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GAC 数学

学习建议

GAC 数学包含四个模块。GAC004 用英语重建基础,从算术、代数一路到解析几何、平面与立体几何、三角学以及指数与对数函数。GAC010 转向数列、金融数学、概率与统计。GAC016 是单变量微积分。GAC024 是离散数学,涵盖集合、计数系统、算法、图论与布尔逻辑。

语言与方法同样被考查。逐单元记录、学期中接受检查的术语记录本是 GAC004 的正式组成部分,所以能说清"斜率"或"残差"是什么,和算出它一样重要。

GAC016 是最常被大学认可学分的模块。多所大学为它公布了微积分课程的对应关系,因此这里的导数与积分内容值得当作大学一年级课程来对待,而不是中学复习。

考核形式是组合式的。通常包括针对前几个单元的课堂小测、一到两个用电子表格完成的项目、期末覆盖全部内容的考试,以及整个学期悄悄累积的平时成绩。

本站的例题、练习与模拟卷均为原创,依据学习目标和这些考核的形式编写。

GAC 数学学习资料

  • 1

    GAC004 数学 I:基础

    • 1.1 术语与算术复习

      Unit 1 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      Module purpose: On completion of this module, students should be able to demonstrate an understanding of the basic concepts of mathematics, and the language used, in preparation for tertiary study within an English-speaking environment.

      The module outcomes this unit works towards:

      Learning Objective GAC004.1: Solve elementary math problems using basic arithmetic operations.

      来源:剑桥国际大纲

    • 1.2 代数 I:代数入门

      Unit 2 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.2: Perform basic algebraic operations and solve equations and inequations using algebraic methods.

      来源:剑桥国际大纲

    • 1.3 代数:函数图像与解析几何

      Unit 3 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.3: Graph algebraic relations and use coordinate geometry to solve problems.

      来源:剑桥国际大纲

    • 1.4 几何:平面、立体与欧氏几何

      Unit 4 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.4: Analyze simple problems involving planar shapes and solids and solve problems in Euclidean geometry.

      来源:剑桥国际大纲

    • 1.5 三角学

      Unit 5 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.5: Calculate solutions to various problems using trigonometric methods.

      来源:剑桥国际大纲

    • 1.6 指数函数与对数函数

      Unit 6 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.6: Solve and graph exponential and logarithmic functions and equations.

      来源:剑桥国际大纲

  • 2

    GAC010 数学 II:概率、统计与金融

    • 2.1 数列与级数

      Unit 1 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      Module purpose: On completion of this module, students should be able to apply a basic knowledge of the principles of probability and statistics to solving and analysing common financial problems.

      The module outcomes this unit works towards:

      Learning Objective GAC010.1: Solve problems using arithmetic and geometric sequences and series.

      来源:剑桥国际大纲

    • 2.2 金融:赚钱与消费

      Unit 2 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.2: Apply algebraic methods to solve financial problems and analyse information.

      来源:剑桥国际大纲

    • 2.3 金融:投资与贷款

      Unit 3 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.2: Apply algebraic methods to solve financial problems and analyse information.

      来源:剑桥国际大纲

    • 2.4 概率:核心概念

      Unit 4 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.3: Solve problems using probability and counting techniques.

      来源:剑桥国际大纲

    • 2.5 统计学

      Unit 5 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.4: Analyse collected data using statistical methods.

      来源:剑桥国际大纲

    • 2.6 统计学:集中趋势的数值度量

      Unit 6 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.4: Analyse collected data using statistical methods.

      来源:剑桥国际大纲

    • 2.7 统计学:离散程度的数值度量

      Unit 7 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.4: Analyse collected data using statistical methods.

      来源:剑桥国际大纲

    • 2.8 分布:正态分布

      Unit 8 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.5: Use the normal distribution to analyse data.

      来源:剑桥国际大纲

  • 3

    GAC016 数学 III:微积分与进阶应用

    • 3.1 微分

      Unit 1 of 3 in GAC016 Mathematics III: Calculus & Advanced Applications (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      Module purpose: On completion of this module, students should be able to demonstrate a basic understanding of the principles of calculus and how they can be applied to the quantitative analysis of practical and financial situations.

      The module outcomes this unit works towards:

      Learning Objective GAC016.1: Determine the derivative (if it exists) of most mathematical functions and use the derivative to analyse functional behaviour.

      来源:剑桥国际大纲

    • 3.2 积分

      Unit 2 of 3 in GAC016 Mathematics III: Calculus & Advanced Applications (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC016.2: Use techniques of integration to find indefinite and definite integrals.

      来源:剑桥国际大纲

    • 3.3 进阶应用

      Unit 3 of 3 in GAC016 Mathematics III: Calculus & Advanced Applications (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC016.3: Apply differentiation and integration techniques in a variety of practical problems.

      来源:剑桥国际大纲

  • 4

    GAC024 离散数学

    • 4.1 集合、关系与函数

      Unit 1 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      Module purpose: On completion of this module, students should be able to demonstrate an understanding of the basic principles of discrete mathematics, particularly the utilisation of mathematical logic. They should also be able to demonstrate the application of these skills to practical situations.

      The module outcomes this unit works towards:

      Learning Objective GAC024.1: Demonstrate understanding of the introductory concepts and properties of sets, relations and functions.

      来源:剑桥国际大纲

    • 4.2 计数系统

      Unit 2 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC024.2: Understand the relationships between different counting systems and be able to perform simple binary arithmetic operations.

      来源:剑桥国际大纲

    • 4.3 二进制应用

      Unit 3 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC024.2: Understand the relationships between different counting systems and be able to perform simple binary arithmetic operations.

      Learning Objective GAC024.5: Use the basic identities of Boolean algebra to analyse logic circuits and understand the basic principles of propositional logic.

      来源:剑桥国际大纲

    • 4.4 算法

      Unit 4 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC024.3: Construct and analyse algorithms and flowcharts for simple mathematical and general procedures.

      来源:剑桥国际大纲

    • 4.5 图与网络

      Unit 5 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC024.4: Identify the basic types, properties and applications of graphs and trees.

      来源:剑桥国际大纲

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