Getting Ready for Calculus
Five lessons to lock down the Advanced Functions skills MCV4U assumes, three to preview the exact rate-of-change-to-derivative sequence it opens with.
Who it's for: Students finishing Advanced Functions (MHF4U) and heading into Calculus & Vectors (MCV4U) who want to start the course already fluent instead of catching up.
The 8-lesson plan
Slides are what your tutor teaches from in the live lesson. The practice module is homework — do it before the next lesson.
Function Toolkit Refresh: Reading Any Function Fast
Rebuild fluency with polynomial, rational, and transformed functions: domain, range, end behaviour, and function notation, the base skills every later lesson leans on, taught this first session as sep
Rational Functions: Every Asymptote, Every Time
Find vertical, horizontal, and oblique asymptotes, holes, and sign behaviour of rational functions with one repeatable procedure, and see how a hole previews the 0/0 limits Lesson 8 will formalize.
Radians, the Unit Circle, and Graphing Trig Functions
Convert between degrees and radians, use the unit circle for exact values, and graph sine, cosine, and tangent with transformations in both directions, equation to graph and graph to equation.
Trig Identities and Solving Trig Equations
Use Pythagorean identities to simplify expressions, give double-angle identities dedicated live teaching time of their own, and solve trig equations over a restricted domain across basic and double-an
Exponential and Logarithmic Functions, Fast
Apply exponent and log laws, convert between exponential and log form, and solve exponential and log equations with domain checks.
Derivative-Ready Algebra: Expansion and Factoring Fluency
Build the exact expansion, factoring, and complex-fraction fluency that Lessons 7 and 8 will demand, before either lesson asks for it, not after.
Average Rate of Change and the Secant-to-Tangent Idea
Calculate average rate of change over an interval, connect it to secant slope, and see how shrinking the interval approaches the tangent, numerically first, with the symbolic version saved as Lesson 8
Limits: Getting Comfortable with Approaching a Value
Evaluate limits by substitution and factoring, then connect the limit of a difference quotient, including a rational-function case, to the derivative at a point, the lesson's payoff, protected as the