MHF4Ur Repeat Advanced Functions – Grade 12 (University)
PREREQUISITE: A final grade of 40% or higher in the same course
GRADE: 12 (University)
AVAILABILITY: Full-time – All Campuses, Part-time – All Campuses, Private – All campuses, Summer School – Accelerated, Blyth Academy Online
THE ONTARIO CURRICULUM: Mathematics
MHF4Ur extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric 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. MHF4Ur online 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
- In this unit, students will investigate the key properties and characteristics of polynomials and use their findings to form connections between algebraic and graphical representations of polynomial functions. Students will develop skills that can be used to analyze and solve polynomial equations and inequalities.
UNIT TWORational Functions
- In this unit, students will examine the key characteristics of rational functions and use them to develop an understanding of their graphical representations. Students will investigate the different cases where horizontal asymptotes occur and use their understanding to solve rational equations and inequalities.
- In this unit, students will build on their understanding of trigonometry acquired from previous studies of mathematics. Students will develop an understanding of radian measure and conceptualize special triangles and the unit circle in terms of radians. Students will explore advanced trigonometric identities and make connections to the graphs of sine and cosine. These graphs will be used to develop the graphs of tangent, cosecant, secant, and cotangent. Lastly, students will apply the understandings developed in this unit to solve trigonometric equations and real-world problems.
UNIT FOURExponential and Logarithmic Functions
- In this unit, students will review exponential functions and make connections to the logarithmic function by applying an understanding of inverse functions. Students will then learn to write expressions in both exponential and logarithmic form. Students will learn about the laws of logarithms and how they can be applied to solve logarithmic equations. Lastly, students will combine the understandings they develop throughout this unit and apply them to solve real-world problems that can be modelled using exponential and logarithmic functions.
UNIT FIVECombining Functions and Rates of Change
- In this unit, students will begin by examining sums, differences, products, and quotients of functions. Students will then substitute functions into other functions in order to form composite functions. The domain, range, and key characteristics of combined functions will then be explored. Students will then turn their attention to rates of change of functions and investigate how the average rate of change can be used to approximate the instantaneous rate of change of a given function.
FINAL EXAMProctored Exam
- This exam is the final evaluation of MHF4Ur online. Students need to arrange their final exam 10 days in advance. All coursework should be completed and submitted before writing the final exam, please be advised that once the exam is written, any outstanding coursework will be given a grade of zero. The exam will be two hours.
- Please consult our Frequently Asked Questions Page or the Exam section within your course for details on exam proctoring options.