representing steady state systems表示稳态系统

9.7: Eigenvalues and eigenvectors特征值和特征向量

Analyzing rates of change: differential calculus变化率分析:微分学

10.1: Limits and derivatives极限和导数

10.2: Differentiation: further rules and techniques差异化:进一步的规则和技术

10.3: Applications and higher derivatives应用和更高阶导数

Approximating irregular spaces: integration and differential equations不规则空间近似:积分和微分方程

11.1: Finding approximate areas for irregular regions为不规则区域寻找近似区域

11.2: Indefinite integrals and techniques of integration不定积分与积分技巧

11.3: Applications of integration集成的应用

11.4: Differential equations微分方程

11.5: Slope fields and differential equations斜率场与微分方程

Modelling motion and change in 2D and 3D: vectors and differential equations建模二维和三维运动和变化:向量和微分方程

12.1: Vector quantities向量

12.2: Motion with variable velocity变速运动

12.3: Exact solutions of coupled differential equations耦合微分方程的精确解

12.4: Approximate solutions to coupled linear equation

建模二维和三维运动和变化:向量和微分方程

Representing multiple outcomes: random variables and probability distributions

呈现多个结果:随机变量和概率分布

13.1: Modelling random behaviour随机行为建模

13.2: Modelling the number of successes in a fixed number of trials固定数量的试验中成功数量的建模

13.3: Modelling the number of successes in a fixed interval固定的时间间隔内成功数量的建模

13.4: Modelling measurements that are distributed randomly随机分布的测量值建模

13.5: Mean and variance of transformed or combined random variables变换后或合并后随机变量的均值和方差

13.6: Distributions of combined random variables组合随机变量的分布

Testing for validity: Spearman's hypothesis testing and x2 test for independence有效性检验:斯皮尔曼假设检验和x2独立性检验

14.1: Spearman's rank correlation coefficient斯皮尔曼秩相关系数

14.2: Hypothesis testing for the binomial probability, the Poisson mean and the product moment correlation coefficient二项式概率、Poisson均值和乘积矩相关系数的假设检验

14.3: Testing for the mean of a normal distribution正态分布均值的检验

14.4: Chi-squared test for independence独立性的卡方检验

14.5: Chi-squared goodness-of-fit test卡方拟合优度检验

14.6: Choice, validity and interpretation of tests测试的选择、有效性和解释

Optimizing complex networks: graph theory优化复杂网络:图论

15.1: Constructing graphs构造图

15.2: Graph theory for unweighted graphs未加权图的图论

15.3: Graph theory for weighted graphs: the minimum spanning tree加权图的图论:最小生成树

15.4: Graph theory for weighted graphs - the Chinese postman problem加权图的图论——中国邮差问题

15.5: Graph theory for weighted graphs - the travelling salesman problem加权图的图论——旅行商问题

数学应用与解析（SL)考纲

Measuring space: accuracy and 2D geometry测量空间:精度和二维几何

1.1: Measurements and estimates测量和估计

1.2: Recording measurements, significant digits and rounding记录测量值、有效位数和舍入

1.3: Measurements: exact or approximate?测量:精确还是近似?

1.4: Speaking scientifically讲科学

1.5: Trigonometry of right-angled triangles and indirect measurements直角三角形三角学和间接测量

1.6: Angles of elevation and depression升降角度

Representing space: non-right angled trigonometry and volumes呈现空间:非直角三角形和体积

2.1: Trigonometry of non-right triangles非直角三角形的三角学

2.2: Area of triangle formula. Applications of right and non-right angled trigonometry非直角三角形的三角学

2.3: Geometry: solids, surface area and volume几何:固体、表面积和体积

Representing and describing data: descriptive statistics表示和描述数据:描述性统计

3.1: Collecting and organising univariate data收集和组织单变量数据

3.2: Sampling techniques抽样技术

3.3: Presentation of data数据的表示

3.4: Bivariate data二元数据

Dividing up space: coordinate geometry, lines, Voronoi diagrams划分空间:坐标几何，线条，Voronoi图

4.1: Coordinates, distance and midpoint formula in 2D and 3D线的梯度及其应用

4.2: Gradient of lines and its applications线的梯度及其应用

4.3: Equations of straight lines; different forms of equations直线方程;方程的不同形式

4.4: Parallel and perpendicular lines平行线和垂直线

4.5: Voronoi diagrams and toxic waste problemVoronoi图与有毒废物问题

Modelling constant rates of change: linear functions建模恒定变化率:线性函数

5.1: Functions功能

5.2: Linear Models线性模型

5.3: Arithmetic Sequences算术序列

5.4: Modelling造型

Modelling relationships: linear correlation of bivariate data建模关系:双变量数据的线性相关

6.1: Measuring correlation测量相关

6.2: The line of best fit最佳配合线

6.3: Interpreting the regression line解释回归曲线

Quantifying uncertainty: probability, binomial and normal distributions量化不确定性:概率、二项分布和正态分布

7.1: Theoretical and experimental probability理论概率和实验概率

7.2: Representing combined probabilities with diagrams用图表表示组合概率

7.3: Representing combined probabilities with diagrams and formulae用图表和公式表示组合概率

7.4: Complete, concise and consistent representations完整、简洁、一致的陈述

7.5: Modelling random behaviour: random variables and probability distributions对随机行为建模:随机变量和概率分布

7.6: Modelling the number of successes in a fixed number of trials在固定数量的试验中建立成功数量的模型

7.7: Modelling measurements that are distributed randomly随机分布的建模测量值

Testing for validity: Spearman's, hypothesis testing and x2 test for independence效度检验:斯皮尔曼检验、假设检验和x2独立性检验

8.1: Spearman's rank correlation coefficient斯皮尔曼秩相关系数

8.2: chi2 test for independence

chi2独立性检验

8.3: chi2 goodness of fit test

chi2拟合优度检验

8.4: The t-test检验

Modelling relationships with functions: power functions与函数的建模关系:幂函数

9.1: Quadratic models二次模型

9.2: Problems involving quadratics二次方程问题

9.3: Cubic models, power functions and direct and inverse variation三次模型、幂函数和正变分与逆变分

9.4: Optimisation优化

Modelling rates of change: exponential and logarithmic functions变化率的建模:指数函数和对数函数

10.1: Geometric sequences and series几何序列与级数

10.2: Compound interest, annuities, amortization复利、年金、摊销

10.3: Exponential models指数模型

10.4: Exponential equations and logarithms指数方程和对数

Modelling periodic phenomena: trigonometric functions周期现象建模:三角函数

11.1: An introduction to periodic functions周期函数简介

11.2: An infinity of sinusoidal functions周期函数简介

11.3: A world of sinusoidal models正弦模型的世界

Analyzing rates of change: differential calculus变化率分析:微分学

12.1: Limits and derivatives极限和导数

12.2: Equation of tangent and normal and increasing and decreasing functions正切函数、法向函数、递增函数、递减函数方程

12.3: Maximum and minimum points and optimization最大和最小点和优化

Approximating irregular spaces: integration近似不规则空间:整合

13.1: Finding areas发现领域

13.2: Integration: the reverse processes of differentiation积分:分化的逆向过程

HL课程有选修内容吗？

目前的数学HL课程的数学内容除了核心课程以外，学员还需要从4个选修内容（概率与统计，集合，关系与群论，微积分，离散数学）中选择一个选修。

在新的课程中，原有的4个选修部分被取消，Mathematics: Analysis and approaches（HL）中加入了统计和高数相关内容，而Mathematics: Applications and interpretation（HL）则会涉及统计和离散相关内容。

想在大学学习数学专业的学员应该选择哪门课程？

学员如果想要修读涉及大量数学内容的大学课程，那么应该选择Mathematics: Analysis and approaches。那些想要学习社会科学、人文科学、某些经济学、统计学和某些工程学课程以及艺术的学员可以选择Mathematics: Applications and interpretation。

有关IB数学的考试大纲分享就到这里。如果你是目标牛剑G5的IB学员，那么就要往42-44这个分数段去努力了，但往往决定IB分数分界线的就是IA和以IA为代表的学术英语写作能力。如果你想接受这方面的专项训练，或者进阶自己其他科目的成绩，点击预约试听【橡沐IB同步培训班】——

点击

IB改革后IB数学选课选错会被目标大学拒绝？附G5院校对于IB数学选课要求

IB数学真题解析这几道代表性的数学题你都学会了吗

查看。