Structure and Content

The bridging modules will run each day from 10am to 3pm. The daily schedule is as follows:

  • Session 1: 10am-12pm
  • Break: 12pm-1pm
  • Session 2: 1pm-3pm

Students will also need to spend time studying outside of class time.

Lecture Style

Each bridging module will comprise two lectures per day, each lasting 2 hours. Each lecture will proceed according to the following format:

  1. Content delivery (45 min)
  2. Q&A session (15 minutes)
  3. Interactive Problem Solving (45 min)
  4. Quiz (15 min)

Bridging Module 1: 10-19 January 2022

(8 consecutive working days)

  • Basic set theory: definition of a set, intersection, union, complement. [One lecture]
  • Real numbers, inequalities, distance between two points, absolute value. [One lecture]
  • Equation of a straight line (slope formula, point-slope equation, slope-intercept), parallel lines, perpendicular lines. [One lecture]
  • Polynomials, long division, factoring polynomials, completing the square, finding roots.[One lecture]
  • How to solve an equation (factoring, completing the square, quadratic formula). [One lecture]
  • Complex numbers: imaginary unit, sum, difference, multiplication, conjugate, reciprocal, quotient of two complex numbers, quadratic equations. [One lecture]
  • How to solve inequalities: interval notation, properties, combined inequalities, inequality involving absolute value. [One lecture]
  • Functions and their graphs: domain,composite functions, even and odd functions, minima and maxima, piecewise defined functions, vertical and horizontal shifts, streches and compressions, reflection. [One lecture]
  • Rational functions: properties, domain of a rational function, graphs, asymptotes. [One lecture]
  • Exponential and logarithm functions. [Two lectures]
  • Trigonometric functions and trigonometric identities. [Two lectures]
  • Polar coordinates, polar equations and graphs, converting from rectangular to polar and from polar to rectangular. [One lecture]
  • Vectors: direction and magnitude, position vector, addition and subtraction, unit vector, dot prduct, cross product. [One lecture]
  • Binomial Theorem. Counting and probability: counting formula, permutations and combinations, compound probabilities. [Two lectures]
  • Basic calculus: finding limits, one-sided limits, continuous functions. [One lecture]
  • Basic calculus: Derivative of a function: product, quotient, chain rule. [One lecture]
  • Basic calculus: Anti-differentiation, definite integral, area under a curve. [One lecture]

Bridging Module 2: 20 January - 2 February 2022

(9 consecutive working days)

  • Functions: Definition, Graph of a Function, Composite Functions. [One lecture] 
  • How to solve inequalities: interval notation, properties, combined inequalities, inequality involving absolute values. [One lecture]
  • Polynomial Functions; Real and Complex Zeros. [One lecture]
  • One to One Functions and Inverse Functions. [One lecture]
  • Exponential and logarithm functions [One lecture]
  • Exponential and Logarithmic Equations. [One lecture]
  • Trigonometric Functions. [One lecture]
  • Inverse Trigonometric Functions. [One lecture]
  • Trigonometric Identities: Sum and Difference Formulas, Double and Half Angles
  • Limits and Continuity. [One lecture]
  • Limits Involving Infinity. [One lecture]
  • The Tangent Problem, Definition of the Derivative. [One lecture]
  • Rules for Differentiation. [One lecture]
  • Derivatives of the Trigonometric Functions. [One lecture]
  • Product Rule, Quotient Rule, Chain Rule. [One lecture]
  • Implicit Differentiation and related rates. [One lecture]
  • First and Second Derivatives; Curve Sketching. [One lecture]
  • Antiderivatives. [One lecture]
  • The Area Problem; the Definite Integral. [One lecture]
  • Evaluating Definite Integrals: The Fundamental Theorem of Calculus. [One lecture] 
  • The Substitution Rule.[One lecture]
  • Integration by Parts. [One lecture]
  • Areas between Curves. [One lecture]

Bridging Module 3:  3-15 February 2022

(9 consecutive working days)

  • Functions and their representations. [One lecture]
  • How to solve inequalities: interval notation, properties, combined inequalities, inequality involving absolute values. [One lecture]
  • Precise definition of a limit. [One lecture] 
  • Limits and continuity. [One lecture]
  • Limits involving infinity. [One lecture] 
  • Formal definition of derivative and rules for differentiation [One lecture]
  • Implicit differentiation. [One lecture]
  • Trigonometric functions and their inverse. [One lecture]
  • Hyperbolic functions and their inverse. [One lecture] 
  • Indeterminate forms and L’Hopital’s Rule. [One lecture] 
  • First and second derivatives; curve sketching. [One lecture]
  • Antiderivatives. [One lecture]
  • The area problem; the definite integral. [One lecture]
  • Evaluating definite integrals: The Fundamental Theorem of Calculus. [One lecture]
  • The Substitution Rule.[One lecture]
  • Integration by Parts. [One lecture]
  • Trigonometric integrals and substitutions. [Two lectures]
  • Partial Fractions. [Two lectures]