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Mathematics

MCV4U

Calculus and Vectors

This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in threedimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course. Note: The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U).

Tuition

$580

One Ontario credit, enrolled online.

Grade
12
Credit
1.0
Delivery
Online

No prerequisite. Open to all eligible students.

Tuition

$580

About this course

This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in threedimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course. Note: The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U).

What you'll learn

  1. Find and apply the derivatives of polynomial, exponential, rational, trigonometric, and radical functions.

  2. Solve problems involving vectors, lines, and planes in three-dimensional space.

  3. Model real-world relationships with rates of change, from velocity and acceleration to optimization.

  4. Prepare for the calculus, linear algebra, and physics courses that science and engineering programs require.

Curriculum expectations

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

A. Rate of Change

  • A1demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit;
  • A2graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative;
  • A3verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.

B. Derivatives and Their Applications

  • B1make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching;
  • B2solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.

C. Geometry and Algebra of Vectors

  • C1demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;
  • C2perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications;
  • C3distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space;
  • C4represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.

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

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