CSCA Mathematics Exam Preparation Course Outline

Lecture Sheet 1: Foundations – Sets & Logic

• Topics Covered:
  • Definition, representation (roster, set builder), and properties of sets.
  • Relationships between sets: subsets, proper subsets, and the empty set.
  • Set operations: union ($A \cup B$), intersection ($A \cap B$), and complement ($C_U A$)³

Lecture Sheet 2: Inequalities

• Topics Covered:
  • Basic properties and axioms of inequalities.
  • Solution methods for quadratic inequalities (e.g., $ax^2 + bx + c > 0$).
  • Solution methods for rational inequalities (e.g., $\frac{P(x)}{Q(x)} \ge 0$).

Lecture Sheet 3: Core Concepts of Functions

• Topics Covered:
  • Definition of a function, domain, and range.
  • Properties of functions: monotonicity (increasing/decreasing) and parity (even/odd functions).
  • Graphical representation of functions and transformations (shifting, stretching).

Lecture Sheet 4: Elementary Functions

• Topics Covered:
  • Power functions ($y=x^a$).
  • Exponential functions ($y=a^x$) and logarithmic functions ($y=\log_a x$).
  • Trigonometric functions (sine, cosine, tangent), their graphs, and basic identities.

Lecture Sheet 5: Sequences & Introduction to Calculus

• Topics Covered:
  • Arithmetic sequences: general term formula ($a_n$) and summation ($S_n$).
  • Geometric sequences: general term formula and summation.
  • Introduction to derivatives: definition and geometric meaning (slope of a tangent).
  • Simple applications of derivatives, such as finding the monotonicity of a function.

Lecture Sheet 6: Plane Analytic Geometry I (Lines & Circles)

• Topics Covered:
  • Equations of lines (slope-intercept, point-slope, general form).
  • Relationships between lines (parallel, perpendicular).
  • Standard and general equations of a circle.
  • Positional relationship between lines and circles (tangent, secant).
• Gaokao Context: Analytic geometry is a major component of the exam. Problems often combine algebraic manipulation with geometric intuition.

Lecture Sheet 7: Plane Analytic Geometry II (Conic Sections)

• Topics Covered:
  • Definitions and standard equations of the ellipse, hyperbola, and parabola¹⁸.
  • Key properties: foci, vertices, eccentricity, and asymptotes (for hyperbolas)¹⁹.

Lecture Sheet 8: Vectors, Complex Numbers & Solid Geometry

• Topics Covered:
  • Vector concepts and operations (addition, subtraction, scalar multiplication).
  • Basic concepts and operations of complex numbers (addition, subtraction, multiplication).
  • Rectangular coordinate system in 3D space.
  • Properties of simple geometric solids (cubes, prisms, pyramids).

Lecture Sheet 9: Probability & Statistics

• Topics Covered:
  • The classical probability model and methods for calculating probability.
  • Numerical characteristics of data: mean and variance.
  • Basic understanding of the normal distribution and its properties^.

Lecture Sheet 10: Final Review & Exam Strategy

• Topics Covered:
  • Comprehensive review of all content modules.
  • Timed practice drills focusing on the exam format: 48 multiple-choice questions in 60 minutes.
  • Strategies for single-answer multiple-choice questions: elimination, substitution, and special value testing.
  • Time management to ensure all questions are attempted.

CSCA Physics Preparatory Course: 10-Lecture Outline

This 10-lecture course is designed to provide a comprehensive review of the CSCA Physics Syllabus (2025) with a preparation intensity inspired by the Gaokao. The primary goal is to build deep conceptual mastery, rapid problem-recognition, and strategic test-taking skills for a high-pressure, multiple-choice environment.

Module 1: Mechanics (Lectures 1-3)

Lecture 1: Foundations of Motion (Kinematics & Newton’s Laws)

• Core Concepts:
  • Kinematics: Displacement, velocity (average vs. instantaneous), acceleration.
  • Uniform acceleration motion: Key equations, graphical analysis ($v-t$, $x-t$ graphs).
  • Free-fall motion.
  • Newton’s laws of motion: First, Second ($F=ma$), and Third laws.
  • Application: Free-body diagrams, static and kinetic friction, forces on inclines, connected objects (e.g., pulley systems).
• CSCA Focus:
  • Mastery of free-body diagrams.
  • Rapidly interpreting kinematic graphs.
  • Identifying the correct frame of reference and system to analyze.

Lecture 2: The Conservation Laws (Work, Energy & Momentum)

• Core Concepts:
  • Work and power (constant and variable forces).
  • Work-Energy Theorem.
  • Kinetic Energy ($KE$) and Potential Energy ($PE$ – gravitational and elastic).
  • Law of Conservation of Mechanical Energy.
  • Impulse and Momentum ($p=mv$).
  • Impulse-Momentum Theorem.
  • Law of Conservation of Momentum (1D and 2D collisions).
• CSCA Focus:
  • Quickly determining if energy, momentum, or both are conserved.
  • Problem-solving using “before and after” state analysis.
  • Applying conservation laws vs. $F=ma$ (knowing which is faster).

Lecture 3: Rotational & Oscillatory Motion (Circular, Gravitation & SHM)

• Core Concepts:
  • Uniform circular motion: Centripetal acceleration and centripetal force.
  • Applications: Banked curves, objects in vertical circles.
  • Newton’s law of universal gravitation ($F=G \frac{m_1 m_2}{r^2}$).
  • Gravitational force as centripetal force (orbits).
  • Simple Harmonic Motion (SHM): Key characteristics, period, frequency.
  • Mechanical waves: Transverse vs. longitudinal, wavelength, frequency, wave speed.
• CSCA Focus:
  • Identifying the source of centripetal force in various scenarios.
  • Distinguishing SHM from other oscillatory motion.
  • Understanding the relationship between gravitation and satellite/planetary motion.

Module 2: Electromagnetism (Lectures 4-6)

Lecture 4: Static Charges & Steady Currents (Electrostatics & DC Circuits)

• Core Concepts:
  • Electrostatics: Coulomb’s Law, electric field strength ($E$), electric potential ($V$).
  • Relationship between $E$-field and electric potential.
  • Direct Current (DC) Circuits: Ohm’s Law ($V=IR$).
  • Series and parallel circuits: Calculating equivalent resistance.
  • Electric work ($W=qU$) and power ($P=IV$).
• CSCA Focus:
  • Superposition principle for $E$-fields and potentials.
  • Rapidly simplifying complex resistor networks (series/parallel).
  • Analyzing changes in circuit (e.g., “what happens to the brightness of bulb A if bulb B burns out?”).

Lecture 5: Moving Charges & Magnetic Fields (Magnetism)

• Core Concepts:
  • Magnetic field (magnetic induction, $B$).
  • Magnetic force on a current-carrying wire (Ampere’s force: $F=ILB$).
  • Magnetic force on a moving charge (Lorentz force: $F=qvB$).
  • Right-hand rules (for force direction, field from current).
  • Application: Charged particle motion in a uniform magnetic field (circular path).
• CSCA Focus:
  • Mastery of all right-hand rules; 3D visualization.
  • Combining electric and magnetic fields (e.g., velocity selectors).
  • Deriving radius and period for charged particles in $B$-fields.

Lecture 6: Dynamic Fields (Electromagnetic Induction)

• Core Concepts:
  • Magnetic flux ($\Phi$).
  • Faraday’s Law of Induction: Induced electromotive force (EMF).
  • Lenz’s Law: Determining the direction of induced current.
  • Applications: Motional EMF ($E=BLv$), generators.
• CSCA Focus:
  • Lenz’s Law is critical: “opposing the change in flux.”
  • Interpreting graphs of $\Phi$ vs. $t$ to find induced EMF.
  • Problems combining induction with forces and energy.

Module 3: Thermodynamics, Optics & Modern Physics (Lectures 7-9)

Lecture 7: Thermodynamics

• Core Concepts:
  • Kinetic theory of gases (microscopic origin of pressure and temperature).
  • Ideal gas equation of state ($PV=nRT$).
  • First Law of Thermodynamics ($\Delta U = Q + W$).
  • Understanding $U$ (internal energy), $Q$ (heat), and $W$ (work).
  • Isobaric, isochoric, isothermal, and adiabatic processes.
• CSCA Focus:
  • Applying the First Law to different processes.
  • Interpreting $P-V$ diagrams (calculating work, identifying processes).
  • Connecting microscopic kinetic theory to macroscopic variables.

Lecture 8: Optics

• Core Concepts:
  • Geometrical Optics: Law of reflection.
  • Law of refraction (Snell’s Law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$).
  • Total internal reflection (TIR) and critical angle.
  • Physical Optics: Young’s double-slit interference (path difference, fringe spacing).
  • Single-slit diffraction.
• CSCA Focus:
  • Rapidly applying Snell’s Law and TIR.
  • Distinguishing interference and diffraction patterns and their cause (path difference).
  • Understanding the conditions for constructive and destructive interference.

Lecture 9: Modern Physics

• Core Concepts:
  • Photoelectric effect: Einstein’s equation ($E_k = hf – W$), threshold frequency, work function.
  • Particle-wave duality (photons).
  • Atomic structure: Bohr model for hydrogen (energy levels, quantization).
  • Atomic transitions (emission and absorption of photons).
  • Fundamentals of nuclear physics: Nuclear composition (protons, neutrons).
  • Nuclear reactions: Alpha, Beta, Gamma decay; nuclear fission and fusion.
  • Mass-energy equivalence ($E=mc^2$).
• CSCA Focus:
  • Conceptual mastery: (e.g., intensity vs. frequency in the photoelectric effect).
  • Calculating energy/wavelength of photons from atomic transitions.
  • Balancing nuclear reaction equations and applying conservation laws.

Module 4: Final Synthesis (Lecture 10)

Lecture 10: Final Review & Timed Exam Strategy

• Core Concepts:
  • Review of all 5 modules, focusing on high-yield formulas and concepts.
  • Connecting concepts across modules (e.g., energy conservation in mechanics, E&M, and thermodynamics).
• CSCA Focus:
  • Strategy for 48 Questions in 60 Minutes:
    • Triage: Identifying “quick-win” questions vs. “time-sink” questions.
    • Pacing: Maintaining an average of 1.25 minutes per question.
    • “Process of elimination” for multiple-choice.
    • Guessing strategies when stuck.
  • Activity: Timed mini-exam (e.g., 24 questions in 30 minutes) followed by a detailed walkthrough of the solutions and strategies.

CSCA Chemistry Preparatory Course: 10-Lecture Outline

This course is designed to comprehensively cover the CSCA Chemistry Examination Syllabus (2025 Edition) with a focus on the problem-solving strategies and depth of understanding required in a Gaokao-style preparatory context.

Lecture 1: Core Concepts & The Mole

• Syllabus Module: Basic Chemical Concepts and Calculations
• Key Topics:
  • Classification of matter (elements, compounds, mixtures) and states of matter.
  • Chemical notation: Writing and interpreting chemical formulas and names.
  • The mole: Mastering calculations involving the amount of substance (Avogadro’s constant, molar mass).
  • Writing and balancing chemical equations (including net ionic equations).
  • Stoichiometry: Mass-mole, mass-volume, and mole-mole calculations in chemical reactions.
• Focus Skill: High-speed stoichiometric calculations and unit conversions.

Lecture 2: Solutions and Gases

• Syllabus Module: Basic Chemical Concepts and Calculations
• Key Topics:
  • Solutions: Understanding molarity, mass percentage, and dilution calculations.
  • Introduction to electrolytes: Strong vs. weak electrolytes.
  • Solution pH: Calculations involving pH, pOH, [H+], and [OH-] for strong acids and bases.
  • Gases: Application of the Ideal Gas Law (PV=nRT) and its relationship to molar volume.
• Focus Skill: Quantitative problem-solving for solutions and gases.

Lecture 3: Atomic Structure & The Periodic Table

• Syllabus Module: Chemical Theories and Laws
• Key Topics:
  • Atomic structure: Protons, neutrons, electrons, isotopes, and electron configuration (up to Z=36).
  • The Periodic Law: Understanding periods, groups, and blocks (s, p, d).
  • Periodic trends: Atomic radius, ionization energy, electronegativity, and metallic/non-metallic character.
  • Positional relationships: Deducing element properties based on table position.
• Focus Skill: Predicting chemical and physical properties using periodic trends.

Lecture 4: Chemical Bonds & Intermolecular Forces

• Syllabus Module: Chemical Theories and Laws
• Key Topics:
  • Chemical bonds: Ionic bonds, covalent bonds (polar and nonpolar), and metallic bonds.
  • Lewis structures and simple molecular geometry (VSEPR for basic shapes like linear, trigonal planar, tetrahedral).
  • Intermolecular forces: Hydrogen bonds, dipole-dipole forces, and London dispersion forces.
  • Impact of bonding and IMFs on physical properties (melting point, boiling point, solubility).
• Focus Skill: Relating molecular structure to macroscopic properties.

Lecture 5: Inorganic Chemistry I: Non-Metals

• Syllabus Module: Properties and Reactions of Substances
• Key Topics:
  • In-depth review of key non-metal elements: Halogens (Cl, Br, I), Oxygen (Ozone), Sulfur, Nitrogen, Phosphorus, Carbon, and Silicon.
  • Properties of their common oxides (e.g., SO₂, SO₃, NO, NO₂, CO, CO₂, SiO₂) and corresponding acids (e.g., H₂SO₄, HNO₃, H₂CO₃, H₃PO₄).
  • Reactions of common bases (e.g., ammonia).
• Focus Skill: Memorization and application of key non-metal reactions.

Lecture 6: Inorganic Chemistry II: Metals

• Syllabus Module: Properties and Reactions of Substances
• Key Topics:
  • Properties of common metals: Alkali metals (Na), Alkaline earth metals (Mg, Ca), and key transition/main group metals (Al, Fe, Cu).
  • Reactions with water, acids, and non-metals.
  • Properties of their oxides and hydroxides (e.g., Al(OH)₃ amphoterism).
  • Common salts: Properties and reactions of carbonates, sulfates, nitrates, and chlorides.
• Focus Skill: Identifying metals and their compounds’ characteristic reactions.

Lecture 7: Redox & Ionic Reactions

• Syllabus Module: Properties and Reactions of Substances / Chemical Theories and Laws
• Key Topics:
  • Redox Reactions: Identifying oxidizing/reducing agents and assigning oxidation states.
  • Balancing complex redox reactions (half-reaction method recommended).
  • Theories of electrolyte solutions: Ionization and dissociation.
  • Ionic Reactions: Writing and balancing net ionic equations.
  • Ionic coexistence: Determining which ions can (and cannot) exist together in solution.
  • Ionic testing methods: Qualitative analysis for common ions (e.g., Cl⁻, SO₄²⁻, CO₃²⁻, NH₄⁺, Fe³⁺, Cu²⁺).
• Focus Skill: Mastering net ionic and redox equation balancing.

Lecture 8: Chemical Kinetics & Equilibrium

• Syllabus Module: Chemical Theories and Laws
• Key Topics:
  • Reaction Rate: Factors affecting rate (concentration, temperature, pressure, catalyst).
  • Chemical Equilibrium: The concept of dynamic equilibrium and the equilibrium constant (Kc, Kp).
  • Le Chatelier’s Principle: Predicting shifts in equilibrium due to changes in concentration, pressure, and temperature.
  • Weak electrolyte equilibrium: Ionization of weak acids/bases (qualitative understanding).
• Focus Skill: Qualitative and quantitative analysis of equilibrium systems.

Lecture 9: Basic Organic Chemistry

• Syllabus Module: Properties and Reactions of Substances
• Key Topics:
  • Hydrocarbons: Alkanes, alkenes (addition reactions), alkynes (addition reactions), and aromatic compounds (Benzene).
  • Nomenclature of simple organic compounds.
  • Isomerism (structural and cis-trans).
  • Common derivatives: Alcohols (oxidation), aldehydes (oxidation), carboxylic acids (esterification), and esters (hydrolysis).
  • Introduction to basic organic polymers (e.g., polyethylene, PVC).
• Focus Skill: Identifying functional groups and predicting their characteristic reactions.

Lecture 10: Chemical Experiments & Applications

• Syllabus Module: Chemical Experiments and Applications
• Key Topics:
  • Laboratory safety rules and recognition of hazard symbols.
  • Use of common laboratory apparatus (e.g., volumetric flask, burette, condenser).
  • Methods for separation and purification of substances: Filtration, distillation, extraction, and chromatography.
  • Preparation and identification of common gases (e.g., H₂, O₂, Cl₂, NH₃, CO₂).
  • Analysis of industrial processes: Principles of ammonia synthesis (Haber-Bosch process) as an application of equilibrium.
• Focus Skill: Connecting experimental design to chemical principles.