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GAC Mathematics

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GAC Mathematics is four modules. GAC004 rebuilds the fundamentals in English, from arithmetic and algebra through coordinate geometry, plane and solid geometry, trigonometry and the exponential and logarithmic functions. GAC010 turns to sequences, financial mathematics, probability and statistics. GAC016 is single-variable calculus. GAC024 is discrete mathematics, from sets and counting systems to algorithms, graphs and Boolean logic.

Language is assessed alongside method. A terminology logbook, kept unit by unit and inspected during the semester, is a real component of GAC004, so being able to say what a gradient or a residual is matters as much as computing one.

GAC016 is the module universities most often credit. Several publish a calculus equivalency for it, which makes the derivative and integral work here worth treating as a first-year course rather than as school revision.

The events are a mixture. Expect a short in-class test on the early units, one or two projects built in a spreadsheet, an examination covering everything at the end, and coursework marks that accumulate quietly all semester.

Worked examples, drills and mock papers here are ours, written to the outcomes and the format of those events.

GAC Mathematics Study Materials

  • 1

    GAC004 Mathematics I: Fundamentals
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    • 1.1 Terminology and Arithmetic Review

      Unit 1 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      Module purpose: On completion of this module, students should be able to demonstrate an understanding of the basic concepts of mathematics, and the language used, in preparation for tertiary study within an English-speaking environment.

      The module outcomes this unit works towards:

      Learning Objective GAC004.1: Solve elementary math problems using basic arithmetic operations.

      Source: Cambridge International syllabus

    • 1.2 Algebra I: Introductory Algebra

      Unit 2 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.2: Perform basic algebraic operations and solve equations and inequations using algebraic methods.

      Source: Cambridge International syllabus

    • 1.3 Algebra: Graphs of Algebraic Relations and Coordinate Geometry

      Unit 3 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.3: Graph algebraic relations and use coordinate geometry to solve problems.

      Source: Cambridge International syllabus

    • 1.4 Geometry: Plane, Solid, and Euclidean Geometry

      Unit 4 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.4: Analyze simple problems involving planar shapes and solids and solve problems in Euclidean geometry.

      Source: Cambridge International syllabus

    • 1.5 Trigonometry

      Unit 5 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.5: Calculate solutions to various problems using trigonometric methods.

      Source: Cambridge International syllabus

    • 1.6 Exponential and Logarithmic Functions

      Unit 6 of 6 in GAC004 Mathematics I: Fundamentals (Level I). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC004.6: Solve and graph exponential and logarithmic functions and equations.

      Source: Cambridge International syllabus

  • 2

    GAC010 Mathematics II: Probability, Statistics and Finance
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    • 2.1 Sequence and Series

      Unit 1 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      Module purpose: On completion of this module, students should be able to apply a basic knowledge of the principles of probability and statistics to solving and analysing common financial problems.

      The module outcomes this unit works towards:

      Learning Objective GAC010.1: Solve problems using arithmetic and geometric sequences and series.

      Source: Cambridge International syllabus

    • 2.2 Finance – Earning Money and Purchasing Goods

      Unit 2 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.2: Apply algebraic methods to solve financial problems and analyse information.

      Source: Cambridge International syllabus

    • 2.3 Finance – Investing Money and Loans

      Unit 3 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.2: Apply algebraic methods to solve financial problems and analyse information.

      Source: Cambridge International syllabus

    • 2.4 Probability – Key Concepts

      Unit 4 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.3: Solve problems using probability and counting techniques.

      Source: Cambridge International syllabus

    • 2.5 Statistics

      Unit 5 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.4: Analyse collected data using statistical methods.

      Source: Cambridge International syllabus

    • 2.6 Statistics – Numerical Measures of Central Locations

      Unit 6 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.4: Analyse collected data using statistical methods.

      Source: Cambridge International syllabus

    • 2.7 Statistics – Numerical Measures of Variability

      Unit 7 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.4: Analyse collected data using statistical methods.

      Source: Cambridge International syllabus

    • 2.8 Distributions – The Normal Distribution

      Unit 8 of 8 in GAC010 Mathematics II: Probability, Statistics and Finance (Level II). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC010.5: Use the normal distribution to analyse data.

      Source: Cambridge International syllabus

  • 3

    GAC016 Mathematics III: Calculus & Advanced Applications
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    • 3.1 Differentiation

      Unit 1 of 3 in GAC016 Mathematics III: Calculus & Advanced Applications (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      Module purpose: On completion of this module, students should be able to demonstrate a basic understanding of the principles of calculus and how they can be applied to the quantitative analysis of practical and financial situations.

      The module outcomes this unit works towards:

      Learning Objective GAC016.1: Determine the derivative (if it exists) of most mathematical functions and use the derivative to analyse functional behaviour.

      Source: Cambridge International syllabus

    • 3.2 Integration

      Unit 2 of 3 in GAC016 Mathematics III: Calculus & Advanced Applications (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC016.2: Use techniques of integration to find indefinite and definite integrals.

      Source: Cambridge International syllabus

    • 3.3 Advanced Applications

      Unit 3 of 3 in GAC016 Mathematics III: Calculus & Advanced Applications (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC016.3: Apply differentiation and integration techniques in a variety of practical problems.

      Source: Cambridge International syllabus

  • 4

    GAC024 Discrete Mathematics
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    • 4.1 Sets, Relations and Functions

      Unit 1 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      Module purpose: On completion of this module, students should be able to demonstrate an understanding of the basic principles of discrete mathematics, particularly the utilisation of mathematical logic. They should also be able to demonstrate the application of these skills to practical situations.

      The module outcomes this unit works towards:

      Learning Objective GAC024.1: Demonstrate understanding of the introductory concepts and properties of sets, relations and functions.

      Source: Cambridge International syllabus

    • 4.2 Counting Systems

      Unit 2 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC024.2: Understand the relationships between different counting systems and be able to perform simple binary arithmetic operations.

      Source: Cambridge International syllabus

    • 4.3 Binary Applications

      Unit 3 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC024.2: Understand the relationships between different counting systems and be able to perform simple binary arithmetic operations.

      Learning Objective GAC024.5: Use the basic identities of Boolean algebra to analyse logic circuits and understand the basic principles of propositional logic.

      Source: Cambridge International syllabus

    • 4.4 Algorithms

      Unit 4 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC024.3: Construct and analyse algorithms and flowcharts for simple mathematical and general procedures.

      Source: Cambridge International syllabus

    • 4.5 Graphs and Networks

      Unit 5 of 5 in GAC024 Discrete Mathematics (Level III). The module is taught over about 40 class hours plus 20 hours of independent study, and is assessed at the teaching centre and moderated by ACT — there is no external exam.

      The module outcomes this unit works towards:

      Learning Objective GAC024.4: Identify the basic types, properties and applications of graphs and trees.

      Source: Cambridge International syllabus

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