IB analysis and approaches Teachers:

Mr. Garrett Mott

What topics are covered in SL (or year 1 of HL)? 

Sample methods and bias, methods of presenting data, measures of central tendency and dispersion, concepts of simple probability, conditional probability, binomial distribution, normal distribution, inverse normal and binomial, standard normal curve, discrete and continuous random variables, calculus based relationships to describe continuous distributions, limits, definition of derivative, derivative rules for various functions, product and quotient and chain rules for derivatives, tangent and normal lines, definite and indefinite integrals including chain rule, total and net area with the x-axis and between curves, volumes of revolution about vertical and horizontal lines, optimization, kinematics. 

SL 4.7 Discrete Random Variables, Probability and Distribution, Expected Value, and Applications

SL 4.8 Binomial Distribution, Mean and Variants

SL 4.9 Normal Distribution and the Curve, Normal Probability, Inverse Normal Calculations

SL 4.10 Equation of Regression Line of x on y

SL 4.11 Conditional Probabilities and Probabilities for Independent Events

SL 4.12 Standardization of Normal Variables

SL 5.1 Introduction to Limits and Derivatives as a Rate of Change

SL 5.2 Increasing and Decreasing Functions, Interpreting Derivatives that are less than or greater than 0 from a Graph

SL 5.3 Derivative Power Rule

SL 5.4 Tangent and Normal Lines to a given point

SL 5.5 Intro to Integration as an anti-differentiation of functions, Anti-differentiation with a boundary condition, Definite Integrals

using technology, Area of a Region enclosed by a curve and the x-axis

SL 5.6 Derivative of Power, Sine, Cosine, ex, and Natural Log Functions, Derivative of a Sum and Multiple of those functions,

Chain, Product and Quotient Rules

SL 5.7 Graphic Behavior of First and Second Derivatives, the relationship between f(x), f’(x), and f’’(x)

SL 5.8 Testing for Local Max andMins, and Points of Inflection of Functions, Optimization

SL 5.9 Kinematic Problems involving Displacement, Velocity, Acceleration and Total Distance

SL 5.10 Indefinite Integral of Power, Sine, Cosine, 1/x, and ex functions, Composition of Indefinite Integrals, Reverse Chain Rule

Integration by Substitution

SL 5.11 Definite Integrals, Area of a Region between a curve and the x-axis, Area of a Region between 2 curves

What topics are covered in HL? 

Vectors in 2d and 3d, vector equation of a line, angle between vectors or lines, points of intersection in 3d between lines and planes, vector and cartesian equation of a plane, cross and dot product between vectors, continuity and differentiability, l'hopital's rule, maclaurin series, implicit differentiation, related rates of change, derivative of inverse trig functions, partial fractions to evaluate integrals, integration by substitution, first order differential equations, euler's method for zeros, solving differential equations by separable variables, integrating factor, series with differential equations. 

HL 1.10 Permutations and Combinations

HL 1.11 Partial Fractions

HL 1.12 Complex Numbers and the Complex Plane

HL 1.13 Polar and Euler Forms of Complex Numbers, Sums, Products and Quotients of these forms

HL 1.14 Complex Conjugate Roots of Quadratics and other Polynomials, DeMoivre’s Theorem for Powers and Roots

HL 1.15 Proof by Mathematical Induction and Contradiction

HL 1.16 Systems of Linear Equations

HL 2.16 Solutions of Modulus Equations and Inequalities

HL 3.9 Reciprocal Pythagorean Properties, Inverse Trig Functions

HL 3.10 Compound and Double Angle Identities

HL 3.11 Symmetry of Trig Graphs

HL 3.12 Three Dimension Vectors

HL 3.13 Scalar Product of Vectors, Angles between two Vectors, Applications of Parallel and Perpendicular Vectors

HL 3.14 Vector Equations of Lines

HL 3.15 Coinciding, Parallel, Intersecting and Skew Lines

HL 3.16 Vector Scalar and Cross Products and their Applications

HL 3.17 Vector Equations of Planes and Normal Vectors

HL 3.18 Intersections of Lines and Planes and the Angles between them

HL 4.13 Use of Bayes Theorem for a Maximum of 3 Events

HL 4.14 Variance of a Discrete Random Variable, Continuous Random Variables and their Probability Density Functions,

Mean Variance and Standard Deviation of both Discrete and Continuous Random Variables, the effect of Linear Transformations of x

HL 5.12 Informal Understanding of Continuity and Differentiability of a Function at a Specific Point, Convergent and Divergent

Limits, Definition of Derivative, Higher Order Derivatives

HL 5.13 Evaluation of Limits using L’Hopitals Rules and the MacLaurin Series

HL 5.14 Implicit Differentiation, Related Rates of Change, Optimization Problems

HL 5.15 Derivatives of Tangent, Secant, Cosecant, Cotangent, ax, logax, arcsin, arccos, and arctan, Indefinite Integrals of the

aforementioned functions, use of Partial Fractions in the Integrand

HL 5.16 Integration by Substitution, by Parts, and repeated Integration by Parts

HL 5.17 Area of a Region enclosed by a curve and the y-axis, Volumes of Revolution about the x or y axes

HL 5.18 First Order Differential Equations, Numerical Solution of dy/dx = f(x,y) using Euler’s Method, Variable Separation

of Homogenous Differentiable Equations dy/dx = f(y/x), using the Substitution of y = vx Solution of y’ +p(x)y = Q(x) using the integrating factor

HL 5.19 Use of MacLaurin Series to obtain expansions for ex, Sine, Cosine, ln(1+x), (1+x)n, use of Simple Substitution Products

Integration and Differentiation to other Series, MacLaurin Series developed from Differentiable Equations

What makes your class unique?

The class works on proofs and deriving expressions in as many topics as possible. The students have a formula book, so we have no need to focus on memorizing formulas, we supplement with proofs and explorations. The students are always in a group setting and are prompted to answer writing prompts and question deeper. Students will often present their ideas to the class or each other and the teachers try to use student generated definitions as often as possible. 

The Analysis and Approaches course relies heavily on collaboration among peers with an inquiry based learning approach. 

How much homework is required in your class? 

Less than one hour per day every day. We often have time in class to start working together. 

There is daily homework, except after tests. Students are also required to work outside of class on their Internal Assessment 

What is your favorite thing about teaching IB? 

The students are so great about questioning the topics in a productive way. I love when someone goes "what if we did this instead?" and the whole class gets to explore that tangent thought without loss of instruction. 

I like teaching IB because the program plays to the strengths of individual students based on their values and academic passions. There is not one set pathway. I love to see the community of students lifting each other up during discussions and helping them to understand material they did not previously get. 

Video

• Ms. Wells

• Ms. Howitt

Course Syllabus

• Analysis 2

• Analysis 3

Which AP test does your IB Course align with? What percentage of the AP test is covered in your course. Please list topics students would need to self study if they choose to also challenge the AP exam.

This document sums it up. HL: https://drive.google.com/file/d/1pwGlEiD4iddZU4I4p0NZ3vwMS3s7Fkja/view?usp=sharing

SL: https://drive.google.com/file/d/1jfZ3UgF5cipfGoTltRL_HEPqH_bua_28/view?usp=sharing 

IB Analysis and Approaches SL covers about 70% of the Calculus AB material. IB Analysis and Approaches HL covers all of the AB topics but does not cover all of the BC topics. Students wanting to take the BC exam after HL will need to self study the following topics.

∙ Limits of Trig & Inverse Trig Functions

∙ Derivative of General Inverse Function

∙ L’Hopital’s Rule with All Indeterminate Forms

∙ Extreme Value Theorem

∙ Newton’s Method

∙ MVT/Rolle’s Theorem

∙ Rectangular and Trapezoidal Approximation

∙ Volumes by Cross Section

∙ Volumes by Revolution about Lines Other Than the x- and y-axis ∙ Arc Length

∙ Surface Area

∙ Trig Substitution

∙ Improper Integrals

∙ Tabular Method for Integration by Parts

∙ 10 Series Convergence/Divergence Tests

∙ Series Error with the Integral Test

∙ Series Error with Alternating Series

∙ Lagrange Error

∙ Absolute Convergence

∙ Interval/Radius of Convergence

∙ Use Known Series to Model Similar Functions

∙ Parametric Equations

∙ Calculus with Parametric Equations and Vectors

∙ Polar Coordinates

∙ Calculus with Polar Coordinates

∙ Arc Length and Area with Polar Coordinates