MHF4U Advanced Functions | Outstanding International Academy

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MHF4U Advanced Functions

University Prep.

Ministry of Education Course Title: Advanced Functions, Grade12, University preparation

Course Code: MHF4U                  

Grade Level: 12

Prerequisite: MCR3U

Department: Mathematics

Course Description:

This course is designed to develop the oral communication, reading, writing, and media literacy skills that students need for success in their secondary school academic programs and in their daily lives. Students will analyse literary texts from contemporary and historical periods, interpret informational and graphic texts, and create oral, written, and media texts in a variety of forms. An important focus will be on the use of strategies that contribute to effective communication. The course is intended to prepare students for the Grade 10 academic English course, which leads to university or college preparation courses in Grades 11 and 12.

Overall Curriculum Expectation - all units are interrelated

Unit 1 Polynomial and Rational Functions

  1. Connecting Graphs and Equations of Polynomial Functions
    •  describe key features of the graphs of polynomial functions

  2. Connecting Graphs and Equations of Rational Functions
    •  sketch the graph of a simple rational function using its key features, given the algebraic representation of the function

  3. Solving Polynomial and Rational Equations
    •  factor polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies

  4. Solving Inequalities
    •  explain, for polynomial and simple rational functions, the difference between the solution to an equation in one variable and the solution to an inequality in one variable, and solve linear inequalities and factorable polynomial inequalities in one variable

Unit 2 Trigonometric Functions

  1. Understanding and Applying Radian Measure
    • recognize the radian as an alternative unit to the degree for angle measurement, define the radian measure of an angle as the length of the arc that subtends this angle at the centre of a unit circle, and develop and apply the relationship between radian and degree measure

  2. Connecting Graphs and Equations of Trigonometric Functions
    • sketch the graphs of and for angle measures expressed in radians, and determine and describe some key properties in terms of radians

  3. Solving Trigonometric Equations
    • recognize equivalent trigonometric expressions by using transformations and verify equivalence using graphing technology

Unit 3 Exponential and Logarithmic Functions

  1. Evaluating Logarithmic Expressions
    • recognize the logarithm of a number to a given base as the exponent to which the base must be raised to get the number, recognize the operation of finding the logarithm to be the inverse operation

  2. Connecting Graphs and Equations of Logarithmic Functions
    • determine, through investigation key features of the graphs of logarithmic functions of the form and make connections between the algebraic and graphical representations of these logarithmic functions

  3. Solving Exponential and Logarithmic Equations
    • recognize equivalent algebraic expressions involving logarithms and exponents, and simplify expressions of these types

Unit 4 Characteristics of Functions

  1. Understanding Rates of Change
    • gather, interpret, and describe information about real-world applications of rates of change, and recognize different ways of representing rates of change

  2. Combining Functions
    • solve problems involving the composition of two functions, including problems arising from real-world applications

  3. Using Function Models to Solve Problems
    • solve problems, using a variety of tools and strategies, including problems arising from real-world applications, by reasoning with functions and by applying concepts and procedures involving functions

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