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Algebraic Techniques & Linear Relationships

Master the algebraic foundations and connect them to the coordinate plane. From simplifying expressions and solving equations to graphing lines and modelling real-world situations with linear relationships. Fully mapped to the NESA Mathematics K-10 Syllabus (2022) Stage 5 Core.

20 Lessons 3 Checkpoints 1 Unit Quiz Stage 5 Core + Paths

NESA Syllabus Outcomes

MAS-ALG-C-01

Simplifies algebraic expressions involving addition, subtraction, multiplication and division.

MAS-ALG-C-02

Expands algebraic expressions using the distributive law and factorises expressions with a common factor.

MAS-EQU-C-01

Solves linear equations and linear inequalities, including those with fractions and brackets.

MAS-EQU-C-02

Changes the subject of a formula and solves simultaneous equations using substitution and elimination.

MAS-LIN-C-01

Determines the gradient and equation of a straight line and graphs linear relationships.

MAS-LIN-C-02

Identifies parallel and perpendicular lines and applies linear models to solve problems.

Lessons

Block A — Algebraic Techniques Lessons 1-7

Simplifying Algebraic Expressions

Combine like terms, work with multiple variables, and simplify complex expressions.

Expanding Algebraic Expressions

Apply the distributive law to single and double brackets. Expand and simplify.

Factorising Common Factors

Identify and extract the highest common factor from algebraic expressions.

Factorising Quadratics

Factorise monic quadratics of the form x² + bx + c. [PATHS extension]

Difference of Squares

Recognise and factorise a² − b². Expand and simplify products of sums and differences.

Mixed Factorisation and Simplification

Combine all factorisation types in multi-step simplification problems.

Algebraic Fractions

Simplify, add, subtract, multiply and divide algebraic fractions. [PATHS extension]

Checkpoint 1 — Algebraic Techniques

Covers Lessons 1-7. Simplifying, expanding, factorising and algebraic fractions.

Block B — Equations and Inequalities Lessons 8-14

Solving Linear Equations

One-step, two-step, multi-step and variables-on-both-sides equations.

Equations with Fractions

Clear fractions using the LCD. Solve algebraic fractions and cross-multiply.

Formulas and Rearrangement

Change the subject of a formula. Work with literal equations in real contexts.

Linear Inequalities

Solve and graph inequalities on a number line. Handle the negative multiplier rule.

Word Problems with Linear Equations

Translate words into equations. Consecutive integers, age, distance and money problems.

Simultaneous Equations — Substitution

Solve pairs of equations by substitution. Check solutions and interpret contexts.

Simultaneous Equations — Elimination

Match coefficients, add or subtract equations, and choose the best method.

Checkpoint 2 — Equations and Inequalities

Covers Lessons 8-14. Linear equations, fractions, formulas, inequalities, word problems and simultaneous equations.

Block C — Linear Relationships Lessons 15-20

Coordinate Geometry — Distance and Midpoint

Apply the distance and midpoint formulas. Solve geometric problems on the Cartesian plane.

Gradient of a Line

Calculate gradient from two points or from an equation. Understand rise over run.

Graphing Linear Relationships

Plot using gradient-intercept and intercept methods. Sketch from equations.

Equations of Lines

Find the equation from gradient and y-intercept, gradient and point, or two points.

Parallel and Perpendicular Lines

Use equal and negative reciprocal gradients. Find equations of parallel and perpendicular lines. [PATHS]

Linear Modelling

Apply linear equations to model costs, distances and temperatures. Interpolate and extrapolate.

Checkpoint 3 — Coordinate Geometry & Linear Modelling

Covers Lessons 15-20. Distance, midpoint, gradient, equations of lines, parallel/perpendicular and linear modelling.

Unit Quiz — Algebraic Techniques & Linear Relationships

Comprehensive assessment covering all 20 lessons, 3 checkpoints and Working Mathematically.