# GENERAL STUDIES

## GENERAL STUDIES

Following the motto of excellence, Atara has designed an excellent college preparatory General Studies program, with a wide variety of course work and an extensive familiarity with the tools and skills that are needed to be successful in the modern world. Each student is provided with a strong educational base, with which she can go on to attend university and pursue the career of her choice. Our curriculum is thorough and engaging enough to challenge the advanced student, and at the same time is accommodating and flexible to cater to a variety of scholastic levels.

## GENERAL STUDIES

### Modern World History

### Course Description:

Modern History surveys world events from the Renaissance to the present. The major

focus is on Western civilization. Political and cultural events associated with the

Renaissance, the rise of nation-states, war and diplomacy, changing economic

systems, and revolutions. The course will end with an in-depth study of World War I

and II. Historical fiction, biographies, films, and other audio-visual materials are part of

the classroom experience. A variety of approaches – chronological, thematic,

historiographic, and biographical – are possible.

### Course Objectives:

**Students will:**

- Read maps and predict the effects of geography on human cultures and societies
- Use primary and secondary sources to construct valid answers to the essential

questions - Defend premises and arguments with valid support from primary and secondary

sources - Debate historical issues and interpretations using precise language and supporting

evidence - Write persuasive paragraphs and papers with strong theses and support from primary

and secondary sources - Develop and apply terms for analyzing religions, and social, political, and economic

organizations - Comprehend and apply elements of art criticism to historical works of art
- Prepare for and argue in debates or discussion
- Apply refined historical skills (construction of written and oral arguments, use of valid

primary and secondary sources to defend arguments, drawing valid inferences, use of

precise language, analysis of maps, charts, and graphs)

### Scope and Sequence:

**Unit 1: Renaissance and Reformation**

- Renaissance art
- Renaissance humanism
- Martin Luther and his ideas
- Calvinism and Anglicanism
- Propaganda in the Protestant Reformation
- The Catholic Reformation and Counter Reformation

**Unit 2: Early Modern Europe and the Old Regime**

- The Price Revolution and changes to daily life in early modern Europe
- Social Hierarchy and daily life in early modern Europe
- Early modern European women and witchcraft
- English Constitutionalism- Elizabeth to William and Mary
- Henry IV and Louis XIII
- Louis XIV as a model of absolutism

**Unit 3: The Scientific Revolution and the Enlightenment**

- Galileo
- Scientific method and discoveries
- Isaac Newton- a scientific view of the universe
- The Enlightenment- Locke, Rousseau, Voltaire

**Unit 4: The French Revolution and Conservative Reaction**

- Enlightenment Ideas
- Social and Economic Background to The French Revolution
- The Summoning of the Estates General
- The Role of Women and Working Classes
- The Liberal Constitution of 1791
- The Radical Phase and the Reign of Terror
- Napoleon
- The lasting effects of the French Revolution
- The Congress of Vienna

**Unit 5: The Industrial Revolution and Early Industrial Europe**

- From the cottage system to the Factory system
- Factory Life
- Worker responses to the Factory system
- Social ranking – middle class and working class
- The Growth of Industrial cities

**Unit 6: Nationalism and Imperialism**

- Nationalism
- The new Imperialism
- Motives and Methods of European Imperialism
- Reactions to European Imperialism

**Unit 7: World War I**

- Long and short term causes of World War I
- Political Geography of Europe in 1914
- The Schlieffen Plan
- Trench Warfare

## GENERAL STUDIES

### American Government

### Course Description:

The American Government course focuses on the United States’ founding principles

and beliefs. Students will study the structure, functions, systems, powers of

government at the national, state, and local levels, and political processes. Content will

include factors that influence U.S. Government. This course prepares students to

become responsible/aware members of American society.

### Course Objectives:

**Students will:**

- understand major political ideas and forms of government in history.
- understand how constitutional government, as developed in the United States, has

been influenced by people, ideas, and historical documents. - understand the roles played by individuals, political parties, interest groups, and the

media in the U.S. political system, past and present. - understand the American beliefs and principles reflected in the U.S. Constitution.
- understand the structure and functions of the government created by the U.S.

Constitution. - understand the processes for filling public offices in the U.S. system of government.
- understand the role of political parties in the U.S. system of government.
- understand the similarities and differences that exist among the U.S. system of

government and other political systems. - understand rights guaranteed by the U.S. Constitution.
- understand the importance of voluntary individual participation in the U.S. democratic

society. - understand the importance of the expression of different points of view in a

democratic society.

### Scope and Sequence:

- Introducing Government in America
- The Constitution
- Federalism
- Civil Liberties and Public Policy
- Civil Rights and Public Policy
- Public Opinion and Political Action
- Political Parties
- Nominations and Campaigns
- Elections and Voting Behavior
- Interest Groups
- Congress
- The Presidency
- The Congress, the President, and the Budget: Taxing and Spending
- The Federal Bureaucracy
- The Federal Courts
- Economic Policymaking
- Social Welfare Policymaking
- Policymaking for Health Care and the Environment
- National Security Policymaking
- The New Face of State and Local Government
- Introduction Government in Ohio
- The Ohio Constitution
- Political Parties, Campaigns, Elections, and Interest Groups in Ohio
- The Ohio Legislature
- The Governor and Bureaucracy of Ohio
- The Texas Court System
- Local Government

## GENERAL STUDIES

### US History

### Course Description:

This course is a comprehensive study of the development of the United States

designed to provide students with the factual knowledge and analytical skills necessary

to deal critically with U.S. history and to introduce students to important issues in the

development of our constitutional democracy. This course provides a one-year survey

of American history from the Colonial Period and the American Revolution to the

present day, with an emphasis on the twentieth century. Students come to understand

the importance of geography in the historical process, the development of a

constitutional democracy, the social/cultural identity of a multi-national and multi-racial

people, the importance of science and technology in the development of an economy

based on both agriculture and industry, and the developing role of the U.S. as a world

power. Using the textbook and primary documents, students will develop skills

necessary to arrive at conclusions on the basis of informed judgment and to present

reasons and evidence clearly and persuasively orally and in writing.

### Course Objectives:

- Reading and Thinking Critically
- Articulating and Defending Thoughts Logically In Oral and Written Form
- Analyzing and Evaluting Primary and Secondary Sources
- Determing Cause and Effect
- Organizing and Ranking Information
- Reading and Using Maps
- Mastering factual material

### Scope and Sequence:

**Unit 1: Colonial America**

- England and the New World
- The Eighteenth Century
- The Colonial Crisis
- The Revolution

**Unit 2: The Revolutionary Period**

- Confederation and Constitution
- Foundations of American Government
- Federalists and Republicans
- The Early Republic

**Unit 3: Antebellum America**

- The Market Revolution
- Jacksonian America
- Abolitionism
- Slavery and Westward Expansion
- Texas and Mexico

**Unit 4: The Civil War Era**

- Secession and War
- The Civil War: Course
- The Civil War: Consequences
- Reconstruction

**Unit 5: The Gilded Age**

- Industrial America
- Urbanization
- The Spanish-American War
- Progressivism

**Unit 6: The World and America**

- The Great War and Versailles
- Laissez-Faire America
- The Great Depression
- The New Deal
- The Second World War: Causes

**Unit 7: Cold War America**

- The Second World War: Course
- Cold War: Containment
- Post-War America
- The Civil Rights Era
- The 1960’s
- Cold War: Détente to Reagan
- The Age of Terror

## GENERAL STUDIES

### Physics

### Course Description:

Physics provides a hands-on experience with the basic principles of physics, as well as

rigorous practice using logical thinking skills. Students use sophisticated computer tools

to gather and analyze data about simple physical phenomena and use their results to

develop various physical laws and to make predictions about additional phenomena.

They then confirm or refute their predictions by experiment. Topics include mechanics,

thermodynamics, electricity and magnetism, light and optics, and waves and sound.

Additional emphasis is placed on the development of computer and laboratory skills.

### Course Objectives:

**Students will be able to:**

- Identify questions and concepts that guide scientific investigations;
- Design and conduct scientific investigations;
- Use technology and mathematics to improve investigations and communications;
- Formulate and revise explanations and models using logic and evidence (critical

thinking); - Recognize and analyze explanations and models; and Communicate and support a scientific argument.

### Scope and Sequence:

**UNIT 1: Motion**

- Graph interpretations
- Position vs. time
- Velocity vs. time
- Acceleration vs. time
- Problem solving
- Using graphs (average velocity, instantaneous velocity, acceleration, displacement, change in velocity)
- Uniform acceleration including free fall (initial velocity, final velocity, time,displacement, acceleration, average velocity)
- Projectiles
- Independence of horizontal and vertical motion
- Problem-solving involving horizontally launched projectiles

**UNIT 2: Forces, momentum and motion**

- Newton’s laws applied to complex problems
- Gravitational force and fields
- Elastic forces
- Friction force (static and kinetic)
- Air resistance and drag
- Forces in two dimensions
- Adding vector forces
- Motion down inclines
- Centripetal forces and circular motion
- Momentum, impulse and conservation of momentum

**UNIT 3: Energy**

- Gravitational potential energy
- Energy in springs
- Nuclear energy
- Work and power
- Conservation of energy

**UNIT 4: Thermodynamics**

- Heat
- Temperature
- Specific heat capacity
- Heat and work
- Basic laws of Thermodynamics

**UNIT 5: Waves**

- Wave properties
- Conservation of energy
- Reflection
- Refraction
- Interference
- Diffraction
- Light phenomena
- Ray diagrams (propagation of light)
- Law of reflection (equal angles)
- Snell’s law
- Diffraction patterns
- Wave – particle duality of light
- Visible spectrum and color

**UNIT 6: Electricity and magnetism**

- Charging objects (friction, contact and induction)
- Coulomb’s law
- Electric fields and electric potential energy
- DC circuits
- Ohm’s law
- Series circuits
- Parallel circuits
- Mixed circuits
- Applying conservation of charge and energy (junction and loop rules)
- Magnetic fields and energy
- Electromagnetic interactions

## GENERAL STUDIES

### Algebra 2

### Course Description:

This course extends the skills and concepts introduced in Algebra 1 and covers the

following topics: absolute value inequalities; linear, quadratic and absolute value

functions (their graphs and defining features); properties of exponents including

negative, zero and fractional values; systems of linear and quadratic equations and

inequalities; quadratics equations with complex number solutions; exponential and

logarithmic functions (properties, graphs, solving equations and applications);

polynomial functions (graphing, finding zeros and important theorems); square root and

cube root functions; rational functions (graphing, finding zeros, and asymptotes); and

conic sections. Also, since problem solving is an integral part of this course, students

spend a considerable amount of time translating problems presented in written form to

equivalent statements in mathematics. Then, the students find solutions to the

problems and express the results in written form. Algebra 2 is a prerequisite for all

advanced math courses.

### Course Objectives:

- Students will be able to analyze and evaluate the characteristics of step, piece-wise,

exponential, and quadratic functions, as well as inverses of functions - Students will interpret and apply the characteristics of functions with regard to a given

context and analyze and evaluate rates of change, both constant and variable, within

the basic function families. - Students will be able to analyze and evaluate geometric and arithmetic sequences as

functions. - Students will analyze and solve quadratic equations using a variety of techniques and

represent, simplify, and operate with complex numbers. - Students will be able to analyze and solve problems involving probabilities,

permutations, and combinations, as well as analyze and evaluate sample data,

making inferences about population means and standard deviations and using these

inferences to compare data sets. - Students will understand and apply algebraic models to quantify the association

between two quantitative variables.

### Scope and Sequence:

**Analyzing Equations and Inequalities**

- Expressions, formulas, and properties of real numbers
- Graphs and measures of central tendency
- Solving equations and solving absolute value equations
- Solving inequalities and solving absolute value inequalities

**Graphing Linear Relations and Functions**

- Relations and functions
- Linear equations
- Slope
- Writing linear equations
- Scatter plots
- Special functions
- Linear inequalities

**Solving Systems of Linear Equations and Inequalities**

- Graphing systems and solving systems algebraically
- Cramer’s Rule
- Graphings systems of inequalities
- Linear programming and applications
- Systems in three variables

**Matrices**

- Adding, subtracting, and multiplying matrices
- Determinants
- Identity and inverse
- Using matrices to solve systems of equations
- Using augmented matrices
- Box and whisker plots

**Exploring Polynomials and Radical Expressions**

- Monomials and polynomials
- Dividing polynomials and factoring
- Roots of real numbers and radical expressions
- Rational exponents
- Solving radical equations and inqualities
- Complex numbers and simplifying expressions with complex numbers

**Exploring Quadratic Functions and Inequalities**

- Solving by graphing, factoring, and completing the square
- Quadratic formula and discriminant
- Sum and product of roots
- Analyzing graphs of quadratic functions
- Graphing and solving quadratic inequalities
- Standard deviation and the normal distribution

**Analyzing Conic Sections**

- Parabolas, circles, ellipses, hyperbolas, conic sections
- Solving quadratic systems

**Exploring Polynomial Functions**

- Graphing and approximating zeros
- Roots and zeros
- Using quadratic techniques to solve
- Composition of functions
- Inverse functions and relations

**Exploring Rational Expressions**

- Graphing Rational Functions
- Direct, inverse, and joint variation
- Multiplying, dividing, adding, and subtracting rational expressions
- Solving rational equations and inequalities

**Exploring Exponential and Logarithmic Functions**

- Real exponents and exponential functions
- Logarithms and logarithmic functions
- Properties of logarithms, common logarithms, natural logarithms
- Solving exponential equations
- Growth and decay

**Investigating Sequences and Series**

- Arithmetic sequences and series
- Geometric sequences and series
- Infinite geometric series
- Recursion and special sequences
- Fractals and the binomial theorem

**Investigating Discrete Mathematics and Probability**

- The counting principle
- Permutations and combinations
- Probability
- Multiplying probabilities and adding probabilities

## GENERAL STUDIES

### Chemistry

### Course Description:

This course is a standards-based study of fundamental chemical concepts, such as atomic theory and its relation to chemical behavior, chemical bonding, the mole and stoichiometry, molecular kinetics, energy relationships, solution dynamics, acids-bases, equilibrium, organic and biological chemistry, and nuclear interactions. This course emphasizes problem-solving skills and is designed to introduce students to both the descriptive and quantitative aspects of chemistry. When possible, new ideas are introduced through experiment or demonstration, with emphasis placed on the interpretation and analysis of data. The course teaches students to understand and apply chemical concepts while gaining an understanding of chemistry’s relationship with current societal issues and everyday life.

### Course Objectives:

- Students will explore the basic building blocks of matter, investigating the quantum structure of atoms, how that structure determines properties and the organization elements on the Periodic Table. They will investigate how atoms interact, bond, and create larger structures with predictable behaviors. Students will investigate basic techniques to quantify various properties and chemical interactions and understand the mathematical means of predicting outcomes of chemical and physical changes. They will also study thermodynamic principles and the mass actions of reaction rates and equilibria that govern chemical processes. Chemistry students also will consider the larger contexts and applications of these concepts, from organic and biochemical to nuclear processes.
- Students will apply measurement, observation, statistical, and technological skills while investigating chemical concepts. Evidence and experimental data will be analyzed for reliability and possible sources of error. The use of well-designed, memorable laboratory experiences will facilitate this application of scientific knowledge and methodology and is essential in helping students to analyze the content critically. Students will learn how ethical considerations play an important role in modern chemistry-related fields and explore the importance of personal accountability in both individual and group work situations.
- Students will improve their ability to learn independently by researching and drawing generalizations from science related articles, books, graphs, charts, and diagrams. Regular opportunities are provided for students to clearly communicate their understanding through oral and written explanations of science concepts and laboratory experiences.
- Students will study the applications of chemistry to develop critical thinking skills.

### Scope and Sequence:

**Introduction to Chemistry**

- What is Chemistry
- Using the Scientific Approach and Scientific Method

**Measurements**** and Calculations**

- Units
- Length, Volume, and Mass
- Uncertainty in Measurements and Significant Figures
- Unit Conversions
- Density

**Matter**

- Physical and Chemical Properties and Changes
- Elements and Compounds
- Pure Substances and Mixtures
- Separation of Mixtures

**Chemical Foundations: Elements, Atoms, and Ions**

- The Elements and Symbols
- Dalton’s Atomic Theory
- Formulas and Compounds
- Structure of an Atom
- Isotopes
- Periodic Table
- Natural States of Elements

**Nomenclature**

- Naming Compounds
- Naming Binary Compounds
- Naming Compounds with Polyatomic Ions
- Naming Acids
- Writing Formulas with Names

**Chemical Reactions**

- Evidence of Chemical Reactions
- Chemical Equations
- Balancing Chemical Equations

**Reactions in Aqueous Solutions**

- Predicting Reactions
- Reactions in Which a Solid Forms
- Acid Base Reactions
- Reactions of Metals and Non-Metals
- Classifying Reactions

**Chemical Composition**

- Atomic Masses: Counting Atoms by Weighing
- The Mole and Molar Mass
- Percent Compositions and Formulas of Compounds
- Empirical Formula and Molecular Formula

**Chemical Quantities**

- Information Given by Chemical Reactions
- Mole-Mole Relationships and Mass Calculations
- Limiting Reactants
- Percent Yield

**Energy**

- The Nature of Energy
- Temperature and Heat; Exothermic and Endothermic Processes
- Thermodynamics and Measuring Changes in Energy
- Enthalpy – Thermochemistry
- Hess’ Law
- Quality vs. Quantity of Energy

**Modern Atomic Theory**

- Rutherford’s Atom
- Electromagnetic Radiation and Emission of Energy by Atoms
- Energy Levels of Hydrogen
- Bohr Model and Wave Mechanical Model
- Hydrogen Orbitals and Electron Configurations
- Atomic Properties of the Periodic Table

**Chemical Bonding **

- Types of Chemical Bonds
- Electronegativity, Bond Polarity, and Diapole Moments
- Stable Electron Configurations and Charges
- Ionic Bonding and Ionic Compounds
- Lewis Structures and Multiple Bonds
- Molecular Structure and VSEPR Model
- Molecules with Double Bonds

**Gases **

- Pressure
- Pressure and Volume: Boyle’s Law
- Volume and Temperature: Charles’ Law
- Volume and Moles: Avogadro’s Law
- The Ideal Gas Law
- Dalton’s Law of Partial Pressures
- Kinetic Molecular Theory of Gases
- Gas Stoichiometry

**Liquids and Solids **

- Water and Phase Changes
- Energy Requirements for Changes of State
- Inter-Molecular forces, Vapor Pressure, and Evaporation
- Solid State – types of Solids
- Bonding in Solids

**Solutions**

- Solutions
- Mass Percent and Molarity
- Dilution
- Stoichiometry of Solution Reactions
- Neutralization Reactions
- Solution Composition

**Acids and Bases**

- Acid Strength
- Water as an Acid and a Base
- The pH Scale
- Buffered Solutions

**Equilibrium**

- How Chemical Reactions Occur and Conditions that Alter Reaction Rates
- The Equilibrium Condition: a Dynamic Condition
- The Equilibrium Constant
- Heterogeneous Equilibrium
- Le Chatlier’s Principle
- Solubility Equilibrium

**Oxidation-Reduction Reactions and Electrochemistry**

- Oxidation States
- Oxidation-Reduction Between Non-Metals
- Electrochemistry and Electrolysis

**Organic Chemistry**

- Carbon Bonding
- Alkanes
- Structural Formulas and Isomerism
- Alkenes and Alkynes
- Aromatic Hydrocarbons
- Functional Groups
- Alcohols, Aldehydes, and Ketones
- Carboxylic Acids and Esters
- Polymers

**Biochemistry**

- Proteins
- Enzymes
- Carbohydrates
- Nucleic Acids
- Lipids

## GENERAL STUDIES

### Biology

### Course Description:

This course introduces students to the study of the life sciences. The ultimate goal is to produce students who are more scientifically literate and environmentally aware; therefore, the curriculum addresses attitudes, processes, knowledge science, technology, society, the environment, and careers. Topics covered include the nature of science, the structure and function of the cell, chemistry of living organisms, genetics, nucleic acid formation and function, taxonomy, a study of the characteristics of the six kingdoms of organisms, origin and diversity of life, and ecological relationships. Various laboratory investigations and other activities strengthen the mastery of topics covered.

### Course Objectives:

- Understanding Organization and Development: Living organisms are composed of cellular units (structures) that carry out functions required for life. Cellular units are composed of molecules, which also carry out biological functions.
- Understanding Matter and Energy Transformations: Food is required for energy and building cellular materials. Organisms in an ecosystem have different ways of obtaining food, and some organisms obtain their food directly from other organisms. All animals and most plants depend on both other organisms and their environment to meet their basic needs.
- Understanding Heredity and Reproduction: Organisms reproduce, develop, and have predictable life cycles. Organisms contain genetic information that influences their traits, and they pass this on to their offspring during reproduction.
- Understanding Evolution and Diversity: Sometimes, differences between organisms of the same kind provide advantages for surviving and reproducing in different environments. These selective differences may lead to dramatic changes in characteristics of organisms in a population over extremely long periods of time.
- Understanding Science Practices:
- Understand Scientific Explanations: Students understand core concepts and principles of science and use measurement and observation tools to assist in categorizing, representing, and interpreting the natural and designed world.
- Generate Scientific Evidence Through Active Investigations: Students master the conceptual, mathematical, physical, and computational tools that need to be applied when constructing and evaluating claims.
- Reflect on Scientific Knowledge: Scientific knowledge builds on itself over time.
- Participate Productively in Science: The growth of scientific knowledge involves critique and communication, which are social practices that are governed by a core set of values and norms.

### Assessments:

Attendance and participation: 15%

Assignments and homework: 25%

- Nightly reading will be given as homework.
- Periodic written homework will be given as a review of material covered in class.

Tests and quizzes: 30%

- Quizzes will be given half way through each unit.
- Tests will be given at the end of each unit.
- Labs will be done at least once per unit, and lab reports will count as quiz grades.

Midterm or final: 30%

** **

### Scope and Sequence:

**The Nature of Life**

- The Science of Biology
- What is science? How do Scientists work?
- Tools and Procedures
- The Chemistry of Life
- The nature of matter
- The properties of water
- Carbon compounds
- Chemical reactions and enzymes

**Cells**

- Cell Structure and Function
- Cell Theory and structure of a cell
- Plasma membrane and diffusion and osmosis
- Prokaryotic vs. Eukaryotic
- Photosynthesis
- Energy and life
- Photosynthesis overview and its chemical reactions
- Cellular Respiration
- Chemical Pathways
- Krebs Cycle and Electron Transport
- Cell Growth and Division and Regulating the Cell Cycle

**Genetics**

- Introduction to genetics
- Gregor Mendel
- Probability and Punnett Squares
- Mendelian Genetics
- Meiosis
- Gene linkage and maps
- DNA and RNA
- Genetic engineering
- The human genome
- Human heredity
- Human chromosomes
- Human molecular genetics

**Evolution**

- Darwin’s Theory of Evolution
- Evolution of populations
- Classifications

**Microorganisms and Fungi**

- Bacteria and viruses
- Protists
- Fungi

**Plants**

- Diversity
- Roots, stems and leaves
- Reproduction
- Adaptation

**Invertebrates**

- Sponges and Cnidarians
- Worms and mollusks
- Arthropods and echinoderms
- Comparing invertebrates

**Chordates**

- Non-vertebrate chordates, fish, and amphibians
- Reptiles and birds
- Mammals
- Comparing chordates
- Animal behavior

**The Human Body**

- Nervous system
- Skeletal, muscular, and integumentary systems
- Circulatory and respiratory systems
- Digestive and excretory systems
- Endocrine and reproductive systems
- The immune system and disease

## GENERAL STUDIES

### Pre-calculus

### Course Description

In this course emphasis is placed on the many trigonometric, geometric and algebraic techniques needed for the preparation of the study of Calculus. The course takes a functional point of view towards topics and is designed to strengthen and enhance conceptual understanding and mathematical reasoning used when solving problems. The course also emphasizes the use of the graphing calculator as a tool to interpret results as well as a method of obtaining an answer. Mastery of algebraic skills is an essential prerequisite. This course surveys a variety of pre-calculus topics including polynomial, rational, exponential, and trigonometric functions over the real and complex numbers. Much emphasis is placed on theory, and breadth and depth of understanding as well as efficacy. A pupil who successfully completes this course is prepared for Calculus AP/AB.

### Course Objectives

- Students will understand the structure of the systems of real and complex numbers, and the concept of functions and their unifying role in mathematics.
- Students will utilize algebraic and trigonometric concepts and skills, will be able to analyze and graph a variety of functions, and will acquire the necessary skills used in calculus such as evaluating limits and the concept of continuity.
- Students are expected to apply the following common skills that are relevant across all curriculum areas and career pathways: students will use technology, apply problem solving and critical thinking skills, and adapt to varied roles and responsibilities.
- Students communicate precisely about quantities, logical relationships, and unknown values through the use of signs, symbols, models, graphs, and mathematical vocabulary. Regular opportunities are provided for students to communicate through oral and written explanations of math concepts.
- Students learn to apply mathematics to everyday life.

** **

### Assessments:

Attendance and participation: 15%

Assignments and homework: 25%

- Nightly homework will be given as a review of what was covered in class

Tests and quizzes: 30%

- Quizzes will be given half way through each unit.
- Tests will be given at the end of each unit.

Midterm or final: 30%

** **

### Scope and Sequence

**Linear Relations and Functions**

- Relations and Functions
- Compositions of Functions
- Graphing Linear Equations
- Writing Equations
- Equations of Parallel and Perpendicular Lines
- Modeling Real World Data with Linear Functions
- Absolute Value Functions
- Graphing Linear Inequalities

**Systems of Linear Equations and Inequalities**

- Solving Systems of Equations in Two and Three Variables
- Using Matrices to Model Motion and Real World Data
- Determinants and Multiplicative Inverses of Matrices
- Solving Systems of Inequalities
- Linear Programming

**The Nature of Graphs**

- Symmetry and Coordinate Graphs
- Families of Graphs
- Graphs of Nonlinear Inequalities
- Inverse Functions and Relations
- Continuity and End Behavior
- Critical Points and Extrema
- Graphs of Rational Functions
- Direct, Indirect, and Joint Variation

**Polynomial and Rational Functions**

- Polynomial Functions
- Quadratic Equations
- The Remainder and Factor Theorems and the Rational Root Theorem
- Locating Zeros of a Polynomial Function
- Rational Equations and Partial Fractions
- Radical Equations and Inequalities
- Modeling Real World Data with Polynomial Functions

**The Trigonometric Functions**

- Angles and Degree Measure
- Trigonometric Ratios in Right Triangles
- Trigonometric Functions on the Unit Circle
- Applying Trigonometric Functions
- Solving Right Triangles
- The Law of Sines and The Law of Cosines

**Graphs of Trigonometric Functions**

- Angles and Radian Measure
- Linear and Angular Velocity
- Graphing Sine and Cosine Functions
- Amplitude and Period of Sine and Cosine Functions
- Horizontal and Vertical Shifts of Sine and Cosine Functions
- Modeling Real World Data with Sinusoidal Functions
- Graphing Other Trigonometric Functions and their Inverses

**Trigonometric Identities and Equations**

- Basic Trigonometric Identities
- Verifying Trigonometric Identities
- Sum and Difference Identities and Double Angle and Half Angle Identities
- Solving Trigonometric Equations
- Normal Form of a Linear Equation
- Distance From a Point to a Line

**Vectors and Parametric Equations**

- Geometric and Algebraic Vectors
- Vectors in Three Dimensional Space
- Perpendicular Vectors
- Applications with Vectors
- Vectors and Parametric Equations
- Modeling Motion Using Parametric Equations
- Transformational Matrices in Three Dimensional Space

**Polar Coordinates and Complex Numbers**

- Polar Coordinates
- Graphs of Polar Equations
- Polar and Rectangular Coordinates
- Polar Form of a Linear Equation
- Simplifying Complex Numbers
- The Complex Plan and Polar Form of Complex Numbers
- Products and Quotients of Complex Numbers in Polar Form
- Powers and Roots of Complex Numbers

**Conics**

- Introduction to Analytic Geometry
- Circles, Ellipses, Hyperbolas, and Parabolas
- Rectangular and Parametric Forms of Conic Sections
- Transformation of Conics
- Systems of Second Degree Equations and Inequalities

**Exponential and Logarithmic Functions**

- Real Exponents
- Exponential Functions
- The Number e
- Logarithmic Functions
- Common Logarithms and Natural Logarithms
- Modeling Real World Data with Exponential and Logarithmic Functions

**Sequences and Series**

- Arithmetic and Geometric Sequences and Series
- Infinite Sequences and Series
- Convergent and Divergent Series
- Sigma Notation and the nth Term
- The Binomial Theorem
- Special Sequences and Series
- Sequences and Iterations
- Mathematical Induction

**Combinatorics and Probability**

- Permutations and Combinations
- Permutations with Repetitions and Circular Permutations
- Probability and Odds and Probabilities of Compound Events
- Conditional Probabilities
- The Binomial Theorem and Probabilities

**Statistics and Data Analysis**

- The Frequency Distribution
- Measures of Central Tendency
- Measures of Variability
- The Normal Distribution
- Sample Sets of Data

## GENERAL STUDIES

### Algebra

### Course Description:

Students will explore a variety of methods to solve equations, graph functions, use mathematical symbols to represent aspects of the physical world, and learn to communicate effectively using mathematical notation. The course covers the following topics: basic operations on polynomial expressions, solutions to linear and quadratic equations, linear functions (graphing, the slope and y-intercepts of lines, writing the equations of lines), systems of linear equations and inequalities, quadratic and exponential functions (graphing and their properties), properties of exponents, properties of rational and irrational numbers, and simplification of radical expressions. Also, since problem solving is an integral part of this course, students spend a considerable amount of time translating problems presented in written form to equivalent statements in mathematics. Then, the students find solutions to the problems and express the results in written form.

### Course Objectives:

- Students will translate, evaluate and simplify expressions, order of operation; Words to symbols and graph on a coordinate plane: ordered pairs, linear equations, linear inequalities, relations and functions.
- Students will solve equations and inequalities involving angle measures.
- Students will classify numbers into their appropriate systems.
- Students will calculate the probability and odds of a simple event using the results to predict the outcome of future events, and differentiate between odds and probability of a simple event.
- Students will recognize, analyze and extend patterns and recognize and use properties of Algebra.
- Students will formulate a linear equation or inequality given a word problem and vice versa.
- Students will determine if a relation is a function and evaluate a function for a given value and will identify the domain, range, and inverse of a relation showing the relation as sets of ordered pairs, tables, mappings and graphs.
- Students will perform the four basic operations on rational numbers.
- Students will determine the slope of a line given two points, a linear equation or a graph.
- Students will compare and order real numbers including square roots.
- Students will solve and graph compound inequalities.
- Students will determine the x and y intercepts of linear graphs from their equations and will solve linear equations and inequalities and graph solutions on a number line.
- Students will classify polynomials and determine the degree for any polynomial.
- Students will solve quadratic equations by factoring.
- Students will solve rational equations and identify and solve proportions using them in applications.
- Students will simplify polynomials using appropriate exponent rules and give answers in either descending or ascending order of exponents.
- Students will multiply polynomials using FOIL on the distributing property and appropriate exponent rules and give answers in either descending or ascending order of exponents.
- Students will factor out the GCF of a polynomial and factor polynomials completely using difference of two squares, perfect square trinomials, trial and error, or regrouping.
- Students will simplify rational expressions using the four basic operations and determine the undefined values.

### Assessments:

Attendance and participation: 15%

Assignments and homework: 25%

- Nightly homework will be given as a review of what was covered in class

Tests and quizzes: 30%

- Quizzes will be given half way through each unit.
- Tests will be given at the end of each unit.

Midterm or final: 30%

### Scope and Sequence:

**Exploring Expressions, Equations, and Functions**

- Variables and Patterns
- Order of Operations
- Properties
- Identity and Equality
- Distributive
- Associative and Commutative

**Exploring Rational Numbers**

- Integers and Number Line
- Rational Numbers
- Adding/Subtracting
- Multiplying/Dividing
- Square Roots and Real Numbers

**Solving Linear Equations**

- With Addition/Subtraction
- With Multiplication/Division
- Multi-Step Equations and with Variables on Both Sides
- Formulas

**Proportional Reasoning**

- Ratios and Proportions
- Percent and Percent Change
- Probability and Odds
- Direct and Inverse Variation

**Graphing Relations and Functions**

- The Coordinate Plane
- Relations and Functions
- Graphing Linear Equations
- Writing Equations from Patterns

**Analyzing Linear Equations**

- Slope
- Writing Linear Equations
- Point Slope and Standard Form
- Slope Intercept From
- Graphing Linear Equations
- Midpoints
- Perpendicular and Parallel Lines

**Solving Linear Inequalities**

- With Addition/Subtraction
- With Multiplication/Division
- Multi-Step
- Compound Inqualities
- Absolute Value
- Graphing Inequalities with Two Variables

**Solving Systems of Linear Equations and Inequalities**

- Using Graphing
- Using Substitution
- With Elimination Using Addition/Subtraction and Multiplication
- Graphing Systems of Inequalities

**Exploring Polynomials**

- Multiplying and Dividing Monomials
- Scientific Notation
- Polynomials
- Addition/Subtraction
- Multiplying by a Monomial
- Multiplying by another Polynomial
- Special Products

**Using Factoring**

- GCF and Distributive Property
- Factoring Trinomials
- Difference of Squares and Perfect Squares
- Solving Equations by Factoring

**Exploring Quadratic and Exponential Functions**

- Graphing Quadratic Functions
- Solving Quadratics by Graphing
- The Quadratic Formula
- Exponential Functions and Growth and Decay

**Exploring Rational Expressions and Equations**

- Simplifying
- Multiplying/Dividing
- Dividing Polynomials
- Rational Expressions with Like and Unlike Denominators
- Mixed Expressions and Complex Fractions
- Solving Rational Equations

**Exploring Radical Expressions and Equations**

- Simplifying
- Operations with Radical Expressions
- Radical Equations
- Completing the Square

## GENERAL STUDIES

### Economics

### Course Description:

The general objective of this course is for students to master fundamental economic concepts, appreciate how the principal concepts of economics relate to each other and understand the structure of economic systems. Students will use economic concepts in a reasoned, careful manner in dealing with personal, community, national and global economic issues. They will use measurement concepts and methods such as tables, charts, graphs, ratios, percentages and index numbers to understand and interpret relevant data. They should learn to make reasoned decisions on economic issues as citizens, workers, consumers, business owners, managers and members of civic groups.

### Course Objectives:

- Students understand common economic terms and concepts and economic reasoning.
- Students analyze the elements of the United States market economy in a global setting.
- Students analyze the influence of the U.S. government on the American economy.
- Students analyze the elements of the United State labor market in a global setting.
- Students analyze the aggregate economic behavior of the U.S. economy.
- Students analyze issues of international trade, and explain how the U.S. economy affects, and is affected by, economic forces beyond its borders.
- Students will demonstrate an understanding of income and spending issues facing individuals and businesses.
- Students will demonstrate an understanding of how banks and other financial institutions operate.
- Students will demonstrate an understanding of effective investment practices.
- Students will analyze the role and importance of credit in personal and business finance.

** **

### Assessments:

Attendance and participation: 15%

Assignments and homework: 25%

- Nightly reading will be given as homework.
- Periodic written homework will be given as a review of material covered in class.
- Writing assignments and/or projects will be given quarterly.

Tests and quizzes: 30%

- Quizzes will be given half way through each unit.
- Tests will be given at the end of each unit.

Midterm or final: 30%

** **

### Scope and Sequence:

**Unit 1: Introduction to Economics**

- What is Economics?
- Economic Systems
- American Free Enterprise

**Unit 2: Introduction to Microeconomics: How Markets Work**

- Demand and Supply
- Prices
- Market Structures

**Unit 3: Business and Labor**

- Business Organizations
- Labor

**Unit 4: Money, Banking, and Finance**

- Money and Banking
- Financial Markets

**Unit 5: Introduction to Macroeconomics: Measuring Economic Performance**

- Gross Domestic Product and Growth
- Economic Challenges

**Unit 6: Government and the Economy**

- Taxes and Government Spending
- Fiscal Policy
- The Federal Reserve and Monetary Policy

**Unit 7: The Global Economy**

- International Trade
- Economic Development and Transition

**Unit 8: Financial Literacy**

- Planning and goals
- Career preparation
- Spending and credit
- Consumer protection
- Income
- Money management
- Saving and investing
- Risk management