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
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
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.
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
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.
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