Mathematics, Physics and Engineering Preparatory Course

Lesson 1 • Algebraic Expressions and Equations

Introduces variables, expression simplification, and linear equation solving. Provides the symbolic reasoning tools needed for physics formulas and engineering models.

Lesson 2 • Polynomials and Rational Expressions

Covers polynomial arithmetic, factoring techniques, and rational expression simplification. Prepares students for function analysis and algebraic manipulation in calculus.

Lesson 3 • Exponents, Radicals, and Logarithms

Develops rules for powers, roots, and logarithmic operations. These tools appear directly in exponential growth models and decibel or pH calculations in applied science.

Lesson 4 • Systems of Equations and Inequalities

Teaches substitution, elimination, and graphical methods for solving systems. Directly applicable to circuit analysis and equilibrium problems in engineering.

Lesson 1 • Exponential and Logarithmic Functions

Examines growth, decay, and logarithmic models graphically and analytically. Prepares students for half-life, RC circuit, and signal attenuation problems.

Lesson 2 • Coordinate Plane and Basic Graphing

Establishes the Cartesian coordinate system and techniques for plotting and interpreting graphs. Forms the visual language used throughout calculus and data analysis.

Lesson 3 • Function Concepts and Notation

Defines functions formally, covering domain, range, and function notation. Builds the conceptual framework for calculus derivatives and integrals.

Lesson 4 • Transformations and Piecewise Functions

Covers shifts, reflections, stretches, and piecewise-defined functions. Enables students to adapt standard models to real-world boundary conditions.

Lesson 1 • Trigonometric Identities and Equations

Covers Pythagorean, sum, difference, and double-angle identities and their use in solving equations. Enables algebraic manipulation of wave and oscillation expressions.

Lesson 2 • Trigonometric Functions and Their Graphs

Analyses amplitude, period, phase shift, and graphs of all six trig functions. Prepares students to model sinusoidal signals and mechanical vibrations.

Lesson 3 • Unit Circle and Radian Measure

Extends trigonometry to all angles using the unit circle and radian notation. Essential for describing periodic phenomena such as oscillations and AC signals.

Lesson 4 • Right Triangle Trigonometry

Defines sine, cosine, and tangent via right triangles and applies them to angle and side calculations. Directly used in resolving vectors and analysing inclined planes.

Lesson 1 • Dot Product and Cross Product

Computes and interprets dot and cross products with geometric and physical meaning. Enables work calculations, torque analysis, and normal vector determination.

Lesson 2 • Matrices and Matrix Operations

Introduces matrix notation, arithmetic, and the transpose operation. Provides the algebraic structure for representing and solving multi-variable engineering systems.

Lesson 3 • Vector Fundamentals in 2D and 3D

Defines vectors geometrically and algebraically, covering addition, subtraction, and scalar multiplication. Establishes the language for describing forces, velocities, and fields.

Lesson 4 • Gaussian Elimination and Applications

Applies row reduction to solve linear systems and interpret solution types. Directly used in nodal analysis of circuits and truss force calculations.

Lesson 1 • Chain Rule and Implicit Differentiation

Extends differentiation to composite and implicitly defined functions. Enables differentiation of complex physical relationships such as pressure-volume equations.

Lesson 2 • Derivative Definition and Basic Rules

Derives the derivative from the limit definition and introduces power, product, and quotient rules. Provides the core differentiation toolkit for physics and engineering formulas.

Lesson 3 • Optimisation and Applied Derivatives

Solves real-world maximum and minimum problems using calculus. Applies directly to minimising material cost, maximising efficiency, and analysing velocity and acceleration.

Lesson 4 • Curve Analysis Using Derivatives

Uses first and second derivatives to determine increasing/decreasing behaviour, concavity, and extrema. Connects calculus to graphing and structural load optimisation.

Lesson 1 • Integration Techniques

Covers substitution, integration by parts, and partial fractions. Expands the range of integrals solvable in thermodynamic work and signal processing problems.

Lesson 2 • Introductory Differential Equations

Solves separable and first-order linear ODEs with initial conditions. Models exponential decay, Newton's cooling, and RC circuit charging directly.

Lesson 3 • Applications of Integration

Applies integrals to area, volume, arc length, and physical quantities such as work and centre of mass. Bridges pure calculus to mechanical and civil engineering calculations.

Lesson 4 • Definite Integrals and the Fundamental Theorem

Defines the definite integral via Riemann sums and applies the Fundamental Theorem of Calculus. Connects area under a curve to accumulated physical quantities.

Lesson 1 • Work, Energy, and Power

Defines work, kinetic and potential energy, and the work-energy theorem. Connects energy methods to efficiency calculations and mechanical system design.

Lesson 2 • Momentum and Collisions

Covers linear momentum, impulse, and conservation laws for elastic and inelastic collisions. Applied to impact analysis, rocket propulsion, and safety engineering.

Lesson 3 • Newton's Laws and Force Analysis

Applies Newton's three laws to free-body diagrams and net force calculations. Enables systematic analysis of static and dynamic loading in mechanical structures.

Lesson 4 • Rotational Motion and Torque

Extends kinematics and Newton's laws to rotating bodies using angular quantities and torque. Essential for gear, shaft, and motor analysis in mechanical engineering.

Lesson 1 • AC Circuits and Impedance

Analyses sinusoidal sources, phasors, and impedance in RLC circuits. Prepares students for power factor correction, resonance, and frequency-domain circuit design.

Lesson 2 • DC Circuit Analysis

Applies Ohm's law and Kirchhoff's laws to analyse resistive DC circuits. Enables systematic solution of multi-loop networks found in electronic and power systems.

Lesson 3 • Capacitors and Inductors

Analyses energy storage in capacitors and inductors and their transient behaviour in RC and RL circuits. Directly applicable to filter design and power supply analysis.

Lesson 4 • Magnetic Fields and Electromagnetic Induction

Covers magnetic force on charges and currents, and Faraday's and Lenz's laws of induction. Underpins transformer, motor, and generator operation in electrical engineering.