Syllabus and Course Information:

This course is closely aligned with the topics you can expect to find on the AP Calculus AB exam. You will explore the concepts, methods, and applications of differential and integral calculus. You’ll work to understand the theoretical basis and solve problems by applying your knowledge and skills. The lessons will help you improve your understanding of foundational calculus terms, formulas and concepts to help you strengthen your calculus skills. 

Skills You'll Learn

• Determining Expressions and values using mathematical procedures and rules

• Connecting representations

• Justifying reasoning and solutions

• Using correct notation, language, and mathematical conventions to communicate results or solutions

Units and Topics

Unit 1: Limits and Continuity

• Concept of a Limit

• Calculating Limits

• Continuity

• Asymptotes and IVT

Unit 2: Differentiation : Definition and Fundamental Properties

• Definition and Existence of Derivatives

• Calculating Derivatives

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions: 

• Advanced Derivative Rules

• Inverse Functions and Higher-Order Derivatives

Unit 4: Contextual Applications of Differentiation:

• Derivatives in context

• Related Rates

• Linearity and L'Hospital's Rule

Unit 5:  Analytical Applications of Differentiation

• MVT and EVT

• Function Behavior

• Optimization

Unit 6: Integration and Accumulation of Change

• Concept of integration

• Fundamental Theorem of Calculus

• Integration Techniques

Unit 7: Differential Equations

•  Analyzing Differential Equations

• Solving Differential Equations

• Modeling Differential Equations

Unit 8: Applications of Integration

• Definite Integrals in Context

• Area Between Curves

• Volumes

Syllabus and Course Information:

AP Calculus BC is a college level course equivalent to a full year of calculus at most universities. The course is based on the College Board’s Advanced Placement Calculus BC curriculum, whose purpose is “developing understanding of the concepts of calculus and providing experience with its methods and applications.” The course will emphasize that most calculus concepts and problems can be viewed or represented several ways: graphically, numerically, algebraically and verbally. Graphing calculators are tools for moving between these representations, so we will use them regularly. The primary purpose of this course is to prepare students for the AP Exam as well as future college math courses students will be required to work the problems from a graphical, numerical or analytical point of view and present their solutions both verbally and in writing. Students are expected to perform college level work. 

Skills You'll Learn

• Determining expressions and values using  mathematical procedures and rules

• Connecting representations

• Justifying reasoning and solutions

• Using correct notation, language, and mathematical conventions to communicate results or solutions

Units and Topics

Unit 1: Limits and Continuity

• Concept of a Limit

• Calculating Limits

• Continuity

• Asymptotes and IVT

Unit 2: Differentiation: Definition and Fundamental Properties

• Definition and Existence of Derivatives

• Calculating Derivates

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

• Advanced Derivative Rules

• Inverse Functions and Higher Order Derivatives

Unit 4: Contextual Applications of Differentiation

• Derivatives in Context

• Related Rates

• Linearity and L'Hospital's Rule

Unit 5: Analytical Applications of Differentiation 

• MVT and EVT

• Function Behavior

• Optimization

Unit 6: Integration and Accumulation of Change

• Concept of Integration 

• Fundamental Theorem of Calculus

• Integration Techniques

Unit 7: Differential Equations

• Analyzing Differential Equations

• Solving Differential Equations

• Modeling Differential Equations

Unit 8: Applications of Integration

• Definite Integrals in Context

• Area Between Curves

• Volume and Arc Length

Unit 9: Parametric Equations, Polar Coordinates, a nd Vector-Valued Functions

• Parametric Equations

• Vector-Valued Functions

• Polar Coordinates

Unit 10: Infinite Sequences and Series

• Infinite Series 

• Tests for Convergence and Divergence

• Sum of Series

• Power Series

Units and Topics

Unit 1: Exploring One-Variable Data

• The Language of Variation: Variables

• Representing a Categorical Variable with Tables

• Representing a Categorical Variable with Graphs

• Representing a Quantitative Variable with Graphs

• Describing the Distribution of a Quantitative Variable

• Summary Statistics for a Quantitative Variable

• Graphical Representations of Summary Statistics

• Comparing Distributions of a Quantitative Variable

• The Normal Distribution

Unit 2: Exploring Two-Variable Data

• Representing Two Categorical Variables 

• Statistics for Two Categorical Variables

• Represent Relationships Between Quantitative Variables

• Correlation

• Linear Regression Models

• Residuals

• Least Squares Regression

• Analyzing Departures from Linearity

Unit 3: Collecting Data

• Introduction to Planning a Study

• Random Sampling and Data Collection

• Potential Problems with Sampling

• Introduction to Experimental Design

• Selecting an Experimental Design

• Inference and Experiments

Unit 4: Probability, Random Variables, and Probability Distributions

• Estimating Probabilities Using Simulations

• Introduction to Probability

• Mutually Exclusive Events

• Conditional Probability

• Independent Events and Unions of Events

• Random Variable and Probability Distributions

• Mean and Standard Deviation of Random Variables

• Combining Random Variables

• Introduction to the Binomial Distribution

• Parameters for a Binomial Distribution

• The Geometric Distribution

Unit 5: Sampling Distributions

• The Normal Distribution, Revisited

• The Central Limit Theorem

• Biased and unbiased Point Estimates

• Sampling Distributions for Sample Proportions

• Sampling Distributions for Sample Proportions

• Sampling Distributions for Sample Means

• Sampling Distributions for Differences in Sample Means

Unit 6: Inference for Categorical Data

• Constructing a Confidence Interval for a Population Proportion

• Justifying a Claim Based on a Confidence Interval for a Population Proportion

• Setting Up a Test for a Population Proportion

• Interpreting p-Values

• Concluding a Test for a Population Proportion

• Potential Errors When Performing Tests

• Confidence Intervals for the Difference of Two Proportions

• Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions

• Setting Up a Test for the Difference of Two Population Proportions

• Carrying Out a Test for the Difference of Two Population Proportions

Unit 7: Inference for Quantitative Data: Means

Unit 8: Inference for Categorical Data: Chi-Square

Unit 9: Inference for Quantitative Data: Slopes

Units and Topics

Unit 1: Chemistry of Life

• Structure of Water and Hydrogen Bonding

• Elements of Life

• Introduction to Biological Macromolecules and their properties

• Structure and Function of Biological Macromolecules

• Nucleic Acids

Unit 2: Cell Structure and Function

• Subcellular Components and Their Functions

• Cell Size

• Plasma Membranes

• Membrane Permeability

• Membrane Transport

• Facilitated Diffusion

• Tonicity and Osmoregulation

• Mechanisms of Transport

• Cell Compartmentalization

• Origins of Cell Compartmentalization

Unit 3: Cellular Energetics

• Enzyme Structure

• Enzyme Catalysis

• Environmental Impacts on Enzyme Function

• Cellular Energy

• Photosynthesis

• Cellular Respiration

• Fitness

Unit 4: Cell Communication and the Cell Cycle

• Cell Communication

• Introduction to Signal Transduction

• Signal Transduction

• Changes in Signal Transduction Pathways

• Feedback

• The Cell Cycle

• Regulation of the Cell Cycle

Unit 5: Heredity

• Meiosis

• Meiosis and Genetic Diversity

• Mendelian Genetics

• Non-Mendelian Genetics

• Environmental Effects on Phenotype

• Chromosomal Inheritance

Unit 6: Gene Expression and Regulation

• DNA and RNA Structure

• Replication, Transcription, and RNA Processing

• Translation

• Regulation of Gene Expression

• Gene Expression and Cell Specialization 

• Mutations

• Biotechnology

Unit 7: Natural Selection

• Introduction to Natural Selection

• Natural Selection

• Artificial Selection

• Population Genetics

• Hardy-Weinberg Equilibrium

• Evidence of Evolution, Common Ancestry, and Continuing Evolution

• Phylogeny

• Speciation

• Extinction

• Variations in Populations

• Origin of Life on Earth

Unit 8: Ecology

• Responses to the Environment

• Energy Flow Through Ecosystems

• Population Ecology

• Effect of Density of Populations

• Community Ecology

• Biodiversity

• Disruptions to Ecosystems

Syllabus and Course Information

You will learn about the fundamental concepts of chemistry including structure and states of matter, intermolecular forces, and reactions. In this course you will explore states and properties of matter, atomic structure and types of chemical bonds. this course helps you refresh your understanding of basic chemistry terms, and you'll get practice analyzing different types of chemical reactions and equations.

Units, Topics, and Sub-Topics

Unit 1: Atomic Structure and Properties

Moles and Molar Mass:

• The Mole Concept and Avogadro's Number

• Atomic Mass Unit

Mass Spectroscopy of Elements:

• Identifying Elements by Mass Spectrometry

• Average Atomic Mass

Elemental Composition of Pure Substances:

• Pure Samples

• Law of Definite Proportions

• Empirical Formulas

Composition of Mixtures:

• Mixtures

• Mass Percent

Atomic Structure and Electron Configuration:

• Atomic Structure

• Coulomb's Law

• Electron Configuration

• Ionization Energy

• Photoelectron Spectroscopy (PES)

Periodicity and the Periodic Table:

• Periodic Table Organization

• Periodic Trends

• Valence Electrons and Ionic Compounds

Unit 2: Molecular and Ionic Compound Structure and Properties

Types of Chemical Bonds:

• Electronegativity

• Nonpolar Covalent Bonds

• Polar Covalent Bonds

• Covalent and Ionic Bonds

• Metallic Bonds

Intermolecular Force and Potential Energy

• Graphs of Potential Energy Versus Internuclear Distance

• Properties of Covalent Bonds

• Properties of Ionic Bonds

Structure of Ionic and Metallic Solids

• Structure of Ionic Solids

• Structure of Metals

• Structure of Alloys

Representing Molecules using Lewis Structures

• Lewis Diagrams

• Resonance Structures

• Formal Charge

• Limitations of the Lewis Structure Model

VSEPR and Bond Hybridization

• Predicting Molecular Properties Using VSEPR Theory and Lewis Structures

• Orbital Hybridization

• Atomic Orbitals and Bond Formation

Unit 3: Intermolecular Forces and Properties

Intermolecular Forces

• London Dispersion Forces

• Dipole-Dipole Interactions

• Ion-Dipole Interactions

• Hydrogen Bonding

• Intermolecular Forces Impacting Biological Systems

Properties of Solids

• Intermolecular Forces Impacting Physical Properties

• Properties of Ionic Solids

• Properties of Covalent Network Solids

• Physical Properties of Molecular Solids

• Properties of Metallic Solids

• Properties of Biomolecules and Polymers

Solids, Liquids, and Gases

• Particulate Model of Solids

• Particulate Model of Liquids

• Particulate Model of Gases

Gas Laws

• Ideal Gas Law

• Combined Gas Law

• Dalton's Law of Partial Pressures

• Graphical Representations of Gas Laws

• Kinetic Molecular Theory

• Deviations from Ideal Gas Law

Properties of Solutions

• Solutions as Homogeneous Mixtures 

• Molarity

• Representations of Solutions

Separations of Solutions and Mixtures

• Chromatography

• Distillation

Solubility

• Solute-Solvent Interactions

Interactions Between Light and Matter

• Spectroscopy and the Electromagnetic Spectrum

• Photon Absorption/Emission and Molecular Motion

• Photelectric Effect

• Beer-Lambert Law

Unit 4: Chemical Reactions

Introduction to Reactions

• Physical and Chemical Changes

• Balanced Reactions

• Net Ionic Equations

• Representations of Reactions

Stoichiometry

• Conservation of Mass

• Stoichiometric Calculations

• Stoichiometric Calculations Using Gas Laws

Introduction to Titration

• Acid-Base Titrations

• Redox Titrations

Types of Chemical Reactions

• Oxidation-Reduction (Redox) Reactions

• Precipitation Reactions

• Introduction to Acid-Base Reactions

Unit 5: Kinetics

Reaction Rates

• Reaction Kinetics

• Reaction Conditions and Rate

• Experimental Determination of Reaction Rate

Introduction to Rate Laws

• Rate Law

• Rate Constant

Concentration Changes over Time

• Reaction Order

• Half-life

Collision Model

• Elementary Reactions

• Molecular Collisions in Reactions

• Maxwell-Boltzmann Distribution

Reaction Mechanisms and Energy Profiles

• Energy Diagram

• Arrhenius Equation

• Introduction to Reaction Mechanisms

• Reaction Intermediates

• Reaction Mechanism and Rate Law

• Steady-State Approximation

• Multistep Reaction Energy Profiles

Catalysis

• Activation Energy and Catalysis

• Catalyst Regeneration

• Catalytic Mechanisms

Unit 6: Thermodynamics

Endothermic and Exothermic Processes

• Enthalpy as Internal Energy

• Enthalpy of Dissolution

• Energy Diagrams

Heat Transfer and Thermal Equilibrium

• Heat and Temperature

• Heat Transfer

Heat Capacity and Calorimetry

• Calorimetry

• Heat Capacity

Energy of Chemical and Physical Processes

• Energy of Phase Changes

• Introduction to Enthalpy of Reactions

Energy of Chemical Bonds

• Bond Enthalpy

• Enthalpy of Formation

Hess's Law

• Applying Hess's Law

Unit 7: Equilibrium 

Introduction to Equilibrium

• Equilibrium Characteristics

• Dynamic Equilibrium

• Direction of Reversible Reactions

Equilibrium Constant

• Reaction Quotient and Equilibrium Constant

• Calculation the Equilibrium Constant

• Magnitude of the Equilibrium Constant

• Properties of the Equilibrium Constant

Equilibrium Position

• Calculation Equilibrium Concentrations

• Representations of Equilibrium

Le Chatelier's Principle

• Introduction to Le Chatelier's Principle

• Reaction Quotient and Le Chatelier's Principle

Solubility Equilibria

• Introduction to Solubility Equilibria

• Common-Ion Effect

• pH and Solubility

• Free Energy of Dissolution

Unit 8: Acids and Bases

Introduction to Acids and Bases

• Autoionization, pH, and pOH

pH and pOH of Strong Acids and Bases

• Strong Acids

• Strong Bases

Weak Acid and Base Equilibria

• Weak Acids

• Weak Bases

• Ionization of Weak Acids and Bases

Acid-Base Reactions and Buffers

• Reactions Between Strong Acids and Strong Bases

• Reactions Between Weak Acids and Strong Bases

• Reactions Between weak Bases and Strong Acids

• Reactions Between Weak Bases and Weak Acids

Acid-Base Titrations

• Acid-Base Titration Curves

• Acid-Base Titration Equivalence Point

• Titration Experiments

• Titration Curves of Polyprotic Acids

Structural Influences on the Strength of Acids and Bases

• Molecular Structure of Acids and Bases

• pH and pKa

Buffers

• Properties of Buffers 

• Henderson-Hasselbalch Equation

• Buffer Capacity

Unit 9: Applications of Thermodynamics

Entropy

• Introduction to Entropy

• Absolute Entropy and Entropy Change

Gibbs Free Energy and Thermodynamic Favorability

• Standard Gibbs Free Energy and Favorability

• Relationship Between Gibbs Free Energy, Enthalpy, and Entropy

Thermodynamic and Kinetic Control

• Kinetic Control of Favorable Reactions

Free Energy and Equilibrium

• Equilibrium Thermodynamics

Driving Unfavorable Reactions

• External Energy Sources

• Coupled Reactions

Galvanic (Voltaic) and Electrolytic Cells

• Components and Characteristics of Electrochemical Cells

• Thermodynamic Favorability of Electrochemical Cells

• Oxidation and Reduction in Electrochemical Cells

Cell Potential and Free Energy

• Assessing Standard Cell Potential

• Free Energy of Standard Cells

Cell Potential Under Nonstandard Conditions

• Characteristics of Nonstandard Cells

• Nernst Equation

Electrolysis and Faraday's Law

• Application of Faraday's Law

About the Course

This course is broken down into bite-sized lessons covering all the topics you'll find on the exam in a thorough yet easy-to-follow manner.  You will learn about the foundational principles of physics as you explore Newtonian mechanics; work, energy, and power; mechanical waves and sound; and introductory, simple circuits. You'll do hands-on laboratory work to investigate phenomena.

Note: Save your lab notebooks and reports; colleges may ask to see them before granting you credit.

Skills You'll Learn

• Interpreting and describing representations and models

• Using mathematics to solve science problems

• Formulating scientific question or hypothesis

• Designing an experiment to answer a scientific question or to test a hypothesis

• Analyzing dat and evaluating evidence

• Working with scientific explanations and theories

• Making connections

Units, Topics, and Sub-Topics

Unit 1: Kinematics

Position, Velocity, and Acceleration: 

• • Kinematic variables and vector quantities

  • Reference frames and motion

  • Linear Kinematic Equations

  • Rotational Kinematic Equations

Representations of Motion:

• Center of Mass and Motion Variables

• Relationship between Force and Acceleration

• Kinematics and Center of Mass

Unit 2: Dynamics

Systems:

• Objects, Elementary Particles, and Systems

The Gravitational Field:

• • Gravity as Weight

  • Gravitational Fields and the Gravitational Force

Contact Forces:

• Applications of Contact Forces

Newton's First Law:

• Inertial Mass and Conservation of Inertia

Newton's Third Law and Free-Body Diagrams:

• Newton's 1st Law Applied to Free-Body Diagrams

• Forces as Interactions

• Static Equilibrium

• Net Forces in Free-Body Diagrams

• Motion Using Newton's Third Law

Newton's Second Law:

• Applications of Newton's 2nd Law

• Implicit Free-Body Diagrams

• Explicit Free-Body Diagrams

Unit 3: Circular Motion and Gravitation

Vector Fields:

• • Vector Fields and Vector Transformations

Fundamental Forces:

• Gravitational and Electric Forces

• Magnitude of Gravity and Acceleration of Gravity

Gravitational Field/Acceleration Due to Gravity on Different Planets:

• Position and Gravity

• Concept of Free-Fall

• Relationship between Gravitational Field and Radius

• Concept of Spherical Symmetry

Inertial Vs. Gravitational Mass:

• Concept of Inertial and Gravitational Mass

Centripetal Acceleration and Centripetal Force:

• Force Magnitude and Gravity

• Force Directionality and Gravity

Free-Body Diagrams for Objects in Uniform Circular Motion:

• Implicit Free-Body Diagrams and Gravity

• Explicit Free-Body Diagrams and Gravity

Applications of Circular Motion and Gravitation:

• One-Dimensional Gravitational Kinematics

• Two-Dimensional Gravitational Kinematics

• Angular Quantities and Circular Motion

• Acceleration and Circular Motion

• Period and Velocity in Circular Motion

• Newton's 1st Law and Gravity

• Newton's 2nd Law and Gravity

• Newton's 3rd Law and Gravity

Unit 4: Energy

Open and Closed Systems: Energy:

• Open Systems

• Closed Systems

Work and Mechanical Energy:

• Work Due to Parallel and Perpendicular Forces

• Work and Kinetic Energy

• Translational and Rotational Kinetic Energy

• Energy Dissipation

• Transfers of Mechanical Energy

• Magnitude of Work

Conservation of Energy, the Work-Energy Principle and Power:

• Internal Energy

• Conservative Forces

• Mechanical Potential Energy

• Electrical Potential Energy

• Conservation of Energy

• Power

Unit 5: Momentum

Momentum and Impulse:

• Momentum as a vector

• Concept of Impulse

Representations of Changes in Momentum:

• Linear Momentum

• Momentum and Impulse

Open and Closed Systems: Momentum:

• Conservation of Momentum and Systems

Conservation of Linear Momentum:

• Elastic Collisions

• Inelastic Collisions

• Momentum and Center of Mass

• Velocity and Center of Mass

• Balance and Center of Mass Location

Unit 6: Simple Harmonic Motion

Period of Simple Harmonic Oscillators:

• Period of a Spring

• Period of a Pendulum

• Motion Variables and Simple Harmonic Motion

Energy of a Simple Harmonic Oscillator:

• Potential Energy of a Pendulum

• Potential Energy of a Spring

• Conservation of Energy and Simple Harmonic Motion

Unit 7: Torque and Rotational Motion

Rotational Kinematics:

• Angular Variables and Rotational Motion

• Period and Velocity in Rotational Motion

Torque and Angular Acceleration:

• Lever Arms

• Torque Magnitude

• Rotational Equilibrium

• Conservation between Angular and Linear Variables

• Angular Acceleration

• Concept of Angular Momentum

• Angular Momentum and Torque

• Changes in Angular Momentum

Angular Momentum and Torque:

• Sign Convention of Angular Momentum

• Angular Momentum and Systems

Conservation of Angular Momentum:

• Net Torque and Angular Momentum

• Mass Distribution and Angular Momentum