Twelfth Grade Curriculum
Rhetoric Math Offerings:
Geometry:
I. Points, Lines, Planes and Angles
A. Some Basic Figures
B. Definitions and Postulates
II. Deductive Reasoning
A. Using Deductive Reasoning
B. Theorems about Angles and Perpendicular Lines
III. Parallel Lines and Planes
A. When Lines an Planes are Parallel
B. Applying Parallel Lines to Polygons
IV. Congruent Triangles
A. Corresponding Parts in Congruence
B. Some Theorems Based on Congruent Triangles
C. More about Proof in Geometry
V. Quadrilaterals
A. Parallelograms
B. Special Quadrilaterals
VI. Inequalities in Geometry
A. Inequalities and Indirect Proof
B. Inequalities and Triangles
VII.
Similar Polygons
A. Ratio, Proportion and Similarity
B. Working with Similar Triangles
VIII. Right Triangles
A. Right Triangles
B. Trigonometry
IX. Circles
A. Tangents, Arcs, and Chords
B. Angles and Segments
X. Constructions and Loci
Twelfth Grade Curriculum
A. Basic Constructions
B. More Constructions
C. Locus
XI. Areas of Plane Figures
A. Areas of Polygons
B. Circles, Similar Figures and Geometric Probability
XII.
Areas and Volumes of Solids
A. Important Solid
B. Similar Solid
XIII. Coordinate Geometry
A. Geometry and Algebra
B. Lines and Coordinate Geometry Proofs
XIV. Transformations
A. Some Basic Mappings
B. Composition and Symmetry
Algebra II and Trigonometry:
I. Basic Concepts of Algebra
A. The Language of Algebra
B. Operating with Real Numbers
C. Solving Equations and Solving Problems
II. Inequalities and Proof
A. Working with Inequalities
B. Working with Absolute Value
C. Proving Theorems
III. Linear Equations and Functions
A. Linear Equations and Their Graphs
B. Linear System
C. Functions and Relations
IV. Products and Factors of Polynomials
A. Working with Polynomials
B. Factors of Polynomials
C. Applications of Factoring
V. Rational Expressions
A. Using the Laws of Exponents
Twelfth Grade Curriculum
B. Rational Expressions
C. Problem Solving Using Fractional Equations
VI. Irrational and Complex Numbers
A. Roots and Radicals
B. Real Numbers and Complex Numbers
VII.
Quadratic Equations and Functions
A. Solving Quadratic Equations
B. Roots of Quadratic Equations
C. Quadratic Functions and Their Graphs
VIII. Variation and Polynomial Equations
A. Variation and Proportion
B. Polynomial Equations
C. Solving Polynomial Equations
IX. Analytic Geometry
A. Conic Sections: Circles and Parabolas
B. Conic Sections: Ellipses and Hyperbolas
C. Systems of Equations
X. Exponential and Logarithmic Functions
A. Exponential Functions
B. Logarithmic Functions
C. Applications
XI. Sequences and Series
A. Sequences
B. Series
C. Binomial Expansions
XII.
Triangle Trigonometry
A. Trigonometric Functions
B. Triangle Trigonometry
XIII. Trigonometric Graphs; Identities
A. Circular Functions and Their Graphs
B. Trigonometric Identities
XIV. Trigonometric Applications
A. Vectors
B. Polar Coordinates and Complex Numbers
C. Inverse Functions
XV.
Statistics and Probability
A. Statistics
B. Counting
Twelfth Grade Curriculum
C. Probability
XVI. Matrices and Determinants
A. Matrices
B. Inverses of Matrices
C. Working with Determinants
Statistics and Probability:
I. Interpreting Categorical and Quantitative Data
A. Summarize, represent, and interpret data on a single count or measurement variable
B. Summarize, represent, and interpret data on two categorical and quantitative variables
C. Interpret linear models
II. Making Inferences and Justifying Conclusions
A. Understand and evaluate random processes underlying statistical experiments
B. Make inferences and justify conclusions from sample surveys, experiments and
observational studies
III. Conditional Probability and the Rules of Probability
A. Understand independence and conditional probability and use them to interpret data
B. Use the rules of probability to compute probabilities of compound events in a uniform
probability model
IV. Using Probability to Make Decisions
A. Calculate expected values and use them to solve problems
B. Use probability to evaluate outcomes of decisions
Pre-Calculus:
I. Linear and Quadratic Functions
A. Points and Lines
B. Slopes of Lines
C. Finding Equations of Lines
D. Linear Functions and Models
E. Complex Numbers
F. Solving Quadratic Equations
G. Quadratic Functions and their Graphs
II. Polynomial Functions
A. Polynomials
B. Synthetic Division; Remainder and Factor Theorems
C. Graphing Polynomial Functions
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D.
E.
F.
G.
Finding Maximums and Minimums
Using Technology To Approximate Roots
Solving Polynomial Equations by Factoring
General Results for Polynomial Equations
III. Inequalities
A. Linear Inequalities; Absolute Value
B. Polynomial Inequalities in One Variable
C. Polynomial Inequalities in Two Variable
D. Linear Programming
IV. Functions
A. Functions
B. Operations on Functions
C. Reflecting Graphs; Symmetry
D. Period Functions; Stretching and Translating Graphs
E. Inverse Functions
V. Exponents and Logarithms
A. Growth and Decay: Integral Exponents
B. Growth and Decay: Rational Exponents
C. Exponential Functions
D. The Number e and the Function ex
E. Logarithmic Functions
F. Laws of Logarithms
G. Exponential Equations; Change of Base
VI. Trigonometric Functions
A. Measurement of Angles
B. Sectors of Circles
C. Sine and Cosine Functions
D. Evaluating and Graphing Sine and Cosine
E. The Other Trigonometric Functions
F. The Inverse Trigonometric Functions
VII.
Trigonometric Functions and Applications
A. Simple Trigonometric Equations
B. Sine and Cosine Curves
C. Modeling Periodic Behavior
D. Relationships among the Functions
E. Solving More Difficult Trigonometric Equations
VIII.
Triangle Trigonometry
A. Solving Right Triangles
B. Area of a Triangle
C. Law of Sines
D. Law of Cosines
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E. Applications of Trigonometry
IX. Trigonometric Addition Formulas
A. Sum and Difference Formulas: Sine and Cosine
B. Sum and Difference Formulas: Tangent
C. Double-Angle and Half-Angle Formulas
D. Solving Trigonometric Equations
X. Polar Coordinates
A. Polar Coordinates and Graphs
B. Geometric Representation of Complex Numbers
C. Powers of Complex Numbers
D. Roots of Complex Numbers
XI. Sequences and Series
A. Arithmetic and Geometric Sequences
B. Recursive Definitions
C. Arithmetic and Geometric Series and their Sums
D. Limits of Infinite Sequences
E. Sums of Infinite Geometric Series
F. Sigma Notation
XII.
Limits
A. Limits of Functions
XIII. Introduction to Calculus
A. Slope of a Curve
B. Using Derivatives in Curve Sketching
C. Velocity and Acceleration
Twelfth Grade Curriculum
Science: Physics
I. Planning and Conducting Investigations
A. Components of a System
B. Measurements of Mass, Volume, Temperature, Heat Exchange, Energy
Transformations, Motion, Fields, and Electric Charge
II. Analyze and Interpret Data
A. Mathematical Statements
B. Interpolated, Extrapolated, and Analyzed Trends to Make Predictions
C. Relationships Between Physical Quantities
D. Slope of a Linear Relationship
E. Vectors
III. Demonstrate Scientific Reasoning and Logic
A. Analysis of Scientific Sources to Develop and Refine Research Hypotheses
B. Analysis of How Science Explains and Predicts Relationships
C. Evaluation of Evidence for Scientific Theories
D. New Discoveries Result in Modification of Existing Theories
E. Construction and Defense of a Scientific Viewpoint
IV. Interrelationships Among Mass, Distance, Force and Time
A. Newton’s Laws of Motion
B. Linear, Uniform Circular, Projectile, and Planetary Motion
C. Gravitation
D. Work, Power and Energy
V. Quantities Including Mass, Energy, Momentum, and Charge are Conserved
A. Kinetic and Potential Energy
B. Elastic and Inelastic Collisions
C. Electric Power
VI. Properties of Fluids
A. Density and Pressure
B. Archimedes’ Principle of Buoyancy
C. Pascal’s Principle
D. Fluids in Motion
E. Bernoulli’s Principle
VII.
Transferred and Transformed Energy for Usable Work
A. Transformation of Energy Among Forms Including Mechanical, Thermal, Electrical,
Gravitations, Chemical, and Nuclear
B. Efficiency of Systems
Twelfth Grade Curriculum
VIII. Models of Transverse and Longitudinal Waves to Interpret Wave Phenomena
A. Wave Characteristics (Period, Wavelength, Frequency, Amplitude, and Phase)
B. Fundamental Wave Processes (Reflection, Refraction, Diffraction, Interference,
Polarization, Doppler Effect)
C. Light and Sound in Terms of Wave Models
IX. Electromagnetic Spectrum
A. Properties and Behaviors of Radio Waves, Microwaves, Infrared, Visible Light,
Ultraviolet, X-rays, and Gamma Rays
B. Wave Properties of Each Band
X. Optical Systems
A. Laws of Reflection and Refraction
B. Ray Diagrams
C. Mirror and Lens Equations
D. Real and Virtual Images
XI. Effects of Gravitations, Electric, and Magnetic Force
A. Inverse Square Laws (Newton’s law of Universal Gravitation and Coulomb’s Law)
B. Motors, Generators, Transformers, and Cathode Ray Tubes
XII.
Electrical Circuits
A. Ohm’s Law
B. Series, Parallel, and Combined Circuits
C. Resistors, Batteries, Generators, Fuses, Switches, and Capacitors
Twelfth Grade Curriculum
Humane Letters:
I. History
A. Spielvogel – Western Civilization
B. Bailyn et al., The Great Republic
C. Morison, Oxford History of the American People
D. Hofstadter, Great Issues in American History
E. The Declaration of Independence
F. Alexander Hamilton et al., The Federalist
G. Constitution of the United States
H. De Tocqueville, Democracy in America
1. An Age of Nationalism and Realism
a. The France of Napoleon III
b. National Unification: Italy and Germany
c. Nation Building and Reform: The National State in Mid-Century
d. Industrialization and the Marxist Response
e. Science and Culture in an Age of Realism
2. The Mass Society in an “Age of Progress
a. The Growth of Industrial Prosperity
b. The Emergence of Mass Society
c. The National State
3. An Age of Modernity, Anxiety, and Imperialism
a. Toward the Modern Consciousness: Intellectual and Cultural
Development
b. Politics: New Directions and New Uncertainties
c. The New Imperialism
d. International Rivalry and the Coming of War
4. The Beginning of the Twentieth Century Crisis: War and Revolution
a. The Road to World War I
b. The War
c. War and Revolution
d. The Peace Settlement
5. The Futile Search for Stability: Europe Between Wars
a. An Uncertain Peace: The Search for Security
b. The Democratic States
c. Retreat from Democracy: The Authoritarian and Totalitarian States
d. Dictatorship in the Iberian Peninsula
e. The Expansion of Mass Culture and Mass Leisure
f. Cultural and Intellectual Trends in the Interwar Years
6. The Deepening of the European Crisis: World War II
a. Prelude to War
b. The Course of World War II
c. The New Order
d. The Home Front
Twelfth Grade Curriculum
e. Aftermath of the War: Cold War
7. Cold War and a New Western World
a. Development of Cold War
b. Europe and the World: Decolonization
c. Recovery and Renewal in Europe
d. The United States and Canada: A New Era
e. Postwar Society and Culture in the Western World
8. The contemporary Western World since 1973
a. Toward a New Western Order
b. After the Cold War: New World Order of Age of Terrorism?
c. New Directions and New Problems in Western Society
d. Western Culture Today
e. Toward a Global Civilization?
II. Literature (Poems, Short Stories and Novels)
A. Thoreau – Walden
B. Melville, Moby Dick
C. Charles Dickens – Great Expectations
D. Edgar Allen Poe – The Fall of the House of Usher and other stories
E. Orwell, 1984
F. Hitler, Mein Kampf
G. Dostoyevsky – Brothers Karamazov
H. Steinbeck – Grapes of Wrath
I. Tuchman – Guns of August
J. Whitman, “Song of Myself”, “Leaves of Grass”
K. S. Crane, “The Bride Comes to Yellow Sky”
L. B. Hart, “The Luck of Roaring Camp” “The Outcasts of Poker Flat”
M. Turner, “The Significance of the Frontier in American History”
N. Dickenson, Selected Poems
O. H. James, The American
P. Frost, Selected Poems
Q. Pound, “The White Stag’ The Return” “Portrait d’une femme” “Mauberley”
R. Agee, Let Us Now Praise Famous Men
S. O’Neill, Long Day’s Journey into Night
T. O’Connor, “The Life You Save May Be Your Own” “A Good Man Is Hard To Find”
U. Miller, Death of a Salesman
V. Warren, All the King’s Men
W. Ellison, Invisible Man
X. Oretega y Gasset, The Revolt of the Masses
Y. Shakespeare – Taming of the Shrew, Othello
Z. Shakespeare’s Poetry
AA. Marx – Communist Manifesto
BB. Plutarch’s Lives
CC. The Twelve Caesar’s
DD. Charles Darwin – “Origin of Species”
EE.
Lincoln – The Man of the People
Twelfth Grade Curriculum
FF.
Faulkner – The Unvanquished
GG. The Education of Henry Adams
HH. The Great Gatsby
II.
Huckleberry Finn
JJ.
Innocence of Father Brown
KK. Leo Tolstoy – Anna Karenina
LL.
Their Eyes Were Watching God
MM. Our Town
NN. Animal Farm
OO. All Rivers Run to Sea
PP.
The Crucible
QQ. A Man for All Seasons
RR. The Gulag of Archipelago
SS.
Rosencrantz and Guildenstern Are Dead
III. Problems of Knowledge and Faith
A. Kant – Critique of Pure Reason
B. Spinoza – Ethics
C. Plato – Republic, Phaedo, Symposium
D. Paul- Epistle to the Romans, First Epistle to the Corinthians
E. Selections from Origen, Basil of Caesarea, and Gregory of Nyssa
F. Chesterton, The Everlasting Man
G. Schumacher, A Guide for the Perplexed
H. Friedrich Nietzsche Thus Spoke Zarathustra,
IV. Rhetoric II
A. A Manual for Writers of Term Papers, Theses, and Dissertations
B. Ten Lessons in clarity and Grace
C. Elements of Style
D. Modern Rhetoric for the Classical Student
E. The Lost Tools of Writing
V. Memory
A. MacLeish, “You, Andrew Marvell”
B. Crane, “Repose of Rivers”
C. Stevens, “The Emperor of Ice Cream”
D. Auden, “Musee des Beaux Arts”
E. Warren, “Bearded Oaks”
F. Markham, “The Man with a Hoe”
VI. Spring Film series:
A. “Citizen Kan”
B. “Dodsworth”
C. “Streetcar Named Desire”
Twelfth Grade Curriculum
D.
E.
F.
G.
H.
I.
“The Grapes of Wrath”
“The Caine Mutiny”
“Casablanca”
“The Quiet American”
Readings from: Max Lerner, America as a Civilization
Orson Wells, “The Third Man”
VII. Senior Thesis
Twelfth Grade Curriculum
Greek IV:
I. Grammar
A. Grammar review
B. Translation
C. Recitation and oratory
D. Reading and discussion of Greek scripture
E. Reading and discussion of Greek and Hellenistic authors
I. Primary Texts
A. The Greek New Testament
B. The Old Testament (Septuagint)
C. Antigone, Sophocles
D. Meno, Plato
E. Nichomachean Ethics, Aristotle