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11/12th Grade Language Arts

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Grades Eleven & Twelve Reading

1.0 Word Analysis, Fluency, and Systematic Vocabulary Development Students apply their knowledge of word origins to determine the meaning of new words encountered in reading materials and use those words accurately. Vocabulary and Concept Development 1.1 Trace the etymology of significant terms used in political science and history. 1.2 Apply knowledge of Greek, Latin, and Anglo-Saxon roots and affixes to draw inferences concerning the meaning of scientific and mathematical terminology. 1.3 Discern the meaning of analogies encountered, analyzing specific comparisons as well as relationships and inferences. 2.0 Reading Comprehension (Focus on Informational Materials) Students read and understand grade-level-appropriate material. They analyze the organizational patterns, arguments, and positions advanced. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition, by grade twelve, students read two million words annually on their own, including a wide variety of classic and contemporary literature, magazines, newspapers, and online information. Structural Features of Informational Materials 2.1 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. Comprehension and Analysis of Grade-Level-Appropriate Text 2.2 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. 2.3 Verify and clarify facts presented in other types of expository texts by using a variety of consumer, workplace, and public documents. 2.4 Make warranted and reasonable assertions about the author's arguments by using elements of the text to defend and clarify interpretations. 2.5 Analyze an author's implicit and explicit philosophical assumptions and beliefs about a subject. Expository Critique 2.6 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). 3.0 Literary Response and Analysis 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 themes. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. Structural Features of Literature 3.1 Analyze characteristics of subgenres (e.g., satire, parody, allegory, pastoral) that are used in poetry, prose, plays, novels, short stories, essays, and other basic genres. Narrative Analysis of Grade-Level-Appropriate Text 3.2 Analyze the way in which the theme or meaning of a selection represents a view or comment on life, using textual evidence to support the claim. 3.3 Analyze the ways in which irony, tone, mood, the author's style, and the "sound" of language achieve specific rhetorical or aesthetic purposes or both. 3.4 Analyze ways in which poets use imagery, personification, figures of speech, and sounds to evoke readers' emotions. 3.5 Analyze recognized works of American literature representing a variety of genres and traditions: a. Trace the development of American literature from the colonial period forward. b. Contrast the major periods, themes, styles, and trends and describe how works by members of different cultures relate to one another in each period. c. Evaluate the philosophical, political, religious, ethical, and social influences of the historical period that shaped the characters, plots, and settings. 3.6 Analyze the way in which authors through the centuries have used archetypes drawn from myth and tradition in literature, film, political speeches, and religious writings (e.g., how the archetypes of banishment from an ideal world may be used to interpret Shakespeare's tragedy Macbeth). 3.7 Analyze recognized works of world literature from a variety of authors: a. Contrast the major literary forms, techniques, and characteristics of the major literary periods (e.g., Homeric Greece, medieval, romantic, neoclassic, modern). b. Relate literary works and authors to the major themes and issues of their eras. c. Evaluate the philosophical, political, religious, ethical, and social influences of the historical period that shaped the characters, plots, and settings. Literary Criticism 3.8 Analyze the clarity and consistency of political assumptions in a selection of literary works or essays on a topic (e.g., suffrage, women's role in organized labor). (Political approach) 3.9 Analyze the philosophical arguments presented in literary works to determine whether the authors' positions have contributed to the quality of each work and the credibility of the characters. (Philosophical approach) Writing 1.0 Writing Strategies 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. Organization and Focus 1.1 Demonstrate an understanding of the elements of discourse (e.g., purpose, speaker, audience, form) when completing narrative, expository, persuasive, or descriptive writing assignments. 1.2 Use point of view, characterization, style (e.g., use of irony), and related elements for specific rhetorical and aesthetic purposes. 1.3 Structure ideas and arguments in a sustained, persuasive, and sophisticated way and support them with precise and relevant examples. 1.4 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. 1.5 Use language in natural, fresh, and vivid ways to establish a specific tone. Research and Technology 1.6 Develop presentations by using clear research questions and creative and critical research strategies (e.g., field studies, oral histories, interviews, experiments, electronic sources). 1.7 Use systematic strategies to organize and record information (e.g., anecdotal scripting, annotated bibliographies). 1.8 Integrate databases, graphics, and spreadsheets into word-processed documents. Evaluation and Revision 1.9 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. 2.0 Writing Applications (Genres and Their Characteristics) 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. Using the writing strategies of grades eleven and twelve outlined in Writing Standard 1.0, students: 2.1 Write fictional, autobiographical, or biographical narratives: a. Narrate a sequence of events and communicate their significance to the audience. b. Locate scenes and incidents in specific places. c. Describe with concrete sensory details the sights, sounds, and smells of a scene and the specific actions, movements, gestures, and feelings of the characters; use interior monologue to depict the characters' feelings. d. Pace the presentation of actions to accommodate temporal, spatial, and dramatic mood changes. e. Make effective use of descriptions of appearance, images, shifting perspectives, and sensory details. 2.2 Write responses to literature: a. Demonstrate a comprehensive understanding of the significant ideas in works or passages. b. Analyze the use of imagery, language, universal themes, and unique aspects of the text. c. Support important ideas and viewpoints through accurate and detailed references to the text and to other works. d. Demonstrate an understanding of the author's use of stylistic devices and an appreciation of the effects created. e. Identify and assess the impact of perceived ambiguities, nuances, and complexities within the text. 2.3 Write reflective compositions: a. Explore the significance of personal experiences, events, conditions, or concerns by using rhetorical strategies (e.g., narration, description, exposition, persuasion). b. Draw comparisons between specific incidents and broader themes that illustrate the writer's important beliefs or generalizations about life. c. Maintain a balance in describing individual incidents and relate those incidents to more general and abstract ideas. 2.4 Write historical investigation reports: a. Use exposition, narration, description, argumentation, or some combination of rhetorical strategies to support the main proposition. b. Analyze several historical records of a single event, examining critical relationships between elements of the research topic. c. Explain the perceived reason or reasons for the similarities and differences in historical records with information derived from primary and secondary sources to support or enhance the presentation. d. Include information from all relevant perspectives and take into consideration the validity and reliability of sources. e. Include a formal bibliography. 2.5 Write job applications and résumés: a. Provide clear and purposeful information and address the intended audience appropriately. b. Use varied levels, patterns, and types of language to achieve intended effects and aid comprehension. c. Modify the tone to fit the purpose and audience. d. 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. 2.6 Deliver multimedia presentations: a. 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). b. Select an appropriate medium for each element of the presentation. c. Use the selected media skillfully, editing appropriately and monitoring for quality. d. Test the audience's response and revise the presentation accordingly. Written and Oral English Language Conventions The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills. 1.0 Written and Oral English Language Conventions Students write and speak with a command of standard English conventions. 1.1 Demonstrate control of grammar, diction, and paragraph and sentence structure and an understanding of English usage. 1.2 Produce legible work that shows accurate spelling and correct punctuation and capitalization. 1.3 Reflect appropriate manuscript requirements in writing. Listening and Speaking 1.0 Listening and Speaking Strategies 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. Comprehension 1.1 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). 1.2 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. 1.3 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). Organization and Delivery of Oral Communication 1.4 Use rhetorical questions, parallel structure, concrete images, figurative language, characterization, irony, and dialogue to achieve clarity, force, and aesthetic effect. 1.5 Distinguish between and use various forms of classical and contemporary logical arguments, including: a. Inductive and deductive reasoning b. Syllogisms and analogies 1.6 Use logical, ethical, and emotional appeals that enhance a specific tone and purpose. 1.7 Use appropriate rehearsal strategies to pay attention to performance details, achieve command of the text, and create skillful artistic staging. 1.8 Use effective and interesting language, including: a. Informal expressions for effect b. Standard American English for clarity c. Technical language for specificity 1.9 Use research and analysis to justify strategies for gesture, movement, and vocalization, including dialect, pronunciation, and enunciation. 1.10 Evaluate when to use different kinds of effects (e.g., visual, music, sound, graphics) to create effective productions. Analysis and Evaluation of Oral and Media Communications 1.11 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. 1.12 Identify logical fallacies used in oral addresses (e.g., attack ad hominem, false causality, red herring, overgeneralization, bandwagon effect). 1.13 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. 1.14 Analyze the techniques used in media messages for a particular audience and evaluate their effectiveness (e.g., Orson Welles' radio broadcast "War of the Worlds"). 2.0 Speaking Applications (Genres and Their Characteristics) 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. Using the speaking strategies of grades eleven and twelve outlined in Listening and Speaking Standard 1.0, students: 2.1 Deliver reflective presentations: a. Explore the significance of personal experiences, events, conditions, or concerns, using appropriate rhetorical strategies (e.g., narration, description, exposition, persuasion). b. Draw comparisons between the specific incident and broader themes that illustrate the speaker's beliefs or generalizations about life. c. Maintain a balance between describing the incident and relating it to more general, abstract ideas. 2.2 Deliver oral reports on historical investigations: a. Use exposition, narration, description, persuasion, or some combination of those to support the thesis. b. Analyze several historical records of a single event, examining critical relationships between elements of the research topic. c. Explain the perceived reason or reasons for the similarities and differences by using information derived from primary and secondary sources to support or enhance the presentation. d. Include information on all relevant perspectives and consider the validity and reliability of sources. 2.3 Deliver oral responses to literature: a. Demonstrate a comprehensive understanding of the significant ideas of literary works (e.g., make assertions about the text that are reasonable and supportable). b. Analyze the imagery, language, universal themes, and unique aspects of the text through the use of rhetorical strategies (e.g., narration, description, persuasion, exposition, a combination of those strategies). c. Support important ideas and viewpoints through accurate and detailed references to the text or to other works. d. Demonstrate an awareness of the author's use of stylistic devices and an appreciation of the effects created. e. Identify and assess the impact of perceived ambiguities, nuances, and complexities within the text. 2.4 Deliver multimedia presentations: a. 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. b. Select an appropriate medium for each element of the presentation. c. Use the selected media skillfully, editing appropriately and monitoring for quality. 2.5 Recite poems, selections from speeches, or dramatic soliloquies with attention to performance details to achieve clarity, force, and aesthetic effect and to demonstrate an understanding of the meaning (e.g., Hamlet's soliloquy "To Be or Not to Be"). d. Test the audience's response and revise the presentation accordingly. 2.5 Recite poems, selections from speeches, or dramatic soliloquies with attention to performance details to achieve clarity, force, and aesthetic effect and to demonstrate an understanding of the meaning (e.g., Hamlet's soliloquy "To Be or Not to Be").Be or Not to Be").

Algebra II

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Algebra II Math Content Standards

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. 1.0 Students solve equations and inequalities involving absolute value. 2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. 3.0 Students are adept at operations on polynomials, including long division. 4.0 Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. 5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane. 6.0 Students add, subtract, multiply, and divide complex numbers. 7.0 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. 8.0 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. 9.0 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. 10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function. 11.0 Students prove simple laws of logarithms. 11.1 Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 11.2 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. 12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. 13.0 Students use the definition of logarithms to translate between logarithms in any base. 14.0 Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. 15.0 Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true. 16.0 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. 17.0 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. 18.0 Students use fundamental counting principles to compute combinations and permutations. 19.0 Students use combinations and permutations to compute probabilities. 20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. 21.0 Students apply the method of mathematical induction to prove general statements about the positive integers. 22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series. 23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series. 24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions. 25.0 Students use properties from number systems to justify steps in combining and simplifying functions.

Chemistry

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Chemistry

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Chemistry Content Standards

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 (*). Atomic and Molecular Structure 1. 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: a. Students know how to relate the position of an element in the periodic table to its atomic number and atomic mass. b. Students know how to use the periodic table to identify metals, semimetals, nonmetals, and halogens. c. 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. d. Students know how to use the periodic table to determine the number of electrons available for bonding. e. Students know the nucleus of the atom is much smaller than the atom yet contains most of its mass. f. * Students know how to use the periodic table to identify the lanthanide, actinide, and transactinide elements and know that the transuranium elements were synthesized and identified in laboratory experiments through the use of nuclear accelerators. g. * Students know how to relate the position of an element in the periodic table to its quantum electron configuration and to its reactivity with other elements in the table. h. * Students know the experimental basis for Thomson's discovery of the electron, Rutherford's nuclear atom, Millikan's oil drop experiment, and Einstein's explanation of the photoelectric effect. i. * Students know the experimental basis for the development of the quantum theory of atomic structure and the historical importance of the Bohr model of the atom. j. * Students know that spectral lines are the result of transitions of electrons between energy levels and that these lines correspond to photons with a frequency related to the energy spacing between levels by using Planck's relationship (E = hv). Chemical Bonds 2. 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: a. Students know atoms combine to form molecules by sharing electrons to form covalent or metallic bonds or by exchanging electrons to form ionic bonds. b. Students know chemical bonds between atoms in molecules such as H2 , CH4 , NH3 , H2 CCH2 , N2 , Cl2 , and many large biological molecules are covalent. c. Students know salt crystals, such as NaCl, are repeating patterns of positive and negative ions held together by electrostatic attraction. d. Students know the atoms and molecules in liquids move in a random pattern relative to one another because the intermolecular forces are too weak to hold the atoms or molecules in a solid form. e. Students know how to draw Lewis dot structures. f. * Students know how to predict the shape of simple molecules and their polarity from Lewis dot structures. g. * Students know how electronegativity and ionization energy relate to bond formation. h. * Students know how to identify solids and liquids held together by van der Waals forces or hydrogen bonding and relate these forces to volatility and boiling/ melting point temperatures. Conservation of Matter and Stoichiometry 3. 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: a. Students know how to describe chemical reactions by writing balanced equations. b. Students know the quantity one mole is set by defining one mole of carbon 12 atoms to have a mass of exactly 12 grams. c. Students know one mole equals 6.02x1023particles (atoms or molecules). d. 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. e. Students know how to calculate the masses of reactants and products in a chemical reaction from the mass of one of the reactants or products and the relevant atomic masses. f. * Students know how to calculate percent yield in a chemical reaction. g. * Students know how to identify reactions that involve oxidation and reduction and how to balance oxidation-reduction reactions. Gases and Their Properties 4. The kinetic molecular theory describes the motion of atoms and molecules and explains the properties of gases. As a basis for understanding this concept: a. Students know the random motion of molecules and their collisions with a surface create the observable pressure on that surface. b. Students know the random motion of molecules explains the diffusion of gases. c. 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. d. Students know the values and meanings of standard temperature and pressure (STP). e. Students know how to convert between the Celsius and Kelvin temperature scales. f. Students know there is no temperature lower than 0 Kelvin. g. * Students know the kinetic theory of gases relates the absolute temperature of a gas to the average kinetic energy of its molecules or atoms. h. * Students know how to solve problems by using the ideal gas law in the form PV = nRT. i. * Students know how to apply Dalton's law of partial pressures to describe the composition of gases and Graham's law to predict diffusion of gases. Acids and Bases 5. Acids, bases, and salts are three classes of compounds that form ions in water solutions. As a basis for understanding this concept: a. Students know the observable properties of acids, bases, and salt solutions. b. Students know acids are hydrogen-ion-donating and bases are hydrogen-ion-accepting substances. c. Students know strong acids and bases fully dissociate and weak acids and bases partially dissociate. d. Students know how to use the pH scale to characterize acid and base solutions. e. * Students know the Arrhenius, Brønsted-Lowry, and Lewis acid-base definitions. f. * Students know how to calculate pH from the hydrogen-ion concentration. g. * Students know buffers stabilize pH in acid-base reactions. Solutions 6. Solutions are homogeneous mixtures of two or more substances. As a basis for understanding this concept: a. Students know the definitions of solute and solvent. b. Students know how to describe the dissolving process at the molecular level by using the concept of random molecular motion. c. Students know temperature, pressure, and surface area affect the dissolving process. d. Students know how to calculate the concentration of a solute in terms of grams per liter, molarity, parts per million, and percent composition. e. * Students know the relationship between the molality of a solute in a solution and the solution's depressed freezing point or elevated boiling point. f. * Students know how molecules in a solution are separated or purified by the methods of chromatography and distillation. Chemical Thermodynamics 7. Energy is exchanged or transformed in all chemical reactions and physical changes of matter. As a basis for understanding this concept: a. Students know how to describe temperature and heat flow in terms of the motion of molecules (or atoms). b. Students know chemical processes can either release (exothermic) or absorb (endothermic) thermal energy. c. Students know energy is released when a material condenses or freezes and is absorbed when a material evaporates or melts. d. Students know how to solve problems involving heat flow and temperature changes, using known values of specific heat and latent heat of phase change. e. * Students know how to apply Hess's law to calculate enthalpy change in a reaction. f. * Students know how to use the Gibbs free energy equation to determine whether a reaction would be spontaneous. Reaction Rates 8. Chemical reaction rates depend on factors that influence the frequency of collision of reactant molecules. As a basis for understanding this concept: a. Students know the rate of reaction is the decrease in concentration of reactants or the increase in concentration of products with time. b. Students know how reaction rates depend on such factors as concentration, temperature, and pressure. c. Students know the role a catalyst plays in increasing the reaction rate. d. * Students know the definition and role of activation energy in a chemical reaction. Chemical Equilibrium 9. Chemical equilibrium is a dynamic process at the molecular level. As a basis for understanding this concept: a. Students know how to use Le Chatelier's principle to predict the effect of changes in concentration, temperature, and pressure. b. Students know equilibrium is established when forward and reverse reaction rates are equal. c. * Students know how to write and calculate an equilibrium constant expression for a reaction. Organic Chemistry and Biochemistry 10. 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: a. Students know large molecules (polymers), such as proteins, nucleic acids, and starch, are formed by repetitive combinations of simple subunits. b. Students know the bonding characteristics of carbon that result in the formation of a large variety of structures ranging from simple hydrocarbons to complex polymers and biological molecules. c. Students know amino acids are the building blocks of proteins. d. * Students know the system for naming the ten simplest linear hydrocarbons and isomers that contain single bonds, simple hydrocarbons with double and triple bonds, and simple molecules that contain a benzene ring. e. * Students know how to identify the functional groups that form the basis of alcohols, ketones, ethers, amines, esters, aldehydes, and organic acids. f. * Students know the R-group structure of amino acids and know how they combine to form the polypeptide backbone structure of proteins. Nuclear Processes 11. 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: a. Students know protons and neutrons in the nucleus are held together by nuclear forces that overcome the electromagnetic repulsion between the protons. b. 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. c. Students know some naturally occurring isotopes of elements are radioactive, as are isotopes formed in nuclear reactions. d. Students know the three most common forms of radioactive decay (alpha, beta, and gamma) and know how the nucleus changes in each type of decay. e. Students know alpha, beta, and gamma radiation produce different amounts and kinds of damage in matter and have different penetrations. f. * Students know how to calculate the amount of a radioactive substance remaining after an integral number of half-lives have passed. g. * Students know protons and neutrons have substructures and consist of particles called quarks.

Chemical Change

A change that results in the formation of one or more new substances

Physical Change

A change to a substance that does not alter its chemical composition

Chemical Property

A property inherent in the chemical makeup of a substance that is revealed during a chemical reaction

Physical Property

A measurable or observable characteristic of an object or substance, such as size, shape, color, or state of matter

History/Social Science

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Grade 11 History-Social Science Content Standards

United States History and Geography: Continuity and Change in the Twentieth Century Students in grade eleven study the major turning points in American history in the twentieth century. Following a review of the nation's beginnings and the impact of the Enlightenment on U.S. democratic ideals, students build upon the tenth grade study of global industrialization to understand the emergence and impact of new technology and a corporate economy, including the social and cultural effects. They trace the change in the ethnic composition of American society; the movement toward equal rights for racial minorities and women; and the role of the United States as a major world power. An emphasis is placed on the expanding role of the federal government and federal courts as well as the continuing tension between the individual and the state. Students consider the major social problems of our time and trace their causes in historical events. They learn that the United States has served as a model for other nations and that the rights and freedoms we enjoy are not accidents, but the results of a defined set of political principles that are not always basic to citizens of other countries. Students understand that our rights under the U.S. Constitution are a precious inheritance that depends on an educated citizenry for their preservation and protection. 11.1 Students analyze the significant events in the founding of the nation and its attempts to realize the philosophy of government described in the Declaration of Independence. 1. Describe the Enlightenment and the rise of democratic ideas as the context in which the nation was founded. 2. Analyze the ideological origins of the American Revolution, the Founding Fathers' philosophy of divinely bestowed unalienable natural rights, the debates on the drafting and ratification of the Constitution, and the addition of the Bill of Rights. 3. Understand the history of the Constitution after 1787 with emphasis on federal versus state authority and growing democratization. 4. Examine the effects of the Civil War and Reconstruction and of the industrial revolution, including demographic shifts and the emergence in the late nineteenth century of the United States as a world power. 11.2 Students analyze the relationship among the rise of industrialization, large-scale rural-to-urban migration, and massive immigration from Southern and Eastern Europe. 1. Know the effects of industrialization on living and working conditions, including the portrayal of working conditions and food safety in Upton Sinclair's The Jungle. 2. Describe the changing landscape, including the growth of cities linked by industry and trade, and the development of cities divided according to race, ethnicity, and class. 3. Trace the effect of the Americanization movement. 4. Analyze the effect of urban political machines and responses to them by immigrants and middle-class reformers. 5. Discuss corporate mergers that produced trusts and cartels and the economic and political policies of industrial leaders. 6. Trace the economic development of the United States and its emergence as a major industrial power, including its gains from trade and the advantages of its physical geography. 7. Analyze the similarities and differences between the ideologies of Social Darwinism and Social Gospel (e.g., using biographies of William Graham Sumner, Billy Sunday, Dwight L. Moody). 8. Examine the effect of political programs and activities of Populists. 9. Understand the effect of political programs and activities of the Progressives (e.g., federal regulation of railroad transport, Children's Bureau, the Sixteenth Amendment, Theodore Roosevelt, Hiram Johnson). 11.3 Students analyze the role religion played in the founding of America, its lasting moral, social, and political impacts, and issues regarding religious liberty. 1. Describe the contributions of various religious groups to American civic principles and social reform movements (e.g., civil and human rights, individual responsibility and the work ethic, antimonarchy and self-rule, worker protection, family-centered communities). 2. Analyze the great religious revivals and the leaders involved in them, including the First Great Awakening, the Second Great Awakening, the Civil War revivals, the Social Gospel Movement, the rise of Christian liberal theology in the nineteenth century, the impact of the Second Vatican Council, and the rise of Christian fundamentalism in current times. 3. Cite incidences of religious intolerance in the United States (e.g., persecution of Mormons, anti-Catholic sentiment, anti-Semitism). 4. Discuss the expanding religious pluralism in the United States and California that resulted from large-scale immigration in the twentieth century. 5. Describe the principles of religious liberty found in the Establishment and Free Exercise clauses of the First Amendment, including the debate on the issue of separation of church and state. 11.4 Students trace the rise of the United States to its role as a world power in the twentieth century. 1. List the purpose and the effects of the Open Door policy. 2. Describe the Spanish-American War and U.S. expansion in the South Pacific. 3. Discuss America's role in the Panama Revolution and the building of the Panama Canal. 4. Explain Theodore Roosevelt's Big Stick diplomacy, William Taft's Dollar Diplomacy, and Woodrow Wilson's Moral Diplomacy, drawing on relevant speeches. 5. Analyze the political, economic, and social ramifications of World War I on the home front. 6. Trace the declining role of Great Britain and the expanding role of the United States in world affairs after World War II. 11.5 Students analyze the major political, social, economic, technological, and cultural developments of the 1920s. 1. Discuss the policies of Presidents Warren Harding, Calvin Coolidge, and Herbert Hoover. 2. Analyze the international and domestic events, interests, and philosophies that prompted attacks on civil liberties, including the Palmer Raids, Marcus Garvey's "back-to-Africa" movement, the Ku Klux Klan, and immigration quotas and the responses of organizations such as the American Civil Liberties Union, the National Association for the Advancement of Colored People, and the Anti-Defamation League to those attacks. 3. Examine the passage of the Eighteenth Amendment to the Constitution and the Volstead Act (Prohibition). 4. Analyze the passage of the Nineteenth Amendment and the changing role of women in society. 5. Describe the Harlem Renaissance and new trends in literature, music, and art, with special attention to the work of writers (e.g., Zora Neale Hurston, Langston Hughes). 6. Trace the growth and effects of radio and movies and their role in the worldwide diffusion of popular culture. 7. Discuss the rise of mass production techniques, the growth of cities, the impact of new technologies (e.g., the automobile, electricity), and the resulting prosperity and effect on the American landscape. 11.6 Students analyze the different explanations for the Great Depression and how the New Deal fundamentally changed the role of the federal government. 1. Describe the monetary issues of the late nineteenth and early twentieth centuries that gave rise to the establishment of the Federal Reserve and the weaknesses in key sectors of the economy in the late 1920s. 2. Understand the explanations of the principal causes of the Great Depression and the steps taken by the Federal Reserve, Congress, and Presidents Herbert Hoover and Franklin Delano Roosevelt to combat the economic crisis. 3. Discuss the human toll of the Depression, natural disasters, and unwise agricultural practices and their effects on the depopulation of rural regions and on political movements of the left and right, with particular attention to the Dust Bowl refugees and their social and economic impacts in California. 4. Analyze the effects of and the controversies arising from New Deal economic policies and the expanded role of the federal government in society and the economy since the 1930s (e.g., Works Progress Administration, Social Security, National Labor Relations Board, farm programs, regional development policies, and energy development projects such as the Tennessee Valley Authority, California Central Valley Project, and Bonneville Dam). 5. Trace the advances and retreats of organized labor, from the creation of the American Federation of Labor and the Congress of Industrial Organizations to current issues of a postindustrial, multinational economy, including the United Farm Workers in California. 11.7 Students analyze America's participation in World War II. 1. Examine the origins of American involvement in the war, with an emphasis on the events that precipitated the attack on Pearl Harbor. 2. Explain U.S. and Allied wartime strategy, including the major battles of Midway, Normandy, Iwo Jima, Okinawa, and the Battle of the Bulge. 3. Identify the roles and sacrifices of individual American soldiers, as well as the unique contributions of the special fighting forces (e.g., the Tuskegee Airmen, the 442nd Regimental Combat team, the Navajo Code Talkers). 4. Analyze Roosevelt's foreign policy during World War II (e.g., Four Freedoms speech). 5. Discuss the constitutional issues and impact of events on the U.S. home front, including the internment of Japanese Americans (e.g., Fred Korematsu v. United States of America) and the restrictions on German and Italian resident aliens; the response of the administration to Hitler's atrocities against Jews and other groups; the roles of women in military production; and the roles and growing political demands of African Americans. 6. Describe major developments in aviation, weaponry, communication, and medicine and the war's impact on the location of American industry and use of resources. 7. Discuss the decision to drop atomic bombs and the consequences of the decision (Hiroshima and Nagasaki). 8. Analyze the effect of massive aid given to Western Europe under the Marshall Plan to rebuild itself after the war and the importance of a rebuilt Europe to the U.S. economy. 11.8 Students analyze the economic boom and social transformation of post-World War II America. 1. Trace the growth of service sector, white collar, and professional sector jobs in business and government. 2. Describe the significance of Mexican immigration and its relationship to the agricultural economy, especially in California. 3. Examine Truman's labor policy and congressional reaction to it. 4. Analyze new federal government spending on defense, welfare, interest on the national debt, and federal and state spending on education, including the California Master Plan. 5. Describe the increased powers of the presidency in response to the Great Depression, World War II, and the Cold War. 6. Discuss the diverse environmental regions of North America, their relationship to local economies, and the origins and prospects of environmental problems in those regions. 7. Describe the effects on society and the economy of technological developments since 1945, including the computer revolution, changes in communication, advances in medicine, and improvements in agricultural technology. 8. Discuss forms of popular culture, with emphasis on their origins and geographic diffusion (e.g., jazz and other forms of popular music, professional sports, architectural and artistic styles). 11.9 Students analyze U.S. foreign policy since World War II. 1. Discuss the establishment of the United Nations and International Declaration of Human Rights, International Monetary Fund, World Bank, and General Agreement on Tariffs and Trade (GATT) and their importance in shaping modern Europe and maintaining peace and international order. 2. Understand the role of military alliances, including NATO and SEATO, in deterring communist aggression and maintaining security during the Cold War. 3. Trace the origins and geopolitical consequences (foreign and domestic) of the Cold War and containment policy, including the following: o The era of McCarthyism, instances of domestic Communism (e.g., Alger Hiss) and blacklisting o The Truman Doctrine o The Berlin Blockade o The Korean War o The Bay of Pigs invasion and the Cuban Missile Crisis o Atomic testing in the American West, the "mutual assured destruction" doctrine, and disarmament policies o The Vietnam War o Latin American policy 4. List the effects of foreign policy on domestic policies and vice versa (e.g., protests during the war in Vietnam, the "nuclear freeze" movement). 5. Analyze the role of the Reagan administration and other factors in the victory of the West in the Cold War. 6. Describe U.S. Middle East policy and its strategic, political, and economic interests, including those related to the Gulf War. 7. Examine relations between the United States and Mexico in the twentieth century, including key economic, political, immigration, and environmental issues. 11.10 Students analyze the development of federal civil rights and voting rights. 1. Explain how demands of African Americans helped produce a stimulus for civil rights, including President Roosevelt's ban on racial discrimination in defense industries in 1941, and how African Americans' service in World War II produced a stimulus for President Truman's decision to end segregation in the armed forces in 1948. 2. Examine and analyze the key events, policies, and court cases in the evolution of civil rights, including Dred Scott v. Sandford, Plessy v. Ferguson, Brown v. Board of Education, Regents of the University of California v. Bakke, and California Proposition 209. 3. Describe the collaboration on legal strategy between African American and white civil rights lawyers to end racial segregation in higher education. 4. Examine the roles of civil rights advocates (e.g., A. Philip Randolph, Martin Luther King, Jr., Malcolm X, Thurgood Marshall, James Farmer, Rosa Parks), including the significance of Martin Luther King, Jr. 's "Letter from Birmingham Jail" and "I Have a Dream" speech. 5. Discuss the diffusion of the civil rights movement of African Americans from the churches of the rural South and the urban North, including the resistance to racial desegregation in Little Rock and Birmingham, and how the advances influenced the agendas, strategies, and effectiveness of the quests of American Indians, Asian Americans, and Hispanic Americans for civil rights and equal opportunities. 6. Analyze the passage and effects of civil rights and voting rights legislation (e.g., 1964 Civil Rights Act, Voting Rights Act of 1965) and the Twenty-Fourth Amendment, with an emphasis on equality of access to education and to the political process. 7. Analyze the women's rights movement from the era of Elizabeth Stanton and Susan Anthony and the passage of the Nineteenth Amendment to the movement launched in the 1960s, including differing perspectives on the roles of women. 11.11 Students analyze the major social problems and domestic policy issues in contemporary American society. 1. Discuss the reasons for the nation's changing immigration policy, with emphasis on how the Immigration Act of 1965 and successor acts have transformed American society. 2. Discuss the significant domestic policy speeches of Truman, Eisenhower, Kennedy, Johnson, Nixon, Carter, Reagan, Bush, and Clinton (e.g., with regard to education, civil rights, economic policy, environmental policy). 3. Describe the changing roles of women in society as reflected in the entry of more women into the labor force and the changing family structure. 4. Explain the constitutional crisis originating from the Watergate scandal. 5. Trace the impact of, need for, and controversies associated with environmental conservation, expansion of the national park system, and the development of environmental protection laws, with particular attention to the interaction between environmental protection advocates and property rights advocates. 6. Analyze the persistence of poverty and how different analyses of this issue influence welfare reform, health insurance reform, and other social policies. 7. Explain how the federal, state, and local governments have responded to demographic and social changes such as population shifts to the suburbs, racial concentrations in the cities, Frostbelt-to-Sunbelt migration, international migration, decline of family farms, increases in out-of-wedlock births, and drug abuse. increases in out-of-wedlock births, and drug abuse.

Physics

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Physics State Standards

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 1. Newton's laws predict the motion of most objects. As a basis for understanding this concept: a. Students know how to solve problems that involve constant speed and average speed. b. 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). c. Students know how to apply the law F=ma to solve one-dimensional motion problems that involve constant forces (Newton's second law). d. 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). e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth. f. 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). g. Students know circular motion requires the application of a constant force directed toward the center of the circle. h. * 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. i. * Students know how to solve two-dimensional trajectory problems. j. * Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components. k. * Students know how to solve two-dimensional problems involving balanced forces (statics). l. * Students know how to solve problems in circular motion by using the formula for centripetal acceleration in the following form: a=v2/r. m. * 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 2. 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: a. Students know how to calculate kinetic energy by using the formula E=(1/2)mv2 . b. 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). c. Students know how to solve problems involving conservation of energy in simple systems, such as falling objects. d. Students know how to calculate momentum as the product mv. e. Students know momentum is a separately conserved quantity different from energy. f. Students know an unbalanced force on an object produces a change in its momentum. g. Students know how to solve problems involving elastic and inelastic collisions in one dimension by using the principles of conservation of momentum and energy. h. * 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 3. 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: a. Students know heat flow and work are two forms of energy transfer between systems. b. 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. c. 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. d. Students know that most processes tend to decrease the order of a system over time and that energy levels are eventually distributed uniformly. e. 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. f. * Students know the statement "Entropy tends to increase" is a law of statistical probability that governs all closed systems (second law of thermodynamics). g. * 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 4. Waves have characteristic properties that do not depend on the type of wave. As a basis for understanding this concept: a. Students know waves carry energy from one place to another. b. Students know how to identify transverse and longitudinal waves in mechanical media, such as springs and ropes, and on the earth (seismic waves). c. Students know how to solve problems involving wavelength, frequency, and wave speed. d. Students know sound is a longitudinal wave whose speed depends on the properties of the medium in which it propagates. e. 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). f. Students know how to identify the characteristic properties of waves: interference (beats), diffraction, refraction, Doppler effect, and polarization. Electric and Magnetic Phenomena 5. Electric and magnetic phenomena are related and have many practical applications. As a basis for understanding this concept: a. Students know how to predict the voltage or current in simple direct current (DC) electric circuits constructed from batteries, wires, resistors, and capacitors. b. Students know how to solve problems involving Ohm's law. c. 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. d. Students know the properties of transistors and the role of transistors in electric circuits. e. Students know charged particles are sources of electric fields and are subject to the forces of the electric fields from other charges. f. 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. g. Students know how to determine the direction of a magnetic field produced by a current flowing in a straight wire or in a coil. h. Students know changing magnetic fields produce electric fields, thereby inducing currents in nearby conductors. i. Students know plasmas, the fourth state of matter, contain ions or free electrons or both and conduct electricity. j. * Students know electric and magnetic fields contain energy and act as vector force fields. k. * 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. l. * Students know how to calculate the electric field resulting from a point charge. m. * Students know static electric fields have as their source some arrangement of electric charges. n. * 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. o. * Students know how to apply the concepts of electrical and gravitational potential energy to solve problems involving conservation of energy.

Geometry

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Geometry Content Standards

The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems. 1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. 2.0 Students write geometric proofs, including proofs by contradiction. 3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. 4.0 Students prove basic theorems involving congruence and similarity. 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. 6.0 Students know and are able to use the triangle inequality theorem. 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 9.0 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. 10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. 11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. 12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. 13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. 14.0 Students prove the Pythagorean theorem. 15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 17.0 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. 18.0 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. 19.0 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. 20.0 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. 21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. 22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.

Pascal's Theorem

In projective geometry, Pascal's theorem states that if an arbitrary hexagon is inscribed in any conic section, and opposite pairs of sides are extended until they meet, the three intersection points will lie on a straight line, the Pascal line of that configuration. In the Euclidean plane, the theorem has exceptions; its natural home is the projective plane.

Linear Algebra

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Gauss

A famous story about Gauss is when he was in primary school. He had continued to rattle off answers within seconds and his probably perplexed teacher, J.G. Büttner, frustrated with young Gauss, gave the young boy a presumably difficult task to keep the boy busy. He asked Gauss to add a list of integers,1 to 100. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher. Gauss's presumed method was to realize that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050.

Earth Science

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Robotics

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Math

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What is Pi?

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213 Pi is a number, approximately 3.142. It is one of the most constant numbers in mathematics. It is the circumference of any circle divided by its diameter. The value of Pi (pronounced 'pie') 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609... and it continues on in a non repeating pattern

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Area enclosed by a circle From Latin: area - "level ground, an open space," The number of square units it takes to exactly fill the interior of a circle. A circle is actually a line, one that connects back to itself making a loop. Imagine the circle to be a loop of string. The string itself has no area, but the space inside the loop does. So strictly speaking a circle has no area. However, when we say "the area of a circle" we really mean the area of the space inside the circle. If you were to cut a circular disk from a sheet of paper, the disk would have an area, and that it what we mean here. If you know the radius Given the radius of a circle, the area inside it can be calculated using the formula where: R is the radius of the circle π is Pi, approximately 3.142 If you know the diameter If you know the diameter of a circle, the area inside it can be found using the formula where: D is the diameter of the circle π is Pi, approximately 3.142 If you know the circumference If you know the circumference of a circle, the area inside it can be found using the formula where: C is the circumference of the circle π is Pi, approximately 3.142

Biology

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Astronomy

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