AP®Courses / Subjects
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AP Calculus AB
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
AP Calculus BC
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
Ap Statistics
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
AP Biology
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
AP Chemistry
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
Ap Physics 1
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
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