MHF4U Advanced Functions – Grade 12 (University)
PREREQUISITE: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation
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
MHF4U 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. MHF4U 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
UNIT ONE
Functions
Essential Question: What are the characteristics of a function? How can we transform a function? How do we find the inverse of a function?
- In this unit, students will learn how to determine if a relation is a function, and how to state the domain an range. Students will also learn how to identify important properties of a function: end behaviour, intervals of increase and decrease, whether a function is even, odd or neither, and continuity. Students will be identifying and graphing transformations as well as identifying and finding inverse relations, and restricting the domain to make a function. Students will learn how to use and write equations of piecewise functions and will learn the key features of functions created by adding, subtracting, multiplying, and dividing functions.
UNIT TWO
Rates of Change
Essential Question: What is the average and instantaneous rate of change of a function?
- In this unit, students will learn how to find the average rate of change graphically, numerically and algebraically and how to estimate the instantaneous rate of change of a function. Students will also learn how to solve problems related to rates of change.
UNIT THREE
Polynomial Functions
Essential Question: How can we generalize the behaviour of functions of degree up to 4?
- In this unit, students will discover the key features of cubic and quartic functions and the transformations of cubic or quartic functions. Students will divide polynomial functions and solve polynomial equations and inequalities graphically and algebraically.
UNIT FOUR
Polynomial Equations and Inequalities
Essential Question: How can we solve polynomial equations and inequalities?
- In this unit, students will learn how to solve polynomial equations algebraically and how to solve polynomial inequalities algebraically and graphically. Students will also solve problems using polynomials.
UNIT FIVE
Rational Functions, Equations, and Inequalities
Essential Question: How can we graph and solve rational equations and inequalities? What behaviours are generalizable for equations of the form y = f(x)/g(x) where f(x) is degree 0 to 2, and g(x) is degree 1 or 2?
- In this unit, students will identify the key features of rational functions and will learn how to graph rational functions. Students will solve rational equations and inequalities graphically or algebraically and learn how to find the average and estimate the instantaneous rate of change of a rational function.
UNIT SIX
Trigonometric Functions
Essential Question: How can we graph and transform trigonometric functions and their reciprocals? How can we use special angles to find exact solutions? How can we model real life situations with trig functions?
- In this unit, students will learn about a new angle measurement called radians. Students will learn how to convert from degrees to radians and from radians to degrees and how to find exact solutions to some trigonometric equations using the special triangles, composite angle formulas and double angle formulas. Students will discover how to graph trigonometric functions using transformations and will learn about the reciprocal trigonometric functions. Students will model situations with trigonometric equations and learn how to find the average and estimate the instantaneous rate of change of trigonometric equations.
UNIT SEVEN
Trigonometric Identities and Equations
Essential Question: How can we use trigonometric identities to solve trigonometric equations?
- In this unit, students will learn how to recognize equivalent trigonometric equations and how to find exact solutions to some trigonometric equations using the special triangles, composite angle formulas and double angle formulas. Students will also learn how to prove trigonometric identities and how to solve trigonometric equations.
UNIT EIGHT
Exponential and Logarithmic Functions
Essential Question: What are the characteristics of exponential and logarithmic functions? What are the rates of change?
- In this unit, students will discover how logarithmic equations relate to exponential equations and will learn about the key features of logarithms. Students will simplify and evaluate logarithmic expressions and solve logarithmic and exponential equations. Students will model situations using logarithmic and exponential functions, including exponential growth and decay, decibels, pH, and the Richter scales.
UNIT NINE
Combinations of Functions
Essential Question: How can we combine functions? What are the characteristics of combined functions? How can we model situations by combining functions?
- In this unit, students will learn how to combine functions by addition, subtraction, multiplication and composition, graphically, numerically, and algebraically. Students will also learn about the key features of combined functions. Students will solve equations with combined functions numerically and graphically and create mathematical models.
CULMINATING PROJECT
5% of Final Grade
- This project is one of the final evaluations of MHF4U online. This project will be worth 5% of the final grade.
FINAL EXAM
Proctored Exam
25% of Final Grade
- This exam is the final evaluation of MHF4U 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. There are three options for taking the exam:
- WRITE EXAM AT BLYTH ACADEMY CAMPUS: If you live close to a Blyth Academy Campus, or if you attend a Blyth Academy Campus, you can take your exam there. Once inside the exam scheduling interface, please click Login/Create Account. Check for an available time and date at the campus of your choosing. The earliest available date will be open within the next 3-5 business days. You cannot book an exam in more than one campus or multiple times at the same campus. You will receive an automatic confirmation email with next steps and exam information. You can cancel and reschedule anytime using the same link.
- ARRANGE YOUR OWN PROCTOR: If you want to arrange a proctor yourself, you can do that. The proctor will need to be approved by us and will need to supervise the exam at his or her place of work, or at a public place such as a library. Some libraries and study centres offer this service themselves. The proctor must be approved by us and must be a working professional (eg teacher, doctor, businessperson, and must provide a work email address for correspondence (no Gmail, Hotmail, etc.). Please note that the final exam cannot be proctored by a family member or by a tutor for that specific subject. Once inside the exam scheduling interface, please click Login/Create Account. Select Arranging My Own Proctor and proceed to schedule your exam.
- USE EXAMITY PROCTORING SERVICE: For a fee of 22 USD*, students can arrange to take their exam in the comfort of their own home, at any time, on any day. Please select Examity Exam in the exam section of your course to set up your Examity profile and schedule your exam. Exams must be scheduled at least 24 hours in advance. *Price is subject to change.
- Please email exams@blythacademyonline.com if you need assistance.