Grade 10

Students who have completed MTH1WE at Merivale or Colonel By may choice either

MCR3U2 Functions: Models & Analysis

MCR3U1: Functions: Theory & Approaches

Students who have completed math students outside of Merivale or Colonel By may choose

MCR3U2: Functions: Methods & Models

Models:     Implies the process of using mathematical structures to represent, analyze, and map real-world or spatial relationships.

Analysis:   Implies the breaking of complex systems down into their parts to understand how they work.

Theory:      Implies a focus on more abstract reasoning and the artistic nature of mathematics

Approaches: Implies the focus on the methods, proofs, and logical structures used to attack abstract problems.

At Merivale High School the pre-IB math pathway has a choice for students.

 This choice is provided for two reasons.

1.   Grade 9 Level of Learning

To continue the students’ learning from whichever level has been reached by the end of grade 9.

2.   Future Desires

To prepare students for their future aspiration in their mathematics learning within the IB program.

This choice DOES NOT impact post secondary options.

This choice IS NOT provided to support post secondary applications. 

Any decision that is made WILL lead to any post secondary application. The mathematics choice in grade 10 is centered around helping students mature in their math understanding and preparing for the IB math pathway only.

This course focuses on the application and construction of mathematics. It is designed for students who help develop a how-to approach, building a strong toolkit of skills before applying them to complex functions. We begin by grounding our studies in coordinate geometry and concrete relationships as a review from MTH1WE followed by using tools like Voronoi Diagrams to build a bridge toward function analysis. This course is ideal to help students appreciate seeing the steps, methods, and real-world connections behind the math.

Units of Study:

Unit 1

• Distance and Midpoint of the Line Segment

• Review of Equation of a Line

• Review of Parallel and Perpendicular Lines

• Medians and Perpendicular Bisectors

• Solving Linear Systems with Tech

• Solving Polynomial Systems with Tech

• Centroid and Circumcenter

• Voronoi Diagrams

• Voronoi Diagrams II

Unit 2

• Polynomial Review & Common Factoring

• Factoring Trinomials (Simple & Complex)

• Factoring Special Cases

• Factoring More Practice

• Primary Trig Ratios Review

• Specials Angles

• Angles & the Cartesian Plane

• Intro to Functions vs Relation

• Functions Notation

• Parent Functions and Key Characteristics

• Transformations - Translations

• Transformations - Stretch/Compression

• Combinations of Transformations

Unit 3 

• Quadratic Transformations

• Exponential Functions - Graphs & Transformations

• Logarithmic Functions - Graphs & Key Characteristics

• Trigonometric Functions - Graphs & Key Characteristics

• Trigonometric Functions - Transformations

• Rational Functions - Key Characteristics & Restrictions

• Multiply & Divide Rational Expressions

• Adding & Subtraction Rational Expressions

Unit 4

• Inverse Function

• Basic Exponential Equations and Logarithm Connections

• Log Laws and Exponential Equations II

• Basic Logarithmic Equations

• Rational Equations

• Linear Trigonometric Equations

• Quadratic Equations by factoring

• Quadratic Trig Equations by factoring

• Quadratic Equations by Completing the Square

• Quadratic Equations by Quadratic Formula

Unit 5

• Intro to Radians

• Trig Identities - with restrictions, radians only

• Trig Identities - radians only

• Solve using Trig Identities

• Solve using Trig Identities II

This course focuses on the architecture of mathematics. It is designed to foster a joy of abstract reasoning and help students understand why mathematical systems behave the way they do. The course begins quicker than MCR3U2 but forgoes the mathematical constructions before entering function analysis. This course is ideal for students who want to build their understanding of theory and the logical structure behind the mathematical models.

Units of Study:

Unit 1

• Review of Factoring Trinomials I

• Review of Factoring Special Cases

• Review of Primary Trig Ratios and Intro to Reciprocals

• Angles & Cartesian Plane

• Trigonometric Special Angles

• Intro to Functions vs Relation

• Functions Notation

• Parent Functions and Key Characteristics

• Transformations - Translations

• Transformations - Stretch/Compression

• Combinations of Transformations 

Unit 2

• Quadratic Transformations

• Exponential Functions - Graphs & Transformations

• Logarithmic Functions - Graphs & Key Characteristics

• Trigonometric Functions - Graphs & Key Characteristics

• Trigonometric Functions - Transformations

• Problem Solving & Review

• Rational Functions - Key Characteristics & Restrictions

• Multiply & Divide Rational Expressions

• Adding & Subtraction Rational Expressions

Unit 3 

• Inverse Functions

• Basic Exponential Equations and Logarithmic Connections

• Log Laws and Exponential Equations II

• Basic Logarithmic Equations

• Rational Equations

• Linear Trigonometric Equations

• Quadratic Equations by factoring

• Quadratic Trig Equations by factoring

• Quadratic Equations by Completing the Square

• Graphing from 3 Forms, KCs and Partial Factoring

• Determining the nature of Roots

• Quadratic Equations by Quadratic Formula

• Solving Composite Equations

Unit 4

• Quadratic Scenarios

• Quadratic Scenarios - Revenue & Dimension

• Quadratic Scenarios - Mixtures & Solutions

• Trigonometry Problems include 3D

• Trigonometric Scenarios

• Trigonometric Scenarios - Create Equation & Solve

• Exponential Scenarios

• Logarithms Scenarios

Unit 5

• Pascal's Triangle and Combinations

• Binomial Expansion

• Intro to Radians

• Trig Identities - with restrictions, radians only

• Trig Identities - radians only

• Solve using Trig Identities

• Solve using Trig Identities II