HSC Mathematics Standard 2 topic guide

Algebra

Algebra is a core part of HSC Mathematics Standard 2. This guide connects the syllabus ideas behind Formulae and Equations, Linear Relationships, Types of Relationships, shows how they appear in worked problems, and points you to the formulas and full lessons needed for exam revision.

What you will learn

Algebra syllabus outline

The units below follow the structure used in the full Study to Learn course. Use the outline to identify exactly which idea needs attention, then work through the public example before continuing to the complete lesson path.

A.1

Formulae and Equations

Substituting into Formulas · Solving Linear and Non-Linear Equations

A.2

Linear Relationships

Graphing Linear Equations · Simultaneous Equations

A.3

Types of Relationships

Quadratic and Exponential Graphs · Modelling Growth and Decay · Reciprocal Relationships & Inverse Variation · Graphing with Tables of Values

Free worked preview

Substituting into Formulas

This complete preview comes from the Formulae and Equations unit. It introduces the core language, shows the method in context, and gives you a real example of the lesson quality before you create an account.

Working with Formulas

Formulas are everywhere in everyday and working life — from calculating how much paint to buy, to working out a car loan repayment, to converting a recipe for a different number of guests. Every one of them boils down to the same two skills: plugging known values into the right places, and rearranging when the value you want isn't the one the formula is "solved for". This lesson builds that fluency before you meet dozens of specific formulas across the rest of the course. After this lesson you will be able to substitute confidently into any formula and rearrange it to solve for a different pronumeral.

A formula relates two or more quantities. To use one, substitute known values for the pronumerals and evaluate, following the correct order of operations.

Rearranging a Formula

Sometimes you need to find a different pronumeral than the one the formula is "solved for" — rearrange first using inverse operations (the same way you'd solve an equation), then substitute.

Common ErrorSubstitute the given value everywhere the pronumeral appears — missing an occurrence (in formulas where a letter appears more than once) is a common mistake.
Worked Example The formula for simple interest is I=PrnI=Prn. Find r if I = $450, P = $3000, n = 3.
1Substitute known values450=3000×r×3450 = 3000 \times r \times 3
2Simplify 3000 × 3450=9000r450 = 9000r
3Divide both sides by 9000r=450÷9000r = 450 \div 9000
4Simplify 450 ÷ 9000r=0.05r = 0.05
r=0.05=5%r = 0.05 = 5\%
Practice QuestionThe formula for the area of a trapezium is A=12(a+b)hA=\frac12(a+b)h. Find h if A = 60, a = 8, b = 12.

Use the formulas

Keep the formula sheet beside you

Revision becomes faster when you practise locating the right equation and understand what every variable means. The full reference is public and searchable on any device.

Open HSC Mathematics Standard 2 Formula Sheet →

Reviewed by the Study to Learn editorial team · Updated 2026-07-24