MCV4U Calculus and Vectors: Online Tutoring in Ontario

1. 01
   Rates of change

   • Average rate of change
   • Instantaneous rate of change
   • Secant lines and their slopes
   • Tangent lines and their slopes
   • Limits and limit notation
   • Evaluating limits graphically and numerically
   • Difference quotient
   • Derivatives from first principles
   • Equation of a tangent line
2. 02
   Derivatives and differentiation rules

   • Derivative notation and derivative functions
   • Power rule
   • Constant multiple rule
   • Sum and difference rules
   • Product rule
   • Quotient rule
   • Chain rule
   • Derivatives of polynomial functions
   • Derivatives of rational and radical functions
   • Second and higher-order derivatives
3. 03
   Applications of derivatives

   • Increasing and decreasing functions
   • Critical numbers and stationary points
   • Local maxima and minima
   • First derivative test
   • Second derivative test
   • Concavity and points of inflection
   • Curve sketching using derivatives
   • Optimization problems
   • Velocity and acceleration in motion
   • Modelling real-world problems
4. 04
   Derivatives of sinusoidal functions

   • Review of sine and cosine functions
   • Derivative of the sine function
   • Derivative of the cosine function
   • Derivatives of transformed sinusoidal functions
   • Rates of change in periodic motion
   • Oscillations and waves
5. 05
   Exponential functions and their derivatives

   • Review of exponential and logarithmic functions
   • Derivatives of exponential functions
   • Chain rule with exponential functions
   • Exponential growth and decay
   • Continuous growth and changing rates
6. 06
   Geometric vectors

   • Introduction to vectors
   • Scalars and vectors
   • Magnitude and direction
   • Vector addition and subtraction
   • Scalar multiplication
   • Resultant vectors
   • Geometric representation of vectors
   • Applications with force and velocity
7. 07
   Cartesian vectors

   • Components in two and three dimensions
   • Position and displacement vectors
   • Vector operations using components
   • Magnitude of a Cartesian vector
   • Unit vectors
   • Dot product
   • Angle between two vectors
   • Perpendicular and parallel vectors
   • Cross product
   • Applications in geometry and physics
8. 08
   Lines and planes in three-dimensional space

   • Equations of lines in 2D and 3D
   • Vector equations of lines
   • Parametric equations of lines
   • Symmetric equations of lines
   • Equations of planes
   • Normal vectors to planes
   • Intersections of lines and planes
   • Intersections of two and three planes
   • Parallel intersecting and skew lines
   • Systems of equations involving lines and planes

Best for: Grade 12 students planning engineering, sciences, economics or any calculus-based university programme.

What is MCV4U?

Calculus and Vectors (MCV4U) is an Ontario Grade 12 University Preparation mathematics course. It covers rates of change and limits, derivative rules, applications of derivatives, derivatives of sinusoidal and exponential functions, vectors, and lines and planes in three-dimensional space.

What do I need before taking MCV4U?

The usual prerequisite is MHF4U (Advanced Functions), and many schools allow it to be taken at the same time.

Are the online MCV4U classes one-to-one, or do I have to join a group?

Classes are live and one-to-one with Janvi Mam, Ph.D., on Zoom or Google Meet, so you never have to join a group or share the class with other students. If you prefer to study with a friend, small-group sessions of 2-3 students in the same course are available at a reduced per-student rate.

What are the benefits of one-to-one MCV4U tutoring?

The lesson follows your own pace and gaps instead of a class average. Every minute goes to your questions, so you can ask anything without worrying about others. Weak topics are spotted and fixed quickly, and the plan can be matched to your school tests and exams.

Can classes fit Ontario time zones?

Yes. Timings are arranged to suit students in Ontario, so you can ask for a slot that works after school hours.

Can I try a class before I commit?

Yes. You can book a free demo class, meet the teacher and see how the class runs before deciding.