Renseignements sur les cours
Functions and Applications - MCF3M
Code du cours CEI : MCF3M-C
11e année, University / College Preparation, 1,0 crédit
Description de cours
This course introduces basic features of the function by extending your experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modelling real-world situations. You will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. You will reason mathematically and communicate your thinking as you solve multi-step problems.
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Unit 1: Solving Quadratic Equations
In this unit, you will learn to use quadratic models and apply these models to solve real-world problems. You will expand, simplify, and factor quadratic expressions. You will learn to solve quadratic equations by factoring and by using the quadratic formula. You will discover the relationship between the roots of the equation and the x-intercepts of the corresponding graph. You will distinguish between a function and a relation and learn how to test if a relation is a function. You will graph quadratic functions and identify their key features. You will also describe transformations of these functions from their equations and sketch the related graphs.
Unit 2: Quadratic Functions
Unit 2 continues the quadratic functions work that was started in Unit 1. In this unit, the focus is on analyzing and transforming the graphs of quadratic functions. The algebraic skills you learned in Unit 1 will be applied to determine the key features of the graphs of quadratic functions and to convert between different forms of the equations that represent quadratic functions. All the concepts are applied at the end of the unit to solve a wide variety of real-world application problems that involve quadratic functions.
Unit 3: Exponential Functions
In Unit 3, you will learn about a new type of function called an exponential function. These functions are related to powers. They occur in a wide variety of real-world situations, such as the unrestricted growth of the human population, the unrestricted growth of bacteria or viruses, the growth of money invested at a guaranteed rate of interest, the decay of a chemical substance, and the depreciation of the value of a new car. Lesson 11 reviews and extends the laws of exponents. In Lesson 12, you will learn about the properties of the graphs of exponential functions. In Lessons 13 through 15, you will solve a variety of problems involving exponential functions.
Unit 4: Trigonometric Functions
In the first three units, you studied quadratic functions and exponential functions. In Unit 4, you will expand your knowledge of functions to include trigonometric functions. You will sketch and analyze the graphs of trigonometric functions and solve related problems. Before you begin, you will first review the primary trigonometric ratios and apply them to solve problems involving two right triangles. You will also learn about the sine law and cosine law and how these are used to solve triangles that do not have a right angle.
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