HSC Maths Notes: How to Take Notes That Actually Help

Last updated: 20 July 2026

Most HSC Maths notes are a waste of time. Students spend hours copying formulas from textbooks into colourful notebooks, then never look at them again. The notes look impressive but don't improve exam performance.

Here's how to take notes that actually work for HSC Maths.

The problem with most maths notes

Copying without thinking

If you're copying a formula from the textbook into your notes, you're not learning. You're transcribing. The textbook already has the formula. Your notes are just a second copy.

Too much content

Notes that try to summarise the entire syllabus end up being a worse version of the textbook. They're too long to review quickly and too shallow to explain anything properly.

No examples

A formula without a worked example is useless. You know the formula exists but not how to use it.

No mistakes

Notes that only show correct solutions don't help you avoid errors. The most valuable notes show what goes wrong and how to fix it.

What good maths notes look like

Good HSC Maths notes have four components:

1. Formula + when to use it

Don't just write the formula. Write when you'd use it.

Example:

• Cosine rule: c² = a² + b² - 2ab cos C
• Use when: you have two sides and the included angle, or all three sides
• Don't use when: it's a right-angled triangle (use Pythagoras instead)

2. One worked example per formula

For each formula or technique, include one worked example. Not five. One. Pick a representative question and write out the full solution.

The example should show:

• What the question looks like
• How you identify which method to use
• The full working
• The final answer with units

3. Common mistakes

For each topic, write down the mistakes you personally make. Not generic mistakes from a textbook. Your mistakes. The ones that keep showing up in your mistakes journal.

Example:

• I keep forgetting the chain rule on sin(2x). DERIVATIVE IS 2cos(2x), NOT cos(2x).
• I mix up upper and lower in area between curves. SKETCH FIRST.

4. A summary sheet (not a textbook)

Your notes should be reviewable in 10-15 minutes. If they're longer than 10 pages, they're too long. Condense. Use bullet points, not paragraphs. Use symbols and shorthand.

How to structure your notes

By topic, not by textbook chapter

Organise your notes by syllabus topic, not by textbook chapter. This makes it easier to find what you need when studying a specific topic.

For HSC Maths Advanced:

1. Functions
2. Trigonometric Functions
3. Calculus: Differentiation
4. Calculus: Integration
5. Financial Mathematics
6. Statistical Analysis

One page per topic

Aim for one page (both sides) per major topic. This forces you to be selective. If you can't fit it on one page, you're including too much detail.

Include a "quick reference" page

A single page with:

• Every formula you need to memorise (the ones NOT on the reference sheet)
• Trig values in radians
• Log laws
• Derivative/integral rules

This is the page you review the night before the exam.

When to take notes

During class

Don't copy everything the teacher writes. Write down:

• New formulas or techniques
• Things the teacher emphasises (if they say "this is always on the exam," write it down)
• Questions you got wrong in class and why
• Things that surprised you or that you didn't understand

After a practice set

After doing 10-15 questions on a topic, take 5 minutes to add to your notes:

• Any new mistake pattern you discovered
• A particularly good worked example from the questions
• Any technique that was different from what you expected

When reviewing your mistakes journal

Your mistakes journal is raw data. Your notes should be the summary. When you see a pattern ("I've gotten chain rule wrong 5 times this week"), add it to your notes with a specific fix.

What to put on your formula sheet cheat page

This is the one page you review before the exam. It should contain only things you need to memorise that are NOT on the NESA reference sheet:

Trig values (radians):

$$sin(0) = 0, sin(\pi/6) = 1/2, sin(\pi/4) = 1/\sqrt2, sin(\pi/3) = \sqrt3/2, sin(\pi/2) = 1$$

$$cos(0) = 1, cos(\pi/6) = \sqrt3/2, cos(\pi/4) = 1/\sqrt2, cos(\pi/3) = 1/2, cos(\pi/2) = 0$$

$$tan(\pi/4) = 1$$

Log laws:

• log(xy) = log(x) + log(y)
• log(x/y) = log(x) - log(y)

$$log(x^{n}) = n·log(x)$$

Derivatives to know cold:

$$d/dx(e^{x}) = e^{x}$$

• d/dx(ln x) = 1/x
• d/dx(sin x) = cos x
• d/dx(cos x) = -sin x

$$d/dx(tan x) = sec^{2}x$$

Integration by parts (Ext 2):

$$\int u dv = uv - \int v du$$

Your personal mistakes:

• [Fill in with your top 5 recurring errors]

Digital vs handwritten

Handwritten notes are better for retention. The physical act of writing helps you remember. But digital notes are easier to search and update.

Use whatever works for you. The format matters less than the content.

If you go digital, don't spend hours making them look beautiful. A plain text file with formulas and examples is more useful than a beautifully designed document that took 5 hours to format.

The bottom line

Good maths notes are short, personal, and focused on your specific weaknesses. They're not a textbook replacement. They're a tool for quick review and for documenting the patterns in your own mistakes.

If your notes don't help you do questions you couldn't do before, they're not working. Revise them.

Want to practise?

PracticePapers.io tracks your mistakes automatically and shows you exactly which topics need work. Free during beta.

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