# BRIDGING COURSES TO UNIVERSITY MATHS

## Standard to Advanced Mathematics

**Bridging Course – Standard to Advanced Maths**

## Course Outline

General or Standard Mathematics may have got you a high ATAR to get into university but it does not adequately prepare you for succeeding in University Mathematics. A robust understanding of algebra, geometry, trigonometry, exponentials and logarithms are essential to avoid difficulties in in your first year. This course prepares students to undertake study in pharmacy, life sciences, economics and some computer science courses (most require Extension 1 mathematics) at University.

### This intensive course is designed for:

- Students who studied Standard 2 Mathematics but need Advanced Mathematics for their University Course;
- Students who had difficulty with one or more topics, or did not do as well as they wanted to in the HSC Advanced Mathematics exam; and
- Students who want to refresh their Advanced Mathematics before commencing their University Course.

### In this course, the topics covered include:

#### DAY 1:

Polynomials-Remainder Theorem, Factor Theorem, Consequences of The Factor Theorem, Zeros and Coefficients

#### DAY 2:

Functions: Introduction, Composite, Exponential, Logarithmic and Trigonometric (circular) functions

#### DAY 3:

Inverse Functions (Composite, Exponential, Logarithmic and Trigonometric)

#### DAY 4:

Limits (Intuitive approach), Computing limits, Limits at infinity, End behaviour of limits, Introduction to differentiation, Tangent line and Rates of change.

#### DAY 5:

Derivative function, Introduction to techniques of differentiation (Product and Quotient Rules, Chain rule, Implicit differentiation)

#### DAY 6:

Derivatives of Exponential and Logarithmic functions, circular functions. Derivatives of Inverse Trigonometric Functions

#### DAY 7:

The Derivative in curve sketching. Analysis of functions 1: Increase, decrease, concavity. Analysis of functions 2: Relative extrema, first and second derivative tests, maxima and minima, points of inflection, curve sketching.

#### DAY 8:

Overview of the area problem. The indefinite integral, integration by substitution, fundamental theorem of calculus I. The definite integral, fundamental theorem of calculus II.

#### DAY 9:

Evaluating definite integrals by substitution, Integration of exponential, logarithmic, and trigonometric functions.

#### DAY 10:

Area between two curves, volumes by slicing, volumes by cylindrical shells,

#### DAY 11:

Length of a plane curve, Area of a surface of revolution, Overview of course

#### DAY 12:

Course Review

Free Day - No Charge

### Timetable and Fees:

#### WHEN:

4-8, 11-14, 18-20 February 2019

#### TIME:

9:00am to 1:00pm (4 hours)

#### COST:

**$440**

We have deliberately kept this cost as low as we could to make this intense course **affordable**.

We **WANT **you to succeed and to embrace Mathematics with a Passion.

#### INCLUDED:

Detailed notes with examples and exercises with solutions

Morning tea**FREE **weekly revision session 9:00 to 12:00 pm Saturdays during Semester 1. You can use this tutorial to clarify conceptual mathematical issues you may be experiencing in your first semester maths programme at University.