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Mathematics

MCR3U

Functions

This course 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. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Tuition

$580

One Ontario credit, enrolled online.

Grade
11
Credit
1.0
Delivery
Online

Prerequisite for this course: MPM2D

  1. Principles of MathematicsMPM2D
  2. FunctionsMCR3UThis course

Tuition

$580

About this course

This course 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. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

What you'll learn

  1. Work fluently with the concept of a function, representing exponential and trigonometric relationships as graphs, tables, and equations.

  2. Investigate inverse functions and develop facility in finding equivalent algebraic expressions.

  3. Solve problems involving sequences, series, and financial applications such as annuities and compound interest.

  4. Build the algebraic foundation that Advanced Functions and university science programs assume.

Curriculum expectations

The overall expectations set by the Ontario curriculum, grouped by strand. Drawn from The Ontario Curriculum, Grades 11–12: Mathematics (2007).

A. Characteristics of Functions

  • A1demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations;
  • A2determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications;
  • A3demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

B. Exponential Functions

  • B1evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways;
  • B2make connections between the numeric, graphical, and algebraic representations of exponential functions;
  • B3identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications.

C. Discrete Functions

  • C1demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle;
  • C2demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems;
  • C3make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities.

D. Trigonometric Functions

  • D1determine 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;
  • D2demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;
  • D3identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications.

How you'll study

DeliveryOnline
Delivered fully online through Vaughan College's learning platform, with live teacher support. Online students can also call into the live in-person classroom through Google Classroom anytime they want extra guidance.
Fast-trackAvailable
Complete the credit in a condensed schedule. Useful for upgrading, course recovery, or summer acceleration.
Credit value1.0 OSSD credit
Counts toward the 30 credits required for the Ontario Secondary School Diploma.

Assessment and evaluation

Every Vaughan College course follows Ontario’s Growing Success policy. Assessment is continuous: teachers gather evidence of learning through observation, conversation, and student work, and give feedback that helps a student improve before the work is graded.

Evaluation — the judgement that produces a mark — measures achievement of the Ontario curriculum expectations across four categories: Knowledge and Understanding, Thinking, Communication, and Application. A student’s grade reflects how well they have met the expectations, with greatest weight given to their most consistent and most recent work.

The final grade

The final percentage grade is based on two parts. Seventy percent comes from work completed throughout the course, weighted toward more recent and more consistent achievement. The remaining thirty percent comes from a final evaluation near the end of the course — an examination, performance, essay, or other culminating task suited to the subject.

Grades are reported against the provincial standard, where Level 3 (70 to 79 percent) represents the standard expected of students at that grade. A grade of 50 percent or higher earns the credit.

The report card

Achievement is reported on the Ontario Provincial Report Card, which records the percentage grade and the credit earned for each course. Grades for completed credits carry forward onto the Ontario Student Transcript, the official record used for graduation and post-secondary admission.

The report card also reports six learning skills and work habits, separately from the academic grade: responsibility, organisation, independent work, collaboration, initiative, and self-regulation. These describe how a student approaches their learning, and universities and colleges do read them.

Considerations for program planning

The Ontario curriculum asks every course to account for a set of cross-curricular considerations — the ways a subject connects to students’ broader development and to the world beyond the classroom. They shape how each course is planned and taught.

Students with special education needs

Teachers plan for the full range of learners. Where a student has an Individual Education Plan, the accommodations, modifications, or alternative expectations it sets out are built into how the course is taught and assessed, so the student can demonstrate learning in the way that works for them.

English language learners

Students who are still developing their English receive scaffolding — adjusted materials, extra time, and language support — while working toward the same curriculum expectations. Assessment separates what a student knows and can do from their stage of English acquisition.

Environmental education

Wherever the subject allows, coursework draws connections to the environment and sustainability, helping students understand how the topics they study relate to the natural world and their responsibilities within it.

Healthy relationships

Every course contributes to a school culture built on respect. Students practise the communication and collaboration skills that underpin healthy, equitable relationships with peers and teachers.

Equity and inclusive education

Materials and discussion reflect a range of experiences and perspectives so every student sees themselves in the work. An inclusive classroom holds high expectations for all learners and treats difference as a strength.

Financial literacy

Where it fits the subject, students apply mathematical and analytical thinking to real financial questions — budgeting, credit, and informed decision-making — so the skills carry into life after graduation.

Literacy, mathematical literacy, and inquiry skills

Reading, writing, oral communication, numeracy, and structured inquiry are developed in every subject, not only in English and mathematics. These are the cross-curricular skills that make learning in every other course possible.

Critical thinking and critical literacy

Students learn to weigh evidence, question assumptions, and interpret what they read, watch, and hear — distinguishing fact from opinion and recognising point of view and bias.

The role of the school library

Library and information resources support research and independent reading. Students learn to locate, evaluate, and use sources responsibly, building the research habits that post-secondary study assumes.

Information and communications technology

Technology is used to support learning and to build the digital skills students need, alongside an understanding of how to work online safely, responsibly, and with attention to their own well-being.

Education and career/life planning

Coursework helps students connect what they are learning to their goals beyond high school, so each credit is a step in a deliberate plan rather than an isolated requirement.

Cooperative education and experiential learning

Where a subject supports it, hands-on and experiential learning connect classroom study to real settings, giving students a clearer sense of how the material is used in work and in the community.

Health and safety

In any course involving activity, equipment, or materials, safe practice is taught and expected. Students learn the procedures that protect themselves and others.

Ethics

Many subjects raise questions of right and wrong. Students learn to examine ethical issues thoughtfully, consider more than one position, and support a view with reasons — including academic honesty in their own work.

Teaching and learning at Vaughan College

Courses are taught in small classes, which lets teachers adapt to how each student learns. A single lesson might combine direct instruction, discussion, independent practice, collaborative work, and hands-on or inquiry-based tasks, chosen to suit the material and the students in the room.

Students receive regular, specific feedback and can move at a pace that fits their goals, whether they are working ahead, recovering a credit, or balancing school with other commitments. The aim is that every student understands not just what they are learning, but why it matters and where it leads.

In-class learning, from anywhere

Be in the classroom from anywhere in the world.

Some of our online courses run alongside a live class in our Vaughan classroom, and which ones changes each semester. When a course offers it, you’ll see a Live now tag on the course or a Hybrid toggle on its page. Turn it on and you can join the real in-person lesson through Google Classroom instead of a separate online-only section, with the same teacher as it happens. Add it when you enrol or anytime after; in-person students can join the same way on the days they study from home.

How it works

Next Step

Ready to add this credit?

Add the course to your cart for enrolment, or speak with our admissions team about pathway sequencing, prerequisites, and credit equivalency from a previous school.

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