Mathematics 1A

Objectives

The objective is to develop mathematical knowledge and skills in subject areas including pre-calculus, calculus (including techniques of antidifferentiation), complex numbers, linear programming, statistics and probability, as preparation for a wide variety of university courses (including science and engineering).

Course outline

Semester 1

• Review of algebra and trigonometry.
• Functions, domain, range, graphs, transformations of graphs.
• Composition of functions, inverse functions (including logarithms and exponential functions, and inverse trigonometric functions).
• Limits, continuity, differentiability, differentiation from first principles.
• Differentiation formulae, including the product rule, quotient rule, chain rule.
• Applications of derivatives, including rates of change, equations of tangents and normals, stationary points, curve-sketching, applied maximum/minimum problems.
• Antidifferentiation, fundamental theorem of calculus, evaluation of areas.

Semester 2

• Techniques of antidifferentiation, including substitution, integration by parts and integrating rational functions.
• Volumes of solids of revolution.
• Complex numbers, including cartesian form, polar form, DeMoivre’s Theorem.
• Linear programming, setting up of variables, constraints, objective functions.
• Graphical methods for linear programming.
• Permutations and combinations.
• Statistics, including tabulation and graphical representation of data, mean, median, mode, standard deviation, variance, quartiles.
• Introduction to probability, including addition rule, multiplication rule, independent events, tree diagrams.
• Probability distributions, expected value, standard deviation.
• Binomial, hypergeometric, geometric and Poisson distributions, as examples of discrete probability distributions.
• Normal distribution.
• Approximation of the Binomial distribution by the normal distribution.

Assessment

Term 2 exam 15%

Term 3 exam 20%

Term 4 exam 65%

Required texts

Maths 1 Lecture Notes (available from the Maths 1 lecturer-in-charge at Trinity College).