Essential Mathematics 1: Algebra and Trigonometry


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Level of study: What does Undergraduate Level 1 mean?

Undergraduate Level 1

EFTSL: What does EFTSL mean?


Delivery Method: What does delivery method mean?

Fully Online

Prerequisites: What are the prerequisites?


Availability: What is a Study period?



13 weeks

Government loans available:


Domestic student fee:

$1,099.00 (AUD)

HECS student fee:

$1,045.00 (AUD)

International student fee:

$1,349.00 (AUD)


This unit aims to increase confidence and ability in mathematical skills, to provide an introduction to the understanding of mathematical principles of algebra and trigonometry and to introduce systematic problem solving techniques. It includes a review of basic algebra; involving introduction to algebraic functions and their graphs; trigonometric functions, properties and identities; elementary theory of vectors; elementary matrices and linear algebra.


There are no prerequisites for this unit.

Special Requirements

  • Audio/Visual equipment — Audio headset with microphone are required to access weekly consultation and help desk facilities.
  • Broadband access — Recommended
  • Other special requirement — To pass this unit a student must achieve 50% in the overall assessment and a minimum of 40% of the available marks in the final examination.


  • Assignment 1 (20%)
  • Assignment 2 (20%)
  • Invigilated Exam (50%)
  • Quizzes — Online quizzes: 5 (10%)
For more information on invigilated exams see Exams and results

Learning Outcomes

At the completion of this unit students will be able to:

  1. apply elementary manipulative skills to solve mathematical problems
  2. formulate simple applied problems in mathematical language
  3. use the principles of elementary trigonometry, vectors, and linear algebra, in the solution of problems.


This unit addresses the following topics.

1Sets of numbers; axioms and laws of the real number system; the real number line; absolute values; complex numbers; order of operations
2Exponents, laws of integer exponents; rational exponents. Equivalent fractions; addition, subtraction, multiplication, and division of fractions
3Solving linear equations; solving quadratic equations; completing the square and the quadratic formula; the discriminant; equations involving radicals
4Properties of absolute values; absolute values in equations; absolute value in inequalities. Ordered pairs and the Cartesian coordinate system
5Definition of a function; notation; domain and range; increasing, decreasing, constant, even, odd functions; average rate of change
6Graphs of quadratic functions; maximum and minimum values; domain and range; integer power functions; zeros; division of one polynomial by another
7Trigonometric functions; points on the unit circle; definition of trigonometric functions; periodicity; notation; trigonometric identities
8Angles, radian measure; degree measure; complementary, supplementary, and coterminal angles; trigonometric ratios of special angles
9Triangles, right triangles; oblique triangles; law of sines; law of cosines; bearing and heading; elevation and depression
10Vectors and scalars; addition of vectors; vector algebra; the dot product. Linear equations in two variables; dependent and independent systems
11Matrix notation; row-equivalent matrices; linear equations; row-echelon form; Gaussian elimination; Gauss-Jordan elimination. Definition of a matrix
12Multiplication of two matrices; the identity matrix; the inverse of a 2x2 matrix; laws of matrix multiplication

Study Resources

This unit is delivered using the following methods and materials:

Instructional Methods

  • Audio/Video conferencing
  • Discussion Forum/Discussion Board
  • Embedded Multimedia
  • Glossary
  • Online Quizzes/Tests
  • Online assignment submission
  • Podcasting/Lecture capture
  • Standard Media
  • Streaming Multimedia
  • Web links
  • Wikis

Print based materials

  • Welcome Letter

Online materials

  • Audio/Video - Streaming
  • Printable format materials
  • Quizzes
  • Resources and Links

Textbooks are subject to change within the academic year. Students are advised to purchase their books no earlier than one to two months before the start of a unit.

Click on the titles of the listed books below to find out more:

Required textbooks

Schaum's Outline of Precalculus

By:Safier, Fred



Supplier:Go to Unibooks

Relevant Courses

This unit is not currently a requirement for any courses, but may be eligible for credit.

  1. Many undergraduate courses on offer through OUA include 'open elective' where any OUA unit can be credited to the course. You need to check the Award Requirements on the course page for the number of allowed open electives and any level limitations.
  2. In other cases, the content of this unit might be relevant to a course on offer through OUA or elsewhere. In order to receive credit for this unit in the course you will need to supply the provider institution with a copy of the Unit Profile in the approved format, which you can download here. Note that the Unit Profile is set at the start of the year, and if textbooks change this may not match the Unibooks textbook list.
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