Grade 11

There are two courses each with two levels. Here at Merivale these courses are also matched with grade 12 Ontario courses which allows students to obtain both diplomas. As a result, the IB curriculum courses must be supplemented to meet Ontario standards of learning. This means all courses in grade 11 are rigorous and content rich allowing students to access any desired post secondary program of study. Selecting a grade 11 course should be based upon a student’s current level of learning and interest in different areas of mathematics.

Applications and Interpretations (AI)

The Philosophy:          This course is designed for the Analyst.

It aligns with the Applied Math and Statistics tradition.

The Name:       Applications implies using math as a tool to solve external problems.

Interpretations implies looking at data or results and explaining what they mean in a       real-world context.

Analysis and Approaches (AA)

The Philosophy:         This course is designed for the Architect.

   It aligns with the Pure Math tradition.

The Name:         Analysis implies breaking complex systems down into their parts to understand how they work.

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

IB math courses WILL NOT impact post secondary options.

Any decision that is made WILL lead to any post secondary application process. The mathematics choice in grade 11 is centered around helping students mature in their math understanding and preparing for the IB math pathway only.

Applications and Interpretations (AI) is a course that allows students to mature in their advanced mathematical skills. This option focuses on applied mathematics and offers a pathway that can best meet a student wherever their learning is currently standing. This course is a one-year IB course that examines in May of the grade 11 year. Students are granted a MDM4U Ontario credit alongside their AI Standard Level credit. AI Higher Level is not offered here at Merivale. Since students IB expectations will have been met in grade 11 students have the option to continue their mathematics studies in either the MHF4U or MCV4U Ontario functions and calculus courses during their grade 12 year. As a result, students can receive up to three Ontario grade 12 credits by choosing this pathway. This results in a pathway that has more time for students to mature in their mathematical abilities.

The IB DP Mathematics: applications and interpretation course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. To give this understanding a firm base, this course includes topics that are traditionally part of a pre-university mathematics course such as calculus and statistics. Students are encouraged to solve real-world problems, construct and communicate this mathematically and interpret the conclusions or generalizations. Students should expect to develop strong technology skills and will be intellectually equipped to appreciate the links between the theoretical and the practical concepts in mathematics. All external assessments involve the use of technology. Students are also encouraged to develop the skills needed to continue their mathematical growth in other learning environments.

Units of Study:

Unit 1 - Review

• Straight Lines

• Arithmetic Series and Sequences

• Geometric Series and Sequences

• Approximation

• 3D Space

• Functions

Unit 2 – Review II

• Triangle Trig

• Apps and Bearings

• Circles

• Systems of Equations

• Compound Interest

• Annuities

• Perpendicular Bisectors

Unit 3 – Statistics and Probability

• Collection/Presentation of Data

•  Collection/Presentation

•  Central Tendency

•  Linear Correlation

•  Probability Outcomes

•  Probability Calculations I

• Probability Calculations II

Unit 4 – Modelling with Functions

• Functions Key Features

• Graphing Functions with GDC

• Functions as Models/Inverse

• Intro to Modelling

• More Modelling

Unit 5 – Further Statistics

• Discrete Random Variables

• Binomial Distribution

• Normal Distribution

• Further Regression

• Hypothesis Testing

• Hypothesis Testing Day 2

Unit 6 – Polynomials & Calculus

• Differentiation

• Increasing & Decreasing

• Applying Derivatives I

• Applying Derivatives II

• Equations of Tangents & Normals

• Integration

• Stationary Points

• Optimisation

• Area under a Polynomial Curve

Analysis and Approaches (AA) is a course that allows students to extend their functions analysis and continue to explore abstract mathematical skills. This option focuses on mathematics for mathematics and offers a pathway that best meets students with a consistent excellent level of learning in MCR3U2 or MCR3U1. This is a two-year IB course that examines in May of the grade 12 year. Students are granted a MHF4U credit after their grade 11 year and a MCV4U credit in their grade 12 year. Both AA standard level and higher level are offered here at Merivale. As a result, students will receive two Ontario grade 12 credits by choosing this pathway. This results in a pathway that is fast paced and requires dedication and commitment to using students strong learning skills.

The AA SL is a rigorous course that combines Ontario Advanced Functions, Ontario Calculus and Vectors with the IB DP analysis and approaches standard level topics. This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. The focus is on developing important mathematical concepts in a comprehensible, coherent and rigorous way, achieved by a carefully balanced approach. Students are encouraged to apply their mathematical knowledge to solve abstract problems as well as those set in a variety of meaningful contexts. Mathematics: analysis and approaches have a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments. Students should expect to develop insight into mathematical form and structure and should be intellectually equipped to appreciate the links between concepts in different topic areas. Students are also encouraged to develop the skills needed to continue their mathematical growth in other learning environments. Throughout the course students are encouraged to take a considered approach to various mathematical activities and to explore different mathematical ideas.

Year I Units of Study

Unit 1 - Polynomials

• Transformations, Vector Notation, Transformations in Standard Form

• Composite & Inverse Function

• Characteristics of Polynomial Functions

• Limits I

• Limits II

• Rates of Change

• Intro to Derivative - Power Rule

• Intro to Derivative - Chain Rule

• Local Extrema & Intervals of Increase and Decrease

• Local Extrema & Product Rule

• Intro to Kinematics I

Unit 2 – Polynomials II

• Polynomial Division & Remainder and Factor Theorem

• Polynomial Division & Remainder and Factor Theorem

• Graphing Polynomials

• Integrals of Polynomials

• Definite/Indefinite Integrals and Bounded Area

• Solving Equations/Inequalities & Sketching

Unit 3 – Exponential & Logarithmic Functions

• Exponents and Solving Exponential Equations

• Sketching and Characteristics of Exponential and Log Functions

• Log Laws & Change of Base

• Solving Exponential Equations with Logs

• Solving Log Equations with different bases

•  Derivatives of Exponential and Logarithms

• Intro to Derivative - Product Rule

• Intro to Kinematics - Polynomial/Exponential

• Integrals - u-substitution

• Kinematics - Distance Travelled

• Applications

Unit 4 – Rational Functions

• Rational Functions Review

• Rational Functions Characteristics - Sketching

• Intro to Derivative - Quotient Rule

• Equations of Tangents II

• Curve Sketching Rational Functions

• Integral - u-substitution

• Rational Equations

• Rational Inequalities

• Equations and Inequalities

Unit 5 – Further Statistics

• Review of Trig Applications - Ambiguous case, 3D, Bearings

• Arc Length Arc Sector

• Trig Functions Review

• Trig Equations and Applications Review

• Trig Identities

• Differentiate and Integrate Trig Functions

• Double Angle Formulas

• Compound Angle Formulas

• Trig Identities Practice

• Trig Equations with Identities

• Trig Inequalities Practice

• Kinematics I

• Kinematics II

Year II Units of Study

Unit 1 – Year I Review

• Polynomial: Characteristics, Sketching & Solving

• Polynomials: Area between Curves

• Rational Functions: Sketching, Solving, Inequalities

• Inverse and Composite Functions

• Exponential & Logarithmic Curve Sketching

• Solving Exponential & Logarithmic Equations

• Tangents & Normals

• Kinematics I

• Trigonometric Functions I

• Trig II

• Integration by sub/Kinematics II

Unit 2 – Polynomials II

• Data Types, Sources & Sampling

• Measures of Central Tendency & Frequency Tables

• Measures of Spread, Data Transformations

• Quartiles, Boxplots & IQR

• Normal Distribution

• Standardized Scores & Applications

• Linear Correlation, Pearson's Correlation & Further Regression

Unit 3 – Exponential & Logarithmic Functions

• Binomial Theorem

• Binomial Distribution

•  Events & Expected Values

• Venn Diagrams & Combined Events

• Conditional Probability

• Discrete Probability Distributions & Fair Game

• Mean & Variance of Binomial Distribution

Unit 4 – Series & Proofs

• Sequences

• Applications I

• Infinite Series

• Applications II

• Direct Proofs

Unit 5 – Vectors

• Introduction to Vectors

• 3-Space & Components

• Scalar Product and Properties

• Vector Product & Properties

• Equation of Lines in 3 Space

• Equation of Planes

• Intersections of Lines & Planes

Analysis and Approaches (AA) is a course that allows students to extend their functions analysis and continue to explore abstract mathematical skills. This option focuses on mathematics for mathematics and offers a pathway that best meets students with a consistent excellent level of learning in MCR3U2 or MCR3U1. This is a two-year IB course that examines in May of the grade 12 year. Students are granted a MHF4U credit after their grade 11 year and a MCV4U credit in their grade 12 year. Both AA standard level and higher level are offered here at Merivale. As a result, students will receive two Ontario grade 12 credits by choosing this pathway. This results in a pathway that is fast paced and requires dedication and commitment to using students strong learning skills.

The AA SL is a rigorous course that combines Ontario Advanced Functions, Ontario Calculus and Vectors with the IB DP analysis and approaches higher level topics. This results in a course that will examine a full 50 topics more than AA SL. All these topics are topics that will again be covered in first year university. As such, AA HL is not a prerequisite for any university program given that students in AA SL must also cover all Ontario diploma requirements. This course recognizes the beauty in mathematics and the love for the subject as pure theory. This course combines additional topics with an in-depth theory of knowledge lens. Due to the 50 extra topics students learn each topic with great number of connections and thus develop a wider view of pure mathematics.  Students are also encouraged to develop the skills needed to continue their mathematical growth in other learning environments. Throughout the course students are encouraged to take a considered approach to various mathematical activities and to explore different mathematical ideas.

Year I Units of Study

Unit 1 – Polynomials I

• Permutations & Combinations

• Binomial Theorem

• Review of Parents, Transformations, Piecewise & Graphing

• Characteristics of Functions

• Characteristics of Polynomial Functions

• Limits

• Limits II

• Rates of Change

• Intro to Derivative - Power Rule, use Binomial theorem, Chain rule.

• Local Extrema, Derivative Tests and Characteristics

Unit 2 – Polynomials II

• Intro to Kinematics, Optimisation and Related Rates

• Polynomial Division & Remainder and Factor Theorem

• Factoring Higher Order Polynomials

• Solving Equations & Sketching

• Antiderivatives of Polynomials with Fundamental Theorem of Calculus

• Definite Integrals, Indefinite Integrals and Bounded Areas

• Integration by Substitution

Unit 3 – Exponential & Logarithmic Functions

• Exponentials & Intro to Log as Inverse

• Log Laws & Change of Base

• Solving Exponential Equations with Logs

• Derivatives of Exponential and Logarithms from First Principles

• Derivatives of Exponential and Logarithms

• Modelling with Exponential and Logarithmic Functions

• Optimisation and Related Rates III

• Antiderivative of Exponential and Logarithm

• Integration by Parts

Unit 4 – Rational Functions

• Rational Functions Characteristics - Sketching

• Sketching Rational Functions

• Solving Rational Equations and Inequalities

• Quotient Rule and Product Rule

• Implicit Differentiation

• Optimisation and Related Rates II

• Rational Functions Characteristics - Curve Sketching

• Partial Fractions and Integration

• L’Hôpital’s Rule

Unit 5 – Trigonometric Functions

• Trig Functions Review, Radian Measure

• Applications of Trig Functions

• Reciprocal Trig Functions and Inverse Trig Functions

• Double Angle Formulas

• Compound Angle Formulas

• Portfolio Group Solution and Discussion Day

• Derivative of Trigonometric Functions - from first principles

• Derivative of Trigonometric Functions

• Derivative of Reciprocal and Inverse

• Optimisation & Kinematics

• Related Rates

• Integration by Parts II - Repeating

• Integration Problems

Unit 6 – Proofs

• Deduction - Direct Proofs

• Proof by Contradiction, Counter examples

• Proof by Induction

• Proof by Induction II

• Sum of Infinite Series - Geometric

Year II Units of Study

Unit 1 – Year I Review

• Differentiation

• Integration

• Optimisation/Related Rates

• Induction

• Implicit Relations

• Trigonometric Functions

Unit 2 – Statistics

• Data Sources & Sampling & Bias

• Frequency Tables/Diagrams, Histograms

• Central tendency & Spread I

• Central tendency & Spread I1

• Quartiles, IQR and Box Plots

• Data Transformations

• Standardized Scores & Applications

• Linear Correlation & Pearson's Correlation

• Linear Correlation, Predictions and coefficient of Determination

Unit 3 – Ordinary Differential Equations

• Differential Equations - Intro & Numerical Method

• Differential Equations - Separable & Homogeneous

• Differential Equations - Practice & Linear

• Maclaurin Series

• Binomial Series and Further Expansions

• Solids of Revolution x-axis

• Solids of Revolution y-axis

Unit 4 – Probability

• Intro to Probability

• Probability of Related Events

• Independence Test and Conditional Probability

• Bayes Theorem

• Discrete Probability Distributions (DRV)

• Probability using Normal Distribution

• Probability Density Function & CRVs

• Mean, Median and Mode of CRVs

• Effect of Linear Transformation of X

Unit 5 – Vectors

• Introduction to Vectors

• 3-Space & Components

• Scalar Product and Properties

• Vector Product & Properties

• Equation of Lines in 3 Space

• Equation of Planes

• Intersections of Lines & Planes

Unit 6 – Complex Numbers

• Complex Numbers & Fundamental Theorem of Algebra

• Polar/Euler Form

• Operations with Complex Numbers

• De Moivre's Theorem & Complex Roots

• Conjugate Root Theorem and Applications