HSC Mathematics Standard 1 topic guide

Algebra

Algebra is a core part of HSC Mathematics Standard 1. This guide connects the syllabus ideas behind Formulae and Equations, Linear 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 Equations

A.2

Linear Relationships

Graphing Linear Equations · Direct Proportion

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

A formula is an equation that relates two or more quantities — e.g. converting temperature, calculating wages, or finding the area of a shape. To use one, substitute known values for the letters (pronumerals) and evaluate.

Order of Operations

Always follow the correct order: brackets, powers/roots, then multiplication/division, then addition/subtraction (sometimes remembered as BODMAS/BIMDAS). Substitute the given values first, then simplify step by step.

Example Formula: Temperature Conversion
F=95C+32F = \frac{9}{5}C + 32
where
FFtemperature in degrees Fahrenheit
CCtemperature in degrees Celsius
Common ErrorSubstitute the given value everywhere the pronumeral appears in the formula — missing one occurrence, or substituting into the wrong letter, is the most common mistake when a formula has the same letter used more than once.
Worked Example Convert 25°C to Fahrenheit.
1Substitute C = 25F=95(25)+32F = \frac{9}{5}(25) + 32
2Simplify the multiplication first: (9/5)(25) = 45F=45+32F = 45 + 32
3Add 45 + 32F=77F = 77
F=77°FF = 77°F
Practice QuestionThe formula for the perimeter of a rectangle is P=2l+2wP = 2l + 2w. Find P when l = 8 m and w = 5 m.

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 1 Formula Sheet →

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