How Do You Use the HSC Maths Formula Sheet?

Every HSC Maths student walks into the exam with the same document: the reference sheet. It's there for Maths Advanced, Maths Standard, and Maths Extension students, and it contains formulas you're not expected to memorise — but you are expected to use fluently.

Here's the thing most students don't realise: the formula sheet doesn't help you if you don't already understand what the formulas mean. Students who use it effectively aren't just copying numbers — they know what each variable represents, which formula applies to which type of question, and how to substitute correctly without losing marks to arithmetic errors.

This guide walks through every major section of the HSC Maths formula sheet with worked examples, so you can walk into your exam knowing exactly where to look and what to do when you find it.

📌 Quick Summary
- The HSC formula sheet is provided in every Maths Advanced and Standard exam — you don't need to memorise the formulas it contains, but you do need to understand them.
- Knowing which formula to apply, and why, is the skill the exam tests — not memorisation.
- Practise working with the reference sheet open during your trial papers and past papers so the format feels natural by exam day.

Table of Contents

1. What Is the HSC Maths Formula Sheet?
2. Trigonometry — Formulas and Worked Example
3. Calculus — Formulas and Worked Example
4. Statistics and Probability — Formulas and Worked Example
5. Financial Maths — Formulas and Worked Example
6. HSC Standard Maths Formula Sheet
7. Tips for Using the Formula Sheet Under Exam Pressure
8. FAQ

What Is the HSC Maths Formula Sheet?

The HSC Maths reference sheet (officially called the Mathematics Reference Sheet) is a one-page document provided to all students in HSC Mathematics Advanced, Mathematics Standard 1, Mathematics Standard 2, and Mathematics Extension 1 and 2 exams.

It includes:

• Financial Maths formulas — compound interest, present/future value of annuities
• Trigonometric ratios and identities — sine rule, cosine rule, exact values
• Statistical formulas — mean, standard deviation, z-scores, normal distribution
• Calculus formulas — standard derivatives and integrals
• Geometric formulas — area, volume, and arc/sector formulas

The sheet is identical for all students — so your advantage doesn't come from having the sheet; it comes from knowing how to use it faster and more accurately than the next student.

What the Reference Sheet Does NOT Include

• How to choose which formula to apply (that's your job)
• Algebraic manipulation steps (you need to do these yourself)
• Formulas for topics not listed — some formulas you still need to memorise (e.g., the quadratic formula is on the sheet, but some algebraic identities are not)

Download the current official reference sheet from the NESA website to make sure you're working with the correct version for your exam year.

Trigonometry — Formulas and Worked Example

Formulas on the Sheet

The trigonometry section includes:

• Sine rule: a/sin A = b/sin B = c/sin C
• Cosine rule: c² = a² + b² − 2ab cos C
• Area of a triangle: A = ½ ab sin C
• Arc length: l = rθ (where θ is in radians)
• Area of a sector: A = ½ r²θ

When to Use Each

Worked Example

Question: In triangle ABC, AB = 8 cm, BC = 11 cm, and angle ABC = 65°. Find the area of the triangle.

Solution:

The angle given (65°) is the included angle between sides AB (= 8) and BC (= 11).

Using the area formula: A = ½ ab sin C

Here, a = 8, b = 11, C = 65°

A = ½ × 8 × 11 × sin(65°)
A = ½ × 88 × 0.9063...
A = ½ × 79.75...
A ≈ 39.9 cm²

Common mistake: Using degrees in radian formulas (arc length, sector area). Always check whether the angle given is in degrees or radians, and convert if necessary.

Calculus — Formulas and Worked Example

Formulas on the Sheet

The calculus section provides standard derivatives and integrals:

Derivatives:

• d/dx [xⁿ] = nxⁿ⁻¹
• d/dx [eˣ] = eˣ
• d/dx [ln x] = 1/x
• d/dx [sin x] = cos x
• d/dx [cos x] = −sin x
• d/dx [tan x] = sec²x

Integrals:

• ∫ xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)
• ∫ eˣ dx = eˣ + C
• ∫ 1/x dx = ln|x| + C
• ∫ sin x dx = −cos x + C
• ∫ cos x dx = sin x + C
• ∫ sec²x dx = tan x + C

The Chain Rule and Product Rule

These are not on the reference sheet for Advanced — you need to know these from memory:

• Chain rule: d/dx [f(g(x))] = f'(g(x)) × g'(x)
• Product rule: d/dx [uv] = u'v + uv'

Worked Example

Question: Find the equation of the tangent to the curve y = 3x² − 2x + 1 at the point where x = 2.

Solution:

Step 1: Find the y-coordinate at x = 2.
y = 3(2)² − 2(2) + 1 = 12 − 4 + 1 = 9
Point: (2, 9)

Step 2: Find dy/dx.
Using d/dx [xⁿ] = nxⁿ⁻¹:
dy/dx = 6x − 2

Step 3: Find the gradient at x = 2.
m = 6(2) − 2 = 10

Step 4: Write the equation of the tangent.
Using y − y₁ = m(x − x₁):
y − 9 = 10(x − 2)
y = 10x − 11

Common mistake: Forgetting to add the constant of integration (+C) in indefinite integrals. This is a mark-losing error that's easy to avoid.

Statistics and Probability — Formulas and Worked Example

Formulas on the Sheet

• Mean: x̄ = Σx / n (or Σfx / Σf for frequency tables)
• Sample standard deviation: s = √[Σ(x − x̄)² / (n−1)]
• z-score: z = (x − μ) / σ
• Normal distribution — 68-95-99.7 rule (empirical rule)

When to Use These

The statistics formulas appear most often in:

• Questions about data sets (finding mean, standard deviation)
• Normal distribution questions (using z-scores to find probabilities)
• Comparing datasets (using z-scores to standardise values from different distributions)

Worked Example

Question: A student's score in a Maths test was 72. The class mean was 65 and the standard deviation was 8. Calculate the student's z-score and interpret what it means.

Solution:

Step 1: Apply the z-score formula.
z = (x − μ) / σ = (72 − 65) / 8 = 7/8 = 0.875

Step 2: Interpret.
A z-score of 0.875 means the student scored 0.875 standard deviations above the class mean. Using the 68-95-99.7 rule, approximately 68% of students scored within one standard deviation of the mean — so this student performed above average but within the top 30% of the distribution.

Common mistake: Using σ (population standard deviation) when the question gives you s (sample standard deviation). Read the question carefully — the formula sheet gives you both, and which one to use depends on context.

Financial Maths — Formulas and Worked Example

Formulas on the Sheet

• Compound interest: A = P(1 + r)ⁿ
• Present value of annuity: PV = M × [1 − (1+r)⁻ⁿ] / r
• Future value of annuity: FV = M × [(1+r)ⁿ − 1] / r

Where:

• P = principal (initial amount)
• A = final amount
• r = interest rate per period (as a decimal)
• n = number of periods
• M = payment per period

When to Use Each

Worked Example

Question: Sarah invests $5,000 at an interest rate of 4.5% per annum, compounded quarterly, for 3 years. How much will she have at the end of the 3 years?

Solution:

Step 1: Identify the variables.
P = 5,000
r = 4.5% ÷ 4 = 1.125% per quarter = 0.01125 (quarterly rate)
n = 3 × 4 = 12 (quarters)

Step 2: Apply the compound interest formula.
A = P(1 + r)ⁿ
A = 5,000 × (1 + 0.01125)¹²
A = 5,000 × (1.01125)¹²
A = 5,000 × 1.14396...
A ≈ $5,719.80

Common mistake: Using the annual rate instead of converting it to the period rate. If interest is compounded quarterly, divide the annual rate by 4 and multiply n by 4. If monthly, divide by 12 and multiply n by 12.

HSC Standard Maths Formula Sheet

Students sitting Maths Standard 1 or Standard 2 receive the same reference sheet, but the questions they're asked require a subset of the formulas available.

Key Differences for Standard Students

• Financial Maths is heavily weighted — annuity formulas appear frequently in Standard 2, so practise these until substitution is automatic.
• Trigonometry in Standard — you'll use sine and cosine rules, and the area formula, but you won't need radian measure (that's Extension territory).
• Statistics in Standard — z-scores, normal distribution, and data analysis appear prominently. Practise interpreting z-scores in real-world contexts (comparing exam results, medical data, etc.).
• No calculus — Standard students don't need the calculus section of the reference sheet.

Standard Maths Exam Strategy

Because Standard Maths questions are often multi-step problems set in real-world contexts, the formula sheet alone isn't enough. You need to:

1. Identify which formula applies from the context of the question.
2. Correctly extract the variables from the question's wording.
3. Substitute accurately.
4. Interpret the answer in context (e.g., "so the loan will take 7 years and 3 months to repay").

Step 4 is where many Standard students lose marks — they calculate correctly but don't give a contextualised conclusion.

Tips for Using the Formula Sheet Under Exam Pressure

Before the Exam

1. Annotate your practice sheet. During study, write small pencil notes next to formulas reminding you when to use them (you won't be able to annotate the real sheet, but the mental associations will stick).
2. Do every past paper with the reference sheet open. Don't try to memorise the formulas — practise finding and applying them quickly.
3. Know which formulas are NOT on the sheet. You'll need to memorise: the quadratic formula (it is on the sheet), product and chain rules (not on the sheet for Advanced), geometric series formulas (check your syllabus), and probability rules.
4. Practise converting units and rates. The most common errors in financial maths come from incorrect rate conversion, not from misapplying the formula itself.

During the Exam

1. Read the question fully before reaching for the formula sheet. Understand what you're being asked first — then find the relevant formula. Going to the sheet first and then reading the question is a common time-wasting mistake.
2. Highlight the variables you've been given. Before substituting, write out what each variable equals. This prevents substitution errors and helps you check your work.
3. Check your units at every step. Are you working in years or months? Dollars or cents? Degrees or radians? Unit errors are preventable mark losses.
4. Don't panic if you can't immediately find the right formula. Read the section headings on the reference sheet methodically — Financial, Trigonometry, Calculus, Statistics. The formula you need is there.

Working With a KIS Tutor

Knowing the formula sheet is there is reassuring. Actually using it fluently under exam pressure is something most students need to practise — and practice is most effective with targeted feedback.

Our tutors average a 99.50 ATAR, with many having achieved top results in HSC Maths Advanced and Extension. Working with 5,600+ students, we've seen that the students who use the formula sheet most effectively are those who've done extensive past paper practice with a tutor who can identify when they're making substitution errors, using the wrong formula, or losing marks on the final contextualisation step.

If you're preparing for HSC Maths — Advanced or Standard — and you'd like personalised support, book a free 30-minute study skills consultation. No commitment required.

Conclusion

The HSC Maths formula sheet is one of your most powerful exam tools — but only if you use it with intention. Every formula on that sheet represents a type of problem you'll encounter, and your job is to match problem types to formulas quickly and accurately.

Start by working through all past NESA papers with the reference sheet open. Flag any questions where you weren't sure which formula to use, then build those connections deliberately. By the time you walk into the exam, reaching for the right section should feel automatic.

For help with HSC Maths tutoring, or to explore our KIS Plus online resources, visit kisacademics.com.

FAQ

Is the HSC Maths formula sheet the same every year?

The reference sheet is updated periodically by NESA and may change when the HSC syllabus is revised. Always download the current version from the NESA website and check the year printed on the document. Using an outdated formula sheet for practice is a common mistake.

Do HSC Maths Extension 1 and Extension 2 students get the same formula sheet?

Extension 1 and Extension 2 students receive an additional reference sheet that includes more advanced formulas (integration techniques, complex number results, etc.) alongside the standard sheet. Check the NESA website for the Extension-specific reference sheet.

Should I memorise anything even though the formula sheet is provided?

Yes. While the reference sheet covers many formulas, there are still things you need to know from memory: the product and chain rules (for Advanced), how to interpret and apply each formula correctly, and how to manipulate formulas algebraically. The sheet tells you what the formula is — the exam tests whether you know how to use it.

What if I use the wrong formula in an HSC Maths exam?

HSC Maths marking guidelines often include marks for correct working even when the final answer is wrong. If you use the wrong formula but apply it consistently and correctly, you may still receive some method marks. However, using the wrong formula from the outset generally means you won't receive marks for the answer. Choosing the correct formula is a fundamental skill the exam tests.

Can I write on the HSC Maths formula sheet?

You cannot annotate the formula sheet that is issued in the exam. However, you can use the working-out pages of the exam booklet to organise your substitution steps before transferring them to your answer. During study, annotating a personal copy of the reference sheet is excellent practice — the annotations won't be there in the exam, but the mental connections will be.