• Mathematics General
  • Year 12

Algebra and Modelling

approx. 19 hrs

4 topics

40 concepts

Develop an aptitude for Algebra and Modelling and select and apply algebraic techniques for exam success.

Available in


The Year 12 Algebra and Modelling program is aligned with the content contained in the NSW General Mathematics syllabus. We show students how to apply algebraic skills and techniques to interpret and use linear and non-linear mathematical models in a range of contexts.  

Topics & Concepts We Cover

This learning program is made up of the following 4 topics, broken down into 40 concepts.

  • Algebraic Expressions 8 concepts

    1. The zero index

    2. Apply index laws for dividing

    3. Apply index laws for multiplying

    4. Add or subtract algebraic fractions with binomial numerators or denominators

    5. Simplifying algebraic fractions multiplication/ division with a numerical denominator or single algebraic term

    6. Simplify algebraic expressions by adding or subtracting like terms

    7. Identify like terms

    8. Substitute positive or negative values into an algebraic expression and evaluate the result

  • Equations 9 concepts

    1. Solve linear equations involving more than three steps

    2. Solve three-step equations

    3. Solve two-step equations

    4. Solve one-step equations

    5. Rearrange a formula to change the subject of the equation

    6. Substitute positive or negative integers into a given formula

    7. Solve linear simultaneous equations using elimination method where one or both of the equations need to be modified

    8. Solve linear simultaneous equations using substitution method

    9. Solve linear simultaneous equations using elimination method

  • Modelling Linear Relationships 14 concepts

    1. Classify the nature of a gradient from a linear function

    2. Use the gradient and y-intercept to graph a linear equation

    3. Reading the x and y intercept from a graph

    4. Sketch a linear relationship from a table of values on a cartesian plane

    5. Finding the y - intercept at x=0

    6. Find the gradient of a line between two points using rise over run

    7. Determine the gradient and y-intercept using the gradient-intercept form of a linear relationship

    8. Identify independent and dependent variables in a practical context

    9. Solving practical problems with linear relationships

    10. Graph two intersecting lines on the same set of axes and read off the point of intersection

    11. Interpolation and Extrapolation

    12. Analyse step graphs

    13. Establish meaning for the gradient and intercepts in a practical context

    14. Apply break-even analysis to linear models

  • Modelling Non-Linear Relationships 9 concepts

    1. Sketch hyperbola graphs - positive quadrant

    2. Sketch cubic graphs - positive quadrant

    3. Develop non-linear equations where one variable varies directly as a power of another

    4. Sketch parabolic graphs - positive quadrant

    5. Sketch exponential graphs - positive quadrant

    6. Recognise the limitations of non-linear modelling - interpolating and extrapolating

    7. Solve contextual problems - including determining minimum and maximum values

    8. Develop linear equations from practical contexts where one variable directly varies with another

    9. Solve inverse variation problems

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Algebra and Modelling


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

Ready to start this program?

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Starting at

$49(inc. GST)

per session

Fully flexible

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Access to practice questions

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