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HIGH SCHOOL SELECTED TOP PRIORITY STANDARDS

**GRADE 9 ****SELECTED TOP PRIORITY STANDARDS**

**ENGLISH**

- Students apply their knowledge of word origins to determine the meaning of new words encountered in reading materials and use those words accurately.
- Students read and understand grade-level-appropriate material. They analyze the organizational patterns, arguments, and positions advanced.
- Students read and respond to historically or culturally significant works of literature that reflect and enhance their studies of history and social science. They conduct in-depth analyses of recurrent patterns and themes. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.
- Students write coherent and focused essays that convey a well-defined perspective and tightly reasoned argument. The writing demonstrates students’ awareness of the audience and purpose.
- Students combine the rhetorical strategies of narration, exposition, persuasion, and description to produce texts of at least 1,500 words each. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies.
- Write biographical or autobiographical narratives or short stories; Write responses to literature; Write expository compositions, including analytical essays and research reports; Write persuasive compositions; Write business letters; & Write technical documents (e.g., a manual on rules of behavior for conflict resolution, procedures for conducting a meeting, minutes of a meeting).
- Students write and speak with a command of standard English conventions.
- Students deliver polished formal and extemporaneous presentations that combine the traditional rhetorical strategies of narration, exposition, persuasion, and description. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies and must be able to deliver persuasive arguments (including evaluation and analysis of problems and solutions and causes and effects).

MATH

- Students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems.
- Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
- Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.
- Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
- Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.
- Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
- Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.
- Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
- Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.
- Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 + (cos(x)) 2 = 1.
- Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
- Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.
- Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
- Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.

**SCIENCE**

**Physical Science**

Physical Science helps to prepare students to enroll in Chemistry and Physics. Motion, forces, matter and structures are a few of the topics integrated into the curricula. Students will be introduced to basic ideas that build into a greater understanding of Chemistry and Physics in later years. Students will also examine the formation and evolution of the universe, the solar system, the earth, and the oceans. Investigations will highlight the methodologies and technologies of earth science and the development use, and depletion of the earth’s resources.

- Laboratory is an essential part of this course and students learn the importance of observation and data organization as they produce formal laboratory reports for each activity.
- Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations.
- The students will gain basic understanding of the following concepts: velocity of an object is the rate of change of its position; Newton’s laws predict the motion of most objects; Electric and magnetic phenomena are related and have many practical applications; etc.

**Earth Science**

Students understand that astronomy and planetary exploration reveal the solar system’s structure, scale, and change over time.

- Earth-based and space-based astronomy reveal the structure, scale, and changes in stars, galaxies, and the universe over time.

Students know accelerators boost subatomic particles to energy levels that simulate conditions in the stars and in the early history of the universe before stars formed.

Students know the evidence indicating that the color, brightness, and evolution of a star are determined by a balance between gravitational collapse and nuclear fusion.

Students know how the red-shift from distant galaxies and the cosmic background radiation provide evidence for the “big bang” model that suggests that the universe has been expanding for 10 to 20 billion years.

- Plate tectonics operating over geologic time has changed the patterns of land, sea, and mountains on Earth’s surface.

Students know the explanation for the location and properties of volcanoes that are due to hot spots and the explanation for those that are due to subduction.

Students know the relative amount of incoming solar energy compared with Earth’s internal energy and the energy used by society.

Students know how differential heating of Earth results in circulation patterns in the atmosphere and oceans that globally distribute the heat.

Students know the interaction of wind patterns, ocean currents, and mountain ranges results in the global pattern of latitudinal bands of rain forests and deserts.

Students know features of the ENSO (El Niño southern oscillation) cycle in terms of sea-surface and air temperature variations across the Pacific and some climatic results of this cycle.

Students know how computer models are used to predict the effects of the increase in greenhouse gases on climate for the planet as a whole and for specific regions.

Students know how the composition of Earth’s atmosphere has evolved over geologic time and know the effect of outgassing, the variations of carbon dioxide concentration, and the origin of atmospheric oxygen.

**Investigation & Experimentation**

Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other four strands, students should develop their own questions and perform investigations. Students will:

Select and use appropriate tools and technology (such as computer-linked probes, spreadsheets, and graphing calculators) to perform tests, collect data, analyze relationships, and display data.

- Identify and communicate sources of unavoidable experimental error.
- Identify possible reasons for inconsistent results, such as sources of error or uncontrolled conditions.
- Formulate explanations by using logic and evidence.
- Solve scientific problems by using quadratic equations and simple trigonometric, exponential, and logarithmic functions.
- Distinguish between hypothesis and theory as scientific terms.
- Recognize the usefulness and limitations of models and theories as scientific representations of reality.
- Read and interpret topographic and geologic maps.
- Analyze the locations, sequences, or time intervals that are characteristic of natural phenomena (e.g., relative ages of rocks, locations of planets over time, and succession of species in an ecosystem).
- Recognize the issues of statistical variability and the need for controlled tests.
- Recognize the cumulative nature of scientific evidence.
- Analyze situations and solve problems that require combining and applying concepts from more than one area of science.

Investigate a science-based societal issue by researching the literature, analyzing data, and communicating the findings. Examples of issues include irradiation of food, cloning of animals by somatic cell nuclear transfer, choice of energy sources, and land and water use decisions in California.

Know that when an observation does not agree with an accepted scientific theory, the observation is sometimes mistaken or fraudulent (e.g., the Piltdown Man fossil or unidentified flying objects) and that the theory is sometimes wrong (e.g., the Ptolemaic model of the movement of the Sun, Moon, and planets).

SOCIAL STUDIES

**World History and Geography: Ancient Civilizations**

Students in grade six expand their understanding of history by studying the people and events that ushered in the dawn of the major Western and non-Western ancient civilizations. Geography is of special significance in the development of the human story. Continued emphasis is placed on the everyday lives, problems, and accomplishments of people, their role in developing social, economic, and political structures, as well as in establishing and spreading ideas that helped transform the world forever.

Students develop higher levels of critical thinking by considering why civilizations developed where and when they did, why they became dominant, and why they declined. Students analyze the interactions among the various cultures, emphasizing their enduring contributions and the link, despite time, between the contemporary and ancient worlds.

Students describe what is known through archaeological studies of the early physical and cultural development of humankind from the Paleolithic era to the agricultural revolution.

Discuss the climatic changes and human modifications of the physical environment that gave rise to the domestication of plants and animals and new sources of clothing and shelter.

Trace the development of agricultural techniques that permitted the production of economic surplus and the emergence of cities as centers of culture and power.

- Understand the relationship between religion and the social and political order in Mesopotamia and Egypt.
- Know the significance of Hammurabi’s Code.
- Trace the evolution of language and its written forms.

Students analyze the geographic, political, economic, religious, and social structures of the Ancient Hebrews.

- Describe the origins and significance of Judaism as the first monotheistic religion based on the concept of one God who sets down moral laws for humanity.
- Identify the sources of the ethical teachings and central beliefs of Judaism (the Hebrew Bible, the Commentaries): belief in God, observance of law, practice of the concepts of righteousness and justice, and importance of study; and describe how the ideas of the Hebrew traditions are reflected in the moral and ethical traditions of Western civilization.
- Explain the significance of Abraham, Moses, Naomi, Ruth, David, and Yohanan ben Zaccai in the development of the Jewish religion.
- Discuss the locations of the settlements and movements of Hebrew peoples, including the Exodus and their movement to and from Egypt, and outline the significance of the Exodus to the Jewish and other people.
- Discuss how Judaism survived and developed despite the continuing dispersion of much of the Jewish population from Jerusalem and the rest of Israel after the destruction of the second Temple in A.D. 70.

Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of Ancient Greece.

- Discuss the connections between geography and the development of city-states in the region of the Aegean Sea, including patterns of trade and commerce among Greek city-states and within the wider Mediterranean region.
- Trace the transition from tyranny and oligarchy to early democratic forms of government and back to dictatorship in ancient Greece, including the significance of the invention of the idea of citizenship (e.g., from Pericles’ Funeral Oration).
- Outline the founding, expansion, and political organization of the Persian Empire.
- Compare and contrast life in Athens and Sparta, with emphasis on their roles in the Persian and Peloponnesian Wars.
- Trace the rise of Alexander the Great and the spread of Greek culture eastward and into Egypt.
- Describe the enduring contributions of important Greek figures in the arts and sciences (e.g., Hypatia, Socrates, Plato, Aristotle, Euclid, Thucydides).

Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of India.

- Discuss the significance of the Aryan invasions.
- Explain the major beliefs and practices of Brahmanism in India and how they evolved into early Hinduism.
- Outline the social structure of the caste system.
- Know the life and moral teachings of Buddha and how Buddhism spread in India, Ceylon, and Central Asia.
- Describe the growth of the Maurya empire and the political and moral achievements of the emperor Asoka.
- Discuss important aesthetic and intellectual traditions (e.g., Sanskrit literature, including the Bhagavad Gita; medicine; metallurgy; and mathematics, including Hindu-Arabic numerals and the zero).

Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of China.

- Locate and describe the origins of Chinese civilization in the Huang-He Valley during the Shang Dynasty.
- Explain the geographic features of China that made governance and the spread of ideas and goods difficult and served to isolate the country from the rest of the world.
- Know about the life of Confucius and the fundamental teachings of Confucianism and Taoism.
- Identify the political and cultural problems prevalent in the time of Confucius and how he sought to solve them.
- List the policies and achievements of the emperor Shi Huangdi in unifying northern China under the Qin Dynasty.
- Detail the political contributions of the Han Dynasty to the development of the imperial bureaucratic state and the expansion of the empire.
- Cite the significance of the trans-Eurasian “silk roads” in the period of the Han Dynasty and Roman Empire and their locations.
- Describe the diffusion of Buddhism northward to China during the Han Dynasty.

Students analyze the geographic, political, economic, religious, and social structures during the development of Rome.

- Identify the location and describe the rise of the Roman Republic, including the importance of such mythical and historical figures as Aeneas, Romulus and Remus, Cincinnatus, Julius Caesar, and Cicero.
- Describe the government of the Roman Republic and its significance (e.g., written constitution and tripartite government, checks and balances, civic duty).
- Identify the location of and the political and geographic reasons for the growth of Roman territories and expansion of the empire, including how the empire fostered economic growth through the use of currency and trade routes.
- Discuss the influence of Julius Caesar and Augustus in Rome’s transition from republic to empire.
- Trace the migration of Jews around the Mediterranean region and the effects of their conflict with the Romans, including the Romans’ restrictions on their right to live in Jerusalem.
- Note the origins of Christianity in the Jewish Messianic prophecies, the life and teachings of Jesus of Nazareth as described in the New Testament, and the contribution of St. Paul the Apostle to the definition and spread of Christian beliefs (e.g., belief in the Trinity, resurrection, salvation).
- Describe the circumstances that led to the spread of Christianity in Europe and other Roman territories.
- Discuss the legacies of Roman art and architecture, technology and science, literature, language, and law.

GRADE 10 **SELECTED TOP PRIORITY STANDARDS**

**ENGLISH**

- Students apply their knowledge of word origins to determine the meaning of new words encountered in reading materials and use those words accurately.
- Students read and understand grade-level-appropriate material. They analyze the organizational patterns, arguments, and positions advanced.
- Students read and respond to historically or culturally significant works of literature that reflect and enhance their studies of history and social science. They conduct in-depth analyses of recurrent patterns and themes. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.
- Students write coherent and focused essays that convey a well-defined perspective and tightly reasoned argument. The writing demonstrates students’ awareness of the audience and purpose.
- Students combine the rhetorical strategies of narration, exposition, persuasion, and description to produce texts of at least 1,500 words each. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies.
- Write biographical or autobiographical narratives or short stories; Write responses to literature; Write expository compositions, including analytical essays and research reports; Write persuasive compositions; Write business letters; & Write technical documents (e.g., a manual on rules of behavior for conflict resolution, procedures for conducting a meeting, minutes of a meeting).
- Students write and speak with a command of standard English conventions.
- Students deliver polished formal and extemporaneous presentations that combine the traditional rhetorical strategies of narration, exposition, persuasion, and description. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies and must be able to deliver persuasive arguments (including evaluation and analysis of problems and solutions and causes and effects).

MATH

**Algebra II**

This discipline complements and expands the mathematical content and concepts of algebra I and geometry. Students who master algebra II will gain experience with algebraic solutions of problems in various content areas, including the solution of systems of quadratic equations, logarithmic and exponential functions, the binomial theorem, and the complex number system.

- Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices
- Students are adept at operations on polynomials, including long division.
- Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.
- Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator.
- Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.
- Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b) 2+ c.
- Students prove simple laws of logarithms.
- Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
- Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step.
- Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.
- Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.
- Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it.

Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.

- Students use fundamental counting principles to compute combinations and permutations.
- Students use combinations and permutations to compute probabilities.
- Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.
- Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.
- Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.
- Students use properties from number systems to justify steps in combining and simplifying functions.

**Science**

The fundamental life processes of plants and animals depend on a variety of chemical reactions that occur in specialized areas of the organism’s cells.

- Students know how eukaryotic cells are given shape and internal organization by a cytoskeleton or cell wall or both.
- Mutation and sexual reproduction lead to genetic variation in a population.
- A multicellular organism develops from a single zygote, and its phenotype depends on its genotype, which is established at fertilization.
- Genes are a set of instructions encoded in the DNA sequence of each organism that specify the sequence of amino acids in proteins characteristic of that organism.

The genetic composition of cells can be altered by incorporation of exogenous DNA into the cells. As a basis for understanding this concept:

- Stability in an ecosystem is a balance between competing effects.
- The frequency of an allele in a gene pool of a population depends on many factors and may be stable or unstable over time.
- Students know why natural selection acts on the phenotype rather than the genotype of an organism.
- As a result of the coordinated structures and functions of organ systems, the internal environment of the human body remains relatively stable (homeostatic) despite changes in the outside environment.

Organisms have a variety of mechanisms to combat disease.

As a basis for under-standing the human immune response:

- Students know the role of the skin in providing nonspecific defenses against infection.
- Students know the role of antibodies in the body’s response to infection.
- Students know how vaccination protects an individual from infectious diseases.
- Students know there are important differences between bacteria and viruses with respect to their requirements for growth and replication, the body’s primary defenses against bacterial and viral infections, and effective treatments of these infections.
- Students know why an individual with a compromised immune system (for example, a person with AIDS) may be unable to fight off and survive infections by microorganisms

**SOCIAL STUDIES**

**World History, Culture, and Geography: The Modern World**

Students relate the moral and ethical principles in ancient Greek and Roman philosophy, in Judaism, and in Christianity to the development of Western political thought.

Students compare and contrast the Glorious Revolution of England, the American Revolution, and the French Revolution and their enduring effects worldwide on the political expectations for self-government and individual liberty.

Students analyze the effects of the Industrial Revolution in England, France, Germany, Japan, and the United States.

- Analyze why England was the first country to industrialize.
- Examine how scientific and technological changes and new forms of energy brought about massive social, economic, and cultural change (e.g., the inventions and discoveries of James Watt, Eli Whitney, Henry Bessemer, Louis Pasteur, Thomas Edison).
- Describe the growth of population, rural to urban migration, and growth of cities associated with the Industrial Revolution.
- Trace the evolution of work and labor, including the demise of the slave trade and the effects of immigration, mining and manufacturing, division of labor, and the union movement.
- Understand the connections among natural resources, entrepreneurship, labor, and capital in an industrial economy.
- Analyze the emergence of capitalism as a dominant economic pattern and the responses to it, including Utopianism, Social Democracy, Socialism, and Communism.
- Describe the emergence of Romanticism in art and literature (e.g., the poetry of William Blake and William Wordsworth), social criticism (e.g., the novels of Charles Dickens), and the move away from Classicism in Europe.

Students analyze patterns of global change in the era of New Imperialism in at least two of the following regions or countries: Africa, Southeast Asia, China, India, Latin America, and the Philippines.

- Describe the rise of industrial economies and their link to imperialism and colonial-ism (e.g., the role played by national security and strategic advantage; moral issues raised by the search for national hegemony, Social Darwinism, and the missionary impulse; material issues such as land, resources, and technology).
- Discuss the locations of the colonial rule of such nations as England, France, Germany, Italy, Japan, the Netherlands, Russia, Spain, Portugal, and the United States.
- Explain imperialism from the perspective of the colonizers and the colonized and the varied immediate and long-term responses by the people under colonial rule.
- Describe the independence struggles of the colonized regions of the world, including the roles of leaders, such as Sun Yat-sen in China, and the roles of ideology and religion.
- Students analyze the causes and course of the First World War.
- Analyze the arguments for entering into war presented by leaders from all sides of the Great War and the role of political and economic rivalries, ethnic and ideological conflicts, domestic discontent and disorder, and propaganda and nationalism in mobilizing the civilian population in support of “total war.”
- Examine the principal theaters of battle, major turning points, and the importance of geographic factors in military decisions and outcomes (e.g., topography, waterways, distance, climate).
- Explain how the Russian Revolution and the entry of the United States affected the course and outcome of the war.
- Understand the nature of the war and its human costs (military and civilian) on all sides of the conflict, including how colonial peoples contributed to the war effort.
- Discuss human rights violations and genocide, including the Ottoman government’s actions against Armenian citizens.

Students analyze the effects of the First World War.

- Analyze the aims and negotiating roles of world leaders, the terms and influence of the Treaty of Versailles and Woodrow Wilson’s Fourteen Points, and the causes and effects of the United States’s rejection of the League of Nations on world politics.
- Describe the effects of the war and resulting peace treaties on population movement, the international economy, and shifts in the geographic and political borders of Europe and the Middle East.
- Understand the widespread disillusionment with prewar institutions, authorities, and values that resulted in a void that was later filled by totalitarians.
- Discuss the influence of World War I on literature, art, and intellectual life in the West (e.g., Pablo Picasso, the “lost generation” of Gertrude Stein, Ernest Hemingway).

Students analyze the rise of totalitarian governments after World War I.

- Understand the causes and consequences of the Russian Revolution, including Lenin’s use of totalitarian means to seize and maintain control (e.g., the Gulag).
- Trace Stalin’s rise to power in the Soviet Union and the connection between economic policies, political policies, the absence of a free press, and systematic violations of human rights (e.g., the Terror Famine in Ukraine).
- Analyze the rise, aggression, and human costs of totalitarian regimes (Fascist and Communist) in Germany, Italy, and the Soviet Union, noting especially their common and dissimilar traits.

Students analyze the causes and consequences of World War II.

- Compare the German, Italian, and Japanese drives for empire in the 1930s, including the 1937 Rape of Nanking, other atrocities in China, and the Stalin-Hitler Pact of 1939.
- Understand the role of appeasement, nonintervention (isolationism), and the domestic distractions in Europe and the United States prior to the outbreak of World War II.
- Identify and locate the Allied and Axis powers on a map and discuss the major turning points of the war, the principal theaters of conflict, key strategic decisions, and the resulting war conferences and political resolutions, with emphasis on the importance of geographic factors.
- Describe the political, diplomatic, and military leaders during the war (e.g., Winston Churchill, Franklin Delano Roosevelt, Emperor Hirohito, Adolf Hitler, Benito Mussolini, Joseph Stalin, Douglas MacArthur, Dwight Eisenhower).
- Analyze the Nazi policy of pursuing racial purity, especially against the European Jews; its transformation into the Final Solution; and the Holocaust that resulted in the murder of six million Jewish civilians.
- Discuss the human costs of the war, with particular attention to the civilian and military losses in Russia, Germany, Britain, the United States, China, and Japan.

Students analyze the international developments in the post-World World War II world.

- Compare the economic and military power shifts caused by the war, including the Yalta Pact, the development of nuclear weapons, Soviet control over Eastern European nations, and the economic recoveries of Germany and Japan.
- Analyze the causes of the Cold War, with the free world on one side and Soviet client states on the other, including competition for influence in such places as Egypt, the Congo, Vietnam, and Chile.

Students analyze instances of nation-building in the contemporary world in at least two of the following regions or countries: the Middle East, Africa, Mexico and other parts of Latin America, and China.

- Understand the challenges in the regions, including their geopolitical, cultural, military, and economic significance and the international relationships in which they are involved.
- Describe the recent history of the regions, including political divisions and systems, key leaders, religious issues, natural features, resources, and population patterns.
- Discuss the important trends in the regions today and whether they appear to serve the cause of individual freedom and democracy.

Students analyze the integration of countries into the world economy and the information, technological, and communications revolutions (e.g., television, satellites, computers).

**GRADE 11 ****SELECTED TOP PRIORITY STANDARDS**

**ENGLISH**

Students read and understand grade-level-appropriate material. They analyze the organizational patterns, arguments, and positions advanced.

Analyze both the features and the rhetorical devices of different types of public documents (e.g., policy statements, speeches, debates, platforms) and the way in which authors use those features and devices.

Analyze the way in which clarity of meaning is affected by the patterns of organization, hierarchical structures, repetition of the main ideas, syntax, and word choice in the text.

Verify and clarify facts presented in other types of expository texts by using a variety of consumer, workplace, and public documents.

Make warranted and reasonable assertions about the author’s arguments by using elements of the text to defend and clarify interpretations.

Analyze an author’s implicit and explicit philosophical assumptions and beliefs about a subject.

Critique the power, validity, and truthfulness of arguments set forth in public documents; their appeal to both friendly and hostile audiences; and the extent to which the arguments anticipate and address reader concerns and counterclaims (e.g., appeal to reason, to authority, to pathos and emotion).

Analyze ways in which poets use imagery, personification, figures of speech, and sounds to evoke readers’ emotions.

Students write coherent and focused texts that convey a well-defined perspective and tightly reasoned argument. The writing demonstrates students’ awareness of the audience and purpose and progression through the stages of the writing process.

Demonstrate an understanding of the elements of discourse (e.g., purpose, speaker, audience, form) when completing narrative, expository, persuasive, or descriptive writing assignments.

Structure ideas and arguments in a sustained, persuasive, and sophisticated way and support them with precise and relevant examples.

Enhance meaning by employing rhetorical devices, including the extended use of parallelism, repetition, and analogy; the incorporation of visual aids (e.g., graphs, tables, pictures); and the issuance of a call for action.

Develop presentations by using clear research questions and creative and critical research strategies (e.g., field studies, oral histories, interviews, experiments, electronic sources).

Use systematic strategies to organize and record information (e.g., anecdotal scripting, annotated bibliographies).

Integrate databases, graphics, and spreadsheets into word-processed documents.

Revise text to highlight the individual voice, improve sentence variety and style, and enhance subtlety of meaning and tone in ways that are consistent with the purpose, audience, and genre.

Students combine the rhetorical strategies of narration, exposition, persuasion, and description to produce texts of at least 1,500 words each. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies.

Write reflective compositions: Explore the significance of personal experiences, events, conditions, or concerns by using rhetorical strategies (e.g., narration, description, exposition, persuasion); Draw comparisons between specific incidents and broader themes that illustrate the writer’s important beliefs or generalizations about life; Maintain a balance in describing individual incidents and relate those incidents to more general and abstract ideas.

Write job applications and résumés; Provide clear and purposeful information and address the intended audience appropriately; Use varied levels, patterns, and types of language to achieve intended effects and aid comprehension.

Modify the tone to fit the purpose and audience.

- Follow the conventional style for that type of document (e.g., résumé, memorandum) and use page formats, fonts, and spacing that contribute to the readability and impact of the document.

Deliver multimedia presentations:

- Combine text, images, and sound and draw information from many sources (e.g., television broadcasts, videos, films, newspapers, magazines, CD-ROMs, the Internet, electronic media-generated images).

- Select an appropriate medium for each element of the presentation.
- Use the selected media skillfully, editing appropriately and monitoring for quality.
- Test the audience’s response and revise the presentation accordingly.

Students write and speak with a command of standard English conventions.

- Demonstrate control of grammar, diction, and paragraph and sentence structure and an understanding of English usage.
- Produce legible work that shows accurate spelling and correct punctuation and capitalization.
- Reflect appropriate manuscript requirements in writing.

Students formulate adroit judgments about oral communication. They deliver focused and coherent presentations that convey clear and distinct perspectives and demonstrate solid reasoning. They use gestures, tone, and vocabulary tailored to the audience and purpose.

Recognize strategies used by the media to inform, persuade, entertain, and transmit culture (e.g., advertisements; perpetuation of stereotypes; use of visual representations, special effects, language).

Analyze the impact of the media on the democratic process (e.g., exerting influence on elections, creating images of leaders, shaping attitudes) at the local, state, and national levels.

Distinguish between and use various forms of classical and contemporary logical arguments, including:

- Inductive and deductive reasoning
- Syllogisms and analogies

Use research and analysis to justify strategies for gesture, movement, and vocalization, including dialect, pronunciation, and enunciation.

Students deliver polished formal and extemporaneous presentations that combine traditional rhetorical strategies of narration, exposition, persuasion, and description. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies.

MATH

**PreCalculus with Trigonometry**

- Understand patterns, relations, and functions on PreCal with Trigo
- Represent and analyze mathematical situations and structures using algebraic symbols
- Use mathematical models to represent and understand quantitative relationships
- Analyze change in various contexts
- Organize and consolidate their mathematical thinking through communication
- Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
- Analyze and evaluate the mathematical thinking and strategies of others
- Use the language of mathematics to express mathematical ideas precisely

**Trigonometry**

Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Facility with these functions as well as the ability to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college.

- Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.
- Students know the definition of sine and cosine as y-and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.
- Students know the identity cos2 (x) + sin2 (x) = 1:
- Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity).
- Students prove other trigonometric identities and simplify others by using the identity cos2 (x) + sin2 (x) = 1. For example, students use this identity to prove that sec2 (x) = tan2 (x) + 1.
- Students graph functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.
- Students know the definitions of the tangent and cotangent functions and can graph them.
- Students know the definitions of the secant and cosecant functions and can graph them.
- Students know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line.
- Students know the definitions of the inverse trigonometric functions and can graph the functions.
- Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.
- Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs and can use those formulas to prove and/or simplify other trigonometric identities.
- Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/or simplify other trigonometric identities.
- Students use trigonometry to determine unknown sides or angles in right triangles.
- Students know the law of sines and the law of cosines and apply those laws to solve problems.
- Students determine the area of a triangle, given one angle and the two adjacent sides.
- Students are familiar with polar coordinates. In particular, they can determine polar coordinates of a point given in rectangular coordinates and vice versa.
- Students represent equations given in rectangular coordinates in terms of polar coordinates.
- Students are familiar with complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in their polar form.
- Students know DeMoivre’s theorem and can give nth roots of a complex number given in polar form.
- Students are adept at using trigonometry in a variety of applications and word problems.

SCIENCE

**Atomic and Molecular Structure**

The periodic table displays the elements in increasing atomic number and shows how periodicity of the physical and chemical properties of the elements relates to atomic structure. As a basis for understanding this concept:

- Students know how to relate the position of an element in the periodic table to its atomic number and atomic mass.
- Students know how to use the periodic table to identify metals, semimetals, nonmetals, and halogens.
- Students know how to use the periodic table to identify alkali metals, alkaline earth metals and transition metals, trends in ionization energy, electronegativity, and the relative sizes of ions and atoms.

Biological, chemical, and physical properties of matter result from the ability of atoms to form bonds from electrostatic forces between electrons and protons and between atoms and molecules. As a basis for understanding this concept:

- Students know atoms combine to form molecules by sharing electrons to form covalent or metallic bonds or by exchanging electrons to form ionic bonds.
- Students know chemical bonds between atoms in molecules such as H2 , CH4 , NH3 , H2 CCH2 , N2 , Cl2, and many large biological molecules are covalent.
- Students know salt crystals, such as NaCl, are repeating patterns of positive and negative ions held together by electrostatic attraction.

The conservation of atoms in chemical reactions leads to the principle of conservation of matter and the ability to calculate the mass of products and reactants. As a basis for understanding this concept:

- Students know how to describe chemical reactions by writing balanced equations.
- Students know the quantity one mole is set by defining one mole of carbon 12 atoms to have a mass of exactly 12 grams.
- Students know one mole equals 6.02x1023particles (atoms or molecules).
- Students know how to determine the molar mass of a molecule from its chemical formula and a table of atomic masses and how to convert the mass of a molecular substance to moles, number of particles, or volume of gas at standard temperature and pressure.

The kinetic molecular theory describes the motion of atoms and molecules and explains the properties of gases. As a basis for understanding this concept:

- Students know the random motion of molecules and their collisions with a surface create the observable pressure on that surface.
- Students know the random motion of molecules explains the diffusion of gases.
- Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.

Acids, bases, and salts are three classes of compounds that form ions in water solutions. As a basis for understanding this concept:

- Students know the observable properties of acids, bases, and salt solutions.
- Students know acids are hydrogen-ion-donating and bases are hydrogen-ion-accepting substances.

Solutions are homogeneous mixtures of two or more substances. As a basis for understanding this concept:

- Students know the definitions of solute and solvent.
- Students know how to describe the dissolving process at the molecular level by using the concept of random molecular motion.

Energy is exchanged or transformed in all chemical reactions and physical changes of matter. As a basis for understanding this concept:

- Students know how to describe temperature and heat flow in terms of the motion of molecules (or atoms).
- Students know chemical processes can either release (exothermic) or absorb (endothermic) thermal energy.

Chemical reaction rates depend on factors that influence the frequency of collision of reactant molecules. As a basis for understanding this concept:

- Students know the rate of reaction is the decrease in concentration of reactants or the increase in concentration of products with time.
- Students know how reaction rates depend on such factors as concentration, temperature, and pressure.

Chemical equilibrium is a dynamic process at the molecular level. As a basis for understanding this concept:

The bonding characteristics of carbon allow the formation of many different organic molecules of varied sizes, shapes, and chemical properties and provide the biochemical basis of life. As a basis for understanding this concept:

- Students know large molecules (polymers), such as proteins, nucleic acids, and starch, are formed by repetitive combinations of simple subunits.

Nuclear processes are those in which an atomic nucleus changes, including radioactive decay of naturally occurring and human-made isotopes, nuclear fission, and nuclear fusion. As a basis for understanding this concept:

- Students know protons and neutrons in the nucleus are held together by nuclear forces that overcome the electromagnetic repulsion between the protons.
- Students know the energy release per gram of material is much larger in nuclear fusion or fission reactions than in chemical reactions. The change in mass (calculated by E = mc2) is small but significant in nuclear reactions.
- Students know some naturally occurring isotopes of elements are radioactive, as are isotopes formed in nuclear reactions.

SOCIAL STUDIES

**Principles of American Democracy**

Students explain the fundamental principles and moral values of American democracy as expressed in the U.S. Constitution and other essential documents of American democracy.

- Analyze the influence of ancient Greek, Roman, English, and leading European political thinkers such as John Locke, Charles-Louis Montesquieu, Niccolò Machiavelli, and William Blackstone on the development of American government.
- Discuss the character of American democracy and its promise and perils as articulated by Alexis de Tocqueville.

Students evaluate and take and defend positions on the scope and limits of rights and obligations as democratic citizens, the relationships among them, and how they are secured.

- Explain how economic rights are secured and their importance to the individual and to society (e.g., the right to acquire, use, transfer, and dispose of property; right to choose one’s work; right to join or not join labor unions; copyright and patent).
- Understand the obligations of civic-mindedness, including voting, being informed on civic issues, volunteering and performing public service, and serving in the military or alternative service.
- Describe the reciprocity between rights and obligations; that is, why enjoyment of one’s rights entails respect for the rights of others.

Students evaluate and take and defend positions on what the fundamental values and principles of civil society are (i.e., the autonomous sphere of voluntary personal, social, and economic relations that are not part of government), their interdependence, and the meaning and importance of those values and principles for a free society.

- Explain how civil society provides opportunities for individuals to associate for social, cultural, religious, economic, and political purposes.
- Explain how civil society makes it possible for people, individually or in association with others, to bring their influence to bear on government in ways other than voting and elections.
- Compare the relationship of government and civil society in constitutional democracies to the relationship of government and civil society in authoritarian and totalitarian regimes.

Students analyze the unique roles and responsibilities of the three branches of government as established by the U.S. Constitution.

- Discuss Article I of the Constitution as it relates to the legislative branch, including eligibility for office and lengths of terms of representatives and senators; election to office; the roles of the House and Senate in impeachment proceedings; the role of the vice president; the enumerated legislative powers; and the process by which a bill becomes a law.
- Explain the process through which the Constitution can be amended.

Students summarize landmark U.S. Supreme Court interpretations of the Constitution and its amendments.

- Understand the changing interpretations of the Bill of Rights over time, including interpretations of the basic freedoms (religion, speech, press, petition, and assembly) articulated in the First Amendment and the due process and equal-protection-of-the-law clauses of the Fourteenth Amendment.

Students evaluate issues regarding campaigns for national, state, and local elective offices.

- Analyze the origin, development, and role of political parties, noting those occasional periods in which there was only one major party or were more than two major parties.
- Discuss the history of the nomination process for presidential candidates and the increasing importance of primaries in general elections.
- Describe the means that citizens use to participate in the political process (e.g., voting, campaigning, lobbying, filing a legal challenge, demonstrating, petitioning, picketing, running for political office).

Students analyze and compare the powers and procedures of the national, state, tribal, and local governments.

- Explain how conflicts between levels of government and branches of government are resolved.

Students evaluate and take and defend positions on the influence of the media on American political life.

- Discuss the meaning and importance of a free and responsible press.
- Describe the roles of broadcast, print, and electronic media, including the Internet, as means of communication in American politics.

Students analyze the origins, characteristics, and development of different political systems across time, with emphasis on the quest for political democracy, its advances, and its obstacles.

- Explain how the different philosophies and structures of feudalism, mercantilism, socialism, fascism, communism, monarchies, parliamentary systems, and constitutional liberal democracies influence economic policies, social welfare policies, and human rights practices.
- Describe for at least two countries the consequences of conditions that gave rise to tyrannies during certain periods (e.g., Italy, Japan, Haiti, Nigeria, Cambodia).
- Identify the forms of illegitimate power that twentieth-century African, Asian, and Latin American dictators used to gain and hold office and the conditions and interests that supported them.
- Identify the successes of relatively new democracies in Africa, Asia, and Latin America and the ideas, leaders, and general societal conditions that have launched and sustained, or failed to sustain, them.

Students formulate questions about and defend their analyses of tensions within our constitutional democracy and the importance of maintaining a balance between the following concepts: majority rule and individual rights; liberty and equality; state and national authority in a federal system; civil disobedience and the rule of law; freedom of the press and the right to a fair trial; the relationship of religion and government.

**Principles of Economics**

Students understand common economic terms and concepts and economic reasoning.

- Examine the causal relationship between scarcity and the need for choices.
- Analyze the role of a market economy in establishing and preserving political and personal liberty (e.g., through the works of Adam Smith).

Students analyze the elements of America’s market economy in a global setting.

- Understand the relationship of the concept of incentives to the law of supply and the relationship of the concept of incentives and substitutes to the law of demand.
- Discuss the effects of changes in supply and/ or demand on the relative scarcity, price, and quantity of particular products.
- Explain the roles of property rights, competition, and profit in a market economy.
- Explain how prices reflect the relative scarcity of goods and services and perform the allocative function in a market economy.
- Understand the process by which competition among buyers and sellers determines a market price.
- Analyze how domestic and international competition in a market economy affects goods and services produced and the quality, quantity, and price of those products.

Students analyze the influence of the federal government on the American economy.

- Understand how the role of government in a market economy often includes providing for national defense, addressing environmental concerns, defining and enforcing property rights, attempting to make markets more competitive, and protecting consumers’ rights.
- Describe the aims of government fiscal policies (taxation, borrowing, spending) and their influence on production, employment, and price levels.

Students analyze the elements of the U.S. labor market in a global setting.

- Understand the operations of the labor market, including the circumstances surrounding the establishment of principal American labor unions, procedures that unions use to gain benefits for their members, the effects of unionization, the mini-mum wage, and unemployment insurance.
- Describe the current economy and labor market, including the types of goods and services produced, the types of skills workers need, the effects of rapid technological change, and the impact of international competition.

Students analyze the aggregate economic behavior of the U.S. economy.

- Define, calculate, and explain the significance of an unemployment rate, the number of new jobs created monthly, an inflation or deflation rate, and a rate of economic growth.
- Distinguish between short-term and long-term interest rates and explain their relative significance.

Students analyze issues of international trade and explain how the U.S. economy affects, and is affected by, economic forces beyond the United States’s borders.

- Explain foreign exchange, the manner in which exchange rates are determined, and the effects of the dollar’s gaining (or losing) value relative to other currencies.

**SOCIOLOGY**

- Discuss what is sociology and its practical importance to society.
- Explain the origins and scope of Sociology and the methods used by sociologists in the study of human behavior.
- Describe social issues and note their sociological implications.
- Analyze the ways in which groups influence social institutions, teach individuals what is appropriate and inappropriate, facilitate change and hinder it, indicate status, class and power level and show prejudice and discrimination.
- Discuss the basic characteristics of culture and analyze how cultures differ as well as how cultures passes values, beliefs, and traditions to the next generation and sanction behaviors.
- Differentiate the three major sociological orientations: conflict theory, structural functionalism and symbolic interactionism.

Grade 12 Selected Top Priority Standards

**ENGLISH**

Students apply their knowledge of word origins to determine the meaning of new words encountered in reading materials and use those words accurately.

Analyze both the features and the rhetorical devices of different types of public documents (e.g., policy statements, speeches, debates, platforms) and the way in which authors use those features and devices.

Analyze the way in which clarity of meaning is affected by the patterns of organization, hierarchical structures, repetition of the main ideas, syntax, and word choice in the text.

Verify and clarify facts presented in other types of expository texts by using a variety of consumer, workplace, and public documents.

Make warranted and reasonable assertions about the author’s arguments by using elements of the text to defend and clarify interpretations.

Students write coherent and focused texts that convey a well-defined perspective and tightly reasoned argument. The writing demonstrates students’ awareness of the audience and purpose and progression through the stages of the writing process.

Enhance meaning by employing rhetorical devices, including the extended use of parallelism, repetition, and analogy; the incorporation of visual aids (e.g., graphs, tables, pictures); and the issuance of a call for action.

Use language in natural, fresh, and vivid ways to establish a specific tone.

Develop presentations by using clear research questions and creative and critical research strategies (e.g., field studies, oral histories, interviews, experiments, electronic sources).

Use systematic strategies to organize and record information (e.g., anecdotal scripting, annotated bibliographies).

Integrate databases, graphics, and spreadsheets into word-processed documents.

Revise text to highlight the individual voice, improve sentence variety and style, and enhance subtlety of meaning and tone in ways that are consistent with the purpose, audience, and genre.

Students combine the rhetorical strategies of narration, exposition, persuasion, and description to produce texts of at least 1,500 words each. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies outlined in.

WRITING STANDARD 1.0.

Write reflective compositions: Explore the significance of personal experiences, events, conditions, or concerns by using rhetorical strategies (e.g., narration, description, exposition, persuasion); Draw comparisons between specific incidents and broader themes that illustrate the writer’s important beliefs or generalizations about life; Maintain a balance in describing individual incidents and relate those incidents to more general and abstract ideas.

Write job applications and résumés: Provide clear and purposeful information and address the intended audience appropriately; Use varied levels, patterns, and types of language to achieve intended effects and aid comprehension; Modify the tone to fit the purpose and audience; Follow the conventional style for that type of document (e.g., résumé, memorandum) and use page formats, fonts, and spacing that contribute to the readability and impact of the document.

Deliver multimedia presentations: Combine text, images, and sound and draw information from many sources (e.g., television broadcasts, videos, films, newspapers, magazines, CD-ROMs, the Internet, electronic media-generated images); Select an appropriate medium for each element of the presentation; Use the selected media skillfully, editing appropriately and monitoring for quality; Test the audience’s response and revise the presentation accordingly.

Students write and speak with a command of standard English conventions.

Demonstrate control of grammar, diction, and paragraph and sentence structure and an understanding of English usage.

Produce legible work that shows accurate spelling and correct punctuation and capitalization.

Reflect appropriate manuscript requirements in writing.

Students formulate adroit judgments about oral communication. They deliver focused and coherent presentations that convey clear and distinct perspectives and demonstrate solid reasoning. They use gestures, tone, and vocabulary tailored to the audience and purpose.

Recognize strategies used by the media to inform, persuade, entertain, and transmit culture (e.g., advertisements; perpetuation of stereotypes; use of visual representations, special effects, language).

Interpret and evaluate the various ways in which events are presented and information is communicated by visual image makers (e.g., graphic artists, documentary filmmakers, illustrators, news photographers).

Use rhetorical questions, parallel structure, concrete images, figurative language, characterization, irony, and dialogue to achieve clarity, force, and aesthetic effect.

Distinguish between and use various forms of classical and contemporary logical arguments, including:

Inductive and deductive reasoning

Syllogisms and analogies

Use research and analysis to justify strategies for gesture, movement, and vocalization, including dialect, pronunciation, and enunciation.

Critique a speaker’s diction and syntax in relation to the purpose of an oral communication and the impact the words may have on the audience.

Analyze the four basic types of persuasive speech (i.e., propositions of fact, value, problem, or policy) and understand the similarities and differences in their patterns of organization and the use of persuasive language, reasoning, and proof.

Students deliver polished formal and extemporaneous presentations that combine traditional rhetorical strategies of narration, exposition, persuasion, and description. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Deliver reflective presentations: Explore the significance of personal experiences, events, conditions, or concerns, using appropriate rhetorical strategies (e.g., narration, description, exposition, persuasion); Draw comparisons between the specific incident and broader themes that illustrate the speaker’s beliefs or generalizations about life; Maintain a balance between describing the incident and relating it to more general, abstract ideas.

Deliver multimedia presentations: Combine text, images, and sound by incorporating information from a wide range of media, including films, newspapers, magazines, CD-ROMs, online information, television, videos, and electronic media-generated images; Select an appropriate medium for each element of the presentation; Use the selected media skillfully, editing appropriately and monitoring for quality; Test the audience’s response and revise the presentation accordingly.

MATH

**Calculus**

Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions. This knowledge includes one-sided limits, infinite limits, and limits at infinity. Students know the definition of convergence and divergence of a function as the domain variable approaches either a number or infinity:

Students prove and use theorems evaluating the limits of sums, products, quotients, and composition of functions.

Students use graphical calculators to verify and estimate limits.

Students prove and use special limits, such as the limits of (sin(x))/x and (1-cos(x))/x as x tends to 0.

Students demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function.

Students demonstrate an understanding and the application of the intermediate value theorem and the extreme value theorem.

Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability:

Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function.

Students demonstrate an understanding of the interpretation of the derivative as an instantaneous rate of change. Students can use derivatives to solve a variety of problems from physics, chemistry, economics, and so forth that involve the rate of change of a function.

Students understand the relation between differentiability and continuity.

Students derive derivative formulas and use them to find the derivatives of algebraic, trigonometric, inverse trigonometric, exponential, and logarithmic functions.

Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.

Students find the derivatives of parametrically defined functions and use implicit differentiation in a wide variety of problems in physics, chemistry, economics, and so forth.

Students compute derivatives of higher orders.

Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.

Students know Newton’s method for approximating the zeros of a function.

Students use differentiation to solve optimization (maximum-minimum problems) in a variety of pure and applied contexts.

Students use differentiation to solve related rate problems in a variety of pure and applied contexts.

Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals.

Students apply the definition of the integral to model problems in physics, economics, and so forth, obtaining results in terms of integrals.

Students demonstrate knowledge and proof of the fundamental theorem of calculus and use it to interpret integrals as anti-derivatives.

Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.

Students compute, by hand, the integrals of a wide variety of functions by using techniques of integration, such as substitution, integration by parts, and trigonometric substitution. They can also combine these techniques when appropriate.

Students know the definitions and properties of inverse trigonometric functions and the expression of these functions as indefinite integrals.

Students compute, by hand, the integrals of rational functions by combining the techniques in the standards with the algebraic techniques of partial fractions and completing the square.

Students compute the integrals of trigonometric functions by using the techniques noted above.

Students understand the algorithms involved in Simpson’s rule and Newton’s method. They use calculators or computers or both to approximate integrals numerically.

Students understand improper integrals as limits of definite integrals.

Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges.

Students calculate Taylor polynomials and Taylor series of basic functions, including the remainder term.

Students know the techniques of solution of selected elementary differential equations and their applications to a wide variety of situations, including growth-and-decay problems.

**SCIENCE**

**Physics**

Standards that all students are expected to achieve in the course of their studies are unmarked.

Standards that all students should have the opportunity to learn are marked with an asterisk (*).

**Motion and Forces**

Newton’s laws predict the motion of most objects. As a basis for understanding this concept:

Students know how to solve problems that involve constant speed and average speed.

Students know that when forces are balanced, no acceleration occurs; thus an object continues to move at a constant speed or stays at rest (Newton’s first law).

Students know how to apply the law F=ma to solve one-dimensional motion problems that involve constant forces (Newton’s second law).

Students know that when one object exerts a force on a second object, the second object always exerts a force of equal magnitude and in the opposite direction (Newton’s third law).

Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth.

Students know applying a force to an object perpendicular to the direction of its motion causes the object to change direction but not speed (e.g., Earth’s gravitational force causes a satellite in a circular orbit to change direction but not speed).

Students know circular motion requires the application of a constant force directed toward the center of the circle.

Students know Newton’s laws are not exact but provide very good approximations unless an object is moving close to the speed of light or is small enough that quantum effects are important.

Students know how to solve two-dimensional trajectory problems.

Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components.

Students know how to solve two-dimensional problems involving balanced forces (statics).

Students know how to solve problems in circular motion by using the formula for centripetal acceleration in the following form: a=v2/r.

Students know how to solve problems involving the forces between two electric charges at a distance (Coulomb’s law) or the forces between two masses at a distance (universal gravitation).

**Conservation of Energy and Momentum**

The laws of conservation of energy and momentum provide a way to predict and describe the movement of objects. As a basis for understanding this concept:

Students know how to calculate kinetic energy by using the formula E=(1/2)mv2 .

Students know how to calculate changes in gravitational potential energy near Earth by using the formula (change in potential energy) =mgh (h is the change in the elevation).

Students know how to solve problems involving conservation of energy in simple systems, such as falling objects.

Students know how to calculate momentum as the product mv.

Students know momentum is a separately conserved quantity different from energy.

Students know an unbalanced force on an object produces a change in its momentum.

Students know how to solve problems involving elastic and inelastic collisions in one dimension by using the principles of conservation of momentum and energy.

Students know how to solve problems involving conservation of energy in simple systems with various sources of potential energy, such as capacitors and springs.

**Heat and Thermodynamics**

Energy cannot be created or destroyed, although in many processes energy is transferred to the environment as heat. As a basis for understanding this concept:

Students know heat flow and work are two forms of energy transfer between systems.

Students know that the work done by a heat engine that is working in a cycle is the difference between the heat flow into the engine at high temperature and the heat flow out at a lower temperature (first law of thermodynamics) and that this is an example of the law of conservation of energy.

Students know the internal energy of an object includes the energy of random motion of the object’s atoms and molecules, often referred to as thermal energy. The greater the temperature of the object, the greater the energy of motion of the atoms and molecules that make up the object.

Students know that most processes tend to decrease the order of a system over time and that energy levels are eventually distributed uniformly.

Students know that entropy is a quantity that measures the order or disorder of a system and that this quantity is larger for a more disordered system.

Students know the statement “Entropy tends to increase” is a law of statistical probability that governs all closed systems (second law of thermodynamics).

Students know how to solve problems involving heat flow, work, and efficiency in a heat engine and know that all real engines lose some heat to their surroundings.

**Waves**

Waves have characteristic properties that do not depend on the type of wave. As a basis for understanding this concept:

Students know waves carry energy from one place to another.

Students know how to identify transverse and longitudinal waves in mechanical media, such as springs and ropes, and on the earth (seismic waves).

Students know how to solve problems involving wavelength, frequency, and wave speed.

Students know sound is a longitudinal wave whose speed depends on the properties of the medium in which it propagates.

Students know radio waves, light, and X-rays are different wavelength bands in the spectrum of electromagnetic waves whose speed in a vacuum is approximately 3×108 m/s (186,000 miles/second).

Students know how to identify the characteristic properties of waves: interference (beats), diffraction, refraction, Doppler effect, and polarization.

**Electric and Magnetic Phenomena**

Electric and magnetic phenomena are related and have many practical applications. As a basis for understanding this concept:

Students know how to predict the voltage or current in simple direct current (DC) electric circuits constructed from batteries, wires, resistors, and capacitors.

Students know how to solve problems involving Ohm’s law.

Students know any resistive element in a DC circuit dissipates energy, which heats the resistor. Students can calculate the power (rate of energy dissipation) in any resistive circuit element by using the formula Power = IR (potential difference) × I (current) = I2R.

Students know the properties of transistors and the role of transistors in electric circuits.

Students know charged particles are sources of electric fields and are subject to the forces of the electric fields from other charges.

Students know magnetic materials and electric currents (moving electric charges) are sources of magnetic fields and are subject to forces arising from the magnetic fields of other sources.

Students know how to determine the direction of a magnetic field produced by a current flowing in a straight wire or in a coil.

Students know changing magnetic fields produce electric fields, thereby inducing currents in nearby conductors.

Students know plasmas, the fourth state of matter, contain ions or free electrons or both and conduct electricity.

Students know electric and magnetic fields contain energy and act as vector force fields.

Students know the force on a charged particle in an electric field is qE, where E is the electric field at the position of the particle and q is the charge of the particle.

Students know how to calculate the electric field resulting from a point charge.

Students know static electric fields have as their source some arrangement of electric charges.

Students know the magnitude of the force on a moving particle (with charge q) in a magnetic field is qvB sin(a), where a is the angle between v and B (v and B are the magnitudes of vectors v and B, respectively), and students use the right-hand rule to find the direction of this force.

Students know how to apply the concepts of electrical and gravitational potential energy to solve problems involving conservation of energy.

SOCIAL STUDIES

**Democracy**

Students explain the fundamental principles and moral values of American democracy as expressed in the U.S. Constitution and other essential documents of American democracy.

Discuss the character of American democracy and its promise and perils as articulated by Alexis de Tocqueville.

Students evaluate and take and defend positions on the scope and limits of rights and obligations as democratic citizens, the relationships among them, and how they are secured.

Discuss the meaning and importance of each of the rights guaranteed under the Bill of Rights and how each is secured (e.g., freedom of religion, speech, press, assembly, petition, privacy).

Explain how economic rights are secured and their importance to the individual and to society (e.g., the right to acquire, use, transfer, and dispose of property; right to choose one’s work; right to join or not join labor unions; copyright and patent).

Discuss the individual’s legal obligations to obey the law, serve as a juror, and pay taxes.

Understand the obligations of civic-mindedness, including voting, being informed on civic issues, volunteering and performing public service, and serving in the military or alternative service.

Describe the reciprocity between rights and obligations; that is, why enjoyment of one’s rights entails respect for the rights of others.

Explain how one becomes a citizen of the United States, including the process of naturalization (e.g., literacy, language, and other requirements).

Students evaluate and take and defend positions on what the fundamental values and principles of civil society are (i.e., the autonomous sphere of voluntary personal, social, and economic relations that are not part of government), their interdependence, and the meaning and importance of those values and principles for a free society.

Explain how civil society provides opportunities for individuals to associate for social, cultural, religious, economic, and political purposes.

Explain how civil society makes it possible for people, individually or in association with others, to bring their influence to bear on government in ways other than voting and elections.

Discuss the historical role of religion and religious diversity.

Compare the relationship of government and civil society in constitutional democracies to the relationship of government and civil society in authoritarian and totalitarian regimes.

Students analyze the unique roles and responsibilities of the three branches of government as established by the U.S. Constitution.

Discuss Article I of the Constitution as it relates to the legislative branch, including eligibility for office and lengths of terms of representatives and senators; election to office; the roles of the House and Senate in impeachment proceedings; the role of the vice president; the enumerated legislative powers; and the process by which a bill becomes a law.

Explain the process through which the Constitution can be amended.

Identify their current representatives in the legislative branch of the national government.

Discuss Article II of the Constitution as it relates to the executive branch, including eligibility for office and length of term, election to and removal from office, the oath of office, and the enumerated executive powers.

Discuss Article III of the Constitution as it relates to judicial power, including the length of terms of judges and the jurisdiction of the Supreme Court.

Explain the processes of selection and confirmation of Supreme Court justices.

Students summarize landmark U.S. Supreme Court interpretations of the Constitution and its amendments.

Understand the changing interpretations of the Bill of Rights over time, including interpretations of the basic freedoms (religion, speech, press, petition, and assembly) articulated in the First Amendment and the due process and equal-protection-of-the-law clauses of the Fourteenth Amendment.

Analyze judicial activism and judicial restraint and the effects of each policy over the decades (e.g., the Warren and Rehnquist courts).

Students evaluate issues regarding campaigns for national, state, and local elective offices.

Analyze the origin, development, and role of political parties, noting those occasional periods in which there was only one major party or were more than two major parties.

Discuss the history of the nomination process for presidential candidates and the increasing importance of primaries in general elections.

Evaluate the roles of polls, campaign advertising, and the controversies over campaign funding.

Describe the means that citizens use to participate in the political process (e.g., voting, campaigning, lobbying, filing a legal challenge, demonstrating, petitioning, picketing, running for political office).

Discuss the features of direct democracy in numerous states (e.g., the process of referendums, recall elections).

Analyze trends in voter turnout; the causes and effects of reapportionment and redistricting, with special attention to spatial districting and the rights of minorities; and the function of the Electoral College.

Students analyze and compare the powers and procedures of the national, state, tribal, and local governments.

Explain how conflicts between levels of government and branches of government are resolved.

Identify the major responsibilities and sources of revenue for state and local governments.

Explain how public policy is formed, including the setting of the public agenda and implementation of it through regulations and executive orders.

Compare the processes of lawmaking at each of the three levels of government, including the role of lobbying and the media.

Identify the organization and jurisdiction of federal, state, and local (e.g., California) courts and the interrelationships among them.

Understand the scope of presidential power and decision making through examination of case studies such as the Cuban Missile Crisis, passage of Great Society legislation, War Powers Act, Gulf War, and Bosnia.

Students evaluate and take and defend positions on the influence of the media on American political life.

Discuss the meaning and importance of a free and responsible press.

Describe the roles of broadcast, print, and electronic media, including the Internet, as means of communication in American politics.

Explain how public officials use the media to communicate with the citizenry and to shape public opinion.

Students analyze the origins, characteristics, and development of different political systems across time, with emphasis on the quest for political democracy, its advances, and its obstacles.

Explain how the different philosophies and structures of feudalism, mercantilism, socialism, fascism, communism, monarchies, parliamentary systems, and constitutional liberal democracies influence economic policies, social welfare policies, and human rights practices.

Discuss the advantages and disadvantages of federal, con federal, and unitary systems of government.

Describe for at least two countries the consequences of conditions that gave rise to tyrannies during certain periods (e.g., Italy, Japan, Haiti, Nigeria, Cambodia).

Identify the forms of illegitimate power that twentieth-century African, Asian, and Latin American dictators used to gain and hold office and the conditions and interests that supported them.

Describe the ideologies that give rise to Communism, methods of maintaining control, and the movements to overthrow such governments in Czechoslovakia, Hungary, and Poland, including the roles of individuals (e.g., Alexander Solzhenitsyn, Pope John Paul II, Lech Walesa, Vaclav Havel).

Identify the successes of relatively new democracies in Africa, Asia, and Latin America and the ideas, leaders, and general societal conditions that have launched and sustained, or failed to sustain, them.

Students formulate questions about and defend their analyses of tensions within our constitutional democracy and the importance of maintaining a balance between the following concepts: majority rule and individual rights; liberty and equality; state and national authority in a federal system; civil disobedience and the rule of law; freedom of the press and the right to a fair trial; the relationship of religion and government.

**Civics**

The students will have a broader understanding of the historical foundations of the US government. Further, they will gain knowledge on how to take part in the government processes as well as develop responsible citizenship. Responsibility toward the government is a crucial focus of this study.

**South-East Asia**

The students will be able to review the historical highlights of the countries of South-East Asia. They will be able to value and appreciate the cultural dimensions unique to the Asian cultures. Moreover, the students may be equipped with insights and know-how in applying and contextualizing the best of Western cultures and ideas into their own local government processes.

**PSYCHOLOGY**

Show an understanding of the science of psychology and the scientific method in written formats such as assignments and exams.

Through exams and other assessments, display a breadth of knowledge of current research, concepts, ethical principles, theories and perspectives in psychology, including recent developments and key figures in the field.

Apply the theoretical concepts to personal life as well as to synthesize psychological concepts with local and global consciousness and awareness.

Do independent assignments such as library orientations and writing skills workshops.