PREREQUISITE : Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation
GRADE : 12 (University)
THE ONTARIO CURRICULUM : Mathematics
MHF4U online at Profectus 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. In MHF4U online, 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.
UNIT 1 :
Exponential and Logarithmic Functions (22hrs)
Students will be able to:
Demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions.
Identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically.
Solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.
UNIT 2 :
Trigonometric Functions (22hrs)
Students will be able to:
Demonstrate an understanding of the meaning and application of radian measure.
Make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems.
Solve problems involving trigonometric equations and prove trigonometric identities.
UNIT 3 :
Polynomial and Rational Functions (22hrs)
Students will be able to:
Identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions.
Identify and describe some key features of the graphs of rational functions, and represent rational functions graphically.
Solve problems involving polynomial and simple rational equations graphically and algebraically.
Demonstrate an understanding of solving polynomial and simple rational inequalities.
UNIT 4 :
Characteristics Of Functions (22hrs)
Students will be able to:
Demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point.
Determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems.
Compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.
FINAL 30%
Course Culmination (22hrs)
The Culminating Unit incorporates all four strands of the Mathematics Curriculum, and covers the four achievement chart categories. It consists of two parts:
Culminating Project worth 15% and a
Final Exam worth 15%
Online Course Policies
Listed below are various mandatory policies as you take on this course.
Attendance is regularly tracked through student contributions to online discussion boards, assignment completion, and learning logs. Failure to complete allocated activities may challenge the student’s ability to attain the credit.
This course will be presented using an asynchronistic model whereby work will be posted on the Google Classroom and it is the student’s responsibility to complete it on their own time.
ALL portions of this course are intended to be learned and completed online.
Final Exams and Tests will be written on site at Profectus Academy of Toronto. Course instructors will relay this information to students and families.
The integrity of student work will be checked on an ongoing basis using Quetext or Turnitin. Plagiarism is not tolerated.
Assessment & Evaluation Policies
The primary purpose of assessment and evaluation is to improve student learning. The Achievement Chart for Mathematics will guide all assessment and evaluation.
Knowledge and Understanding
17.5%
Thinking
17.5%
Communication
17.5%
Application
17.5%
The final grade will be determined as follows:
70% based on Assessment OF Learning (including conversations, observations and products) conducted throughout the course.
30% based on Culminating Tasks administered at or towards the end of the course.
Assessment and evaluation is divided into two important parts. The grade the student receives on a midterm or final report indicates achievement/ proficiency in Curriculum Expectations. A level of competence (Needs Improvement, Satisfactory, Good or Excellent) will be assessed and reported in the area of Learning Skills and Work Habits: Independent Work, Collaboration, Responsibility, Initiative, Self-Regulation, and Organization.
