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MCR3U Functions – GRADE 11

PREREQUISITE : Principles of Mathematics, Grade 10, Academic

GRADE : 11 (University)


MCR3U online at Profectus introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. In MCR3U online, students will reason mathematically and communicate their thinking as they solve multi-step problems.

UNIT 1 :

Characteristics of Functions (22hrs)

Students will be able to:

  • Demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations.
  • Determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications.
  • Demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

UNIT 2 :

Exponential Functions (22hrs)

Students will be able to:

  • Evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways.
  • Make connections between the numeric, graphical, and algebraic representations of exponential functions.
  • Identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications.

UNIT 3 :

Discrete Functions (22hrs)

Students will be able to:

  • Demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle.
  • Demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems.
  • Make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities.

UNIT 4 :

Trigonometric Functions (22hrs)

Students will be able to:

  • Determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law.
  • Demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions.
  • Identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications.


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

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.