Getting Ready for Advanced Functions

Eight tutor-led lessons that turn rusty Grade 11 Functions skills into the polynomial, rational, log, and trig foundations Advanced Functions assumes.

Who it's for: Students finishing Grade 11 Functions (MCR3U) and heading into Grade 12 Advanced Functions (MHF4U), taught live in a group of four. Lessons 1-2 rebuild notation and factoring; Lessons 3-7 add new content - remainder theorem, end behaviour, rational functions, logs; Lesson 8 previews composing.

✓ Evaluates, transforms, and finds the inverse of any function on sight, and states domain and range correctly including rational and radical restrictions.✓ Factors any polynomial, including cubics and quartics, using the factor and remainder theorems, and handles rational expressions with restrictions stated.✓ Analyzes a polynomial's end behaviour and zero multiplicity from factored form and graphs it by hand, then graphs a rational function's asymptotes and holes.✓ Converts fluently between exponential and log form, applies the laws of logarithms to condense and expand expressions, and solves log-required equations.✓ Evaluates reciprocal trig functions and simplifies expressions using Pythagorean identities, and combines, composes, and finds rate of change of functions.

The 8-lesson plan

Slides are what your tutor works from in the live lesson. The practice module is homework: do it before the next lesson.

1

Function Toolkit Refresh: Notation, Domain/Range, Transformations, and Inverses

Rebuild fast, accurate fluency with function notation, domain and range including rational and radical restrictions, transformations, and inverse functions - the baseline literacy MHF4U assumes.

Slides Practice module
2

Factoring and Rational Expressions: The Algebra MHF4U Runs On

Rebuild GCF, trinomial, and special-case factoring to full fluency, then simplify, multiply, divide, add, and subtract rational expressions with restrictions stated every time.

Slides Practice module
3

The Factor Theorem and Remainder Theorem: Factoring Any Polynomial

Use the remainder theorem to evaluate a polynomial without dividing, the factor theorem to confirm a factor, and division to fully factor cubic and quartic polynomials.

Slides Practice module
4

Polynomial Functions: End Behaviour, Multiplicity, and Graphing from Factored Form

Read end behaviour from degree and leading coefficient, read zero behaviour from multiplicity, sketch a polynomial from factored form, and reverse the process from a description.

Slides Practice module
5

Rational Functions: Asymptotes and Holes from Scratch

Build rational-function analysis from scratch: state restrictions, classify each denominator zero as a vertical asymptote or hole, find the horizontal or oblique asymptote, and sketch.

Slides Practice module
6

From Exponent Laws to Logarithms: The New Inverse Operation

Refresh exponent laws and common-base exponential equation solving, then introduce logarithms as the inverse of an exponential and the log laws that condense and expand expressions.

Slides Practice module
7

Trig Refresh Plus the New Identity Toolkit

Refresh radians, the unit circle, CAST, and solving a basic trig equation, then introduce reciprocal trig functions and the Pythagorean identities used to simplify and prove.

Slides Practice module
8

Combining, Composing, and the Rate-of-Change On-Ramp to MHF4U

Combine two functions by operation with a stated domain, compose functions and evaluate them numerically and symbolically, and extend average rate of change toward instantaneous.

Slides Practice module
Reserve a seat (4 per cohort)