Algebraic Relationships
Linear modelling, quadratic models, exponential and inverse variation models, simultaneous-equation comparisons, and HSC-style algebra in practical contexts.
Active lessons
9
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
9 of 9 active
Lesson 1
Algebraic Relationships Revision
Consolidate Year 11 skills: solving linear equations, substituting into formulas, gradient and y-intercept, and plotting from tables — preparation for Year 12 non-linear content.
Lesson 2
Linear Relationships and Modelling
Build and interpret linear models from fixed costs, starting values, rates of change, tables, and practical equations.
Lesson 3
Quadratic Models
Recognise and interpret quadratic models including parabola shape, opening direction, vertex, intercepts, and practical context restrictions.
Lesson 4
Exponential and Inverse Variation Models
Recognise and evaluate exponential growth and decay models and inverse variation models, and identify each type from tables, equations, and contexts.
Lesson 5
Reciprocal Relationships
Recognise and sketch y = k/x as a rectangular hyperbola, identify its asymptotes and branches, find k from a given point, and solve practical inverse variation problems.
Lesson 6
Simultaneous Equations in Context
Solve and interpret pairs of practical models, including equal-cost points and option comparisons.
Lesson 7
Linear Inequalities and Modelling
Solve linear inequalities, represent solutions on a number line, and interpret inequality constraints in practical budgeting and threshold contexts.
Lesson 8
Working with Formulae and Substitution
Substitute values into literal equations from science, finance, and measurement contexts, and rearrange simple formulas to find a target variable.
Lesson 9
Algebraic Relationships Exam Practice
Practise HSC-style algebra modelling questions using linear models, non-linear graphs, simultaneous equations, and contextual interpretation.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.