Your AP & College
AI Toolkit

Key Concepts

• Song Dynasty: gunpowder, printing, compass, iron production
• Mali Empire: Mansa Musa hajj (1324) caused Egyptian inflation from excess gold
• Mongol Empire: largest land empire, Pax Mongolica enabled safe Silk Road trade
• Aztec: chinampas farming, tribute system, Tenochtitlan 200,000+ people
• Feudalism in both Europe AND Japan: parallel decentralized power structures

Key Concepts

• Silk Road: overland, China to Mediterranean, luxury goods and ideas
• Indian Ocean: largest + most profitable — monsoon winds key
• Trans-Saharan: gold + salt trade built Mali and Great Zimbabwe
• Black Death: spread via Silk Road → killed 1/3 of Europe

Land-Based Empires

• Ottoman: took Constantinople 1453, devshirme, gunpowder empire
• Mughal: Akbar's religious tolerance, enormous wealth
• Safavid: Shia Islam as state religion — constant conflict with Ottomans
• Qing China: Manchu rulers adopted Confucianism to legitimize rule

Transoceanic Connections

• Portugal: African coast → Indian Ocean monopoly
• Spain: Columbus 1492, Potosí silver mines fund global trade
• Atlantic slave trade: 12.5 million Africans, 2 million died en route
• Silver connected China, Europe, Americas in global economy

Unit 5: Revolutions

• American, French, Haitian (only successful slave revolution), Latin American
• Haitian Revolution = best complexity example on any APWH essay

Unit 6: Industrialization

• Britain first, Berlin Conference (1884) carved up Africa
• Social Darwinism justified imperialism ideologically

Unit 7: Global Conflict

• WWI causes: MAIN. WWII rose from WWI humiliation + Great Depression

Units 8–9

• Decolonization, Cold War, globalization, climate change

Key Concepts

• Renaissance: humanism, secularism, individual achievement — Italy first
• Gutenberg printing press (~1450): mass distribution undermined Church monopoly
• Protestant Reformation (Luther 1517): 95 Theses, faith alone, scripture alone
• Catholic Counter-Reformation: Council of Trent, Jesuits
• 30 Years War (1618–1648) → Peace of Westphalia → state sovereignty established
• Scientific Revolution: Copernicus, Galileo, Newton — reason over religious authority

Key Concepts

• Absolutism: Louis XIV "L'état, c'est moi" — divine right, Versailles as control
• English Exception: Glorious Revolution (1688) → constitutional monarchy
• Enlightenment: Locke (natural rights), Voltaire (tolerance), Rousseau (general will)
• French Revolution: Third Estate, Reign of Terror, Napoleon rises
• Napoleon spread Enlightenment ideas and nationalism across Europe
• Congress of Vienna (1815): conservative reaction, balance of power restored

19th Century

• Industrial Revolution: Britain first, urbanization, new working class
• Nationalism: Italian unification (Garibaldi), German unification (Bismarck/Realpolitik)
• Imperialism: Berlin Conference, Social Darwinism

20th Century

• WWI: alliance systems, total war, Russian Revolution, 17 million dead
• Interwar: Great Depression, rise of fascism, appeasement fails
• WWII: Holocaust (6 million Jews), D-Day, atomic age
• Cold War, Marshall Plan, Berlin Wall, EU formation

All 9 — Know Argument + Constitutional Principle

• Declaration of Independence: natural rights, social contract, right to revolution
• Articles of Confederation: too weak — no taxation, no executive, no courts
• Constitution: federalism, separation of powers, checks and balances
• Federalist No. 10 (Madison): factions controlled by large republic + representation
• Federalist No. 51 (Madison): separation of powers, "ambition must counteract ambition"
• Federalist No. 70 (Hamilton): strong single executive — energy + accountability
• Federalist No. 78 (Hamilton): judicial review, courts as "least dangerous branch"
• Brutus No. 1: large republic can't represent people, standing army danger
• Letter from Birmingham Jail (MLK): just vs unjust laws, civil disobedience justified

Constitutional Power

• Marbury v Madison (1803): established judicial review
• McCulloch v Maryland (1819): implied powers, federal supremacy
• US v Lopez (1995): Commerce Clause has limits

1st Amendment

• Engel v Vitale (1962): no school-sponsored prayer
• Schenck v US (1919): "clear and present danger" limits free speech
• Tinker v Des Moines (1969): students keep 1st Amendment rights at school
• NY Times v US (1971): prior restraint unconstitutional
• Wisconsin v Yoder (1972): free exercise overrides compulsory education

Civil Rights + Voting

• Shaw v Reno (1993): racial gerrymandering violates Equal Protection
• Baker v Carr (1962): redistricting cases are justiciable
• McDonald v Chicago (2010): 2nd Amendment applies to states
• Citizens United v FEC (2010): political spending = protected free speech

Three Branches (Know Formal + Informal Powers)

• Congress: filibuster (Senate, 60 for cloture), declare war, confirm appointments
• President: veto, commander-in-chief, executive orders, bully pulpit
• Courts: judicial review, stare decisis, judicial activism vs restraint

Key Amendments

• 1st: speech, religion, press, assembly, petition
• 14th: equal protection + due process — incorporates Bill of Rights to states

Elections + Participation

• Electoral College: winner-take-all, 270 needed to win
• Iron triangles: interest groups + Congress + bureaucracy
• Linkage institutions: parties, elections, interest groups, media

Core Concepts

• Legitimacy: traditional, charismatic, rational-legal (Weber's three types)
• Political culture: shared values shaping political behavior
• Civil society: organizations between state and family — stronger = more democratic

United Kingdom (Model Democracy)

• Parliamentary system: PM is leader of majority party, fused executive-legislative power
• Unitary state with devolution: Scotland, Wales, N. Ireland have assemblies but Parliament is supreme
• Two-party dominant: Labour vs Conservative

Russia (Competitive Authoritarian)

• Formal democratic institutions exist but not genuinely competitive
• Putin consolidated power via media control + opposition suppression

China (Single-Party Authoritarian)

• Chinese Communist Party controls all institutions — no genuine opposition
• Xi removed term limits (2018); economic liberalization + political control

Iran (Theocratic Republic)

• Supreme Leader = ultimate authority; Guardian Council vets all candidates

Mexico (Federal Presidential Democracy)

• PRI ruled 71 years (1929–2000) → peaceful democratic transition
• Sexenio: 6-year single term, no reelection

Nigeria (Federal with Cleavages)

• North (Muslim) vs South (Christian) ethnic tensions; oil = "resource curse"

Key Concepts

• Absolute vs relative location; formal, functional, and perceptual regions
• Demographic transition model: Stage 1 (high birth+death) → Stage 4 (low both)
• Population pyramids: wide base = young/growing; narrow base = aging/declining
• Push factors (leave): poverty, conflict, disaster. Pull factors (attract): jobs, safety
• Rule of 70: doubling time = 70 ÷ growth rate %

Culture + Political Geography

• Cultural diffusion: relocation, contagious, hierarchical, stimulus
• Nation-state: political boundary matches cultural boundary (ideal, rare)
• Centripetal forces (unite) vs centrifugal forces (divide)
• Supranationalism: EU, UN — countries cede some sovereignty

Urban Geography

• Bid-rent: land value decreases with distance from CBD
• Urban models: concentric zone, sector, multiple nuclei
• Primate city: one dominant city disproportionate to next largest

Development

• HDI: education + income + life expectancy
• Core-periphery: wealthy cores exploit peripheral regions

Supply and Demand

• Equilibrium: where supply meets demand — market-determined price and quantity
• Elasticity: PED = %ΔQd / %ΔP; elastic (>1) vs inelastic (<1)
• Consumer/producer surplus: area above/below price line on S&D graph

Market Structures

• Perfect competition: price takers, zero long-run economic profit
• Monopoly: price maker, produces where MR=MC, deadweight loss exists
• Monopolistic competition: differentiated products, some price control, zero LR profit

Externalities + Factor Markets

• Negative externality: MSC > MPC → government corrects with tax
• MRP = MRC at profit-maximizing labor quantity in factor markets

Measuring the Economy

• GDP = C + I + G + NX
• Unemployment: frictional (between jobs), structural (skills mismatch), cyclical (recession)
• Inflation: demand-pull (too much spending) vs cost-push (supply shock)

Fiscal + Monetary Policy

• Expansionary fiscal: increase G or cut taxes → increase AD → fight recession
• Contractionary fiscal: decrease G or raise taxes → decrease AD → fight inflation
• Fed tools: federal funds rate, reserve requirements, open market operations

Key Models

• AD-AS: aggregate demand + short-run/long-run aggregate supply
• Phillips Curve: inverse unemployment-inflation relationship
• Loanable funds: supply of savings, demand for loans, real interest rate

Research Methods

• Experiment: manipulate IV, measure DV — ONLY method that establishes causation
• Correlation: r = −1 to +1 — relationship but NOT causation
• Confounding variable: alternative explanation — must control for it
• Double-blind: neither participant nor researcher knows who got treatment

Brain + Neurotransmitters

• Hippocampus: memory formation (HM case study). Amygdala: fear
• Frontal lobe: planning, personality (Phineas Gage)
• Dopamine: reward. Serotonin: mood. GABA: inhibitory

Learning

• Classical conditioning: NS + UCS → UCR; after pairing CS → CR (Pavlov)
• Operant: positive reinforcement adds pleasant → behavior INCREASES
• Negative reinforcement: removes unpleasant → behavior INCREASES (NOT punishment)
• Variable ratio: most resistant to extinction (slot machines)

Social Psychology

• Fundamental attribution error: overestimate personality, underestimate situation
• Bystander effect: more observers = less helping (diffusion of responsibility)
• Milgram: 65% delivered max shock — power of authority

Disorders

• Major depressive disorder: 2+ weeks low mood. Schizophrenia: hallucinations + flat affect
• OCD: obsessions (thoughts) + compulsions (rituals)

Exam Breakdown

• MCQ: 45 questions, 60 min — 45% of score — DO NOT ignore
• FRQ 1: Synthesis — 40 min — cite 3+ of 6–7 sources
• FRQ 2: Rhetorical Analysis — 40 min — analyze writer's choices
• FRQ 3: Argument — 40 min — defend your own claim

Key Devices

• Ethos (credibility), Pathos (emotion), Logos (logic)
• Anaphora: repetition at start → rhythm + emphasis
• Juxtaposition: contrasting ideas side by side
• Concession + Rebuttal: acknowledge opposing view then refute

Scoring (same for all three essays)

• Thesis: 1 pt — defensible claim, can be in intro OR conclusion
• Evidence + Commentary: 4 pts — most important category
• Sophistication: 1 pt — complexity, tension, broader significance

Synthesis Essay

• Your argument drives the essay — sources are ammunition, not the essay
• Cite 3+ sources or lose an automatic point
• Disagree with one source while using others = automatic sophistication point

Argument Essay

• Body 3 = concession + rebuttal → earns sophistication point
• Use ANY evidence: history, science, literature, personal experience

Exam

• MCQ: 55 questions, 60 min — 5 passages (prose + poetry)
• FRQ 1: Poetry analysis. FRQ 2: Prose analysis. FRQ 3: Open question (your choice of novel/play)

Must-Know Elements

• Imagery, Tone (author's attitude), Symbolism, Irony (verbal/situational/dramatic)
• Point of view: first/third/omniscient — affects what reader knows and trusts
• Enjambment: line continues without pause. Volta: the "turn" in a poem
• Caesura: pause within a line — slows reader, creates emphasis

Poetry FRQ

• Read twice — first for overall meaning, second for craft choices
• Identify: speaker, situation, shift (volta), unusual word choices
• Thesis: "[Author] uses [devices] to convey [complex claim about theme]"

Open Question FRQ

• Be specific: "In Chapter 4, when Gatsby says..." beats vague references
• Know your works at chapter level — specificity earns points
• Practice adapting same work to 10 different prompt angles

Key Concepts

• Limit: value f(x) APPROACHES as x→a (not necessarily f(a))
• L'Hôpital's Rule: 0/0 or ∞/∞ → take derivatives of top AND bottom
• Continuity at x=a: limit exists + f(a) defined + they equal each other (all three required)
• IVT: f continuous on [a,b] and k between f(a) and f(b) → f(c)=k exists
• EVT: continuous on [a,b] → absolute max AND min are guaranteed

All the Rules

• Power: d/dx[xⁿ] = nxⁿ⁻¹
• Chain: d/dx[f(g(x))] = f'(g(x))·g'(x) — used in ~80% of derivatives
• Product: (uv)' = u'v + uv'. Quotient: (u/v)' = (u'v−uv')/v²
• Key derivatives: sin→cos, eˣ→eˣ, ln x→1/x

Derivatives Applications

• 1st derivative test: + to − = local max; − to + = local min
• MVT: continuous on [a,b], differentiable on (a,b) → f'(c) = (f(b)−f(a))/(b−a)
• Optimization: critical points + test endpoints on closed interval

Integration + FTC

• Indefinite: ∫f(x)dx = F(x) + C (always +C)
• FTC Part 1: d/dx[∫ₐˣf(t)dt] = f(x)
• FTC Part 2: ∫ₐᵇf(x)dx = F(b) − F(a)
• FTC + Chain Rule: d/dx[∫ₐᵍ⁽ˣ⁾f(t)dt] = f(g(x))·g'(x)

Additional Integration

• Integration by parts: ∫u dv = uv − ∫v du; choose u via LIATE order
• Partial fractions: decompose rational functions before integrating
• Improper integrals: use limits when bounds are infinity
• Logistic growth: dP/dt = kP(1−P/L) → S-curve with carrying capacity

Convergence Tests

• Geometric: |r| < 1 converges, sum = a/(1−r)
• p-series: converges if p > 1
• Ratio Test: lim|aₙ₊₁/aₙ| < 1 → converges
• Alternating Series Test: alternating, terms → 0, decreasing → converges

Taylor + Maclaurin

• eˣ = 1 + x + x²/2! + x³/3!... (memorize)
• sin x = x − x³/3! + x⁵/5!... cos x = 1 − x²/2! + x⁴/4!...

Parametric

• dy/dx = (dy/dt)/(dx/dt)
• d²y/dx² = d/dt[dy/dx] / (dx/dt)
• Arc length: ∫√[(dx/dt)² + (dy/dt)²] dt

Polar

• x = rcosθ, y = rsinθ
• Area: A = ½∫r² dθ. Between curves: ½∫[r₁² − r₂²] dθ

Key Concepts

• Rate of change: average rate = (f(b)−f(a))/(b−a)
• Zeros and multiplicity: odd multiplicity = crosses x-axis; even = touches
• Rational functions: vertical asymptotes where denominator = 0
• Exponential: f(x) = abˣ; a = initial value, b = growth/decay factor
• Logarithm laws: log(xy) = log x + log y; log(xⁿ) = n·log x

Trigonometry

• Unit circle: know all 16 standard angles and their sin/cos/tan values
• Transformations: amplitude (a), period (2π/b), phase shift (−c/b)
• Inverse trig: arcsin, arccos, arctan — restricted domains

Polar + Parametric (Intro)

• Convert: x=rcosθ, y=rsinθ, r²=x²+y²
• Parametric: x(t) and y(t) trace a curve as t changes

Key Concepts

• SOCS: Shape, Outliers, Center, Spread — describe EVERY distribution with all four
• Mean vs Median: mean pulled by outliers; median is resistant
• r: correlation (−1 to +1). r²: % of variation in y explained by x
• Residual = actual − predicted (positive = underestimate)
• Outlier: below Q1−1.5(IQR) or above Q3+1.5(IQR)

Sampling

• SRS: gold standard. Stratified: divide then SRS. Cluster: select entire groups
• Experiment: establishes causation. Observational: association only

Probability

• P(A or B) = P(A) + P(B) − P(A and B). P(A and B) = P(A)×P(B|A)
• Binomial: BINS (Binary, Independent, fixed N, Same p)
• Normal: 68-95-99.7 rule; z = (x−μ)/σ

The 4-Step Process

• 1. STATE: H₀ and Hₐ in words + symbols, significance level α
• 2. PLAN: name the test, check conditions (Random, Normal, Independent)
• 3. DO: calculate test statistic + p-value
• 4. CONCLUDE: compare p to α, reject or fail to reject H₀ IN CONTEXT

Java Fundamentals

• Integer division: 7/2 = 3 (not 3.5) — truncates. Cast first: (double)7/2 = 3.5
• Modulo: % gives remainder — 7%2 = 1. Use for even/odd checks
• String: use .equals() not == for comparison

Classes + Inheritance

• Constructor: same name as class, no return type, initializes object
• Private instance variables accessed via getter/setter methods (encapsulation)
• extends: subclass inherits. super(): calls superclass constructor (must be first line)
• Override: redefine method in subclass with same signature

Data Structures

• Arrays: fixed size, 0-indexed, arr.length (no parentheses)
• 2D arrays: arr[row][col]. ArrayList: add, get, set, remove, size()
• Traverse ArrayList with remove() backwards — prevents skipping elements

Sorting + Searching

• Selection sort: find min, swap to front — O(n²)
• Insertion sort: build sorted portion left to right — O(n²)
• Binary search: sorted array only — O(log n)

Key Concepts

• Abstraction: hiding complexity — lists, procedures, libraries are all abstractions
• Iteration + Selection: loops and conditionals — know when to use each
• Binary: all data in bits — 2ⁿ values with n bits
• Lossless vs lossy compression: lossless = exact reconstruction; lossy = some data lost
• Metadata: data about data (file size, creation date, GPS location)

The Internet

• Packets: data broken into pieces, each takes own route, reassembled at destination
• TCP/IP: protocols standardizing how data travels. DNS: domain names → IP addresses
• HTTP vs HTTPS: HTTPS = encrypted connection

Cybersecurity + Society

• Encryption: symmetric (same key) vs asymmetric (public/private pair)
• Phishing, DDoS, malware — know definitions and how each works
• Digital divide: unequal technology access across populations
• Crowdsourcing: using large groups to gather data or solve problems

Macromolecules + Membranes

• Proteins: most diverse — enzymes, receptors, structural, transport, signaling
• Phospholipid bilayer: hydrophilic heads out, hydrophobic tails in
• Osmosis: water moves toward higher solute concentration
• Enzyme: active site + substrate → product; denatured by extreme pH or temperature

Photosynthesis

• Light reactions: THYLAKOID — water splits, O₂ released, ATP + NADPH produced
• Calvin cycle: STROMA — CO₂ fixed, G3P made (sugar precursor)

Respiration

• Glycolysis: CYTOPLASM. Krebs: MATRIX. ETC: INNER MEMBRANE → 32–34 ATP
• Fermentation (no O₂): regenerates NAD+ — lactic acid or ethanol + CO₂

Genetics + Gene Expression

• Transcription: DNA → mRNA. Translation: mRNA → protein at ribosome
• Mutations: silent, missense, nonsense. H-W: p+q=1 AND p²+2pq+q²=1

Evolution

• Natural selection: variation + heritability + differential survival
• H-W equilibrium: large pop, no mutation, no migration, random mating, no selection

Ecology

• 10% rule. Keystone species: remove → trophic cascade
• Positive feedback amplifies change; negative feedback maintains homeostasis

Atomic Structure

• Periodic trends: atomic radius ↑ down/left; IE ↑ up/right; electronegativity ↑ up/right
• Electron config: aufbau, Pauli, Hund — know all three rules

Bonding + IMF

• VSEPR: electron pairs determine molecular geometry
• IMF hierarchy: H-bonding > dipole-dipole > London dispersion (all have LDF)

Key Concepts

• Net ionic equations: exclude spectator ions
• Rate = k[A]ᵐ[B]ⁿ — orders ONLY from experimental data, not balanced equation
• Arrhenius: higher T = faster rate; catalyst lowers activation energy only
• Rate-determining step: slowest step determines rate law

Equilibrium

• Le Chatelier: system shifts to oppose stress
• Q vs K: Q < K → shift right (→); Q > K → shift left (←)

Acids/Bases

• pH = −log[H⁺]; pH + pOH = 14
• ICE tables for weak acid/base calculations
• Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA])

Thermodynamics

• ΔG = ΔH − TΔS; ΔG < 0 = spontaneous
• ΔG° = −RT ln K: connects thermo to equilibrium

Earth Systems + Living World

• 4 spheres: lithosphere, hydrosphere, atmosphere, biosphere — all interact
• 10% rule: only 10% of energy transfers between trophic levels
• Keystone species: remove → trophic cascade → ecosystem collapse

Populations

• J-curve: exponential growth → crash. S-curve: logistic → levels at carrying capacity
• Rule of 70: doubling time = 70 ÷ growth rate %

Soil + Water

• Soil horizons: O→A(topsoil)→B→C→R. Topsoil = most fertile, first lost
• Aquifer over-pumping → subsidence + saltwater intrusion

Land + Water (HIGHEST PRIORITY)

• EUTROPHICATION: N+P runoff → algae bloom → O₂ depletion → dead zone
• Tragedy of the Commons: shared unregulated resources always get overexploited
• Salinization: over-irrigation → salt buildup → infertile soil

Energy

• Coal (most CO₂) → oil → natural gas (least CO₂)
• Nuclear: zero GHG but radioactive waste lasts 10,000+ years
• Solar, wind: clean but have manufacturing/land/wildlife impacts

Atmospheric Pollution

• Photochemical smog: NOₓ + VOCs + sunlight → ground-level ozone (BAD)
• Acid deposition: SOₓ + NOₓ + water → kills ecosystems
• Stratospheric ozone (GOOD): CFCs destroy it. Montreal Protocol (1987) fixed it

Climate Change

• GHGs: CO₂, CH₄ (80× more potent), N₂O. Enhanced greenhouse effect = warming
• Positive feedback AMPLIFIES: ice melts → less albedo → more heat → more melting
• Mitigation = reduce GHGs. Adaptation = adjust to changes already happening

Motion

• Big 4: v=v₀+at; x=v₀t+½at²; v²=v₀²+2ax; x=½(v+v₀)t
• Projectile: horizontal (constant v) and vertical (a=−g) are INDEPENDENT
• Graphs: slope of x-t = velocity; slope of v-t = acceleration

Newton's Laws

• ΣF = ma — sum ALL forces, draw free body diagram first
• 3rd Law: action-reaction pairs are equal, opposite, on DIFFERENT objects

Energy + Momentum

• KE = ½mv²; PE = mgh; W_net = ΔKE
• Conservation of energy: if no non-conservative forces, KE + PE = constant
• Impulse: FΔt = Δp. Conservation of momentum: p_before = p_after (isolated system)
• Elastic: both momentum AND KE conserved. Inelastic: momentum only

Rotation

• Torque: τ = rF sinθ
• Angular momentum L = Iω: conserved when no external torques
• Skater pulling in arms: I decreases → ω increases (L conserved)

Fluids

• Pressure: P = F/A; P = P₀ + ρgh with depth
• Buoyancy: F_buoy = ρ_fluid × V_submerged × g
• Continuity: A₁v₁ = A₂v₂ (narrower = faster)
• Bernoulli: P + ½ρv² + ρgh = constant (faster flow = lower pressure)

Thermodynamics

• 1st Law: ΔU = Q − W (energy conservation for thermal systems)
• 2nd Law: entropy of isolated system never decreases

Electricity + Magnetism

• Coulomb's Law: F = kq₁q₂/r²
• Ohm's Law: V = IR. Series: same I, voltages add. Parallel: same V, currents add
• Magnetic force on charge: F = qvB sinθ (right-hand rule for direction)

Optics

• Snell's Law: n₁sinθ₁ = n₂sinθ₂
• Thin lens: 1/f = 1/d_o + 1/d_i; m = −d_i/d_o

Calculus in Mechanics

• v(t) = dx/dt; a(t) = dv/dt; use integrals when acceleration is not constant
• Work: W = ∫F·dx when force varies with position
• Impulse: J = ∫F dt when force varies with time

Rotation

• Moment of inertia: I = ∫r² dm (given for standard shapes)
• Rolling without slipping: v = Rω connects linear + rotational
• τ = Iα; L = Iω — angular momentum conserved if no external torques

Gravitation

• F = Gm₁m₂/r² — inverse square law
• Gravitational PE: U = −Gm₁m₂/r (negative, zero at infinity)
• Circular orbit: gravity = centripetal force → solve for orbital speed/period

FRQ Strategy

• Set up integral with limits shown before evaluating
• Label all variables — define what each symbol represents
• Partial credit is substantial — show every step even if stuck

Key Concepts

• Gauss's Law: ΦE = Q_enc/ε₀ — use for symmetric distributions (sphere, cylinder, plane)
• Electric potential: V = kq/r; E = −dV/dr
• Conductors in equilibrium: E = 0 inside; charge on surface only

Circuits

• Kirchhoff's laws: ΣI_in = ΣI_out (junction); ΣΔV = 0 (loop)
• RC circuit: τ = RC; exponential charging/discharging
• RL circuit: τ = L/R; exponential current build-up

Magnetism + Induction

• Ampere's Law: ∮B·dl = μ₀I_enc — for symmetric current distributions
• Faraday's Law: EMF = −dΦ_B/dt — changing flux induces EMF
• Lenz's Law: induced current opposes the change in flux

Exam

• Section I: MCQ — reading + listening passages (50%)
• Section II: Email reply + argumentative essay (integrate 3 sources) + speaking (25%+25%)

6 Thematic Units

• Families and Communities. Personal and Public Identities. Contemporary Life
• Science and Technology. Global Challenges. Beauty and Aesthetics

High-Yield Grammar

• Subjunctive: WEIRDO (Wishes, Emotion, Impersonal, Recommendation, Doubt, Ojalá)
• Preterite (completed action) vs imperfect (ongoing/habitual/description)
• Por vs para: por = cause/exchange; para = purpose/recipient/deadline

Cultural Comparisons

• Name a SPECIFIC country (not just "Spanish-speaking countries")
• Use specific cultural products, practices, perspectives
• Know Mexico, Spain, Colombia, Argentina at minimum

Exam Structure

• Section I: MCQ — reading + listening (50%)
• Section II: Writing (email + essay) + Speaking (conversation + cultural comparison) (50%)

Key Grammar

• Subjonctif: after verbs of doubt, emotion, wish, necessity
• Imparfait vs passé composé: imparfait = ongoing; PC = completed action
• Conditionnel: would — hypotheticals and polite requests
• Pronoms relatifs: qui (subject), que (object), dont (de+), où (place/time)

Francophone Countries to Know

• France, Belgium, Québec (Canada), Sénégal, Côte d'Ivoire, Maroc
• Know at least two in depth for cultural comparison examples

Exam Sections

• Reading: passages with MCQ. Listening: conversations + announcements
• Writing: story narration (4 pictures) + email response
• Speaking: conversation simulation + cultural presentation

Strategies

• Story narration: use narrative connectors — 首先、然后、接着、最后
• Heritage speakers: practice formal written Chinese — spoken fluency ≠ exam ready
• Practice Pinyin input or character recognition under time pressure

Required Texts

• Caesar, Gallic Wars: Books 1, 4, 5, 6 (selections) — prose military narrative
• Vergil, Aeneid: Books 1, 2, 4, 6, 10, 12 (selections) — dactylic hexameter epic

Essential Grammar

• 5 declensions: know all cases — nominative, genitive, dative, accusative, ablative, vocative
• Subjunctive: purpose (ut), result, indirect command, cum clauses
• Participles: agree with noun in case/number/gender — present active, perfect passive
• Indirect statement: accusative + infinitive after verbs of thinking/saying

Formal Analysis

• Line, color (hue/value/saturation), space (2D vs 3D, perspective), composition
• Balance (symmetrical vs asymmetrical), focal point, rhythm

Contextual Analysis

• Function: what was this USED for? (religious, political, commemorative)
• Patron: who commissioned it and why? Reveals power relationships
• Audience: who saw it? How would they have responded?
• Historical context: what events or ideologies does it reflect?

Key Periods

• Ancient Greece/Rome: Parthenon, Doryphoros — civic ideals + naturalism
• Medieval: Hagia Sophia, Chartres Cathedral — faith through architecture
• Renaissance: Sistine Chapel, Birth of Venus — humanism + classical revival
• Baroque: Caravaggio, Bernini — drama + Counter-Reformation emotion
• Modern: Picasso, Duchamp — challenging tradition itself
• Non-Western: Great Mosque of Djenné, Taj Mahal, Seated Guanyin — know these deeply

Core Theory

• Key signatures: circle of fifths — sharps (FCGDAEB), flats (BEADGCF)
• Major scale: W-W-H-W-W-W-H pattern
• Minor scales: natural, harmonic (raised 7th), melodic (raised 6+7 ascending)
• Intervals: count letter names inclusive; quality (M, m, P, A, d)

Roman Numeral Analysis

• I IV V = major; ii iii vi = minor; vii° = diminished
• Inversions: root position, 1st inversion (3rd in bass), 2nd inversion (5th in bass)
• V7 → I is the most important cadential motion

4-Part SATB Voice Leading

• Avoid parallel 5ths and parallel octaves between ANY two voices
• Leading tone (7th scale degree) resolves UP to tonic
• 7th of chord resolves DOWN by step