Grade 11 (DP1)

IB-DP Courses

Ontario High School Courses

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All about Explorer Math

Introduction

Course Outline

Course Settings + Grades

⚠️Mandatory Questionnaire to receive Credit for this course

Accomodations

Assessment & Evaluation for Student Success

Curriculum Expectations (Pending Hasina Confirmations)

Welcome to Explorer Math Grade 12 (MHF4U)

Chapter 1: Lesson Plans

Introduction to Characteristics of Functions

Lesson 1: Rates of Change

✍️ (GRADED) Chapter 1 Lesson 1 Quiz

Lesson 1 Mini Challenge

Lesson 2: Explore Situations in Which the Rate of Change is Zero, Constant, or Changing

✍️ (GRADED) Chapter 1 Lesson 2 Quiz

Lesson 2 Mini Challenge

Lesson 3: Calculating Rates of Change for Various Functions

✍️ (GRADED) Chapter 1 Lesson 3 Quiz

Lesson 3 Power Math

Lesson 3 Mini Challenge

Lesson 4: Average Rate of Change vs Instantaneous Rate of Change

✍️ (GRADED) Chapter 1 Lesson 4 Quiz

Lesson 4 Power Math

Lesson 4 Mini Challenge

Lesson 5: What are Tangent Lines & What Does “Normal to the Tangent” Mean?

✍️ (GRADED) Chapter 1 Lesson 5 Quiz

Lesson 5 Power Math

Lesson 5 Mini Challenge

Lesson 6: Making Connections Between the Slope of a Secant on the Graph of a Function & the Average Rate of Change

✍️ (GRADED) Chapter 1 Lesson 6 Quiz

Lesson 6 Power Math

Lesson 6 Mini Challenge

Lesson 7: Connect Tangent Slope at a Point on a Function's Graph to the Instantaneous Rate of Change

 ✍️ (GRADED) Chapter 1 Lesson 7 Quiz

Lesson 7 Power Math

Lesson 7 Mini Challenge

Lesson 8: Estimate a Tangent's Slope Using Secant Slopes and Relate it to Average and Instantaneous Rates of Change

 ✍️ (GRADED) Chapter 1 Lesson 8 Quiz

Lesson 8 Power Math

lesson 8 Mini Challenge

Lesson 9: Solve Problems Involving Average & Instantaneous Rates of Change

✍️ (GRADED) Chapter 1 Lesson 9 Quiz

Lesson 9 Power Math

Lesson 9 Mini Challenge

Lesson 10: What is the Limit of a Function?

✍️ (GRADED) Chapter 1 Lesson 10 Quiz

Lesson 10 Power Math

Lesson 10 Mini Challenge

Lesson 11: Key Features of the Graphs of Functions Created by Adding, Subtracting, Multiplying, or Dividing Functions

✍️ (GRADED) Chapter 1 Lesson 11 Quiz

Lesson 11 Power Math

Lesson 11 Mini Challenge

Lesson 12: Real-World Applications of Combination of Functions

✍️ (GRADED) Chapter 1 Lesson 12 Quiz

Lesson 12 Power Math

Lesson 12 Mini Challenge

Lesson 13: Explain Odd/Even Properties and Increasing/Decreasing Behaviour of Functions Formed by Adding, Subtracting, Multiplying, or Dividing

✍️ (GRADED) Chapter 1 Lesson 13 Quiz

Lesson 13 Mini Challenge

Lesson 14: Composite Functions / Composition of Functions, Interpret the Notation of Composite Functions

✍️ (GRADED) Chapter 1 Lesson 14 Quiz

Lesson 14 Power Math

Lesson 14 Mini Challenge

Lesson 15: Composition of Two Functions: Real World Applications

✍️ (GRADED) Chapter 1 Lesson 15 Quiz

Lesson 15 Power Math

Lesson 15 Mini Challenge

Lesson 16: Algebraically Determine the Composition of Two Functions

✍️ (GRADED) Chapter 1 Lesson 16 Quiz

Lesson 16 Power Math

lesson 16 Mini Challenge

Lesson 17: Understand How to Represent Complex Functions as Composites of Simpler Functions

✍️ (GRADED) Chapter 1 Lesson 17 Quiz

Lesson 17 Power Math

Lesson 17 Mini Challenge

Lesson 18: Demonstrate, by Giving Examples for Functions Represented in a Variety of Ways

✍️ (GRADED) Chapter 1 Lesson 18 Quiz

Lesson 18 Power Math

Lesson 18 Mini Challenge

Lesson 19: Make Connections, Through Investigation Using Technology, Between Transformations

✍️ (GRADED) Chapter 1 Lesson 19 Quiz

Lesson 19 Power Math

Lesson 19 Mini Challenge

Lesson 20/21: Compare Various Functions With One Another

✍️ (GRADED) Chapter 1 Lesson 20 Quiz

Lesson 20 Power Math

Lesson 20 Mini Challenge

✍️ (GRADED) Chapter 1 Lesson 21 Quiz

Lesson 21 Power Math

Lesson 21 Mini Challenge

Lesson 22: Locate Approximately a Root of an Equation, by Means of Graphical Considerations and/or Searching for a Sign Change

✍️ (GRADED) Chapter 1 Lesson 22 Quiz

Lesson 22 Power Math

Lesson 22 Mini Challenge

Math Check-In

Chapter 1 Quiz

Chapter 1: Characteristics of Functions

Chapter 2: Lesson Plans

Introduction to Polynomials and Rational Functions

Lesson 1: Polynomial Expressions and Equations of Polynomial Functions

✍️ (GRADED) Chapter 2 Lesson 1 Quiz

Lesson 1 Power Math

Lesson 2: Finding the Degree From the Equation in Expanded or Factored Form

✍️ (GRADED) Chapter 2 Lesson 2 Quiz

Lesson 2 Power Math

Lesson 3: Finding the Leading Coefficient From the Equation in Expanded or Factored Form

✍️ (GRADED) Chapter 2 Lesson 3 Quiz

Lesson 4: Comparing the Numeric, Graphical, & Algebraic Representations of Polynomial Functions

✍️ (GRADED) Chapter 2 Lesson 4 Quiz

Lesson 5: Describe key features of polynomial graphs, including domain, range, shape, and end behaviour

✍️ (GRADED) Chapter 2 Lesson 5 Quiz

Lesson 6/7: Making Connections Between a Polynomial Function Given in Factored Form & the x-Intercepts of its Graph

✍️ (GRADED) Chapter 2 Lesson 6/7 Quiz

Lesson 6/7 Power Math

Lesson 8: Sketching the Graph of a Polynomial Function Given in Factored Form Using its Key Features

✍️ (GRADED) Chapter 2 Lesson 8 Quiz

Lesson 8 Mini Challenge

Lesson 9: Determining the Roles of the Parameters a, k, d, & c in Functions

✍️ (GRADED) Chapter 2 Lesson 9 Quiz

Lesson 10: Determining an Equation of a Polynomial Function That Satisfies a Given Set of Conditions

✍️ (GRADED) Chapter 2 Lesson 10 Quiz

Lesson 11: Determine the equation of a polynomial family from given zeros and identify the member passing through a given point

✍️ (GRADED) Chapter 2 Lesson 11 Quiz

Lesson 12: Compare the properties of even and odd polynomial functions and determine whether a function is even, odd, or neither

✍️ (GRADED) Chapter 2 Lesson 12 Quiz

Lesson 13: Determining Key Features of the Graphs of Rational Functions

✍️ (GRADED) Chapter 2 Lesson 13 Quiz

Lesson 14: Determining Key Features of the Graphs of Rational Functions That are the Reciprocals of Linear & Quadratic Functions

 ✍️ (GRADED) Chapter 2 Lesson 14 Quiz

Lesson 15: Sketching the Graph of a Simple Rational Function Using its Key Features, Given the Algebraic Representation of the Function

 ✍️ (GRADED) Chapter 2 Lesson 15 Quiz

Level 15 Power Math

Lesson 16: Understanding the Connection Between Vertical Asymptote & Limits That Equal to Infinity

 ✍️ (GRADED) Chapter 2 Lesson 16 Quiz

Lesson 16 Mini Challenge

Lesson 17: Given the Equation of a Rational Function, Determine the Equation of the Horizontal Asymptote

✍️ (GRADED) Chapter 2 Lesson 17 Quiz

Lesson 18/19: Given the Equation of a Polynomial or Rational Function, Draw an Accurate Sketch Showing All Key Features

 ✍️ (GRADED) Chapter 2 Lesson 18/19 Quiz

Lesson 18/19 Power Math

Lesson 20: Performing Long Division of Polynomials, Perform Synthetic Division of Polynomials, State the Restrictions, & Write the Division Statement

✍️ (GRADED) Chapter 2 Lesson 20 Quiz

Lesson 20B: Perform long and synthetic division of polynomials, state restrictions, and write the division statement

✍️ (GRADED) Chapter 2 Lesson 20B Quiz

Lesson 20B Power Math

Lesson 20B Mini Challenge

Lesson 21: Relate polynomial functions, divisors, and remainders to verify the Remainder Theorem and Factor Theorem

 ✍️ (GRADED) Chapter 2 Lesson 21 Quiz

Lesson 22: Using Factor Theorem to Determine Whether a Binomial is a Factor of a Higher-Order Polynomial

✍️ (GRADED) Chapter 2 Lesson 22 Quiz

Lesson 23: Factoring Polynomial Expressions in One Variable, of Degree no Higher Than Four, by Selecting & Applying Strategies

✍️ (GRADED) Chapter 2 Lesson 23 Quiz

Lesson 23 Power Math

Lesson 23 Mini Challenge

Lesson 24: Determine the relationship between the real roots of a polynomial equation and the x-intercepts of its graph

✍️ (GRADED) Chapter 2 Lesson 24 Quiz

Lesson 24 Power Math

Lesson 24 Mini Challenge

Lesson 25/26: Solving Polynomial Equations in One Variable, of Degree no Higher Than Four

✍️ (GRADED) Chapter 2 Lesson 25/26 Quiz

Lesson 25/26 Power Math

Lesson 25/26 Mini Challenge

Lesson 27: Determine the relationship between the real roots of a rational equation and the x-intercepts of its graph

✍️ (GRADED) Chapter 2 Lesson 27 Quiz

Chapter 2: Polynomials and Rational Functions

Mid Term

🎯Midterm

Chapter 3: Lesson Plans

Introduction to Exponential and Logarithmic Functions

Lesson 1: Recognizing the Logarithm of a Number to a Given Base as the Exponent to Which the Base Must be Raised to Get the Number

✍️ (GRADED) Chapter 3 Lesson 1 Quiz

Lesson 2: Recognizing the Operation of Finding the Logarithm to be the Inverse Operation

✍️ (GRADED) Chapter 3 Lesson 2 Quiz

Lesson 3: Determining the Approximate Logarithm of a Number to Any Base, Including Base 10

✍️ (GRADED) Chapter 3 Lesson 3 Quiz

Lesson 4: Making connections between related logarithmic and exponential equations

✍️ (GRADED) Chapter 3 Lesson 4 Quiz

Lesson 5/6: Solving Simple Exponential Equations by Rewriting Them in Logarithmic Form

✍️ (GRADED) Chapter 3 Lesson 5/6 Quiz

Lesson 5/6 Power Math

Lesson 7: Making Connections Between Laws of Exponents & the Laws of Logarithms

 ✍️ (GRADED) Chapter 3 Lesson 7 Quiz

Lesson 6/7 Mini Challenge

Lesson 8: Using the Laws of Logarithms to Simplify & Evaluate Numerical Expressions

✍️ (GRADED) Chapter 3 Lesson 8 Quiz

Lesson 9: Laws of Logs: PROOFS

✍️ (GRADED) Chapter 3 Lesson 9 Quiz

Lesson 10: Solve logarithmic equations using logarithm properties and check for inadmissible solutions with negative bases or arguments

Chapter 3: Exponential and Logarithmic Functions

Course Code: MHF4UCourse Type: University PreparationFormat: Online School CoursePrerequisite: MCR3U, Grade 11 Functions or MCT4C, Grade 12 Mathematics for College TechnologyNeeded for: MHF4U is needed prior to taking MCV4U and for those wishing to consolidate their understanding of mathematics before proceeding to several university programs.Course Format: Online, Learn at your own pace, built-in supports and prompts, Gamified Learning with Pop Quizzes, Online Exams, Auto-grading, Current Grade Displayed Our expertise in MathExplorer Math prepares students from Grades 6-12 to learn advanced international math from the comfort of their homes. Not only will your child be prepared to succeed from a global standpoint, but they will also develop a passion for math that they can actually apply! What will I learn?In this course, you will explore advanced functions and mathematics. You will be learning how to analyze graphs of functions and equations, how to create graphs of functions, and how to obtain useful information from functions and graphs for real-life applications. You will be learning about rates of change, making connections between functions and their key characteristics, and how to critically think to solve advanced math problems. This will allow you to develop an essential skill set of mathematical skills that are highly applicable in real life and in many careers.Topics covered1) Characteristics of Functions2) Polynomials and Rational Functions3) Exponential and Logarithmic Functions4) Trigonometric Functions

MHF4U Advanced Functions: University-preparation Ontario course covering functions, polynomial/rational, exponential/logarithmic, and trigonometric functions, with self-paced learning, supports, quizzes, exams, auto-grading, and grade tracking.

MHF4U - Math Grade 12-7A Ontario

MHF4U - Math Grade 12-7A Ontario

Hasina Lookman

Course Details

Course content

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