Search for Pascal's Triangle and the Binomial Expansion

1. Exploration & Native Americans Christopher Columbus Italian explorer who sailed for Spain in 1492. Wanted to find a western route to Asia. Reached the Caribbean instead. His voyages began sustained European contact with the Americas. Led to European colonization and the Columbian Exchange. Conquistadores Spanish explorers/conquerors who sought gold, land, and converts. Helped Spain conquer large Native American empires. Often used military force and alliances with rival Native groups. Mayas, Incas, Aztecs Major civilizations in the Americas before European conquest. Aztecs: centered in Mexico; conquered by Cortés. Incas: centered in the Andes/South America; conquered by Pizarro. Mayas: Central America; famous for cities, writing, mathematics, and astronomy. Hernando Cortés Spanish conquistador. Conquered the Aztec Empire in 1519–1521. Defeated Montezuma/Moctezuma II and captured Tenochtitlán. Francisco Pizarro Spanish conquistador who conquered the Inca Empire. Operated in present-day Peru. Montezuma Aztec ruler when Cortés arrived. Also called Moctezuma II. His empire was eventually conquered by Cortés and his allies. Hernando de Soto Spanish explorer who explored the southeastern part of what became the United States. His expedition encountered Native peoples and reached the Mississippi River. Francisco de Coronado Spanish explorer who explored the American Southwest and Great Plains. Searched for the legendary Seven Cities of Gold. Jacques Cartier French explorer who explored the St. Lawrence River. His voyages helped France establish claims in North America. John Cabot Italian explorer sailing for England. Explored the North Atlantic coast of North America in 1497. Helped England establish a claim to North American territory. Prince Henry the Navigator Portuguese prince who supported exploration. Helped Portugal develop navigation and sailing technology. Portuguese exploration contributed to the development of the Atlantic slave trade. ⸻ 2. Spanish, French & English Colonization Joint-stock company A company where investors pool money to fund a business. Why important: English colonies such as Virginia were partly financed through joint-stock companies. Virginia Company English joint-stock company. Founded Jamestown in 1607. Investors hoped to make money from the colony. Jamestown First permanent English settlement in North America, 1607. Located in Virginia. Suffered from disease, starvation, conflict, and poor leadership. Tobacco eventually helped make the colony profitable. Tidewater Coastal area of Virginia and surrounding colonies. Early English settlements were concentrated here. Piedmont Inland region between the Tidewater/coastal plain and Appalachian Mountains. Settlement expanded into this area as colonies grew. Coureurs de bois French “runners of the woods.” French colonists/traders who lived and traveled among Native Americans. Participated heavily in the fur trade. Samuel de Champlain French explorer. Founded Quebec in 1608. Known as the “Father of New France.” Developed alliances with Native Americans. ⸻ 3. Roanoke & Early Virginia Sir Walter Raleigh English supporter of colonization. Sponsored the attempted settlement at Roanoke. Roanoke English colony established in the 1580s. Eventually disappeared. Called the “Lost Colony.” John Smith Leader at Jamestown. Helped organize the settlement and enforce discipline. Famous for his relationship with Pocahontas, although later accounts are disputed. “Starving Time” Winter of 1609–1610 at Jamestown. Colonists experienced extreme hunger, disease, and death. Demonstrated how difficult early colonization was. John Rolfe Helped make Virginia economically successful by growing tobacco. Married Pocahontas. Tobacco became Virginia’s major cash crop. Headright system Colonists received land for bringing people to Virginia. Encouraged immigration. Helped create large plantations and contributed to social/economic inequality. Freeman A colonist who possessed certain political rights, including the ability to participate in government. Political rights were generally limited to certain white male colonists. House of Burgesses Created in Virginia in 1619. First representative legislative assembly in the English colonies. Important development in colonial self-government. 1618 reforms of the Virginia Company The Virginia Company changed its policies to attract settlers and make Virginia successful. Included: More representative government. Greater incentives for settlers. Expansion of land ownership. Greater economic opportunity. Result: Virginia became more attractive to settlers. ⸻ 4. Puritans & Religion John Calvin Protestant religious thinker. Developed Calvinism. Believed in predestination. Predestination The belief that God has already determined who will be saved. Puritanism Protestant movement that wanted to reform the Church of England. Puritans believed the English church still contained too many Catholic practices. Separatists Puritans who believed the Church of England could not be reformed. Wanted to separate completely from it. The Pilgrims were Separatists. Non-Separatist Puritans Wanted to reform the Church of England rather than leave it completely. Many settled Massachusetts Bay. Pilgrims Separatist Puritans. Settled at Plymouth in 1620. Signed the Mayflower Compact. Mayflower Compact Agreement signed by Plymouth settlers. Established self-government based on majority rule. Important early example of colonial self-government. Plymouth Colony founded by Pilgrims in 1620. Later became part of Massachusetts. William Bradford Pilgrim leader and governor of Plymouth. Helped maintain the colony. Wrote about Plymouth’s early history. Massachusetts Bay Colony Founded by Puritans in 1630. Much larger than Plymouth. Centered around Boston. Governed according to Puritan religious beliefs. John Winthrop Governor of Massachusetts Bay. Described Massachusetts as a “city upon a hill.” “City upon a hill” Winthrop’s idea that Massachusetts should serve as an example of a successful Christian society to the world. Covenant A religious agreement between God and a community. Puritans believed their communities had a special covenant with God. “Visible saints” Puritans who demonstrated that they had received God’s grace and were considered members of the church. “Invisible saints” Those believed to have God’s grace/salvation, even though humans could not truly know who was saved. “Saving grace” The belief that God’s grace could lead a person to salvation. ⸻ 5. New England Religious Conflicts Anne Hutchinson Puritan woman who challenged Massachusetts religious leaders. Believed faith/grace was more important than following religious rules. Put on trial and banished from Massachusetts. Shows the limits of religious tolerance in Massachusetts. Roger Williams Founded Rhode Island. Believed in: Religious freedom Separation of church and government Fairer treatment of Native Americans Banished from Massachusetts. Fundamental Orders of Connecticut 1639. Established a representative government in Connecticut. Often considered one of the first written constitutions in America. King Philip’s War 1675–1676. Major conflict between New England colonists and Native Americans led by Metacom, whom colonists called King Philip. Resulted in enormous destruction and loss of Native American land and power. Toleration Act of 1649 Maryland law granting religious toleration to Christians. Intended especially to protect Catholics. Important early example of religious toleration, although it was limited. ⸻ 6. Massachusetts Education Massachusetts Education Act of 1647 Required towns to establish schools when they reached certain population sizes. Why? Puritans wanted people to be able to read the Bible. Important: Shows how strongly education and religion were connected in Puritan society. ⸻ 7. Colonial Regions New England Colonies Examples: Massachusetts Plymouth Connecticut Rhode Island New Hampshire Important characteristics Religious motivations Puritan influence Small farms Town-centered communities Fishing Shipbuilding Lumber Commerce Less suitable climate for large cash-crop plantations ⸻ Middle Colonies Examples: New York Pennsylvania New Jersey Delaware Important characteristics Religious diversity More ethnic diversity Fertile farmland Grain production Large ports Trade Cities such as New York and Philadelphia ⸻ Southern Colonies Examples: Virginia Maryland North Carolina South Carolina Georgia Important characteristics Plantation agriculture Tobacco, rice, indigo Slavery Large landowners Warm climate Greater social/economic inequality ⸻ 8. Types of Colonies Corporate colony Colony controlled by a company. Example: Virginia originally operated under the Virginia Company. Royal colony Controlled directly by the English king. Governor appointed by the king. Proprietary colony Granted by the king to an individual or group. Proprietor had significant control. Example: Pennsylvania → William Penn Charter of Liberties Early New York document providing certain rights and outlining representative government. Associated with efforts to establish political participation in the colony. ⸻ 9. William Penn & Quakers William Penn Quaker. Founded Pennsylvania. Wanted a colony based on religious tolerance. Had relatively peaceful relationships with Native Americans. Quakers / Society of Friends Protestant religious group. Believed in spiritual equality. Rejected many traditional church structures. Supported religious tolerance. Women had greater religious participation than in many other colonial communities. George Calvert Also known as Lord Baltimore. Catholic Englishman. Received land that became Maryland. Wanted a place where Catholics could practice their religion more freely. ⸻ 10. Georgia James Oglethorpe Founded Georgia in 1732. Intended Georgia partly as a buffer against Spanish Florida. Also wanted to create opportunities for poor English people. ⸻ 11. Pennsylvania & New York Patroonship Dutch system in New Netherland. Large land grants were given to wealthy individuals called patroons. Encouraged large estates. Quitrent A fee/rent paid to a proprietor for use of land. Common in proprietary colonies. ⸻ 12. Bacon’s Rebellion Bacon’s Rebellion 1676 Virginia. Nathaniel Bacon led settlers against Native Americans and Virginia’s government. Bacon’s followers believed Governor Berkeley was not protecting frontier settlers. Why important? Exposed class tensions between wealthy planters and poorer colonists. Afterward, Virginia increasingly relied on enslaved Africans instead of indentured servants. ⸻ 13. Colonial Social Classes Indentured servants Europeans who agreed to work for a certain number of years in exchange for passage to America. After their contract ended, they could become free. Freedom dues Things given to indentured servants when their contract ended. Could include: Clothing Tools Land or supplies Redemptioners European immigrants who agreed to work for a period of time after arriving in America to pay off transportation costs. ⸻ 14. Slavery Chattel slavery System in which enslaved people were treated legally as property. Slavery became hereditary. Enslaved people had extremely limited/no legal freedom. Middle Passage Forced voyage of enslaved Africans across the Atlantic to the Americas. Part of the triangular trade. Conditions were extremely overcrowded and deadly. Slave codes Laws restricting the rights and freedoms of enslaved people. They often: Prevented movement. Restricted education. Restricted assembly. Defined enslaved people as property. Made slavery hereditary. ⸻ 15. Stono Rebellion Stono Rebellion 1739, South Carolina. Enslaved Africans rebelled and attempted to escape toward Spanish Florida. Colonial authorities eventually suppressed the rebellion. Why important? Led to even stricter slave laws. ⸻ 16. Triangular Trade A trading system connecting Europe, Africa, and the Americas. Simplified: Europe → Africa Manufactured goods Africa → Americas Enslaved Africans Americas → Europe Sugar Tobacco Rice Other raw materials ⸻ 17. Mercantilism Economic theory used by European empires. Basic idea: Colonies exist to benefit the mother country. England wanted colonies to: Supply raw materials. Buy English manufactured goods. Increase England’s wealth. Strengthen England’s economy. ⸻ 18. Navigation Acts English laws regulating colonial trade. They required much colonial trade to: Use English ships. Pass through English-controlled channels. Benefit England. Goal: strengthen mercantilism. ⸻ 19. Molasses Act 1733 Taxed foreign molasses imported into British colonies. Designed to protect British sugar producers in the Caribbean. Colonists often avoided or resisted the tax through smuggling. Woolens Act Restricted colonial production/trade of woolen goods. Intended to protect English manufacturers. Hat Act Restricted colonial production/export of hats. Another example of Britain controlling colonial manufacturing. Iron Act Encouraged production of certain raw iron products in the colonies but restricted production of finished iron goods. Britain wanted colonies to supply raw materials while buying manufactured products from Britain. BIG IDEA: These laws show mercantilism and British attempts to control colonial economies. ⸻ 20. Dominion of New England Dominion of New England Created by King James II in 1686. Combined several New England colonies under one government. Why? Increase royal control. Enforce Navigation Acts. Reduce colonial self-government. Sir Edmund Andros Royal governor of the Dominion of New England. Strongly enforced royal policies. Very unpopular with many colonists. ⸻ 21. Glorious Revolution Glorious Revolution — 1688 English people and Parliament removed James II. William and Mary became monarchs. Increased the power of Parliament. Colonial effect: Colonists overthrew the Dominion of New England government. Sir Edmund Andros was removed. Colonists regained some self-government. ⸻ 22. Political Deference Political deference The belief that ordinary people should respect and defer to wealthy, powerful, or socially prominent leaders. Colonial society was often hierarchical. ⸻ 23. Lower House of the Legislature The elected part of a colonial legislature representing ordinary property-owning colonists. Examples: House of Burgesses Colonial assemblies Important: These assemblies helped establish the tradition of representative government. ⸻ 24. The Great Awakening Great Awakening Religious revival movement in the 1730s–1740s. Preachers emphasized: Personal faith Emotional religious experiences Salvation Individual relationships with God It challenged established churches and religious authorities. Jonathan Edwards Famous Great Awakening preacher. Known for the sermon: “Sinners in the Hands of an Angry God.” Emphasized God’s power and the need for conversion. George Whitefield Extremely popular traveling preacher. Preached throughout the colonies. Helped spread the Great Awakening. Old Lights People who supported traditional, established religious practices. New Lights People who supported the emotional revival-style religion of the Great Awakening. Baptists Protestant group that grew during the Great Awakening. Emphasized personal faith and baptism. Helped increase religious diversity. ⸻ 25. John Peter Zenger John Peter Zenger New York printer/journalist. Put on trial for criticizing the colonial governor. His lawyer argued that truthful statements should not be considered libel. Why important? His trial became an important symbol associated with freedom of the press. ⸻ 26. Maryland & Carolina Fundamental Constitutions of Carolina Document associated with governing Carolina. Created a hierarchical political/social structure. Helped establish an aristocratic plantation society. Slavery became increasingly important in Carolina. Established churches A government-supported official church. In some colonies, taxes helped support the established church. Important contrast: Established churches = government + religion connected. Rhode Island/Pennsylvania = greater religious freedom. ⸻ 27. Great Migration Great Migration, 1630–1643 Large migration of English Puritans to Massachusetts Bay and other New England colonies. Why? Religious motivations Political/religious conflict in England Desire to build Puritan communities Important: This was different from the much later Great Migration of African Americans during the 20th century. ⸻ 28. Enclosure Movement Enclosure Movement In England, landowners enclosed common lands and combined small fields into larger private farms. Effect: Some small farmers lost access to land. Increased movement of people toward cities and overseas colonies. Helped contribute to English migration to America. ⸻ 29. “City Upon a Hill” vs. Religious Tolerance Know this contrast for APUSH: Massachusetts Bay → Puritan religious society → Limited religious tolerance Rhode Island → Roger Williams → Religious freedom Pennsylvania → William Penn → Quakerism + religious tolerance Maryland → Catholic refuge → Toleration Act of 1649 ⸻ ⭐ The MOST IMPORTANT Connections to Know These are the connections your teacher is likely looking for in APUSH questions. Tobacco → Virginia John Rolfe → tobacco → profitable Virginia → plantations → labor demand → indentured servants → slavery Bacon’s Rebellion → slavery Bacon’s Rebellion → class conflict → elites become more suspicious of poor white workers → increased reliance on African slavery Puritans → Massachusetts Puritans → Great Migration → Massachusetts Bay → John Winthrop → “city upon a hill” Separatists → Plymouth Separatists → Pilgrims → Mayflower → Plymouth → Mayflower Compact Religious disagreement → Rhode Island Anne Hutchinson/Roger Williams → conflict with Massachusetts → Rhode Island → religious freedom Quakers → Pennsylvania William Penn → Quakers → Pennsylvania → religious tolerance Mercantilism → Navigation Acts Mercantilism → Britain wants colonies to benefit England → Navigation Acts → trade restrictions Great Awakening → religious change Great Awakening → emotional religion → New Lights → challenges established churches → increased religious diversity Slavery → plantation economy Cash crops → labor demand → African slavery → slave codes → racial hierarchy