# 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:

- Content delivery (45 min)
- Q&A session (15 minutes)
- Interactive Problem Solving (45 min)
- Quiz (15 min)

### Bridging Module 1: 4 - 13 January 2023

*(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: 16 January - 27 January 2023

*(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: 30 January -9 February 2023

*(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]