# 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 offered on 04/01/2021-13/01/2021 (8 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 offered on 14/01/2021-29/01/2021 (10 working days with 25 & 26 January excluded )

• 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 offered on 01/02/2021-12/02/2021 (10 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]