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MHF4U - Advanced Functions ( 高等函数 )

20 小时

网上真人教师

1.0

课程学分

110 小时

课程时数

10  周

课程长度

高三 [第11班]

级别

上课模式

  • 一对一 (一位老师对一位学生)
  • 一对二 (一位老师对兩位学生)
  • 一对四 (一位老师对四位学生)
  • 一对六 (一位老师对六位学生)

课程详情

本课程扩展了学生对函数的经验学生将研究多项式,有理数,对数和三角函数的性质;掌握复合函数的技巧;拓宽他们对变化率的理解;灵巧的掌握的运用这些概念和技巧学生也将完善其在高中数学获得成功的必需的数学过程。本课程目的在于,作为大学课程的先行课程,为学习微积分和向量课作准备,并那些希望在继续各种大学课程的任一分支求学前,巩固其对数学的理解。
 


A. EXPONENTIAL AND LOGARITHMIC FUNCTIONS

OVERALL EXPECTATIONS
By the end of this course, students will:

  1. demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;
  2. identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically;
  3. solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.
     

B. TRIGONOMETRIC FUNCTIONS

OVERALL EXPECTATIONS
By the end of this course, students will:

  1. demonstrate an understanding of the meaning and application of radian measure;
  2. make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems;
  3. solve problems involving trigonometric equations and prove trigonometric identities.
     

C. POLYNOMIAL AND RATIONAL FUNCTIONS

OVERALL EXPECTATIONS
By the end of this course, students will:

  1. identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;
  2. ​identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;
  3. solve problems involving polynomial and simple rational equations graphically and algebraically;
  4. demonstrate an understanding of solving polynomial and simple rational inequalities.

D. CHARACTERISTICS OF FUNCTIONS

OVERALL EXPECTATIONS
By the end of this course, students will:

  1. demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point;
  2. determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems;
  3. compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.
     
More please click MHF4U - Advanced Functions
 

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