IB Analysis and Approaches HL is a rigorous two-year integrated college-level course for prospective STEM major students, with an emphasis on algebraic methods and mathematical thinking. This course is specifically recommended for STEM majors with a heavy focus on abstract mathematics and reasoning: theoretical physics, pure mathematics, computer science, engineering, etc. Analysis and Approaches focuses more on analytic, abstract mathematics. In HL, students are introduced to theories, analysis, and reasoning in different areas of mathematics.

Unlike the standard US subject-specific AP curriculum, IBH Analysis covers various topics in mathematics, such as Quadratics, Functions, Exponentials, Logarithms, Transformations, Complex Numbers and Polynomials, Sequences and Series, Permutations and Combinatorics, Methods of Mathematical Proofs, Trigonometry, Vectors, Differential and Integral Calculus, Advanced Calculus, Statistics and Probability, in a course of two years. At the end of the two-year course, students are expected to take the IBH Analysis exam.

Students are also required to complete an Internal Assessment, which is a mathematical exploration. This is a report based on a topic of the student’s choice, focusing on the mathematics of that topic. The internal assessment comprises 20% of the final external IB marks. The exploration is approximately 6-12 pages long, and written at a level accessible to an audience of the student's peers. It is expected that this internal assessment will require a total of 10 hours of work. We will discuss possible topics in the first year. Students should decide on the final topic over the Summer of the first year, and the writing of the assessment will take place in the first half of the second year.

Every written assignment (HW and tests) must be done with a black or blue pen since every IB Math paper only permits writing with a black or blue pen. However, you may use a pencil for sketching a graph or graphing.

• Grades 11 & 12

• Most recommended for students coming from AP Calculus AB (with a score 4 or 5) or exceptional Pre-Calculus grades in 10th grade

• Teacher Recommendation

• HIGHLY recommended, ONLY IF POSSIBLE (consult with Ms. Lee), to take AP Calculus AB concurrently in junior year, if coming from Pre-Calculus (Not necessary)

• 5% Participation

• 30% Homework

• 25% Journals / IA

• 40% Tests

Participation

• Students are expected to be on time for every class, and be ready for the day's activities when class begins. Students are expected to come to class prepared with all required supplies each day. 

• Each day, students can earn a participation grade on a scale from 0-5 according to: being on time (1), coming prepared (1), engaging in class and staying on task (2), and demonstrating a positive respectful attitude (1).

Homework

• Every homework given on a daily basis will be graded for completion on a scale from 0-5. All homework must be submitted in the submission box before the class starts. Completion is graded on effort, not accuracy, and is not necessarily a reflection of the type of grade a student should expect on assessments. 

• In order to receive full credit on completion, students must show all work and attempt all problems. Even though a student is not able to solve all problems, one must try the best, and keep all the work process for future review and feedback. This is one of the most important attitudes in mathematics. 

Journals / IA

• Throughout the two years, students will write math journals on a shared Google Drive. The journal assignments will be done cooperatively with the IB AI HL class, so that both AI and AA students will gain broader perspectives and knowledge in each other's math. Each journal assignment consists of one main post and two comments. 

• Each main post is graded out of 20 points: 10 points on completion, and 10 points on the quality. Merely paraphrasing the materials, or inserting screenshots/captures of mathematical expressions from the textbook or external source, is not a good quality journal. A good quality journal consists of creative research topics and thoughts, personal engagement, and reflection. 

• Two comments are graded out of 10 points total: 5 points for each comment. Just as in the main post, each comment will be graded on completion and quality. One may write more than two comments, but the maximum points earned will always be 10 points. If a student writes more than two comments, the two comments with the best quality will be accounted for in the grade. 

• Starting the second year, students will work on Internal Assessments, and any related assignments will go under this category. 

Tests

• Tests will be given after each chapter, or two/three depending on the contents and the pace. They will be announced in advance.

• The emphasis on evaluation will be on the methods and procedures taught in that unit, and NOT on the correct answer. A student with an incorrect answer may earn more credit than a student with a correct answer depending on the work shown and justification given. IB and AP standards from math state: "Correct answers with no work shown will receive no credit."

• At the end of each semester, there will be a cumulative semester exam. The Year 1 Semester 1 exam will assess all of the materials covered in the first semester. The Year 1 Semester 2 exam will assess all of the materials covered in the whole year. The Year 2 Semester 1 exam will assess all of the materials covered in the whole year 1 and semester 1 of year 2. Since one of the primary purposes of this class is to be prepared for IB exams at the end of the senior year, the semester exams will consist of problems similar to the actual IB exam problems. Year 2 Semester 2 exam will be replaced with a group video project. 

*** All gradings follow AP/IB. If I cannot read or follow your work, I am NOT grading it ***

** We finish the Core book before the 1st semester ends **

Core Chapter 1: Straight Lines

• Historical Note: Galileo and Parabolas

• A - Lines in the Cartesian Plane

• B - Graphing a Straight Line

• C - Perpendicular Bisectors

• D - Simultaneous Equations

Core Chapter 2: Sets and Venn Diagrams

• A - Sets

• B - Intersection and Union

• C - Complement of a Set

• Investigation 1: Fluid Filling Functions

• D - Special Number Sets

• Theory of Knowledge: Rational and Irrational Numbers

• E - Interval Notation

• F - Venn Diagrams

• G - Venn Diagram Regions

• H - Problem Solving with Venn Diagrams

Core Chapter 3: Surds and Exponents

• A - Surds and Other Radicals

• B - Division by Surds

• C - Exponents

• D - Laws of Exponents

• E - Scientific Notation

Core Chapter 4: Equations

• A - Power Equations

• B - Equation in Factored Form

• C - Quadratic Equations

• Historical Note: The Quadratic Formula

• D - Solving Polynomial Equations Using Technology

• E - Solving Other Equations Using Technology

Core Chapter 5: Sequences and Series

• A - Number Sequence

• B - Arithmetic Sequences

• C - Geometric Sequences

• D - Growth and Decay

• E - Financial Mathematics

• F - Series

• G - Arithmetic Series

• Theory of Knowledge: Sum of Odd Integers

• H - Finite Geometric Series

• I - Infinite Geometric Series

• Theory of Knowledge: Infinite Geometric Series

Core Chapter 6: Measurement

• A - Circles, Arcs and Sectors

• B - Surface Area

• C - Volume

• D - Capacity

Core Chapter 7: Right-Angled Triangle Trigonometry

• A - Trigonometric Ratios

• B - Inverse Trigonometric Ratios

• C - Right Angles in Geometric Figures

• D - Problem Solving with Trigonometry

• E - True Bearings

• F - The Angle Between a Line and a Plane

Core Chapter 8: The Unit Circle and Radian Measure

• A -  Radian Measure

• B - Arc Length and Sector Area

• Theory of Knowledge: Measurement Systems

• C - The Unit Circle

• D - Multiples of π/6 and π/4

• E - The Pythagorean Identity

• F - Finding Angles

• G - The Equation of a Straight Line

Core Chapter 9: Non-Right-Angled Triangle Trigonometry

• A - The Area of a Triangle

• B - The Cosine Rule

• C - The Sine Rule

• D - Problem Solving with Trigonometry

Core Chapter 10: Points in Space

• A - Points in Space

• B - Measurement

• C - Trigonometry

Core Chapter 11: Probability

• A - Experimental Probability

• B - Two-Way Tables

• C - Sample Space and Events

• D - Theoretical Probability

• E - Making Predictions Using Probability

• F - The Addition Law of Probability

• G - Independent Events

• H - Dependent Events

• I - Conditional Probability

• J - Formal Definition of Independence

• K - Bayes’ Theorem

• Theory of Knowledge: What is Probability?

Core Chapter 12: Sampling and Data

• A - Errors in Sampling and Data Collection

• B - Sampling Methods

• Theory of Knowledge: Clinical Trials

• C - Writing Surveys

• D - Types of Data

• E - Simple Discrete Data

• F - Grouped Discrete Data

• G - Continuous Data

Core Chapter 13: Statistics

• A - measuring the Center of Data

• B - Choosing the Appropriate Measure

• C - Using Frequency Tables

• D - Grouped Data

• E - Measuring the Spread of Data

• F - Box and Whiskers Diagrams

• G - Outliers

• H - Parallel Box and Whiskers Diagrams

• I - Cumulative Frequency Graphs

• J - Variance and Standard Deviation

Core Chapter 14: Quadratic Functions

• A - Quadratic Functions

• B - Graphs of Quadratic Functions

• C -  Using the Discriminant

• D - Finding a Quadratic Form Its Graph

• E - The Intersection of Graphs

• F - Problem Solving with Quadratics

• H - Quadratic Inequalities

Core Chapter 15: Functions

• A - Relations and Functions

• B - Function Notation

• C - Domain and Range

• D - Rational Functions

• E - Composite Functions

• F - Inverse Functions

• G - Intersecting Lines

• Theory of Knowledge: Language and Syntax

Core Chapter 16: Transformations of Functions

A - Translations

B - Stretches

C - Reflections

D - Miscellaneous Transformations

E - The Graph of y=1/f(x)

Core Chapter 17: Trigonometric Function

• A - Periodic Behavior

• B - The Sine and Cosine Functions

• C - General Sine and Cosine Functions

• D - Modelling Periodic Behavior

• E - Fitting Trigonometric Models to Data

• F - The Tangent Function

• G - Trigonometric Equations

• H - Using Trigonometric Models

HL Chapter 1: Further Trigonometry

• A - Reciprocal Trigonometric Functions

• B - Inverse Trigonometric Functions

• C - Algebra with Trigonometric Functions

• D - Double Angle Identities

• E - Compound Angle Identities

HL Chapter 2: Exponential Functions

• A - Rational Exponents

• B - Algebraic Expansion and Factorization

• C - Exponential Equations

• D - Exponential Functions

• E - Growth and Decay

• F - The Natural Exponential

HL Chapter 3: Logarithms

• A - Logarithms in Base 10

• B - Logarithms in Base e

• C - Laws of Logarithms

• D - Natural Logarithms

• Theory of Knowledge: Invention vs. Discovery

• E - Logarithmic Equations

• F - The Change of Base Rule

• G - Solving Exponential Equations Using Logarithms

• H - Logarithmic Functions

HL Chapter 4: Introduction to Complex Numbers

• A - Complex Numbers

• B - The Sum of Two Squares Factorization

• C - Operations with Complex Numbers

• D - Equality of Complex Numbers

• E - Properties of Complex Conjugates

HL Chapter 5: Real Polynomials

• A - Polynomials

• B - Operations with Polynomials

• C - Zeros, Roots, and Factors

• D - Polynomial Equality

• E - Polynomial Division

• F - The Remainder Theorem

• G - The Factor Theorem

• H - The Fundamental Theorem of Algebra

• I - Sum and Product of Roots Theorem

• J - Graphing Cubic Functions

• K - Graphing Quartic Functions

• L - Polynomial Equations

• M - Cubic Inequalities
  
  

HL Chapter 6: Further Functions

• A - Even and Odd Functions

• B - The Graph of y=[f(x)]^2

• C - Absolute Value Functions

• D - Rational Functions

• E - Partial Fractions

HL Chapter 7: Counting

• A -  The Product Principle

• B - The Sum Principle

• C - Factorial Notation

• D - Permutations

• E - Combinations

HL Chapter 8: The Binomial Theorem

• A - The Binomial Theorem for Positive Integer Exponent n

• B - The Binomial Theorem for Rational Exponent n

HL Chapter 9: Reasoning and Proof

• A - Logical Connectives

• B - Proof by Deduction

• C - Proof by Equivalence

• Theory of Knowledge: Definitions

• D - Definitions

• Theory of Knowledge: Axioms

• E - Proof by Exhaustion

• F - Disproof by Counter Example

• G - Proof by Contrapositive

• H - Proof by Contradictions: reductio ad absurdum

HL Chapter 10: Proof by Mathematical Induction

• A - The Process of Induction

• B - The Principle of Mathematical Induction

HL Chapter 11: Linear Algebra

• A - Systems of Linear Equations

• B - Row Operations

• C - Solving 2 by 2 Systems of Linear Equations

• D - Solving 3 by 2 Systems of Linear Equations

HL Chapter 12: Vectors

• A - Vectors and Scalars

• B - Geometric Operations with Vectors

• C - Vectors in a Plane

• D - The Magnitude of a Vector

• E - Operations with Plane Vectors

• F - Vectors in Space

• G - Operations with Vectors in Space

• H - Vector Algebra

• I - The Vector Between Two Points

• J - Parallelism

• K - The Scalar Product of Two Vectors

• L - The Angle Between Two Vectors

• M - Proof Using Vector Geometry

• N - The Vector Product of Two Vectors

HL Chapter 13: Vector Applications

• A - Lines in 2 and 3 Dimensions

• B - The Angle Between Two Lines

• C - Constant Velocity Problems

• D - The Shortest Distance From a Point to a Line

• E - Intersecting Lines

• Theory of Knowledge: The Evolution of Mathematics

• F - Relationships Between Lines

• G - Planes

• H - Angles in Space

• I - Intersecting Planes

HL Chapter 14: Complex Numbers

• A - The Complex Plane

• B - Modulus and Argument

• C - Geometry in the Complex Plane

• D - Polar Form

• E- Euler's Form

• F - De Moivre's Theorem

• G - Roots of Complex Numbers

HL Chapter 15: Limits

• A - Limits

• Theory of Knowledge: Paradoxes

• B - The Existence of Limits

• C - Limits at Infinity

• D - Trigonometric Limits

• E - Continuity

HL Chapter 16: Introduction to Differential Calculus 

• A - Rates of Change

• B - Instantaneous Rates of Change

• C - The Gradient of a Tangent

• D - The Derivative Function

• E - Differentiation from First Principles

• F - Differentiability and Continuity

HL Chapter 17: Rules of Differentiation

• A - Simple Rules of Differentiation

• B - The Chain Rule

• C - The Product Rule

• D - The Quotient Rule

• E -  Derivatives of Exponential Functions

• F - Derivatives of Logarithmic Functions

• H - Derivatives of Trigonometric and Inverse Trigonometric Functions

• I - Second and Higher Derivatives

• J - Implicit Differentiation

HL Chapter 18: Properties of Curves

• A - Tangents

• B - Normals

• C - Increasing and Decreasing

• D - Stationary Points

• E - Shape

• F - Inflection Points

• G - Understanding Functions and Their Derivatives

• H - L'Hopital's Rule

HL Chapter 19: Applications of Differentiation

• A - Rates of Change

• B - Optimization

• C - Related Rates

• Theory of Knowledge: Intrinsic vs. Natural

HL Chapter 20: Introduction to Integration

• A - Approximating the Area Under a Curve

• B - The Riemann Integral

• C - Antidifferentiation

• D - The Fundamental Theorem of Calculus

HL Chapter 21: Techniques for Integration

• A - Discovering Integrals

• B - Rules for Integration

• C - Particular Values

• D - Integrating f(ax+b)

• E - Partial Fraactions

• F - Integration by Substitution

• G - Integration by Parts

HL Chapter 22: Definite Integrals

• A - Definite Integrals

• B - Definite Integrals Involving Substitution

• C - The Area Under a Curve

• D - The Area Above a Curve

• E - The Area Between Two Curves

• F - The Area Between a Curve and the y-axis

• G - Solids of Revolution

• H - Problem Solving by Integration

• I - Improper Integrals

HL Chapter 23: Kinematics

• A - Displacement

• B - Velocity

• C - Acceleration

• D - Speed

HL Chapter 24: Maclaurin Series

• A - Maclaurin Series

• B - Convergence

• C - Composite Functions

• D - Addition and Subtraction

• E - Differentiation and Integration

• F - Multiplication

• G - Division

HL Chapter 25: Differential Equations

• A - Differential Equations

• B - Euler's Method for Numerical Integration

• C - Differential Equations of the Form dy/dx = f(x)

• D - Separable Differential Equations

• E - Logistic Growth

• F - Homogeneous Differential Equations dy/dx = f(y/x)

• G - The Integrating Factor Method

• H - Maclaurin Series Developed From a Differential Equation

HL Chapter 26: Bivariate Statistics

• A - Association Between Numerical Variables

• B - Pearson's Product-Moment Correlation Coefficient

• C - Line of Best Fit By Eye

• D - The Least Squares Regression Line

• Theory of Knowledge: Interpolation vs. Extrapolation

• E - The Regression Line of x Against y

• Theory of Knowledge: Men's vs. Women's Salaries

HL Chapter 27: Discrete Random Variables

• A - Random Variables

• B - Discrete Probability Distributions

• C - Expectations

• D - Variance and Standard Deviation

• E - Properties of aX + b

• F - The Binomial Distribution

• G - Using Technology to Find Binomial Probabilities

• H - The Mean and Standard Deviation of a Binomial Distribution

HL Chapter 28: Continuous Random Variables

• A - Probability Density Functions

• B - Measures of Center and Spread

• C - The Normal Distribution

• D - Calculating Normal Probabilities

• E - The Standard Normal Distribution

• F - Normal Quantiles

Mock and Practice Exams until the IB Exam in May

• 50% maximum (2.5 points) can be earned for late submission within 24 hours. No late submission will be accepted after then. 

• If a student is absent with an excuse, he/she has as many days to make up work missed due to absences as the number of excused days of absence that occurred. Excused absence requires an email from the school office or the student's parents/guardians, or the Transit Form entry. 

• IB Math HL courses run at a very rapid pace. For the most of the time, there is no or almost no time in class to discuss the homework or test questions. Therefore, it is extremely important that the students communicate with Ms. Lee, whenever there are questions. It is the student's responsibility to reach out when they need help.

• We will have a class Whatsapp group. Oftentimes, when you have a question on a problem, your classmates might have the same question as well. Or, sometimes your classmate can have a solution to your questions. So, we want to use the group chat effectively, for discussing questions amongst peers. Ms. Lee will be there to guide if you need a hint. 

• "I can proudly assure, that I am probably the fastest responder of any teacher at SJS! I will answer your questions any time, any day, even if it's 3 AM on Sunday, as long as I am awake. So please, PLEASE use me as much as possible! I am the best, free resource that you have!"