Complete Syllabus

Mathematics and Logic for Medical-Scientific Entrance Tests · English

Syllabus Modules

12 modular units covering all topics required for medical-scientific entrance exams. Each unit includes learning objectives, prerequisites, and suggested study timelines.

Module 1

Arithmetic & Number Theory

Fundamental operations, fractions, decimals, percentages, ratios, and number properties.

  • Integers, rational numbers, and real numbers
  • Prime factorization, GCD, and LCM
  • Operations with fractions and decimals
  • Percentages and proportional reasoning

Learning Outcomes

Perform arithmetic operations fluently; solve problems involving ratios and percentages.

Module 2

Algebra & Equations

Linear equations, systems of equations, inequalities, and polynomial operations.

  • Linear equations and inequalities
  • Systems of linear equations
  • Polynomials and factoring
  • Quadratic equations and the quadratic formula

Learning Outcomes

Solve linear and quadratic equations; interpret solutions in context.

Module 3

Geometry & Trigonometry

Plane geometry, solid geometry, and basic trigonometric functions.

  • Angles, triangles, and polygons
  • Circles and arc measures
  • Volume and surface area of solids
  • Sine, cosine, and tangent

Learning Outcomes

Calculate perimeters, areas, and volumes; apply trigonometric ratios to solve triangles.

Module 4

Functions & Graphs

Linear, quadratic, exponential, and logarithmic functions; graphical analysis.

  • Function notation and evaluation
  • Linear and quadratic functions
  • Exponential and logarithmic functions
  • Interpreting graphs and transformations

Learning Outcomes

Analyze and sketch graphs; model real-world phenomena using functions.

Module 5

Probability

Basic probability rules, conditional probability, and counting principles.

  • Sample spaces and events
  • Addition and multiplication rules
  • Conditional probability and independence
  • Permutations and combinations

Learning Outcomes

Compute probabilities for simple and compound events; apply counting techniques.

Module 6

Statistics

Descriptive statistics, data representation, and basic inferential concepts.

  • Mean, median, mode, and range
  • Variance and standard deviation
  • Histograms, box plots, and scatter plots
  • Correlation and basic regression

Learning Outcomes

Summarize and interpret data; draw conclusions from statistical information.

Module 7

Logic & Critical Reasoning

Propositional logic, logical arguments, and critical reasoning for medical-scientific contexts.

  • Propositions and logical connectives
  • Truth tables and logical equivalence
  • Syllogisms and deductive reasoning
  • Identifying logical fallacies

Learning Outcomes

Evaluate logical arguments; apply critical reasoning to scientific problems.

Module 8

Sequences & Series

Arithmetic and geometric sequences, finite and infinite series.

  • Arithmetic and geometric sequences
  • Sum of finite arithmetic series
  • Sum of finite and infinite geometric series
  • Applications in science and medicine

Learning Outcomes

Find terms and sums of sequences; apply series to real-world contexts.

Module 9

Data Interpretation

Reading and interpreting data from tables, charts, and graphs.

  • Reading tables and frequency distributions
  • Bar charts, line graphs, and pie charts
  • Interpreting scientific data
  • Drawing conclusions from data

Learning Outcomes

Extract and interpret information from various data representations.

Module 10

Exponents & Logarithms

Properties of exponents and logarithms; exponential and logarithmic equations.

  • Laws of exponents
  • Logarithmic properties
  • Solving exponential and logarithmic equations
  • Applications in scientific contexts

Learning Outcomes

Simplify expressions and solve equations involving exponents and logarithms.

Module 11

Mathematical Reasoning

Problem-solving strategies, mathematical proofs, and reasoning techniques.

  • Problem-solving heuristics
  • Direct and indirect proofs
  • Mathematical induction
  • Counterexamples and conjectures

Learning Outcomes

Apply mathematical reasoning to solve complex problems; construct logical arguments.

Module 12

Exam Preparation & Review

Comprehensive review of all topics; test-taking strategies; timed practice.

  • Topic-by-topic review
  • Timed practice tests
  • Test-taking strategies
  • Performance analysis and feedback

Learning Outcomes

Demonstrate proficiency in all syllabus topics; perform effectively under exam conditions.

Prerequisites

Recommended knowledge before starting the syllabus.

Basic Arithmetic

Addition, subtraction, multiplication, division, fractions, and decimals.

English Language

Ability to read and understand mathematical texts in English (B1 level or higher).

Critical Thinking

Basic logical reasoning and problem-solving skills.

Digital Literacy

Familiarity with using computers and online learning platforms.

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