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Advanced Placement (AP) exams enable students to earn college credit with the help of exam questions and past exams for effective preparation.

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AP Calculus AB: 2.1.8 Continuity and Discontinuity

A function is continuous at a point if it’s defined there, its limit exists, and the function’s value equals that limit. Discontinuities occur when one or more of these conditions fail, leading to jump, point (removable), or infinite discontinuities.

AP Calculus AB: 2.1.7 The Squeeze Theorem

The Squeeze Theorem helps find the limit of a function by "squeezing" it between two simpler functions whose limits are known and equal. If the given function is always between those two near a point, then its limit at that point is the same.

AP Calculus AB: 2.1.6 One-Sided Limits

One-sided limits examine a function's behavior from only one direction—left (−) or right (+). A limit exists at a point only if both the left-hand and right-hand limits exist and are equal. If they differ, the overall limit does not exist.

AP Calculus AB: 2.1.4 The Limit Laws, Part I

Limits follow the same arithmetic rules as real numbers. You can add, subtract, multiply, or divide limits (if the denominator isn't zero), and constants can be factored out. These properties simplify evaluating complex expressions involving limits.

AP Calculus AB: 2.1.3 The Formal Definition of a Limit

The formal definition of a limit uses ε (epsilon) and δ (delta) to precisely describe how a function approaches a value. It states that for every ε > 0, there exists a δ > 0 such that when x is within δ of c (but not equal to c), f(x) is within ε of the limit L.

AP Calculus AB: 2.1.2 Finding Limits Graphically

Finding limits graphically involves observing the y-value a function approaches as x gets close to a specific point from both sides. If the left and right sides approach the same value, the limit exists; if they differ, the limit does not exist.

AP Calculus AB: 2.1.1 Finding Rate of Change over an Interval

The rate of change measures how a function's output varies with changes in input over an interval, often approximated by the average rate of change. Using position functions, it helps analyze motion by calculating how location changes over time.

AP Calculus AB: Chapter 1 Test

This content focuses on applying geometric formulas (area of semicircles, triangles, and volume of cones) and understanding average rates of change in various real-world contexts, such as motion, sales trends, and growth models. It reinforces interpreting function notation, unit conversions, and est...

AP Calculus AB: Chapter 1 Practice Test

This content blends geometry and real-world rate problems, covering area and volume formulas (like those for semicircles, squares, and cones), and interpreting average rates of change from data and graphs. It includes practical examples involving speed, falling objects, and sales data to strengthen ...

AP Calculus AB: 1.2.3 Parabolas

This content introduces parabolas as the graphs of second-degree polynomial functions, explaining how coefficients affect their direction, width, and position. It also covers simplifying expressions, handling undefined points, and using the distance formula derived from the Pythagorean theorem to ca...

AP Calculus AB: 1.2.2 Graphing Lines

This content covers the fundamentals of graphing linear equations using slope-intercept and point-slope forms. It explains how to calculate slope, determine y-intercepts, and write equations of lines through given points. The section also includes concepts like parallel and perpendicular lines and a...

AP Calculus AB: 1.2.1 Functions

This content introduces the concept of functions as mathematical machines that map each input to exactly one output. It covers function notation, how to evaluate functions for numbers and expressions, and provides examples using equations and graphs to reinforce the concept.

AP Calculus AB: 1.1.3 Average Rates of Change

This content explains the concept of average rate of change using the Greek letter delta (Δ) to represent changes in variables, illustrated with real-world examples like population growth, velocity, and weight loss. It also introduces the challenge of finding instantaneous rates of change, highlight...

AP Calculus AB: 1.1.2 The Two Questions of Calculus

This flashcard set introduces the two central problems calculus aims to solve: finding instantaneous rates of change (differential calculus) and determining areas under curves (integral calculus). It explains how these concepts extend basic rate and area ideas, forming the foundation of modern calcu...

AP® U.S. Government - U.S. Presidents

George Washington served as the first President of the United States from April 30, 1789, to March 4, 1797. He had no political party affiliation and set many precedents for the presidency.

AP® U.S. Government - Foreign and Military Policy

Foreign policy refers to a country's strategy in dealing with other nations. It involves decisions and actions related to diplomacy, trade, defense, and international relations. For example, U.S. foreign policy focuses on managing America's relationships with other countries.

AP® U.S. Government - Domestic and Economic Policy

Domestic policy includes all laws, programs, and government actions that address issues within a country. It covers areas like healthcare, education, and economic regulation to manage internal affairs.

AP® U.S. Government - Civil Liberties

Civil liberties are individual freedoms that limit government power and protect citizens from government overreach. These rights—like freedom of religion and the right to bear arms—are guaranteed by the Bill of Rights to ensure personal freedoms.

AP® U.S. Government - Civil Rights

Civil rights are protections and privileges granted by the government to ensure equal treatment and prevent discrimination based on factors like race, gender, or ethnicity. Unlike civil liberties, which are basic freedoms, civil rights focus on guaranteeing fairness and equality in society.

AP® U.S. Government - The Judiciary

Statutory law refers to laws written and enacted by legislative bodies. These laws are formally passed statutes, such as one making it illegal to harm protected species like the American bald eagle.

AP® U.S. Government - The Bureaucracy

A bureaucracy is a complex administrative system made up of appointed officials. It operates with a clear hierarchy, specialized jobs, and formal rules to manage government functions efficiently.

AP® U.S. Government - The Presidency

To serve as President, a person must be a natural-born U.S. citizen, at least 35 years old, and have lived in the United States for a minimum of 14 years. These requirements are set by the Constitution to ensure experience and national loyalty.

AP® U.S. Government - Congress

Article I of the U.S. Constitution established the legislative branch, known as Congress. It outlines the structure, powers, and responsibilities of the House of Representatives and the Senate, granting them the authority to make federal laws.

AP® U.S. Government - The Media

Mass media includes various forms of communication—like TV, radio, newspapers, and the Internet—that reach large audiences. It plays a key role in shaping public opinion and informing citizens about political events and issues.

AP® U.S. Government - Interest Groups

A linkage institution is a structure that connects citizens to the government, helping their concerns become political issues. Key examples include political parties, interest groups, and the media.

AP® U.S. Government - Political Parties

A political party is an organized group of people with shared political beliefs and goals. Its main purpose is to gain political power by winning elections and influencing government policy.

AP® U.S. Government - Political Participation

Political culture refers to the shared beliefs, values, and norms about how government and politics should function. In the U.S., it includes ideas like respect for the rule of law, democratic processes, and peaceful transitions of power.

AP® U.S. Government - Public Opinion

This deck covers key concepts related to public opinion in U.S. government, including definitions, polling methods, political ideologies, and demographic influences on political beliefs.

AP® U.S. Government - Federalism

Federalism is a system of government where power is shared between a national government and state governments. In the U.S., both levels have their own responsibilities and authority, working together under the Constitution.

AP® U.S. Government - The Constitution

The original purpose of the Philadelphia Convention in 1787 was to revise the Articles of Confederation. However, the delegates soon chose to create an entirely new Constitution, establishing a stronger federal government.

AP® U.S. Government - Foundations of the U.S. Government

An absolute monarchy grants the monarch unlimited power, with no legal or constitutional restraints (e.g., Saudi Arabia). A constitutional monarchy, on the other hand, limits the monarch’s power through a constitution or laws, often placing real political power in the hands of elected officials (e....

US Government AP - Interest Groups and Political Action Committees

These groups focus on protecting and promoting the financial and job-related interests of their members, like AARP for older Americans or SEIU for service workers.

US Government AP - The Constitution

Article II of the Constitution establishes the executive branch, outlining the powers and duties of the president, such as commanding the military, making treaties, and appointing officials with Senate approval. It also defines the Electoral College, the system used to elect the president, which was...

Learn AP® U.S. History - Bush Jr. + Obama 2001- 2016

In Bush v. Gore (2000), the Supreme Court ruled that Florida’s inconsistent vote-counting standards violated due process, effectively awarding the presidency to George W. Bush.

Learn AP® U.S. History - Bush Sr. + Clinton 1989 - 2000

The 1989 Tiananmen Square protest was seen by many as a sign of Communism’s possible decline, but it ended in a violent crackdown, symbolized by the iconic image of a lone man facing down tanks.

Learn AP® U.S. History - Carter + Reagan 1977 - 1988

Carter’s first act as President was to pardon all Vietnam War draft evaders, granting them blanket amnesty through executive order. Jimmy Carter won the 1976 election by presenting himself as a Washington outsider, which appealed to voters still disillusioned by the Watergate scandal.

Learn AP® U.S. History - Nixon + Ford 1969 - 1976

The Nixon Doctrine stated that the U.S. would support allies with aid and arms but expected them to defend themselves, marking a shift away from direct American military involvement.

Learn AP® U.S. History - Kennedy + Johnson 1961 - 1968

The first televised presidential debates debuted in 1960 between Kennedy and Nixon, with Kennedy’s strong on-camera presence playing a key role in his narrow victory.

Learn AP® U.S. History - Eisenhower 1952 - 1961

"We Like Ike" was the popular campaign slogan for Dwight Eisenhower in the 1952 presidential election, reflecting his widespread appeal. Eisenhower’s key campaign promise was to end the Korean War, which he fulfilled shortly after taking office, leaving Korea divided much as it had been before the c...

Learn AP® U.S. History - Truman 1945 - 1951

The Baby Boom was a sharp rise in U.S. birth rates from 1946 to 1957, with more babies born between 1948 and 1953 than in the previous 30 years combined.

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