Online tutoring for Grade 12 Calculus and Vectors (MCV4U)

Grade 12 Calculus and Vectors asks for two kinds of thinking at once: derivatives and their word problems, and vectors, lines and planes in three dimensions. We work the problems with your child, live and online, one to one.

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Who this is for

Grade 12 students enrolled in MCV4U this semester
Students taking Calculus and Vectors in the same year as Advanced Functions
Students aiming at university programs that list calculus as a requirement
Parents who want a short written summary of every lesson: what was worked on, and the next step

Calculus and Vectors (MCV4U)

Grade 12 · Prerequisite: MHF4U (Advanced Functions), taken before or at the same time

Rate of Change

Limits and the slope of a tangent
The derivative from first principles
Instantaneous rate of change as a limit

Derivatives and Their Applications

Power, product, quotient and chain rules
Derivatives of exponential and sinusoidal functions
Curve sketching from the first and second derivative
Optimization problems
Related rates

Geometry and Algebra of Vectors

Vectors in two-space and three-space
Dot and cross product, and projections
Equations of lines and planes
Intersections of lines and planes

Taking MCV4U alongside MHF4U

Many Ontario students take Calculus and Vectors and Advanced Functions in one year. Calculus leans on functions, logarithms and trigonometry from MHF4U, so a gap there shows up as a lost mark on a derivative question.

When a student takes both, we line up the units of the two courses and patch the Advanced Functions topic a calculus problem depends on before it is needed.

Where students get stuck in Calculus and Vectors

The derivative from first principles
Writing the limit of the difference quotient and simplifying it without an algebra slip is the first test of the course, and it reappears on exams long after the shortcut rules arrive.
The chain rule inside product and quotient rules
One expression can need three rules nested in the right order. Students who can apply each rule alone still drop a factor when they meet them together.
Setting up optimization and related-rates problems
The calculus is often the easy part. Turning a paragraph about a box, a ladder or a tank into one function of one variable is where most marks go.
Reading a graph from its first and second derivatives
Intervals of increase, concavity and points of inflection come from sign charts of two different functions, and mixing them up gives a sketch that looks right but is not.
Lines and planes in three dimensions
Vector, parametric, symmetric and scalar equations all describe the same objects. Picturing them in 3-space and finding where they meet is new for most students.
Choosing between the dot and cross product
One gives a number and one gives a vector. Knowing which one finds an angle, a normal, an area or a projection is a decision students make many times per test.

How we teach Calculus and Vectors

In each lesson the student solves MCV4U questions while the teacher checks every line, and a unit is finished only when a new problem set is done with no help.
Our mistakes blueprint for this course tracks calculus and vector slips, such as a lost chain-rule factor or a wrong normal, and practice goes after the ones still open.
Within 24 hours of each lesson the teacher writes down what was covered, the latest test result and the starting point for next time.
A summer start lets a student work through the whole course early, so the school semester becomes a review rather than a first look.

How we teach

The method behind the marks

Four things every lesson is built on.

01
Run the course before the course
A grade 12 course taught front to back the summer before, so the school year is the student's second pass, not their first. Four courses in one summer is possible; one is the usual.
02
Lessons are problems, not lectures
Every lesson is the student doing questions with a teacher beside them. A topic is finished when the student completes the set without instruction, not when it has been explained.
03
The mistakes blueprint
For each course we keep a map of every mistake a student can make on it. Practice targets the ones the student has not cleared yet, before one of them costs a mark that stays on the transcript.
04
Logged within 24 hours
After every lesson the teacher logs what was covered, the latest test score, a confidence rating out of five, and where the next lesson starts. Written the same day, while it is still fresh.

The roster

From the lesson log

Students with a logged test in this subject, read straight off the lesson log. Every lesson is logged within 24 hours, in the teachers' own words. Students are shown by number and initials only.

Student 8
A.L.
Calculus and Vectors (MCV4U)
Alumni
99%
MCV4U · Final
Finished calculus with a 99 and was admitted to Electrical Engineering at Waterloo.
→ Waterloo Electrical Engineering

Updated November 10, 2026

Offers

Two ways to work with us

During the school year

1-on-1 tutoring

$60 / hour

Your first lesson is free.

One student, one instructor, one plan. Grade 11 and 12 math, physics, chemistry and biology, online and live.

Weekly, twice weekly, or ahead of a test
Every lesson logged within 24 hours
Stop any time, no packages

Book a free trial lesson

Before the school year

The course intensive

$600 / subject

Start with lesson 1 for $70.

One grade 12 course front to back in 10 lessons, Monday to Friday over two weeks, before the student takes it for marks.

10 lessons, 1 hour each, same time daily
95+ on our final, or we keep teaching free
Advanced Functions, Calculus, Physics, Chemistry

See the intensive

FAQ

Frequently Asked Questions

What parents ask about Calculus and Vectors tutoring before booking.

Can my child take Calculus and Vectors and Advanced Functions in the same semester?

Yes, and many Ontario students do. We tutor both together and order the lessons so the Advanced Functions skill a calculus unit needs is covered first.

Why does my child understand derivatives but lose marks on word problems?

Because the hard step is building the function from the words. We practise that setup on its own, then the full problem, until it is routine.

How do you help with the vectors half of MCV4U?

With sketches first and algebra second. Students draw the lines and planes they are working with, then write the equations, which makes intersection and distance questions far less abstract.

Can lessons follow my child's school MCV4U unit order?

Yes. Lessons track the order and pace of your child's class, and the week before a test is spent on the kinds of questions that unit usually tests.

Start with a free trial lesson

One lesson, one teacher, on the unit your child is on now. You get the lesson log the same day.

Book a free trial lesson

Online tutoring for Grade 12 Calculus and Vectors (MCV4U)

Who this is for

Calculus and Vectors (MCV4U)

Rate of Change

Derivatives and Their Applications

Geometry and Algebra of Vectors

Taking MCV4U alongside MHF4U

Where students get stuck in Calculus and Vectors

The derivative from first principles

The chain rule inside product and quotient rules

Setting up optimization and related-rates problems

Reading a graph from its first and second derivatives

Lines and planes in three dimensions

Choosing between the dot and cross product

How we teach Calculus and Vectors

The method behind the marks

Run the course before the course

Lessons are problems, not lectures

The mistakes blueprint

Logged within 24 hours

From the lesson log

Two ways to work with us

1-on-1 tutoring

The course intensive

Frequently Asked Questions

Related

Start with a free trial lesson