MHF4U: Advanced Functions (University Preparation)
PREREQUISITE: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation
GRADE: 12 (University)
AVAILABILITY: Spark Asher Academy Online
THE ONTARIO CURRICULUM: Mathematics
Course Overview
MHF4U online is meticulously designed to enhance students’ understanding of advanced functions, pivotal for success in higher-level mathematics and related fields. This course delves into polynomial, rational, logarithmic, and trigonometric functions, rates of change, and a robust integration of mathematical processes essential for problem-solving in real-world scenarios and academic pursuits. Structured to cater to both those aiming for a university program in Calculus and Vectors and those consolidating their understanding before transitioning to various university programs, MHF4U serves as a comprehensive platform for students preparing for advanced studies in mathematics.
Course Content and Structure
The curriculum for MHF4U, set by the Ontario Ministry of Education, ensures consistency across online and in-person formats, covering:
- Polynomials
- Rational Functions
- Trigonometry
- Exponential and Logarithmic Functions
- Combining Functions and Rates of Change
These units build upon each other to develop a thorough understanding of each function’s properties and their applications, reinforcing skills in problem-solving, reasoning, reflecting, selecting tools, making connections, creating representations, and communicating mathematical ideas effectively.
UNIT ONE: Polynomials
Essential Question: How can characteristics of polynomials be used to make connections between functions and their graphical representations?
- Students explore polynomial properties to link algebraic expressions to their graphical counterparts, enhancing their ability to solve related equations and inequalities.
UNIT TWO: Rational Functions
Essential Question: What patterns exist in rational functions and how can they be used to predict their behaviors?
- Investigations into rational functions lead to an understanding of asymptotes, graph behaviors, and solving complex rational equations.
UNIT THREE: Trigonometry
Essential Question: How can the properties of trigonometric functions be applied to model and solve real-world problems?
- Building on previous knowledge, students explore radian measures, special triangles, advanced identities, and their applications in solving trigonometric equations.
UNIT FOUR: Exponential and Logarithmic Functions
Essential Question: How do exponential and logarithmic functions relate, and how can this relationship be applied to solve real-world problems?
- Students review and connect exponential functions to their inverses, exploring the laws of logarithms and their applications in solving practical problems.
UNIT FIVE: Combining Functions and Rates of Change
Essential Question: How can understanding the rates of change enhance comprehension of real-world dynamics?
- Focus on combining functions, forming composite functions, and exploring rates of change to understand motion and changes in various contexts.
Assessment
- 70% Course Work: Continuous evaluation through assignments, projects, and tests reflecting the student’s consistent performance across the course.
- 30% Final Evaluation: Culminates in a proctored final exam, crucial for assessing comprehensive understanding and application of the mathematical concepts covered.
MHF4U is not just a course but a foundational step towards advanced education in mathematics, equipping students with the necessary tools and knowledge to excel in future academic challenges.
For more details on final exams and the exam fee, please consult to us directly via contact page. Additional information can be found in our download section in courses page.
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