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Advanced Functions

MHF4U-GRADE 12

Course Code:

MHF4U

Subject:

Advanced Functions

Course type:

open

Prerequiste:

None

Advance functions
Advance functions
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MHF4U deepens students’ understanding of mathematical functions and their applications.

The course focuses on

  • Algebraic skills
  • Polynomial
  • Rational
  • Expressions
  • Advanced function types including exponential
  • Logarithmic
  • Trigonometric functions.
Emphasis is placed on solving equations, analyzing function behaviour, and modeling real-world situations, preparing students for university-level mathematics, science, and business programs.

Unit 1: Function Properties and Transformations

Students explore the characteristics and manipulation of functions.
Lessons include:

  • Introduction to Functions

  • Adding, Subtracting, and Multiplying Functions

  • Inverse Functions

  • Transformations of Graphs

  • Composition of Functions

  • Average and Instantaneous Rate of Change

Unit 2: Polynomial and Rational Functions

This unit examines algebraic expressions and equations.
Lessons include:

  • Polynomial Functions and Their Features

  • Graphing Polynomial Functions

  • Factoring Techniques

  • Remainder and Factor Theorems

  • Rational Functions and Graphs

  • Solving Polynomial and Rational Equations

  • Inequalities with Polynomials and Rationals

Unit 3: Trigonometric Functions

Students build on prior trigonometry knowledge and expand into advanced applications.
Lessons include:

  • Introduction to Logarithms

  • Laws of Logarithms and Exponent Rules

  • Exponential and Logarithmic Equations

  • Graphing and Transforming Exponential/Log Functions

  • Real-Life Applications in Finance, Biology, and Physics

Unit 5: Final Evaluation

Students apply their knowledge in problem-solving and analysis tasks.
Lessons include:

  • Culminating Mathematical Modeling Project

  • Final Exam

  • 70% of the final grade is based on coursework, including:

    • Function graphing and transformation tasks

    • Algebraic manipulation and identity proofs

    • Application problems involving finance, growth, and motion

      · Unit quizzes, assignments, and reflections

  • 30% of the final grade is based on final evaluations:

    • 10% Culminating application project

    • 20% Final written exam assessing all function types and problem-solving skills

All assessments follow Ontario curriculum standards and are designed to support mathematical fluency, critical thinking, and analytical modeling essential for postsecondary success

Industry-Standard Tools

Access to the latest software and hardware used in the technology industry

Expert Faculty

Learn from experienced professionals with industry background

Project-Based Learning

Develop practical skills through hands-on projects and assignments.

Career Support

Guidance for future education and career opportunities

Where Flexibility Meets Academic Excellence

Your Future Starts with the Right High School:
Get the OSSD Advantage for Top University Admissions

At Futures Canadian School, students earn the Ontario Secondary School Diploma (OSSD) through a fully online, Ministry-inspected program designed for success—anywhere in the world. Our flexible format, expert support, and university-prep focus empower students to reach their academic goals on their terms, while meeting the highest standards of Ontario education. Whether you're aiming for top universities in Canada or abroad, we provide a pathway that fits your pace and ambition.

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Frequently Asked Questions

Q) Is the school accredited by the Ministry of Education?
Ans) Yes, Futures Canadian School is fully inspected and accredited by the Ontario Ministry of Education to ensure that we meet the highest standards of academic quality.
Ans) You can reach us by email, phone or through our website to begin your application or speak directly with an admissions counselor.
Ans) We offer over 80 college and college preparatory courses covering fields such as health sciences, business, engineering, design and more.
Ans) Students receive personalized academic advising, tutoring, and regular progress monitoring to help them succeed.
Ans) Yes! We offer comprehensive college application support, including program selection, personal statement writing, and meeting deadlines.

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