- Limits and Continuity
- Differentiation: Definition and Fundamental Properties
- Differentiation: Composite, Implicit, and Inverse Functions
- Contextual Applications of Differentiation
- Analytical Applications of Differentiation
- Integration and Accumulation of Change
- Differential Equations
- Applications of Integration
- Parametric Equations, Polar Coordinates, and Vector-Valued Functions (
**BC Only**) - Infinite Sequences and Series (
**BC Only**)

## Introduction

## Advanced Placement (AP)

## Tutoring Services

## Course Overview

College Board’s Advanced Placement (AP) program provides students the opportunity to pursue college-level coursework in high school. This not only gives students a chance to push themselves academically, but it also helps them to better prepare for college readiness and success. Also, it provides students the potential to earn college credit, advanced placement, or both while still in high school. In the month of May, students take a comprehensive exam that assesses their critical thinking, argument-based writing skills, and the ability to analyze multiple perspectives—all vital skills for post-secondary academic success. To learn more about the Advanced Placement program, please visit https://apstudents.collegeboard.org/.

## Tutoring Program

###### AP Calculus

Our tutors are educated and trained to teach and reinforce these standards in order to push students to achieve the highest goals of mathematical learning and understanding. *These standards are based on the Massachusetts Department of Education; tutoring lessons can be altered to fit any differing standards or learning points as necessary*

For those students who seek to pursue an even higher level of mathematical learning, Advanced Placement courses are the final step before the college level. The AP courses offered for math are as follows:

AP Calculus AB

AP Calculus BC

AP Statistics

These courses come with strict guidelines set by The College Board and students will take a standardized AP Examination in May of the school year. These are rigorous assessments designed to prepare students for the college-level experience from content to coursework to exams. Depending on their score, students may earn college credit for the AP Exam.

There are two versions of the AP Calculus course and exam: AB and BC. The major difference between the two courses is that the BC course and exam goes into more depth than the AB course and exam; everything covered in AP Calculus AB is covered in BC, plus a few more topics. The material covered is as follows:

Our tutoring will cover these topics in depth as well as test-taking strategies for the AP Exams specifically. Students will be expected to have a strong background in high school math up through Pre-Calculus, as it is a requirement to take either AP Calculus course. There are a number of skills and goals for each topic as outlined by The College Board. A breakdown of some of these key skills that we will focus on in tutoring is as follows:

- Limits and Continuity – Exam Weighting 10-12% AB, 4-7% BC
- Define and estimate limit values using notation, from graphs, and from tables
- Determine limits using algebraic properties and manipulation
- Selecting appropriate procedures for determining limits, and using Squeeze Theorem to determine limits
- Exploring types of discontinuities and removing them, defining continuity at a point, and converming continuity over an interval
- Connecting infinite limits and vertical/horizontal asymptotes
- Working with the Intermediate Value Theorem

- Differentiation: Definition and Fundamental Properties – Exam Weighting 10-12% AB, 4-7% BC
- Defining average and instantaneous rates of change at a point
- Defining and estimating derivatives
- Connecting differentiability and continuity
- Applying derivative rules (power, constant, sum, difference, constant multiple, product, quotient)
- Derivatives of trigonometric functions, exponential functions, and logarithmic functions

- Differentiation: Composite, Implicit, and Inverse Functions – Exam Weighting 9-13% AB, 4-7% BC
- Using differentiation techniques (chain rule, implicit differentiation)
- Differentiating inverse functions and trigonometric functions
- Selecting procedures for calculating derivatives
- Calculating higher-order derivatives

- Contextual Applications of Differentiation – Exam Weighting 10-15% AB, 6-9% BC
- Interpreting the meaning of the derivative in context
- Connecting position, velocity, and acceleration
- Solving related rates problems
- Approximating values of a function using local linearity and linearization
- Using L’Hopital’s Rule for determining limits of indeterminate forms

- Analytical Applications of Differentiation – Exam Weighting 15-18% AB, 8-11% B
- Using the Mean Value Theorem and Extreme Value Theorem
- Determining intervals on which a function is increasing or decreasing
- Using the First Derivative, Second Derivative, and Candidates Tests to determine relative and absolute extrema
- Determining concavity of functions over their domains
- Sketching graphs of functions and their derivatives
- Connecting a function and its first and second derivatives
- Solving Optimization problems
- Exploring behaviors of implicit relations

- Integration and Accumulation of Change – Exam Weighting 17-20% AB, 17-20% B
- Exploring accumulations of change
- Approximating areas with Riemann Sums
- The Fundamental Theorem of Calculus and Accumulation Functions
- Applying Properties of Definite Integrals
- The fundamental Theorem of Calculus and Definite Integrals
- Finding Antiderivatives and Indefinite Integrals
- Integrating using substitution, long division, and completing the square
- Integrating using integration by parts, linear partial fractions, and evaluating improper integrals (
**BC Only**)

- Differential Equations – Exam Weighting 6-12% AB, 6-9% BC
- Modeling situations with and verifying solutions for differential equations
- Sketching and reasoning using Slope Fields
- Finding general and particular solutions using separation of variables
- Exponential models with differential equations
- Approximating solutions using Euler’s Method (
**BC Only**) - Logistic Models with differential equations (
**BC Only**)

- Applications of Integration – Exam Weighting 10-15% AB, 6-9% BC
- Finding average value of a function on an interval
- Connecting position, velocity, and acceleration using integrals
- Using accumulation functions and definite integrals in applied contexts
- Finding the area between curves expressed as functions of x and y
- Finding the area between curves that intersect at more than two points
- Volumes with cross sections (squares, rectangles, triangles, semicircles), disc method, and washer method
- The arc length of a smooth, planar curve and distance traveled (
**BC Only**)

- Parametric Equations, Polar Coordinates, and Vector-Valued Functions – Exam Weighting 11-12%
**BC Only**- Defining and differentiating parametric equations
- Finding arc lengths of curves given by parametric equations
- Defining and differentiating vector-valued functions
- Integrating vector-valued functions
- Solving motion problems using parametric and vector-valued functions
- Defining polar coordinates and differentiating in polar form
- Finding the area of a polar region bounded by a single and two polar curves

- Infinite Sequences and Series – Exam Weighting 17-18%
**BC Only**- Defining convergent and divergent infinite series
- Working with geometric series
- Tests for convergence (nth term test, integral test, comparison tests, alternating series test, ratio test)
- Harmonic Series and p-Series
- Determining absolute or conditional convergence
- Alternating series error bound
- Finding Taylor Polynomial Approximations of functions
- Lagrange Error bound
- Radius and interval of convergence of power series
- Finding Taylor or Maclaurin Series for a function
- Representing functions as power series

These topics and skill points will be the main focus of our tutoring to help students excel in learning calculus and scoring their best on the AP Exam.

###### AP Statistics

Statistics is a branch of mathematics that steers away from the more calculation-heavy algebra and calculus studies, and focuses more on analytical thinking and interpreting data. While it may not be as intensive as some other branches of mathematics, statistics offers its own set of challenges in understanding, analyzing, and interpreting patterns in data. The breakdown of topics for AP Statistics is as follows:

- Exploring Data: Describing Patterns and Departures from Patterns (20% – 30%)
- Constructing and Interpreting Graphical Displays of Distributions of Univariate Data
- Summarizing Distributions of Univariate Data
- Comparing Distributions of Univariate Data
- Exploring Bivariate Data
- Exploring Categorical Data

- Sampling and Experimentation: Planning and Conducting a Study (10% – 15%)
- Overview of Methods of Data Collection
- Planning and Conducting Surveys
- Planning and Conducting Experiments
- Exploring Bivariate Data
- Generalizability of Results and Types of Conclusions that can be Drawn from Observational Studies, Experiments, and Surveys

- Anticipating Patterns: Exploring Random Phenomena Using Probability and Simulation (20% – 30%)
- Probability
- Combining Independent Random Variables
- The Normal Distribution
- Exploring Bivariate Data
- Sampling Distributions

- Statistical Inference: Estimating Population Parameters and Testing Hypotheses (30% – 40%)
- Estimation
- Tests of Significance

Within these topics, our tutoring will focus on some key concepts to reinforce the learning and mastery of statistics, and to help students achieve their highest scores on the AP exam.

- Constructing and Interpreting Graphical Displays of Distributions of Univariate Data
- Center and spread
- Clusters and gaps
- Outliers and other unusual features
- Shape

- Summarizing Distributions of Univariate Data
- Measuring center (median, mean)
- Measuring spread (range, interquartile range, standard deviation)
- Measuring position (quartiles, percentiles, standardized scores [z-scores])
- Using box plots
- The effect of changing units on summary measures

- Comparing Distributions of Univariate Data
- Comparing center and spread within group and between group variation
- Comparing clusters and gaps
- Comparing outliers and other unusual features
- Comparing shapes

- Exploring Bivariate Data
- Analyzing patterns in scatterplots
- Correlation and linearity
- Least-squares regression line
- Residual plots, outliers, and influential points
- Transformations to achieve linearity: logarithmic and power transformations

- Exploring Categorical Data
- Frequency tables and bar charts
- Marginal and joint frequencies for two-way tables
- Conditional relative frequencies and association
- Comparing distributions using bar charts

- Overview of Methods of Data Collection
- Census
- Sample survey
- Experiment
- Observational study

- Planning and Conducting Surveys
- Characteristics of a well-designed and well-conducted survey
- Populations, samples, and random selection
- Sources of bias in sampling and surveys
- Sampling methods (simple random sampling, stratified random sampling, cluster sampling)

- Planning and Conducting Experiments
- Characteristics of a well-designed and well-conducted experiment
- Treatments, control groups, experimental units, random assignments, and replication
- Sources of bias and confounding, including placebo effect and blinding
- Completely randomized design
- Randomized block design, including matched pairs design

- Probability
- Interpreting probability, including long-run relative frequency interpretation
- “Law of Large Numbers”
- Addition and multiplication rules, conditional probability, and independence
- Discrete random variables and their probability distributions, including binomial and geometric
- Simulation of random behavior and probability distributions
- Mean (expected value) and standard deviation of a random variable and linear transformation of a random variable

- Combining Independent Random Variables
- Independence vs dependence
- Mean and standard deviation for sums and differences of independent random variables

- The Normal Distribution
- Properties of the normal distribution
- Using tables of the normal distribution
- The normal distribution as a model for measurements

- Sampling Distributions
- Sampling distribution of a sample proportion and a sample mean
- Central Limit Theorem
- Sampling distribution of a difference between two independent sample proportions and sample means
- Simulation of sampling distributions
- t-distribution
- Chi-square distribution

- Estimation
- Estimating population parameters and margins of error
- Properties of point estimators, including unbiasedness and variability
- Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals
- Large sample confidence interval for a proportion and a difference between two proportions
- Confidence interval for a mean, a difference between two means, and the slopes of a least-squares regression line

- Tests of Significance
- Logic of significance testing, null and alternative hypotheses; p-values;one and two-sided tests; concepts of Type I and Type II errors; concept of power
- Large sample test for a proportion and a difference between two proportions
- Test for a mean and for a difference between two means
- Chi-square test for goodness of fit, homogeneity of proportions, and independence
- Test for the slope of a least-squares regression line

###### AP Comparative Government and Politics

AP Comparative Government and Politics is designed to help students learn and understand the skills needed for the AP Comparative Government and Politics exam in May. In this class, students use critical thinking and writing skills to understand important issues of different countries, how those nations’ governments function, and how those countries solve problems. Students will also focus on how governments address issues like elections, economic development, and cultural ties. AP Comparative Government and Politics will focus on reading and writing to complete the AP Comparative Government and Politics exam in May. Students will learn how to interpret tables and graphs, read legal and government documents, analyze information, and critically explore their findings through writing. Tutors will help students use information and knowledge of different political values around the world to make comparisons and apply knowledge of these different political systems globally.

###### AP European History

AP European History is a rigorous course that examines the history and culture of Europe. Students will focus on events from the Renaissance period to the present. Students will learn about how economics, politics, and social changes shaped Europe. Students will also learn how events and decisions made locally have a broader effect outside the region. We work with students to read a variety of historical documents to look for causes, context, and evaluate points of view of a time period. Students will analyze the results of the events by using different historical texts. In addition to reading historical texts, students will evaluate different perspectives by historians. Students will also be exposed to works of art and music to determine the cultural impact. Our tutors will also work on a variety of skills like writing and interpreting information which will help prepare students for the AP European History exam in May.

###### AP Human Geography

AP Human Geography is designed to help students understand how we live in the world. AP Human Geography also helps students to think critically about the patterns and processes humans have used to create their environment. Tutors help students understand how humans live and use the land and resources of the Earth and better understand how humans have shaped and settled in different regions. They will learn how economies and political systems develop. Tutors will help students make comparisons among different cultural phenomena like language and religion. AP Human Geography also develops writing and analysis skills. Our tutors will teach students how to use maps and data to help analyze how we use the Earth and its resources. AP Human Geography also uses historical events to help explain current issues in geography. Tutors will work with students on the content and skills needed to be successful on the AP Human Geography exam in May.

###### AP Macroeconomics

AP Macroeconomics looks at the entire economic system to analyze how household, business, and government decisions work together. We will look at topics like personal choices along with scarcity and business cycles. Tutors will work with students to apply economic concepts to everyday situations. Tutors also work with students to look at information on tables and graphs to interpret economic change. Students will learn to think critically about how economic information can be used by the consumers and make models representing economic data. Tutors will help apply information to prepare students for the AP Macroeconomics exam in May.

###### AP Microeconomics

Students taking AP Microeconomics will learn how individuals make economic decisions. We will focus on understanding basic economic concepts like supply and demand and how those concepts are used to make complex decisions. Our tutors will work with students to apply these concepts to different economic situations. Tutors also work with students to analyze graphs, charts, and data to understand better and explain these economic concepts. Tutors will help students to apply the content and skills necessary to be ready for the AP Microeconomics exam in May.

###### AP Psychology

In AP Psychology, students will gain an in-depth understanding of behaviors and mental processes of humans. AP Psychology is an in-depth look at how people and groups interact and the results of our action. Students use case studies and research to gain a deeper understanding of human psychology. Our tutors will help prepare students to complete the AP Psychology exam in May by working on writing and analysis skills. We will engage students in discussions to help students gain knowledge of human development, mental processes, and better understand behavior. Tutors will also help students apply knowledge through problem-solving scenarios.

###### AP United States Government and Politics

AP United States Government and Politics takes an advance look at the American government system. Students learn how the US government functions. Students will examine the different branches of government. Tutors will also work with students to understand concepts like political approaches and procedures. Our tutors use case studies, historical information, and US Supreme Court cases to better understand how local, state, and national governments work together. Tutors work with students to analyze documents, understand necessary background information, and work on writing skills. Students will also work on the essential skills and concepts to prepare for the AP United States Government and Politics exam in May.

###### AP United States History

Students working with our tutors in AP US History follow the course and development of the United States by looking at its founding through the present day. Teachers use a variety of historical documents to work on analytical and critical thinking skills. Students will work with tutors to better understand the decisions and choices made that influenced the development of the United States nationally and globally. Students will also use documents like political cartoons and photographs to understand the development of the United States. Tutors will work with students on analytical and argumentation skills to help them support their opinion with credible information. Students also look at a variety of historical viewpoints and sources. Our tutors work with students on writing skills and concepts necessary to complete the AP US History exam in May.

###### AP World History: Modern

In AP World History, students will compare and contrast the social, political, and economic development of the world starting in the 1200s CE to the present. Students will use history skills like document analysis and critical reading to look for causes, context, and evaluate viewpoints. We will help students better understand historical documents and understand the historical events that support those documents. We also work with other interpretations of historical events to better understand the subject and think like a historian. Tutors will work with students on analytical and argumentation skills to help them support their perspective with credible information. Tutors will work with students on skills and concepts necessary to complete the AP World History exam in May.

###### AP Physics

Our tutoring will help reinforce and instill the learning and mastery of physics and the understanding of these concepts. *These standards are based on the Massachusetts Department of Education; tutoring lessons can be altered to fit any differing standards or learning points as necessary*

For those students who seek to pursue an even higher level of physics education, Advanced Placement courses are the final step before the college level. There are four AP courses offered for physics:

**AP Physics 1**

**AP Physics 2**

**AP Physics C: Mechanics**

**AP Physics C: Electricity and Magnetism**

These courses come with strict guidelines set by The College Board and students will take a standardized AP Examination in May of the school year. These are rigorous assessments designed to prepare students for the college-level experience from content to coursework to exams. Depending on their score, students may earn college credit for the AP Exam.

Though there are four distinct sections of AP Physics, there are two major differences between them: AP Physics 1 and 2 are **algebra based** while the two AP Physics C courses are **calculus based**. All four courses are designed to be comparable to the college level, so there is an expectation of rigor and math knowledge associated with all of them. As far as the content of each course, AP Physics 1 and AP Physics C: Mechanics cover roughly the same material, while AP Physics 2 and AP Physics C: Electricity and Magnetism cover roughly the same material, the difference being the use of calculus in the C courses.

The following information is a breakdown of the standards of learning as set by The College Board, as well as an outline of some of the concepts and topics that will be focused on in our tutoring:

###### AP Physics 1

- Kinematics – Exam weighting 10 – 16%
- Position, velocity, and acceleration
- Describe the motion of an object using quantities such as position, displacement, distance, velocity, speed, and acceleration
- Distinguish between vector and scalar quantities
- Understand the three fundamental interactions of forces in nature: gravitational force, electroweak force, and strong force
- Distinguish between linear and circular motion and the appropriate equations of motion for each situation

- Representations of motion
- Describe the linear motion of a system by the displacement, velocity, and acceleration of its center of mass
- Make predictions about the motion of a system based on changes in its acceleration, velocity, and position
- Create mathematical models and analyze graphical relationships for acceleration, velocity, and position of the center of mass of a system

- Position, velocity, and acceleration
- Dynamics – Exam weighting 12 – 18%
- Systems
- Understand that a system is an object or a collection of objects
- Model the properties of a system based on its substructure
- Relate these properties to changes in the system properties over time as variables are changed

- The Gravitational Field
- Apply F = mg to calculate the gravitational force on an object with mass m in a gravitational field of strength g

- Contact Forces
- Make claims about various contact forces between objects based on the causes of these forces
- Explain contact forces (tension, friction, normal, buoyant, spring)

- Newton’s First Law
- Design an experiment for collecting data between the net force exerted on an object, its mass, and its acceleration
- Design a plan for collecting data to measure gravitational and inertial mass and to distinguish between them

- Newton’s Third Law and Free-Body Diagrams
- Represent forces in diagrams or mathematically using appropriately labeled vectors
- Analyze a scenario and make claims about the forces exerted on an object by other objects for different types and components of forces
- Use Newton’s Third Law to make claims and predictions about action-reaction pairs of forces
- Analyze situations involving interactions among several objects by using free-body diagrams

- Newton’s Second Law
- Predict the motion of an object subject to forces using Newton’s Second Law
- Design a plan to collect and analyze data for motion from force measurement
- Re-express a free-body diagram into a mathematical representation and solve for the acceleration of the object
- Create and use free-body diagrams to analyze physical situations and solve problems with motion

- Applications of Newton’s Second Law
- Use representations of the center of mass of an isolated two-object system to analyze the motion of the system
- Evaluate whether all the forces on a system or all the parts of a system have been identified
- Apply Newton’s Second Law to systems to calculate the change in the velocity when an external force is exerted on the system
- Use visual or mathematical representations of the forces between objects in a system to predict whether there will be a change in the velocity of the system

- Systems
- Circular Motion and Gravitation – Exam weighting 4 – 6%
- Vector Fields
- Understand that vector fields are represented by field vectors indicating magnitude and direction
- Use vector fields to make inferences about the number, relative size, and location of sources

- Fundamental Forces
- Articulate situations when the gravitational force is dominant and the electromagnetic, weak, and strong forces can be ignored

- Gravitational and Electric Forces
- Use Newton’s Law of gravitation to calculate the gravitational force between two objects
- Connect the concepts between gravitational force and electric force and compare similarities and differences between them

- Gravitational Field/Acceleration Due to Gravity on Different Planets
- Apply F = mg to calculate the gravitational force on an object with mass m in a gravitational field of strength g
- Calculate the gravitational field strength g using g = (G*m)/r*r
- Approximate the gravitational field strength near the surface of an object from its radius and mass relative to those of Earth or other reference objects

- Inertial vs Gravitational Mass
- Understand that gravitational mass is the property of an object or a system that determines the strength of the gravitational interaction with other objects, systems, or gravitational fields
- Design a plan for collecting data to measure gravitational mass and to measure inertial mass and to distinguish between the two

- Centripetal Acceleration and Force
- Evaluate whether all the forces on a system have been identified using given data and relevant equations

- Free-Body Diagrams for Objects in Uniform Circular Motion
- Design a plan to collect and analyze data for motion from force measurements and carry out an analysis to determine the relationship between the net force and the sum of all forces
- Re-express free-body diagrams into mathematical representations and solve for the acceleration of the object
- Create and use free-body diagrams to analyze physical situations and solve problems with motion

- Applications of Circular Motion and Gravitation
- Express the motion of an object using narrative, mathematical, and graphical representations
- Design an experimental investigation of the motion of an object
- Analyze experimental data describing the motion of an object and express the results using narrative, mathematical, and graphical representations
- Represent forces in diagrams or mathematically using appropriately labeled vectors
- Analyze a scenario and make claims about the forces on an object
- Use Newton’s Third Law to make claims and predictions about the action-reaction pairs of forces when two objects interact

- Vector Fields
- Energy – Exam weighting 16 – 24%
- Open and Closed Systems
- Understand that a system is an object or a collection of objects
- Define open and closed systems and apply conservation concepts for energy, charge, and momentum to those situations

- Work and Mechanical Energy
- Make predictions about changes in kinetic energy of an object based on the net force acting on the object as it moves
- Use net force and velocity vectors to determine changes in kinetic energy
- Use force and velocity vectors to determine the net force on an object and whether the kinetic energy would change
- Apply mathematical methods to determine the change in kinetic energy of an object given the forces on and displacement of the object
- Calculate the total energy of a system and justify the calculation of component types of energy
- Predict changes in the total energy of a system due to changes in position, speed, and frictional interactions of the objects in the system
- Make predictions about the changes in mechanical energy of a system when an external force acts parallel or antiparallel to the displacement of the center of mass
- Apply conservation of energy and the work-energy theorem to determine whether the work done on an object will change the energy of the system

- Conservation of Energy, the Work-Energy Principle, and Power
- Create a representation showing that a single object can only have kinetic energy and calculate that energy
- Translate between a single object and a system that includes that object and the energies they contain
- Calculate the expected behavior of a system and justify using conservation of energy
- Describe and/or make predictions about the internal potential energy of systems
- Calculate changes in energy in a system
- Design an experiment and analyze data to determine changes in work and energy of a system
- Predict and calculate energy transfer to or work done on an object in a system
- Make claims between a system and its environment where there is a transfer of work and/or energy

- Open and Closed Systems
- Momentum – Exam weighting 10 – 16%
- Momentum and Impulse
- Justify the selection of data needed to determine the relationship between the direction of the force acting on an object and the resulting change in momentum
- Use relevant equations to calculate changes in momentum
- Analyze data to characterize the change in momentum of an object
- Design a plan for collecting data to investigate changes in momentum

- Representations of Changes in Momentum
- Calculate the change in linear momentum of a two-object system
- Perform an analysis on data presented in graphs and predict changes in momentum

- Open and Closed Systems
- Define open and closed systems for situations and apply conservation concepts for energy, charge, and linear momentum

- Conservation of Linear Momentum
- Make predictions based on linear momentum and conservation of kinetic energy in elastic collisions
- Apply principles of conservation of momentum and restoration of kinetic energy to solve systems of inelastic and elastic collisions in one and two-dimensions
- Design an experimental test of an application of conservation of linear momentum, predict the outcome of the experiment, analyze data generated by the experiment, and evaluate the prediction vs outcome
- Classify and justify a collision as elastic or inelastic using appropriate principles and calculations, and predict the outcome of such collisions

- Momentum and Impulse
- Simple Harmonic Motion – Exam weighting 2 – 4%
- Period of Simple Harmonic Oscillators
- Predict which properties determine the motion of a simple harmonic oscillator
- Design a plan and collect data to ascertain the characteristics of oscillatory motion in a system
- Analyze data to identify relationships between given values such as force, displacement, acceleration, velocity, period, frequency, spring constant, string length, and mass
- Construct an explanation of oscillatory behavior given a restoring force

- Energy of a Simple Harmonic Oscillator
- Calculate the expected behavior of a system using the model and justify the use of conservation of energy to calculate changes in internal energy
- Apply mathematical reasoning to describe and calculate changes in energy of a system (elastic potential, gravitational potential, kinetic)

- Period of Simple Harmonic Oscillators
- Torque and Rotational Motion – Exam weighting 10 – 16%
- Rotational Kinematics
- Express the motion of an object using narrative, mathematical, and graphical representations
- Use appropriate and relevant equations to calculate angular acceleration, velocity, and position

- Torque and Angular Acceleration
- Use representations of the relationship between force and torque
- Compare and estimate the torque on an object caused by various forces
- Design an experiment and analyze data testing a question about torques in a balanced rigid system
- Calculate torques on a two-dimensional system in static equilibrium
- Make predictions about the change in angular velocity about an axis when a torque is exerted about that axis
- Predict the behavior of rotational collision situations using angular impulse and change of angular momentum
- Plan data-collection and analysis strategies to test the relationship between torques and changes in angular momentum on an object

- Angular Momentum and Torque
- Describe a representation and use it to analyze changes of angular velocity and momentum of a system due to forces acting on it
- Plan data-collection strategies to establish that torque, angular velocity, acceleration, and momentum can be predicted when variables are rotating about an axis
- Use appropriate mathematical routines to calculate values for changes in angular momentum or average torque

- Conservation of Angular Momentum
- Make predictions and calculations regarding the angular momentum of a system where there is no net external torque
- Describe and/or calculate the angular momentum and rotational inertia of a system in terms of positions and velocities of the objects in the system

- Rotational Kinematics
- Electric Charge and Electric Force – Exam weighting 4 – 6%
- Conservation of Charge
- Define open and closed systems and apply conservation of energy, charge, and linear momentum to those situations

- Electric Charge
- Make predictions about the sign and quantity of net charge of objects or systems after charging processes using conservation of electric charge
- Construct an explanation of the two-charge model of electric charge
- Understand that the smallest observed unit of charge is the elementary charge

- Electric Force
- Use Coulomb’s Law to make predictions about the interaction between two point charges
- Connect the concepts of gravitational force and electric force

- Conservation of Charge
- DC Circuits – Exam weighting 6 – 8%
- Definition of a Circuit
- Make predictions about the sign and relative quantity of net charge of objects or systems after charging processes in simple circuits using conservation of charge

- Resistivity
- Choose and justify the data needed to determine resistivity of a given material

- Ohm’s Law, Kirchhoff’s Loop Rule (Resistors in Series and Parallel)
- Construct and/or interpret a graph of the energy changes in an electrical circuit with a single battery and resistors in series and/or parallel
- Apply conservation of energy to design an experiment that will verify Kirchhoff’s Loop Rule in a circuit with one battery and resistors in series or one pair of parallel branches
- Apply Kirchhoff’s Loop Rule in calculations involving total electric potential for complete circuit loops with one battery and resistors in series or one pair of parallel branches

- Kirchhoff’s Junction Rule, Ohm’s Law (Resistors in Series and Parallel)
- Apply Kirchhoff’s Junction Rule to the comparison of electric current in segments of an electrical circuit and predict how those values would change if configurations of the circuit are changed
- Design an investigation of an electrical circuit with one or more resistors in which conservation of charge can be confirmed and analyzed
- Use a description or schematic of an electrical circuit to calculate unknown values of current in various segments or branches of the circuit

- Definition of a Circuit
- Mechanical Waves and Sound – Exam weighting 12 – 16%
- Properties of Waves
- Use a visual representation to explain the distinction between transverse and longitudinal waves
- Describe representations of transverse and longitudinal waves
- Describe sound in terms of transfer of energy and momentum in a medium
- Use graphical representation of a periodic mechanical wave to determine the amplitude of the wave
- Explain and/or predict how the energy carried by a sound wave relates to the amplitude of the wave

- Periodic Waves
- Use a graphical representation of a periodic mechanical wave to determine frequency and period of the wave
- Use a visual representation of a periodic mechanical wave to determine the wavelength of the wave
- Design an experiment to determine the relationship between the wave speed, wavelength, and frequency of a periodic wave
- Create or use a wave front diagram to demonstrate or interpret the observed frequency of a wave depending on the relative motion of the source and observer

- Interference and Superposition (Waves in Tubes and on Strings)
- Use and construct representations of pulses to model the interaction between two pulses to analyze the superposition of two pulses
- Design a suitable experiment and analyze data illustrating the superposition of mechanical waves
- Design a plan for collecting data to quantify the amplitude variations when two or more traveling waves or pulses interact in a medium
- Predict properties of standing waves that are confined to a region and have nodes and antinodes
- Explore the relationship between variables responsible for standing waves on a string or in a column of air
- Explore the relationship between standing wave wavelengths and the size of the region to which it is confined
- Calculate wavelengths and frequencies of standing waves
- Use a visual representation to explain how waves of slightly different frequency give rise to the phenomenon of beats

- Properties of Waves

This extensive list of standards and goals will be followed closely during our tutoring to ensure that students will understand everything they need to know in order to achieve their highest potential for the AP exam.**The standards for the AP Physics C: Mechanics exam are virtually the same as those listed for the AP Physics 1 exam, with the addition of the use of calculus on top of algebra and other mathematical techniques. Students are expected to have taken or concurrently be taking a calculus course in order to succeed in AP Physics C: Mechanics.**

###### AP Physics 2

- Fluids – Exam weighting 10 – 12%
- Fluid Systems
- Construct representations of how the properties of a system are determined by the interactions of its constituent substructures

- Density
- Predict the densities, differences in densities, or changes in densities under different conditions
- Select from experimental data the information necessary to determine or compare the densities of objects

- Fluids: Pressure and Forces
- Make claims about the force on an object due to the presence of other objects with the same properties (mass, charge)
- Make claims and predictions about the action-reaction pairs of forces when two objects interact using Newton’s Third Law
- Analyze situations involving interactions among several objects by using free-body diagrams that include the application of Newton’s Third Law to identify forces

- Fluids and Free-Body Diagrams
- Use a free-body diagram to solve for the acceleration of an object
- Predict the motion of an object subject to external forces using Newton’s Second Law in a variety of situations
- Create and use free-body diagrams to analyze situations and solve problems with motion

- Buoyancy
- Explain contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic electric forces and have certain directions

- Conservation of Energy in Fluid Flow
- Make calculations related to moving fluids using Bernoulli’s equation and/or the relationship between force and pressure, as well as the continuity equation
- Construct an explanation of Bernoulli’s equation in terms of conservation of energy

- Conservation of Mass Flow Rate in Fluids
- Make calculations of quantities related to flow of a fluid using conservation of mass

- Fluid Systems
- Thermodynamics – Exam weighting 12 – 18%
- Thermodynamic Systems
- Construct representations of how the properties of a system are determined by the interactions of its constituent substructures

- Pressure, Thermal Equilibrium, and the Ideal Gas Law
- Make claims about how the pressure of an ideal gas is connected to the force exerted by molecules on the walls of the container and how changes in pressure affect the thermal equilibrium of the system
- Treating a gas molecule as an object, analyze the collisions with a container wall and determine the cause of pressure, and at thermal equilibrium, calculate the pressure, force, or area for a thermodynamic problem
- Connect the average kinetic energy of a system to the temperature of the system
- Connect the statistical distribution of microscopic kinetic energies of molecules to the macroscopic temperature of the system
- Analyze graphical representations of macroscopic variables for an ideal gas to determine the Ideal Gas Law

- Thermodynamics and Forces
- Understand the relationship between forces acting on objects, Newton’s Third Law, and action-reaction pairs regarding thermodynamic systems

- Thermodynamics and Free-Body Diagrams
- Use free-body diagrams and Newton’s Second Law to solve the mathematical representation for the acceleration of an object subject to forces
- Interpret free-body diagrams and re-express them into mathematical representations
- Create and interpret free-body diagrams for thermodynamic systems

- Thermodynamics and Contact Forces
- Explain and make claims about various contact forces (tension, friction, normal, buoyant, spring) using relevant equations f

- Heat and Energy Transfer
- Make predictions about the direction of energy transfer due to temperature changes

- Internal Energy and Energy Transfer
- Calculate expected behavior of a system using the object model and relevant equations
- Describe, make predictions, and calculate changes in the internal energy of a system
- Make claims about the interaction between a system and its environment
- Predict and calculate energy transfer to an object or system
- Design an experiment and analyze graphical data in which the area under a pressure-volume curve is used to determine the work done on or by the object or system
- Describe processes of energy transfer between a system and its environment due to differences in temperature (conduction, convection, radiation)
- Predict changes in the internal energy of a thermodynamic system involving transfer of energy due to heat or work done and justify using conservation of energy
- Make calculations of internal energy changes, heat, or work based on the First Law of Thermodynamics

- Thermodynamics and Elastic Collisions: Conservation of Momentum
- Make predictions of the dynamical properties of a system undergoing a collision using conservation of energy and momentum
- Classify a collision as elastic or inelastic and justify the use of conservation of momentum and energy for an elastic collision

- Thermodynamics and Inelastic Collisions: Conservation of Momentum
- Classify a collision as elastic or inelastic and justify the use of conservation of momentum and energy for an inelastic collision, and recognize that there is a common final velocity for the colliding objects in a totally inelastic case
- Apply conservation of momentum to predict the change in kinetic energy

- Thermal Conductivity
- Design an experiment and analyze data to examine thermal conductivity using relevant equations

- Probability, Thermal Equilibrium, and Entropy
- Construct an explanation based on atomic-scale interactions and probability of how a system approaches thermal equilibrium when energy is transferred in a thermal process
- Connect the Second Law of Thermodynamics in terms of entropy and how it behaves in reversible and irreversible processes

- Thermodynamic Systems
- Electric Force, Field, and Potential – Exam weighting 18 – 22%
- Electric Systems
- Construct representations of how the properties of a system are determined by the interactions of its substructures

- Electric Charge
- Make claims about natural phenomena based on conservation of electric charge
- Make predictions about the sign and quantity of net charge of an object or system after various charging processes
- Construct an explanation of the two charge model and make a prediction about the distribution of positive and negative charges within neutral systems as they undergo various processes

- Conservation of Electric Charge
- Predict electric charges on objects in a system based on conservation of charge
- Design a plan to collect data and justify that data on the electrical charging of objects and charge induction on neutral objects

- Charge Distribution: Friction, Conduction, and Induction
- Make predictions about the redistribution of charge during charging by friction, conduction, and induction, as well as due to other systems
- Construct a representation of the distribution of charge in insulators and conductors
- Plan and/or analyze the results of experiments where electric charges are rearranged by induction

- Electric Permittivity
- Understand that matter has a property called electric permittivity that affects the flow of electrons

- Introduction to Electric Forces
- Represent, understand, and describe forces between objects using relevant equations, free-body diagrams, and Newton’s Laws

- Electric Forces and Free-Body Diagrams
- Create and use free-body diagrams to solve problems and represent situations mathematically using relevant equations

- Describing Electric Force
- Make predictions about the interaction between two electric point charges using Coulomb’s Law
- Connect the concepts of gravitational and electric forces
- Describe the electric force that results from the interaction of point charges using appropriate mathematics

- Gravitational and Electromagnetic Forces
- Connect the strength of the gravitational force between two objects based on their masses with the strength of the electric force between two objects based on their charges

- Vector and Scalar Fields
- Understand that a vector field gives the value of a physical quantity as described by a vector

- Electric Charges and Fields
- Predict the direction and magnitude of the force on an object with charge q in an electric field E using the equation F = qE
- Understand the vector relationship between the electric field and the net electric charge creating that field
- Explain the inverse square relationship between the electric field surrounding a spherically symmetric, electrically charged object
- Distinguish the characteristics that differ between monopole and dipole fields
- Apply mathematical routines to determine the magnitude and direction of the electric field at specified points
- Create representations of and calculate the magnitude and direction of electric fields at various distances between two electrically charged parallel plates
- Represent the motion of an electrically charged particle in the uniform electric field between two oppositely charged parallel plates

- Isolines and Electric Fields
- Construct or interpret visual representation of the isolines of gravitational potential energy and electric potential
- Predict the structure of isolines of electric potential
- Apply mathematical routines to calculate the average value of the magnitude of the electric field in a region

- Conservation of Electric Energy
- Describe, make predictions about, and calculate changes in the internal energy of a system
- Predict and calculate energy transfer to an object or system involving electric charges, fields, and potential

- Electric Systems
- Electric Circuits – Exam weighting 10 – 14%
- Definition and Conservation of Electric Charge
- Make predictions using conservation of charge about changes of charge after various charging processes
- Make predictions about the distribution of positive and negative charges when neutral systems undergo various processes

- Resistivity and Resistance
- Select and justify data needed to determine the resistivity of a material using relevant equations

- Resistance and Capacitance
- Make predictions about the properties of resistors and/or capacitors when placed in a circuit (series or parallel)
- Analyze data to determine changes in resistance or capacitance using relevant equations
- Make and justify predictions of changes in values of resistance and capacitance based off of changes in values of circuit elements in series and/or parallel made of sources of emf, resistors, capacitors, and switches

- Kirchhoff’s Loop Rule
- Analyze data to verify Kirchhoff’s Loop Rule
- Describe and make predictions regarding electric potential, charge, and current using Kirchhoff’s Loop Rule
- Mathematically express the changes in electric potential of a loop in a multiloop electrical circuit and justify using Kirchhoff’s Loop Rule

- Kirchhoff’s Junction Rule and the Conservation of Electric Charge
- Predict or describe current values in series and parallel resistors and other branching circuits using Kirchhoff’s Junction Rule and relate it to conservation of charge
- Determine missing values of current, charge of capacitors, and potential differences in various arrangements of series and parallel circuits using Kirchhoff’s Junction Rule and other relevant equations

- Definition and Conservation of Electric Charge
- Magnetism and Electromagnetic Induction – Exam weighting 10 – 12%
- Magnetic Systems
- Magnetic Permeability and Magnetic Dipole Moment
- Understand that matter has a property called magnetic permeability which affects the degree of magnetization a material obtains in response to a magnetic field
- Understand that matter has a property called magnetic dipole moment which is an intrinsic property of some fundamental particles

- Vector and Scalar Fields
- Monopole and Dipole Fields
- Distinguish the characteristics that differ between monopole and dipole fields

- Magnetic Fields and Forces
- Apply mathematical routines and relevant equations to express the force exerted on a moving charged object in a magnetic field
- Create a verbal or visual representation of a magnetic field around a straight wire or pair of parallel wires
- Describe the orientation of a magnetic dipole placed in a magnetic field (compass in Earth’s magnetic field, iron filings around a bar magnet)
- Analyze the magnetic behavior of a bar magnet composed of ferromagnetic material

- Magnetic Forces
- Use right-hand rules to analyze a current-carrying conductor and a moving electrically charged object to determine the direction of the magnetic force
- Use relevant equations to calculate the magnitude of the magnetic force

- Forces Review
- Connect the strength of electromagnetic forces with the spatial scale of the situation, the magnitude of electric charges, and the motion of the electrically charged objects involved

- Forces Review
- Use representations and models to describe the magnetic properties of some materials that can be affected by magnetic properties of other objects in the system
- Construct an explanation of an electromagnetic device in which an induced emf is produced by changing the magnetic flux through a loop of current or by a constant magnetic field through a changing area (Lenz’s Law)

- Geometric and Physical Optics – Exam weighting 12 – 14%
- Waves
- Describe representations of transverse and longitudinal waves
- Analyze data to identify whether a mechanical wave is polarized
- Contrast mechanical and electromagnetic waves in terms of the need for a medium for wave propagation

- Electromagnetic Waves
- Make qualitative comparisons of the wavelengths of types of electromagnetic radiation
- Describe representations and models of electromagnetic waves that explain the transmission of energy when no medium is present

- Periodic Waves
- Construct an equation relating wavelength and amplitude of a wave from its graphical representation, relating the frequency or period and amplitude at a given position as a function of time

- Refraction, Reflection, and Absorption
- Make claims about the behavior of light as the wave travels from one medium to another (transmission, reflection, absorption)
- Make predictions about the locations of the object and image relative to the location of a reflecting surface using relevant equations
- Describe models of light and make claims and predictions about path changes for light as it travels from one medium to another

- Images from Lenses and Mirrors
- Plan data collection strategies and perform data analysis and evaluation of evidence about the formation of images due to reflection of light from curved spherical mirrors
- Use quantitative and qualitative representations and models to analyze situations and solve problems about image formation occurring due to the reflection of light through surfaces and the refraction of light through thin lenses

- Interference and Diffraction
- Make claims and predictions and construct representations to analyze situations in which two waves overlap (superposition, standing waves)
- Make claims about the diffraction pattern produced when a wave passes through a small opening with a size comparable to the wavelength
- Apply the wave model to describe the generation of interference patterns and make predictions about them
- Predict and explain the ability or inability of waves to transfer energy around corners and behind obstacles in terms of diffraction

- Waves
- Quantum, Atomic, and Nuclear Physics – Exam weighting 10 – 12%
- Systems and Fundamental Forces
- Construct representations of the differences between a fundamental particle and a system composed of fundamental particles
- Understand the structure of an atom in terms of the number of protons, neutrons, electrons, and radioactive emissions
- Construct representations of the energy-level structure of an electron in an atom
- Identify the strong force as the force responsible for holding the nucleus together

- Radioactive Decay
- Analyze conservation of charge for nuclear and elementary particle reactions and make predictions related to these reactions
- Apply inelastic and elastic collision properties to collisions of fundamental particles using conservation of momentum and energy
- Apply conservation of nucleon number and charge to make predictions about nuclear reactions and decays (fission, fusion, alpha/beta/gamma decay)

- Energy in Modern Physics (Radioactive Decay and E = m*c*c
- Describe, make predictions about, and calculate changes in the internal energy of systems
- Describe emission or absorption spectra associated with electronic or nuclear transitions as transitions between allowed energy states
- Apply conservation of mass and energy concepts and use to E = m*c*c make a related calculation

- Mass-Energy Equivalence
- Articulate the reasons that the theory of conservation of mass was replaced by the theory of conservation of mass-energy
- Apply mathematical routines to describe the relationship between mass and energy using E = m*c*c

- Properties of Waves and Particles
- Explain why classical mechanics cannot describe all properties of objects
- Understand that certain phenomena classically thought of as waves can exhibit properties of particles
- Articulate the reasons that classical mechanics must be replaced by special relativity to describe the experimental results and theoretical predictions that show that properties of space and time are not absolute
- Make predictions about using the scale of a problem to determine if a wave or particle model is more appropriate
- Articulate the evidence supporting the claim that a wave model is appropriate to explain the diffraction of matter interacting with a crystal where the particle has momentum corresponding to a de Broglie wavelength smaller than the separation between adjacent atoms in the crystal
- Predict the dependence of major features of a diffraction pattern based on the particle speed and de Broglie wavelength of electrons in an electron beam interacting with a crystal

- Photoelectric Effect
- Support the photon model of radiant energy with evidence provided by the photoelectric effect
- Select a model of radiant energy that is appropriate to the spatial or temporal scale of an interaction with matter

- Wave Functions and Probability
- Use a graphical wave function representation of a particle to predict the probability of finding a particle in a specific spatial region
- Use a standing wave model to explain the existence of specific energy states of an electron
- Predict the number of radioactive nuclei remaining in a sample after a certain period of time as well as the missing species (alpha, beta, gamma) in a radioactive decay
- Construct or interpret representations of transitions between atomic energy states involving the emission and absorption of photons

- Systems and Fundamental Forces

This extensive list of standards and goals will be followed closely during our tutoring to ensure that students will understand everything they need to know in order to achieve their highest potential for the AP exam.**The standards for the AP Physics C: Electricity and Magnetism exam are virtually the same as those listed for the AP Physics 2 exam sections 3-5, with the addition of the use of calculus on top of algebra and other mathematical techniques. Students are expected to have taken or concurrently be taking a calculus course in order to succeed in AP Physics C: Electricity and Magnetism.**