PASUM Mathematics, Physics & Chemistry
Pre-university lecture notes, tutorials, and concept explanations from Universiti Malaya PASUM (Matriculation Programme).
Concepts
Browse the core knowledge units across all subjects:
Mathematics
- Integration Techniques — Methods of integration (substitution, parts, trig)
- Differential Equations — Separable, exact, Bernoulli, non-homogeneous
- Series — Convergence, tests, power series
- Binomial Expansion — Binomial theorem and applications
- Power Series — Taylor & Maclaurin — Series expansions
- Geometry - Circle — Circle equations and properties
- Geometry - Ellipse — Ellipse equations and properties
- Geometry - Hyperbola — Hyperbola equations and properties
- Geometry - Parabola — Parabola equations and properties
- Matrices — Operations, inverses, systems of equations
- Cramer's Rule — Determinant-based solutions
- Complex Numbers — Argand diagram, Euler's formula
- Hyperbolic Functions — Definitions, derivatives, integrals
- Inverse Trigonometric Functions — Domains, ranges, derivatives
- Improper Integrals — Convergence and comparison tests
- Method of Differences — Summation techniques
- Sequences — Limits and convergence
- Summation Formulas — Standard summation results
- Counting & Probability — Permutations, combinations, Bayes' theorem
- Probability Distributions — Binomial, Poisson, normal
- Hypothesis Testing — Testing population parameters
Physics
- Electrostatics — Coulomb's law, electric fields, Gauss's law
- Capacitors & Dielectrics — Capacitance, energy storage, dielectrics
- AC Circuits — Impedance, resonance, phasors
- Magnetism — Magnetic fields, forces, Faraday's law
- Inductance & Transformers — Self/mutual inductance, transformers
- Semiconductors & Diodes — Band theory, pn-junctions
- Operational Amplifiers — Ideal op-amp circuits
- Transistors & Biasing — BJT biasing and configurations
- Atomic Physics — Bohr model, spectra, quantum numbers
- Nuclear Physics — Radioactivity, fission, fusion
- Photoelectric Effect — Photon energy, work function
- Photons — Electromagnetic radiation quanta
- Quantum Mechanics — Wave functions, particle in a box
- Modern Physics — Wave-Particle Duality — De Broglie, uncertainty
- Black Body Radiation — Planck's law, Stefan-Boltzmann
Chemistry
- Electrochemistry — Galvanic cells, electrolysis, Nernst equation
- Chemical Equilibrium — Le Chatelier's principle, Kc, Kp
- Ionic Equilibria — pH, buffers, titrations
- Solubility Product — Ksp, precipitation, common ion effect
- Phase Equilibria — Raoult's law, distillation, phase diagrams
- Thermochemistry — Enthalpy, Hess's law, calorimetry
- Kinetic Chemistry — Rate laws, Arrhenius, mechanisms
- Stereochemistry — R/S configuration, E/Z isomers
- Alcohol & Phenol — Reactions, acidity, oxidation
- Carbonyl Compounds — Aldehydes, ketones, reactions
- Carboxylic Acids & Derivatives — Acyl derivatives, hydrolysis
- Amines & Amino Acids — Basicity, peptide bonds, 20 amino acids
- Polymer Chemistry — Addition, condensation, biopolymers
Sources
Lecture notes and tutorials organized by course (109 files):
- Application of DE - Mixing Problems
- Bernoulli Differential Equation
- EC2526 — Electrochemistry Tutorial
- Electrochemistry Part 2
- Exact Differential Equation
- FAC1004 L01 — Complex Numbers
- FAC1004 L02 — Euler's Formula
- FAC1004 L13 — Inverse Trigonometric Functions
- FAC1004 L14 — Properties of Inverse Trig Functions
- FAC1004 L15-L16 — Derivatives of Inverse Trig Functions
- FAC1004 L17 — Hyperbolic Functions
- FAC1004 L18 — Hyperbolic Functions (Derivatives & Integrals)
- FAC1004 L19-L20 — Inverse Hyperbolic Functions
- FAC1004 L21-L22 — Integrals Involving Hyperbolic Functions
- FAC1004 L5-L6 — Functions of Complex Numbers (n-th Roots)
- FAC1004 L7-L8 — Complex Equations (Geometric Interpretation)
- FAC1004 Tutorial 10 — Integration of Hyperbolic Functions
- FAC1004 Tutorial 2 — Complex Numbers
- FAC1004 Tutorial 3 — Complex Logarithm
- FAC1004 Tutorial 6 — Inverse Trigonometric Functions
- FAC1004 Tutorial 7 — Derivatives of Inverse Trig Functions
- FAC1004 Tutorial 8 — Hyperbolic Functions
- FAC1004 Tutorial 9 — Inverse Hyperbolic Functions
- FAD1007 Final 2021-2022
- FAD1008 Final 2021-2022
- FAD1014 L1-L2 — Integration (Anti-Derivative)
- FAD1014 L11-L12 — Area Under Curves
- FAD1014 L13 — Volume of Solids of Revolution
- FAD1014 L14 — Volume (Area Between Curves)
- FAD1014 L15-L16 — Differential Equations (Separable)
- FAD1014 L20 — Improper Integrals
- FAD1014 L21 — Introduction to Series
- FAD1014 L22 — Finite Series and Summation
- FAD1014 L23-L24 — Binomial Expansion
- FAD1014 L25-L26 — Power Series, Taylor & Maclaurin
- FAD1014 L27-L28 — Geometry I (Circle & Parabola)
- FAD1014 L29-L30 — Geometry (Ellipse)
- FAD1014 L3-L4 — Integration by Substitution
- FAD1014 L5-L6 — Integration by Parts
- FAD1014 L7-L8 — Trigonometric Integrals
- FAD1014 L9-L10 — Trigonometric Substitution
- FAD1014 Tutorial 1 — Indefinite Integrals
- FAD1014 Tutorial 10 — First-Order Linear DEs
- FAD1014 Tutorial 11 — Binomial Theorem
- FAD1014 Tutorial 12 — Taylor & Maclaurin Series
- FAD1014 Tutorial 13 - Circle, Parabola, Ellipse
- FAD1014 Tutorial 2 — Integration by Parts
- FAD1014 Tutorial 3 — Trigonometric Integrals
- FAD1014 Tutorial 4 — Trigonometric Substitution
- FAD1014 Tutorial 5 — Area Enclosed by Curves
- FAD1014 Tutorial 6 — Volume of Solids of Revolution
- FAD1014 Tutorial 7 — Differential Equations
- FAD1015 Final 2023-2024
- FAD1015 Final 2024-2025
- FAD1015 L13 — Binomial Distribution
- FAD1015 L14 — Poisson Distribution
- FAD1015 L15-L16 — Normal Distribution & Approximation
- FAD1015 L17-L18 — Uniform & Exponential Distributions + R Intro
- FAD1015 L19 — Input Data & Descriptive Statistics in R
- FAD1015 L20 — Sampling Distribution of the Mean
- FAD1015 L21-L22 — Estimation of Population Mean
- FAD1015 L23-L24 — Hypothesis Testing About the Mean
- FAD1015 L25-L26 — Hypothesis Testing in R
- FAD1015 L27-L28 — Matrices (Types & Operations)
- FAD1015 L29-L30 — Matrices (Inverse & Systems of Equations)
- FAD1015 Tutorial 13 — Matrices
- FAD1015 Week 1 — Counting Rules & Permutation
- FAD1015 Week 2 — Mutually Exclusive & Conditional Probability
- FAD1015 Week 3 — Independent Events & Bayes' Theorem
- FAD1015 Week 4 — Discrete Random Variables (PDF & CDF)
- FAD1015 Week 5 — Mean & Variance (Discrete & Continuous)
- FAD1015 Week 6 — Continuous Random Variables
- FAD1018 Final 2022-2023
- FAD1018 Final 2023-2024
- FAD1018 Final 2024-2025
- FAD1018 L4-L5 — Electrolytic Cell
- FAD1018 W1 — Chemical Equilibrium
- FAD1018 W11 — Carboxylic Acids & Derivatives
- FAD1018 W12 — Amine & Amino Acids
- FAD1018 W14 — Polymer Chemistry
- FAD1018 W15 — Thermochemistry
- FAD1018 W16 — Chemical Kinetics Part 2
- FAD1018 W16 — Kinetic Chemistry
- FAD1018 W2-W3 — Ionic Equilibria
- FAD1018 W3 (3) — Ionic Equilibria Part 5-6 — Acid-Base Titrations
- FAD1018 W3 — Buffer Solutions
- FAD1018 W4 — Solubility Product
- FAD1018 W5-W6 — Phase Equilibria
- FAD1018 W6 — Stereochemistry
- FAD1018 W7 — Alcohol and Phenol
- FAD1018 W8-W10 — Carbonyl Compounds
- FAD1018 — Topics (Teaching Schedule)
- FAD1022 L1-L3 — Electrostatics
- FAD1022 L14-L16 — AC Analysis
- FAD1022 L17-L21 — AC Series Circuits
- FAD1022 L22-L26 — Magnetism
- FAD1022 L31-L33 — Inductance & Transformers
- FAD1022 L34-L38 — Semiconductors & Op-Amps
- FAD1022 L39-L42 — Atomic & Nuclear Physics
- FAD1022 L43 — Modern Physics
- FAD1022 L44 — Photons and Photoelectric Effect
- FAD1022 L45 — Introduction to Quantum Mechanics
- FAD1022 L7-L9 — Capacitors
- FAD1022 Quick Quiz 2026 — Inductance & Transformers
- L1 L2 Electrochemistry
- L31-L32 Hyperbola
- Non-Homogeneous DE (Linearly Dependent)
- Non-Homogeneous DE (Linearly Independent)
- Revision Faraday and Lenz Law
Tutorials
Practice problems with worked solutions (61 files):
- FAC1004 Tutorial 10 — Integration of Hyperbolic Functions
- FAC1004 Tutorial 2 — Complex Numbers & De Moivre's Theorem
- FAC1004 Tutorial 3 — Complex Logarithms & Loci
- FAC1004 Tutorial 6 — Inverse Trigonometric Functions
- FAC1004 Tutorial 7 — Derivatives of Inverse Trig & Hyperbolic Functions
- FAC1004 Tutorial 8 — Hyperbolic Functions
- FAC1004 Tutorial 9 — Inverse Hyperbolic Functions
- FAD1014 Tutorial 1 — Integration Basics
- FAD1014 Tutorial 10 — Linear First Order Differential Equations
- FAD1014 Tutorial 11 — Binomial Theorem and Power Series
- FAD1014 Tutorial 12 — Power Series and Circle Geometry
- FAD1014 Tutorial 2 — Integration by Parts
- FAD1014 Tutorial 3 — Trigonometric Integrals
- FAD1014 Tutorial 4 — Trigonometric Substitution and Partial Fractions
- FAD1014 Tutorial 5 — Area Under Curves
- FAD1014 Tutorial 6 — Volumes of Revolution
- FAD1014 Tutorial 7 — Differential Equations
- FAD1015 Tutorial 1 — Counting and Permutation
- FAD1015 Tutorial 1-6 — Counting & Probability Fundamentals
- FAD1015 Tutorial 10 — Estimation of Population Mean
- FAD1015 Tutorial 10 — Estimation of the Population Mean
- FAD1015 Tutorial 11 — Hypothesis Testing About the Mean
- FAD1015 Tutorial 12 — Hypothesis Testing in R
- FAD1015 Tutorial 2 — Combination
- FAD1015 Tutorial 3 — Probability and Mutually Exclusive Events
- FAD1015 Tutorial 4 — Conditional Probability and Bayes Theorem
- FAD1015 Tutorial 5 — Discrete Random Variables
- FAD1015 Tutorial 6 — Expected Value, Variance, and Continuous Random Variables
- FAD1015 Tutorial 7 — Normal Distribution
- FAD1015 Tutorial 8 — Uniform & Exponential Distributions
- FAD1015 Tutorial 8 — Uniform and Exponential Distributions
- FAD1015 Tutorial 9 — Sampling Methods
- FAD1015 Tutorial 9 — Sampling and Sampling Distributions
- FAD1018 Tutorial 1 — Chemical Kinetics
- FAD1018 Tutorial 10 — Amines and Amino Acids
- FAD1018 Tutorial 12 — Carbohydrates
- FAD1018 Tutorial 13 — Lipids
- FAD1018 Tutorial 14 — Nucleic Acids
- FAD1018 Tutorial 2 — Chemical Kinetics II
- FAD1018 Tutorial 3 — Buffer Solutions
- FAD1018 Tutorial 4 — Electrochemistry
- FAD1018 Tutorial 5 — Solutions and Raoult's Law
- FAD1018 Tutorial 6 — Stereochemistry
- FAD1018 Tutorial 7 — Acidity of Phenols
- FAD1018 Tutorial 8 — Aldehydes and Ketones
- FAD1018 Tutorial 9 — Carboxylic Acids and Derivatives
- FAD1022 Tutorial 1 — Electrostatics
- FAD1022 Tutorial 10 — Electromagnetism
- FAD1022 Tutorial 11 — Inductance
- FAD1022 Tutorial 12 — Semiconductors and Electronics
- FAD1022 Tutorial 13 — Electronics and Atomic Physics
- FAD1022 Tutorial 14 — Atomic Physics
- FAD1022 Tutorial 15 — Modern Physics
- FAD1022 Tutorial 3 — Capacitors
- FAD1022 Tutorial 4 — DC Circuits
- FAD1022 Tutorial 5 — AC Basics
- FAD1022 Tutorial 6 — AC Circuit Analysis Part 1
- FAD1022 Tutorial 7 — AC Circuit Analysis Part 2
- FAD1022 Tutorial 8 — Magnetism Part 1
- FAD1022 Tutorial 9 — Magnetism and Electromagnetic Induction
- st13-detailed
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