HSC Maths Reference Sheet: What's On It and What Isn't (2026)

Last updated: 20 July 2026

NESA gives you a reference sheet in the HSC Maths exam. It's the same sheet for Standard 2, Advanced, Extension 1, and Extension 2. Most students never practice with it and don't know what's actually on it.

Here's the complete breakdown.

Where to get it

Download the official version from the NESA website. Print it. Use it every time you study. You should know where every formula is before you walk into the exam.

PracticePapers.io also has an interactive version with all 65 formulas across 14 topics, each with explanations and common mistakes.

What's on the sheet

Measurement

• Arc length (degrees and radians)
• Sector area
• Surface area of a cylinder
• Volume of a cylinder, cone, sphere, pyramid
• Triangle area (½bh and ½ab sin C)

Trigonometry

• Sine rule:

$$a/\sin A = b/\sin B = c/\sin C$$

• Cosine rule:

$$c^{2} = a^{2} + b^{2} - 2ab \cos C$$

• Area of triangle:

$$\tfrac{1}{2}ab \sin C$$

Algebra

• Quadratic formula
• Discriminant

Series and sequences

• Arithmetic: nth term and sum
• Geometric: nth term and sum
• Infinite geometric series sum

Calculus

• Differentiation rules: power, product, quotient, chain
• Derivatives of: (e^x), (\ln(x)), (\sin(x)), (\cos(x)), (\tan(x))
• Standard integrals: (x^n), (1/x), (e^x), (\sin(x)), (\cos(x))

Statistics

• Normal distribution (mean and standard deviation)
• Z-score formula
• Expected value
• Variance
• Binomial distribution (mean and standard deviation)

Financial mathematics

• Compound interest
• Annuity (future value and present value)

Vectors (Extension 1)

• Magnitude
• Dot product
• Projection

Complex numbers (Extension 2)

• Modulus and argument
• De Moivre's theorem

Mechanics (Extension 2)

• Equations of motion

What's NOT on the sheet

This is what catches students out. These are formulas and values you must memorise.

Trigonometric values

You need to know these for radians:

• sin(0) = 0, cos(0) = 1

$$sin(\pi/6) = 1/2, cos(\pi/6) = \sqrt3/2$$

$$sin(\pi/4) = 1/\sqrt2, cos(\pi/4) = 1/\sqrt2$$

$$sin(\pi/3) = \sqrt3/2, cos(\pi/3) = 1/2$$

$$sin(\pi/2) = 1, cos(\pi/2) = 0$$

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

Logarithm laws

$$log_{a}(xy) = log_{a}(x) + log_{a}(y)$$

$$log_{a}(x/y) = log_{a}(x) - log_{a}(y)$$

$$log_{a}(x^{n}) = n·log_{a}(x)$$

$$log_{a}(a) = 1$$

$$log_{a}(1) = 0$$

• Change of base:

$$\log_{a}(x) = \log(x)/\log(a)$$

Derivative of tan(x)

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

. This is on the sheet, but students often miss it because it's listed separately from the other trig derivatives.

Trapezoidal rule formula

The structure is on the sheet but you need to know how to apply it with multiple subintervals (the h/2 pattern with coefficients 1, 2, 2, ..., 2, 1).

Integration by parts formula (Extension 2)

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

. Not on the sheet. Must memorise.

Integration by partial fractions (Extension 2)

The decomposition technique. Not on the sheet.

How to use the sheet effectively

1. Practice with it

Every practice session, have the printed sheet next to you. Use it. Get familiar with where every formula is located on the page.

2. Know what's missing

The formulas listed above (trig values, log laws, integration by parts) aren't on the sheet. Memorise them. If you go into the exam expecting them to be there, you'll waste time looking and then panic.

3. Don't over-rely on it

Basic differentiation and integration rules should be automatic. You shouldn't need to look up the power rule. The sheet is for less frequent formulas like the cosine rule, annuity formulas, and z-score.

4. Check notation

The sheet uses specific notation. Make sure you understand what each symbol means (μ for mean, σ for standard deviation, θ for angle, etc.) before the exam.

5. Verify during the exam

After solving a problem, if you used a formula, check it against the sheet. This catches memory errors. Did you write the cosine rule with a + instead of a -? The sheet will tell you.

Common mistakes with the reference sheet

Using the wrong formula. The sheet has similar formulas (arithmetic vs geometric series, future value vs present value of annuities). Read carefully.

Not knowing what's NOT on the sheet. Students assume trig values and log laws are provided. They aren't.

Wasting time searching. In a 3-hour exam, every second counts. Know where everything is on the page.

Ignoring it entirely. Some students never look at the sheet during the exam because they've memorised everything. That's fine if you actually have memorised everything. But if you're unsure of a formula, checking the sheet is faster and more reliable than guessing.

The interactive version

The PracticePapers.io formula sheet goes beyond the NESA sheet. It has:

• 65 formula cards across 14 topics
• Plain-English explanations for every formula
• 10 common mistake warnings
• 9 worked examples
• Course filtering (Standard 2, Advanced, Ext 1, Ext 2)
• Live search
• Print mode for exam revision

View the interactive formula sheet

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Based on the current NESA HSC Mathematics reference sheet. Always check the official NESA website for the latest version. PracticePapers.io is not affiliated with NESA.