The NESA HSC maths reference sheet is one of the most useful exam resources students receive, but it is also one of the easiest to misuse. Students often know that a formula is "on the sheet" without knowing where it is, what the variables mean, or when the formula applies.
This guide links the official NESA PDFs, then explains how to use the reference sheet during study and exam preparation. It covers the Standard maths reference sheet and the Advanced/Extension reference sheet separately, because they are different documents.
What the reference sheet is
NESA publishes official HSC mathematics reference sheets for students to use in exams. The official NSW Government pages describe the resources as containing data and formulas students may need in their HSC exams.
There are two main maths reference-sheet downloads:
- Mathematics Standard 1 and 2 HSC reference sheet
- Mathematics Advanced, Extension 1 and Extension 2 HSC reference sheet
The sheet is not a replacement for learning the course. It is a support document. Students still need to recognise the topic, choose the correct formula, substitute correctly, use their calculator accurately, and communicate the final answer.
That is why formula-sheet practice should start early. If a student first studies the sheet the week before trials, they will waste time looking for formulas instead of solving the question.
The best way to teach the sheet is to treat it as part of the problem-solving process. Students should not say "the formula is on the sheet" as a complete plan. They should say, "This is a compound-interest question, the sheet gives the compound-interest structure, the period rate is monthly, and the answer needs to be rounded to the nearest cent." That sentence is the difference between recall and exam readiness.
Official PDF downloads
Use NESA's official pages rather than a copied version from a third-party site.
Teachers should bookmark the official pages and avoid storing old PDFs in shared drives without checking the publication date. A local copy is convenient, but the official NESA page is the source to check before assessment blocks, trials, and final HSC revision.
Mathematics Standard 1 and 2
Download from NESA: Mathematics Standard 1 and 2 HSC reference sheet
NESA lists this as a data sheet, formula sheet, and reference sheet authored by the NSW Education Standards Authority, with publication date 1 January 2025.
Mathematics Advanced, Extension 1 and Extension 2
Download from NESA: Mathematics Advanced Extension 1 and 2 HSC reference sheet
NESA lists this as a data sheet, formula sheet, and reference sheet authored by the NSW Education Standards Authority, with publication date 1 January 2025.
For calculator rules that sit beside reference-sheet use, read the guide to NESA approved calculators for HSC maths. For Standard 2 finance practice, use the HSC Financial Maths guide.
What's on it, section by section
The Standard sheet is short. The Advanced/Extension sheet is longer and covers more topics. The sections below summarise what appears on the official PDFs.
Standard: Measurement
The Standard sheet includes limits of accuracy, arc length, sector area, trapezium area, an approximate area formula, surface area, volume, and right-triangle/trigonometry rules.
This is useful in practical measurement questions, but students still need to know what diagram feature each symbol represents. The formula is only helpful if the student can identify the two parallel sides and the perpendicular height.
The sheet also includes sine rule, cosine rule, and area of a triangle using . Students should practise deciding between those formulas from the information in the diagram, not from the name of the topic.
A useful classroom drill is to give students three diagrams with no formula names attached. Ask them to circle the values they know, mark the value they need, then choose the formula. This stops students from matching formulas to chapter headings only.
Standard: Financial Mathematics
The Standard sheet includes compound interest or future value, straight-line depreciation, and declining-balance depreciation.
It does not remove the need to understand the context. In a depreciation question, students need to decide whether the value decreases by a fixed amount or by a percentage of the current value. In financial questions, they also need to convert annual rates to period rates when required.
For annuities, students may be given table factors in the question or exam material. They still need to know whether they are using future value or present value. The worked guide to HSC Standard 2 annuities covers that distinction.
The sheet also does not stop students from making calculator mistakes. In financial maths, require a written line for the period rate and the number of periods before students evaluate the expression. That one habit catches many wrong-answer distractors.
Standard: Statistical Analysis
The Standard sheet includes the outlier rule using quartiles and IQR, the z-score formula, and a normal distribution diagram with approximate percentages for one, two, and three standard deviations.
The common error is formula recognition without interpretation. A student may compute a z-score correctly but fail to explain what that z-score means in context. Another may identify an outlier cutoff but forget to compare the actual data value to it.
For statistics, students should write a sentence after the calculation. A z-score, IQR cutoff, or normal-distribution percentage is rarely the whole response. The final mark often depends on interpreting the number in the context of the dataset.
Advanced/Extension: Measurement and Functions
The Advanced/Extension sheet includes measurement formulas similar to the Standard sheet, plus function and relation formulas such as the quadratic formula and the equation of a circle.
It also includes relationships for roots of a cubic equation. Students should not wait until Extension-style algebra questions to notice those formulas. Build them into revision sets earlier so students can recognise when coefficient relationships are being tested.
For Advanced students, this is where "not on the sheet" matters as much as "on the sheet". Basic algebra, factorising, completing the square, and domain restrictions still need to be fluent. The sheet may provide a formula, but it will not repair weak algebra.
Advanced/Extension: Sequences, series, logs and exponentials
The Advanced/Extension sheet includes arithmetic sequence and series formulas, geometric sequence and series formulas, the limiting sum of a geometric series, compound interest, and logarithmic/exponential identities.
This section is powerful, but it can create false fluency. Students may copy a geometric-series formula without identifying the first term or common ratio correctly. In financial contexts, they may use the formula mechanically without checking whether payments occur at the start or end of a period.
Teachers can test this by asking students to annotate a question before solving it: first term, common difference or ratio, number of terms, and whether the context is arithmetic or geometric. If students cannot label those parts, the formula will not save them.
Advanced/Extension: Trigonometric functions and identities
The sheet includes right-triangle ratios, sine rule, cosine rule, sector formulas in radians, reciprocal identities, Pythagorean identity, compound angle formulas, t-formulae, product-to-sum identities, and double-angle forms.
It also includes exact-value triangles for 45 degrees and 30/60 degrees. That helps, but students still need to connect exact values with radians, transformations, and equation solving.
The exact-value diagrams are especially useful when students understand why the values appear. Have them derive the common sine, cosine, and tangent values from the triangles, then practise moving between degrees and radians. Otherwise, they may find the triangle but still choose the wrong angle or quadrant.
Advanced/Extension: Statistical analysis and probability
The sheet includes z-score, outlier rules, normal distribution percentages, expectation and variance, probability laws, conditional probability, continuous random variable integrals, and binomial distribution formulas.
Students often use the probability formulas as if the events are independent without checking the condition. The formula tells them what to calculate; the question tells them whether the formula applies.
When revising probability, make students write the event definitions. For example, define and in words before substituting into a formula. This reduces the common error of calculating the right expression for the wrong event.
Advanced/Extension: Differential and integral calculus
The calculus section is extensive. It includes derivative rules for powers, product rule, chain rule, quotient rule, trigonometric functions, exponential and logarithmic functions, inverse trigonometric functions, plus a table of standard integrals.
It also includes integration by parts and a trapezoidal-rule style numerical approximation. Students still need to choose the method. The sheet will not tell them whether a question wants first principles, a derivative rule, a stationary point test, or an area calculation.
The calculus page can look comforting because it contains many rules. In practice, students lose marks before they reach the rule: choosing the wrong function to differentiate, missing a chain-rule structure, or failing to connect the derivative back to the question context.
Advanced/Extension: Combinatorics, vectors, complex numbers and mechanics
The final page includes permutation and combination formulas, binomial expansion, vector magnitude and dot product formulas, complex-number polar/exponential forms, de Moivre style powers, and mechanics formulas.
This is mostly Extension-heavy material. Students should practise with the sheet open and then without it, because the problem in these topics is usually not locating a formula. It is setting up the structure correctly.
For Extension classes, the reference sheet should be part of proof and modelling practice, not a separate handout. Ask students which lines of the sheet are relevant, which are not, and what extra reasoning is required to connect them.
What's NOT on it
The sheet does not include everything a student needs.
Students still need to know:
- how to rearrange formulas
- when a rate must be divided by the number of compounding periods
- how to round to a stated degree of accuracy
- how to interpret a graph or table
- how to define variables in a model
- how to communicate a conclusion in context
- how to choose between similar formulas
Some formula omissions depend on the course and year, so do not treat any unofficial "missing formulas" list as permanent.
The safest classroom activity is simple: give students a blank topic list and ask them to mark each item as "on the sheet", "partly on the sheet", or "not on the sheet". The discussion matters more than the final table.
For example, a student may mark compound interest as "on the sheet", but rate conversion as "not on the sheet". They may mark trigonometry formulas as "on the sheet", but quadrant reasoning and exact-angle selection as "partly on the sheet". That distinction gives teachers a precise revision target.
How to practise with it
Reference-sheet fluency is a skill. Teach it explicitly.
1. Use the official PDF from the start. Students should use the same NESA PDF during homework, topic tests, and revision. That builds visual memory.
2. Make students name the section. Before using a formula, they should identify the section: measurement, financial mathematics, statistics, trigonometry, calculus, probability, or another area.
3. Require a formula line. Even if the formula is on the sheet, students should write the relevant formula before substitution. That line earns method marks in school marking and makes errors easier to diagnose.
4. Pair formula choice with question wording. Ask students what words in the question told them to use that formula. For example, "compounded monthly" changes the rate and period count.
5. Run sheet-speed drills. Give students two minutes to find five formulas and write what each variable means. This is not busywork; it prevents searching under exam pressure.
6. Practise without the sheet after practising with it. Students should eventually know the common formulas well enough that the sheet becomes a backup, not the main strategy.
7. Build mixed-topic questions. Formula-sheet confidence is often topic-bound. A student can find the z-score formula in a statistics lesson but miss it in a mixed revision set. Use mixed practice once the class has basic fluency.
8. Make students explain non-use. Sometimes the correct move is not to use a formula from the sheet. Ask students why a tempting formula is irrelevant. This trains them to read the question instead of scanning for familiar symbols.
curriq helps teachers build this into worksheets. You can generate a Standard 2 financial set, an Advanced calculus set, or a mixed HSC revision set, then require students to annotate which reference-sheet formulas were used. Browse the HSC Standard 2 and HSC Advanced hubs for outcome-level topic pages.
FAQ
Where can I download the official HSC maths reference sheet?
Download it from NESA's official NSW Government pages: one page for Mathematics Standard 1 and 2, and one page for Mathematics Advanced, Extension 1 and Extension 2.
Is the Standard maths reference sheet the same as the Advanced one?
No. Standard uses a shorter reference sheet. Advanced, Extension 1 and Extension 2 use a longer sheet with additional formulas for functions, calculus, probability, vectors, complex numbers, and mechanics.
Should students memorise formulas that are on the reference sheet?
Students should still know the common formulas well enough to recognise when they apply. The sheet helps with recall, but it does not choose the method or interpret the question.