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University Prep Program

Full preparation for the entrance exams of San Marcos and Peru's most demanding universities, with the same principle as always: quality education within everyone's reach.

Two Only One Coin students going over the syllabus together
  • Duration: 6 months · semester cycle
  • Modality: 100% online · live classes
  • Study plan: 18 subjects
  • Focus: San Marcos admission exam
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Program goal

The program works through every area assessed in admission exams, step by step, with live classes, exam-style exercises and constant assessments to track your progress.

That you master both the content and the problem-solving strategies an entrance exam demands — not memorising, but analysing, interpreting and deciding under pressure.

What you'll study

  • Verbal Reasoning — Reading comprehension, main ideas, semantic relationships and inference.
  • Logical-Mathematical Reasoning — Logical reasoning and problem solving with inductive and deductive strategies.
  • Mathematics — Arithmetic, Algebra, Geometry and Trigonometry applied to admission problems.
  • Sciences — Physics, Chemistry and Biology: core principles and the scientific method.
  • Language & Literature — Grammar, syntax and usage, with analysis of literary and non-literary texts.
  • Social Sciences — History, Geography, Economics, Civics and Philosophy, with a critical view of Peru and the world.

How it is taught

  • Content built up step by step
  • Exam-style exercises throughout
  • Problems analysed and discussed in class
  • Constant assessments to measure progress
  • Study habits and independent learning

By the end of the program you'll be able to

  • Answer admission-exam questions effectively
  • Apply knowledge across different subject areas
  • Analyse information critically and methodically
  • Sustain your academic performance with confidence
  • Face the admission process at a competitive level

The full syllabus

Verbal Reasoning 16 topics
  1. Text hierarchy: identifying the central theme
  2. Text hierarchy: identifying the main idea
  3. Cohesion devices (anaphora, cataphora, ellipsis and connectors)
  4. Text coherence: thematic unity and non-contradiction
  5. Synthesis processes I: selection and generalisation
  6. Synthesis processes II: abstracting information
  7. Semantic-textual relationships: contextual synonymy
  8. Semantic-textual relationships: contextual antonymy
  9. The sense of language: denotation and connotation
  10. Literal compatibility and incompatibility
  11. Inferential compatibility and incompatibility
  12. Inference I: holistic and data-based
  13. Inference II: lexical and causal
  14. Inference III: intention and prospective
  15. Cognitive extrapolation (changing the premises)
  16. Referential extrapolation (changing the context)
Logical-Mathematical Reasoning 16 topics
  1. Optimisation situations: maxima and minima
  2. Measuring strategies: weighings, scales, sectioning and cuts
  3. Recreational logic I: number arrangements, dice, matchsticks and dominoes
  4. Recreational logic II: calendars and transfers
  5. Inductive reasoning: numerical, verbal and geometric
  6. Time and frequency relationships: frequency of events and clock problems
  7. Problem posing: interpreting information (equations)
  8. Moving objects: rotation and translation of figures / wheels, pulleys and gears
  9. Orientation and topology: routes, paths, cardinal points and figure tracing
  10. Figure analysis: counting figures, symmetry and reflections
  11. Spatial vision: visualising figures in space, congruence and similarity
  12. Metric geometry: perimeters and areas of polygonal and circular regions
  13. Data analysis: tables, statistical charts and data sufficiency
  14. Logic of certainty and chance: sports situations and certainty problems
  15. Deductive reasoning: simple/compound deduction and ordering information
  16. Dialectics and algorithms: truths and lies, family ties and flowcharts
Arithmetic 16 topics
  1. Logic and sets
  2. Natural numbers (N)
  3. Numeral systems
  4. Integers (Z)
  5. Divisibility rules
  6. Prime numbers
  7. GCD and LCM
  8. Rational numbers
  9. Decimal numbers
  10. Ratios and proportions
  11. Magnitudes and proportional sharing
  12. Percentages and rates
  13. Sequences and mixtures
  14. Descriptive statistics
  15. Measures of position and dispersion
  16. Combinatorics and probability
Algebra 16 topics
  1. Operations, powers and roots
  2. Polynomials: degree, addition and multiplication
  3. Polynomial division: classic method, Ruffini and Horner
  4. Remainder theorem and factor theorem
  5. Notable products, Newton's binomial and notable quotients
  6. Factoring methods and GCD/LCM of polynomials
  7. Fundamental theorem of algebra and root-coefficient relationships
  8. Operations in R, intervals and complex numbers
  9. Properties of absolute value and their application
  10. Linear, quadratic and biquadratic equations
  11. First- and second-degree inequalities in one variable
  12. Linear systems with 2 and 3 variables (Cramer and Gauss)
  13. Systems of inequalities and linear programming
  14. The notion of function: domain, range and graphing
  15. Elementary functions (linear, quadratic, root) and monotonicity
  16. Special functions: inverse, exponential and logarithmic
Geometry 16 topics
  1. Line segments, angles and perpendicular/parallel lines
  2. Fundamental properties, congruence and inequalities
  3. Notable lines and points of the triangle
  4. Quadrilaterals, parallelograms, trapezoids and general polygons
  5. Angles in the circle and tangency properties
  6. Inscribed and circumscribed figures and related theorems
  7. Thales' theorem and triangle similarity criteria
  8. Angle bisector, median and Pythagorean theorems
  9. Metric relationships in the triangle and the circle
  10. Areas of triangular and quadrangular regions
  11. Circumference, area of the circle and circular sector
  12. Convex and regular polyhedra and prisms
  13. Pyramids and frustums of pyramids and prisms
  14. Solids of revolution
  15. The Cartesian plane: distance between points and equation of the line
  16. Conics: equations of the circle, parabola and ellipse
Trigonometry 16 topics
  1. Angle measurement systems
  2. Arc length and area of the circular sector
  3. Trigonometric ratios
  4. Solving right triangles
  5. Angles in standard position
  6. Reduction to the first quadrant
  7. The unit circle
  8. Trigonometric identities
  9. Trigonometric ratios of the sum and difference of two angles
  10. Double-angle trigonometric ratios
  11. Half-angle trigonometric ratios
  12. Sum-to-product transformations
  13. Trigonometric equations
  14. Laws of sines, cosines and tangents
  15. Applications: angles of elevation and depression
  16. Trigonometric functions (domain, range, graph) and inverses
Physics 16 topics
  1. Dimensional analysis
  2. Vector analysis
  3. Kinematics I: uniform and uniformly accelerated motion, free fall
  4. Kinematics II: uniform and accelerated circular motion
  5. Dynamics and Newton's laws
  6. Torque and momentum
  7. Work and energy
  8. Conservation of energy and power
  9. Thermal physics
  10. Fluid mechanics
  11. Electrostatics
  12. Electrodynamics
  13. Electromagnetism
  14. Oscillatory motion and simple harmonic motion
  15. Wave motion and light
  16. Modern physics
Chemistry 16 topics
  1. Matter and energy
  2. Atomic structure
  3. Periodic table and nomenclature of inorganic compounds
  4. Chemical bonding
  5. Chemical reactions
  6. Stoichiometry: stoichiometric calculations
  7. Stoichiometry: limiting and excess reagents, purity and reaction yield
  8. The gaseous state
  9. Dispersed systems: solutions and concentration units
  10. Acids and bases: neutralisation reactions
  11. Kinetics and chemical equilibrium
  12. Electrochemistry: electrolysis and galvanic cells
  13. Organic chemistry: hydrocarbons
  14. Organic chemistry: oxygenated compounds
  15. Organic chemistry: nitrogen compounds
  16. Natural resources: environment, resources, pollution and the greenhouse effect
Biology 16 topics
  1. The basis of life: living beings, levels of organisation, viruses and bioelements
  2. Biomolecules: carbohydrates, lipids, proteins, nucleic acids (DNA/RNA) and vitamins
  3. Prokaryotic and eukaryotic cells: cell theory, structures, organelles and the nucleus
  4. Plant and animal histology: growth, support, epithelial, connective, muscle and nervous tissues
  5. Energy metabolism: photosynthesis (light/dark phases) and aerobic cellular respiration
  6. Nutrition and digestion: comparative digestive systems (animals) and human anatomy
  7. Transport and circulation: animal and human circulatory systems; transport in plants (xylem/phloem)
  8. Excretion and immunity: the human urinary system, types of animal excretion and the immune response
  9. Chemical coordination: phytohormones (plants) and the human endocrine system (hormones)
  10. Nervous coordination: nerve impulses, the senses and the anatomy of the human nervous system
  11. Reproduction and the cell cycle: mitosis, meiosis, plant reproduction and the human reproductive system
  12. Classical genetics: Mendel's laws, dominance and sex-linked inheritance
  13. Human genetics and evolution: mutations, evolutionary theories (Darwin/Lamarck) and human evolution
  14. Biodiversity: classification of living beings and the Plantae and Animalia kingdoms
  15. Health and disease: infectious diseases, transmission mechanisms and public health
  16. Ecology and conservation: ecosystems, food chains, biogeochemical cycles and protected natural areas
Spanish Language 16 topics
  1. Communication: elements, language and functions
  2. Language, speech and varieties (regional, social and standard)
  3. Spanish in Peru and Peruvian language families
  4. Phonemes, the phoneme-letter relationship and the syllable
  5. Diphthongs, triphthongs, hiatus and syllable division
  6. General accentuation rules (monosyllables and polysyllables)
  7. Special accentuation: diacritic, emphatic and complex forms
  8. Morphemes and word-formation processes
  9. Nouns and adjectives: structure, classes and agreement
  10. The verb phrase: characterisation, structure and conjugation
  11. Adverbs, prepositions and conjunctions: classes and functions
  12. The sentence: definition, structure and classification by speaker attitude
  13. Complex syntax: simple and compound sentences
  14. Commas, periods, parentheses, quotation marks and other punctuation
  15. Standard use of upper- and lower-case letters
  16. The linguistic sign and semantic relationships (polysemy, homonymy, etc.)
Literature 16 topics
  1. Literary theory
  2. Greek classicism
  3. Renaissance and Baroque
  4. The mid-19th century
  5. The avant-garde
  6. The Spanish tradition
  7. Spanish American modernismo
  8. Spanish American narrative
  9. The Latin American Boom
  10. Peru: Colony and Republic
  11. Peru: realism and discourse
  12. Peru: postmodernism
  13. The Peruvian avant-garde
  14. Indigenismo
  15. The Generation of '50
  16. Contemporary Peruvian literature
Psychology 16 topics
  1. Scientific origins and schools (psychoanalysis, behaviourism, humanism, cognitivism)
  2. Biological bases of behaviour
  3. Socialisation and norms of coexistence
  4. The family: parenting styles, values and attitudes
  5. Sensation, perception and attention
  6. Memory: stages, types and processes
  7. Thought and language
  8. The development of intelligence and its main theories
  9. Conditioning (classical and operant) and observational learning
  10. Meaningful, discovery-based, cooperative and self-regulated learning
  11. Factors, dimensions and stages of the life cycle (prenatal and childhood)
  12. Adolescence, adulthood and biopsychosocial changes
  13. Self-knowledge, self-esteem, body image and sexual/cultural identity
  14. Emotions, feelings, passions and emotional intelligence
  15. Motivation: definition, types and the hierarchy of needs
  16. Responsible sexuality, risk behaviours and life plans
Civic Education 16 topics
  1. Human rights I: concept, characteristics and historical evolution
  2. Human rights II: the Universal Declaration and the Convention on the Rights of the Child
  3. International protection: the Pact of San José, the Inter-American Commission and Court
  4. The Political Constitution of Peru: fundamental rights and constitutional guarantees
  5. Citizen participation I: law-making, constitutional reform and referendums
  6. Citizen participation II: recall, removal, accountability and prior consultation
  7. Civil society: institutions, social movements and participatory budgeting
  8. Democratic coexistence: a culture of peace against discrimination and corruption
  9. Conflict resolution: negotiation, mediation, conciliation and arbitration
  10. Historical memory: terrorist violence in Peru, pacification and reconciliation
  11. Identity and interculturality: ethnic and linguistic diversity and belonging
  12. National heritage: valuing Peru's historical and natural heritage
  13. The Peruvian State: characteristics of the rule of law, structure and duties
  14. Branches of the State: organisation and functions of the Legislative, Executive and Judiciary
  15. Autonomous bodies: the Constitutional Court, Ombudsman, Public Ministry, JNJ, Central Bank and Comptroller
  16. Electoral system and defence: JNE, ONPE, RENIEC and the role of the armed forces and police
History of Peru 16 topics
  1. Origins of civilisation: migration routes and the Lithic and Archaic periods
  2. Early Horizon: the Formative period and sociopolitical complexity
  3. Regional developments: the Nazca, Moche and Recuay cultures
  4. Pan-Andean states: the splendour of Tiahuanaco and the Wari Empire
  5. Late Intermediate: the regional states (Chimú, Chincha, Chachapoyas and Aymara kingdoms)
  6. The Tawantinsuyo: origin, expansion and sociopolitical and economic organisation
  7. Fall and resistance: the end of the Tawantinsuyo and the response to the Spanish conquest
  8. Viceroyal order I: colonial consolidation and the Toledan reforms
  9. Viceroyal order II: colonial institutions, economy, society and culture
  10. Reforms and rebellions: the Bourbon reforms and the struggles of Juan Santos and Túpac Amaru II
  11. Peruvian independence: the crisis of the Spanish Empire, the Cortes of Cádiz and the liberation currents
  12. The early Republic: the First Militarism, caudillismo and the False Prosperity (guano)
  13. Crisis and reconstruction: the war with Chile and the Second Militarism
  14. 20th century I: the Aristocratic Republic, Leguía's Oncenio and new ideologies
  15. 20th century II: from Sánchez Cerro to Odría's Ochenio and the reformism of the 1960s
  16. Recent history: military government, the return to democracy, the Fujimori years and the 21st century
World History 16 topics
  1. Introduction to history: definition, sources and universal periodisation
  2. Hominisation and prehistory: from hominids to sapiens and the Metal Ages
  3. Eastern civilisations I: Mesopotamia and Egypt (politics, society and culture)
  4. Eastern civilisations II: India and China (organisation and cultural contributions)
  5. The classical world I: Greece (periods, organisation and cultural legacy)
  6. The classical world II: Rome (from Monarchy to Empire and its disintegration)
  7. Early Middle Ages: Germanic kingdoms, the Carolingian and Byzantine empires
  8. The Islamic world: origin, expansion and cultural contributions of medieval Islam
  9. Late Middle Ages: expansion (11th-13th centuries), medieval society and religiosity
  10. Transition to modernity: humanism, the Renaissance and the Reformation
  11. Absolutism and colonialism: geographic discoveries and European monarchies
  12. Age of revolutions: the Enlightenment, US independence and the French Revolution
  13. Industrial Revolution: the First and Second Revolutions and colonial empires
  14. The political 19th century: Napoleonic wars, the Restoration and the revolutions of 1830 and 1848
  15. Great 20th-century conflicts: the First and Second World Wars and the Russian Revolution
  16. The contemporary world: the Cold War, the end of the USSR, globalisation and the 2008 crisis
Geography 16 topics
  1. The geosystem and cartography: imaginary lines, coordinates and representations
  2. Internal geodynamics: the Earth's structure, plate tectonics and volcanism
  3. External geodynamics: weathering, erosion and the forces that shape the relief
  4. Peru's relief I: features of the submarine relief and the Coast
  5. Peru's relief II: morphology of the Andean region and the Rainforest
  6. Peru's climate: climate factors, the Senamhi classification and the El Niño phenomenon
  7. Global climate crisis: global warming, the greenhouse effect and the Paris Agreement
  8. Peru's hydrography: the Peruvian sea, the Humboldt Current and drainage basins
  9. Water resource management: glaciers and river basin management
  10. Disaster risk management: hazard, vulnerability, resilience and disaster classification
  11. Biodiversity and protected areas: world biomes, protected natural areas and the biosphere
  12. Sustainable development: environmental problems (deforestation) and the 2030 Agenda
  13. Economic activities: extractive, productive and service sectors in Peru
  14. Demography and space: the Peruvian population, structure, dynamics and migration
  15. Territorial organisation: decentralisation, land borders and maritime domain
  16. World geography: physical and social elements and quality of life (HDI) by continent
Economics 16 topics
  1. Economic fundamentals: definition, scarcity, opportunity cost and methods
  2. Needs and circulation: human needs and the circular flow of the economy
  3. Consumer theory: the demand function and elasticities (price and income)
  4. Production theory: production, costs, revenue and the supply function
  5. Market models: perfect competition, monopoly, oligopoly and monopolistic competition
  6. Market failures: externalities, public goods and the role of regulatory bodies
  7. Factor markets: labour, land, capital and the accumulation of human capital
  8. Money and the financial system: types and functions of money, assets and institutions
  9. Monetary policy: the Central Reserve Bank — functions, instruments and the interest rate
  10. Public sector and taxation: the public budget, fiscal instruments and the tax system
  11. Consumption and investment: the consumer basket, CPI, savings and types of investment
  12. External sector I: balance of payments, trade balance and foreign trade theory
  13. External sector II: the exchange market (exchange rates) and economic integration
  14. Growth and development: the economic cycle, sources of growth and human development (HDI)
  15. National reality: the informal economy, income distribution and poverty in Peru
  16. Entrepreneurship and projects: idea management, problem trees, cash flow and evaluation
Philosophy 16 topics
  1. Introduction to philosophy: etymology, origin, characteristics and disciplines
  2. Ancient philosophy I: from myth to logos and the pre-Socratic period
  3. Ancient philosophy II: the Greek apogee — Socrates, Plato and Aristotle
  4. Modern philosophy: rationalism, empiricism and Kant's criticism
  5. Contemporary philosophy: from absolute idealism to existentialism and postmodernity
  6. Latin American thought I: stages of philosophy — colonial, Enlightenment and Romanticism
  7. Latin American thought II: from positivism and spiritualism to the 20th century in Peru
  8. Philosophical anthropology: human nature, subjectivity, the individual and society
  9. Ethics and morality: evaluating ethical problems, moral dilemmas and values
  10. Political philosophy: the origin of power, the State and today's democratic values
  11. Gnoseology and science: characteristics of knowledge and the scientific method
  12. Critical epistemology: problems of the hypothesis and the critique of science and technology
  13. Philosophy of language: relationships between language, truth, science and politics
  14. Logic and argumentation I: analysing arguments — premises and conclusions
  15. Logic and argumentation II: identifying informal fallacies and notable paradoxes
  16. Aesthetics and society: artistic appreciation, contemporary genres and cultural criticism

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