HSC Trial Mathematics Examinations

and Year 11 Final Examinations

Professionally written and formatted examination papers that mirror the rigour and format of the HSC: original, comprehensive and customisable. Prepared by experienced and current Mathematics teachers, with complete worked solutions and marking guidelines, and branded with your school’s crest.

A Trial counts toward your students’ HSC assessment mark and is their last full rehearsal. Every question is original, properly graded and checked, so the paper holds up in the exam room, in marking and in moderation.

See a sample paper

Question 26, 4 marks. A wading pool consisting of a semicircle and a trapezium, drawn in blue inside a brick-paved surround, with dimensions of 10, 15, 18, 20 and 26 metres. Find the total cost of the paving at $52.70 per square metre. — Question 26 · 4 marks · Standard 2

Samples

Sample questions, by course

Every course we write, as it appears on the page. Tap a question to see it at full size.

Year 12 Trial · Standard 2

Question 29, 3 marks. A shaded blue sphere of diameter 30 millimetres inside a wireframe cube with 30 millimetre sides. Calculate the volume of the empty space in the box. — **Question 29 · 3 marks** — A 30 mm sphere in a 30 mm box; the volume of the empty space.

Question 31, 3 marks. A factory production line described in full, then a flow network from Start to Finish through workstations A to G with a capacity on each conveyor and a dashed line marking a proposed cut. Part a: state the capacity of the cut. — **Question 31 · 3 marks** — Maximum flow through a production line; the capacity of a cut.

Question 20, 8 marks. An activity network from Start to Finish with activities A to H and their durations in hours, each node drawn as a circle split for earliest and latest starting times. — **Question 20 · 8 marks** — Critical path analysis: earliest and latest starting times.

Question 22, 6 marks. A plan of a rectangular site 18 by 10 metres with a swimming pool of 13 by 5 metres and two semicircular sections of radius 3 metres, surrounded by hatched green grass. — **Question 22 · 6 marks** — Soil removed for a swimming pool with semicircular ends; grass laid around it.

Question 18, 4 marks. A drawing of an EMV card chip at a scale of 3 to 1, measuring 3.3 centimetres by 2.4 centimetres. Write down the actual dimensions to the nearest millimetre. — **Question 18 · 4 marks** — A scale drawing of an EMV chip at 3 : 1; its actual dimensions.

Question 14, multiple choice. A box plot on a grid of the ages of 228 cyclists in the 2025 Tour de France, with two outliers. Which of 50, 100, 150 or 200 is the only possible number of competitors younger than 30? — **Question 14 · multiple choice** — A box plot of the ages of Tour de France riders; what the quartiles imply.

Question 3, multiple choice. Five playing cards numbered 2, 3, 5, 7 and 11 face down; the first is turned over to show 7. What is the probability that a second card chosen is odd? Options one half, three fifths, two thirds, three quarters. — **Question 3 · multiple choice** — Five prime-numbered cards; the probability of an odd number after one is revealed.

Question 37, 3 marks. An airline refunds fares when the Sydney to Wagga Wagga flight time, normally distributed with a mean of 75 minutes and a standard deviation of 9 minutes, exceeds the mean by t minutes, and wants to refund no more than 1 per cent of fares. A sketch of the standard normal distribution with the region below z shaded pink, and a table of probabilities for z from 2.30 to 2.39. Find t to the nearest minute. — **Question 37 · 3 marks** — Refunds on a flight that runs late; the standard normal curve and a table of z values.

Want to read a whole paper?

Email us from your school address and we will send a complete, watermarked paper for the course you teach.

Request a full paper

The care

Why choose The Exam Room?

Only Mathematics exams — that is our specialty and where our expertise lies.
Content adjusted to match your teaching scope and sequence — no insert sheets.
Professionally prepared diagrams and formatting.
Alignment with current HSC standards and expectations.
Original and expertly crafted questions that test genuine understanding.
Balanced and well-structured papers that differentiate within a cohort.
Detailed solutions that support teacher feedback and student learning.
Professionally branded materials that enhance your school’s reputation.

Question 14, 6 marks, use the Question 14 writing booklet. The complex number z equals cos theta plus i sin theta. Show that z plus 1 equals 2 cos theta on 2 times cos theta on 2 plus i sin theta on 2, then apply the result to two complex numbers z1 and z2. — HSC conventions, down to the writing-booklet line

What you get

Everything you need as PDF files — just print

The examination paper, branded with your school’s crest.
Multiple-choice answer sheets.
Writing booklets, with students’ NESA numbers pre-printed if you wish.
Complete worked solutions, including the multiple-choice questions.
Marking guidelines with syllabus references and outcomes.
A spreadsheet that calculates marks by topic and outcome, with suggested moderation in line with recent HSC results.

Customisation

Made for your school

White-labelled. Papers, answer sheets and writing booklets carry your school’s crest and present as your own.
Your scope and sequence. We adapt papers and specific questions to the topics you have covered.
Your cover page. Instructions particular to your school, in your format if you prefer.
Your marking allocation. Standard and Advanced papers can be split into booklets to suit it.
NESA numbers printed on papers and writing booklets if desired.

Pricing

The cost

Year	Course	Exam format	Time	Regular price*
Year 11 Final	Extension	60 marks (6 MC)	1½ hours	$500
	Advanced	80 marks (8 MC)	2 hours	$600
	Standard	80 marks (10 MC)	2 hours	$600
Year 12 Trial	Extension 2	100 marks (10 MC)	3 hours	$1,100
	Extension 1	70 marks (10 MC)	2 hours	$800
	Advanced	100 marks (10 MC)	3 hours	$950
	Standard 2	100 marks (15 MC)	2½ hours	$950
	Standard 1	80 marks (10 MC)	2 hours	$800

*Excluding GST.

Discounts for 2027

For orders placed by December 2026.

1 exam	40% off the regular price
2 exams	45% off the regular price
3 exams	50% off the regular price
4 exams	55% off the regular price
5 exams	60% off the regular price
6 exams	65% off the regular price
7 exams	70% off the regular price
8 exams	75% off the regular price

This page prints cleanly if you need to pass it on.

How it works

From order form to exam day

Order online, or email us the completed PDF order form, noting any topics to omit and any special requests. Your school’s crest can follow as a PDF, now or later.
We call you to make sure everything is completely clear.
Once the details are final, we invoice your school at the address you nominate.
On payment, all examination materials are emailed to you in the first week of Term 3. The order cut-off for 2027 is to be advised.
On commitment to purchase, a secured viewing of the final paper can be arranged so you are fully satisfied before it is printed.
Examinations are held on the specified dates, aligned with the customary Trial HSC timetable observed by NSW independent schools. Other arrangements are possible by negotiation. The 2027 examination dates and security period will be confirmed in Term 2, 2027.
A security period follows. Papers and completed scripts stay confidential until we declare it over; your school may then release the papers and solutions to students.

From 2027, two additional Year 11 and 12 assessments may also be purchased, by negotiation.

Who writes them

Current teachers, only Mathematics

The Exam Room is run by Stephen Ewington. Our papers are written by very experienced Mathematics teachers, HSC markers and writers.

Contact

Any questions?

Please feel free to contact us about anything. We are happy to find workable solutions to fit your school’s needs.

Email: hello@theexamroom.com.au
Phone: +61 424 977 252

Order online

To pass on

The Exam Room brochure (PDF, 2026)
Order form, with terms and conditions (PDF, 2026)