MHF4U
University Preparation
Advanced Functions
Course Summary
Subject Area Subject: Mathematics
Grade 12
Prerequisites:
MCR3U
or
MCT4C
1 Credit
4 Units, 41 learning activities
This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.
Course outline
Learning Activity 1 Recognizing applications of polynomial expressions
Learning Activity 2 Describing polynomial expressions
PreviewLearning Activity 3 Identifying polynomial functions
Learning Activity 4 Classifying polynomial functions
Learning Activity 5 Exploring the effect of degree on polynomial functions
Learning Activity 6 Determining the end behaviours of polynomial functions
Learning Activity 7 Describing polynomials in factored form
Learning Activity 8 Developing the factor theorem and remainder theorem
Learning Activity 9 Applying long division to polynomial functions
Learning Activity 10 Investigating transformations of polynomial functions
Learning Activity 11 Using symmetry to characterize odd and even polynomial functions
Learning Activity 12 Exploring the graphs of reciprocal functions
Learning Activity 13 Connecting algebraic and graphical representations of rational functions
Learning Activity 14 Solving rational equations
Learning Activity 15 Solving inequalities
Learning Activity 1 Defining logarithmic functions
Learning Activity 2 Exploring the characteristics of logarithmic functions
Learning Activity 3 Connecting exponential and logarithmic functions
Learning Activity 4 Solving logarithmic and exponential equations: part 1
Learning Activity 5 Solving logarithmic and exponential equations: part 2
Learning Activity 6 Exploring transformations of logarithmic functions
Learning Activity 1 Introducing trigonometric functions
Learning Activity 2 Introducing radian measure
Learning Activity 3 Exploring angles expressed in radian measure
Learning Activity 4 Exploring characteristics of the sine, cosine, and tangent functions
Learning Activity 5 Graphing the reciprocal trigonometric functions
Learning Activity 6 Investigating transformations of sinusoidal functions
Learning Activity 7 Connecting algebraic and graphical representations of sinusoidal functions
Learning Activity 8 Solving trigonometric equations
Learning Activity 9 Verifying and applying the compound angle formulas
Learning Activity 10 Exploring equivalent trigonometric expressions
Learning Activity 11 Deriving and applying the double angle and Pythagorean formulas
Learning Activity 12 Solving trigonometric equations
Learning Activity 1 Expressing a function as the combination of other functions
Learning Activity 2 Combining functions by adding, subtracting or multiplying
Learning Activity 3 Combining functions by dividing or applying one function to another
Learning Activity 4 Determining the domain and range of combined functions
Learning Activity 5 Exploring the average rate of change of a function
Learning Activity 6 Determining the instantaneous rate of change of a function
Learning Activity 7 Describing composite functions using symmetry
Learning Activity 8 Solving the equations of composite functions arising from real world applications
Interested in enrolling?
Please connect with the guidance counsellor at your school to see if this course is available to you. Your counsellor will support you in accessing the course, if available, or work with you to find an alternative in which you can enroll.
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