A jacket is marked down by 20% in a sale. In a further sale the discounted price is reduced by another 10%. Explain why the total discount is not 30%, and calculate the single percentage discount that would give the same final price.

The second discount is applied to the already-reduced price, not to the original, so it removes 10% of a smaller amount than the first discount did. After both reductions the price is 0.80 × 0.90 = 0.72 of the original, so the customer pays 72% and the single equivalent discount is 28%.

The mean of five numbers is 14. When a sixth number is included, the mean becomes 15. Find the sixth number.

Sum of the first five = 5 × 14 = 70. Sum of all six = 6 × 15 = 90. The sixth number = 90 − 70 = 20.

Does Year 10 maths count towards the HSC?

No, it is not assessed. It matters because Year 11 assumes it from the first week — the algebra especially — and a gap costs an afternoon to fix now against a term later.

Which Year 10 topics matter most for senior maths?

Rearranging equations, working with indices and surds exactly, and reading between a graph and its equation. Those three carry more weight in Year 11 than anything else on the Year 10 course.

Should I choose Advanced or Standard?

That is a school and family decision, but a useful test is whether algebra currently feels like a tool or a task. If it still takes conscious effort, spend a term making it automatic before deciding — the choice is easier from a position of fluency.

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HSC · Year 10

Year 10 Maths practice tests with worked solutions

Year 10 is where the algebra that Year 11 assumes gets built. These tests cover the whole year by topic, with a worked solution for every question rather than an answer key.

What the course asks of you

Algebra: Expanding, factorising and solving — the skills every later subject leans on.
Linear and non-linear relationships: Straight lines, parabolas, and reading a graph back into a rule.
Measurement and geometry: Surface area and volume, similar figures, and trigonometry in right-angled triangles.
Statistics and probability: Comparing data sets, and calculating probabilities from tables and diagrams.

Sample questions

Written for this site, in the style of the exam. Answer first, then see the model response and what the marks were for.

Question 1
2 marks
Factorise fully: 3x² − 12
Question 2
1 mark
A ladder 5.0 m long leans against a wall, with its foot 1.5 m from the base of the wall. The angle the ladder makes with the ground, to the nearest degree, is:
Question 3
3 marks
A jacket is marked down by 20% in a sale. In a further sale the discounted price is reduced by another 10%. Explain why the total discount is not 30%, and calculate the single percentage discount that would give the same final price.
Question 4
2 marks
The mean of five numbers is 14. When a sixth number is included, the mean becomes 15. Find the sixth number.

What Year 11 will assume you already have

Nothing on this page is assessed. It is here because Year 11 begins by assuming it, and the assumption is rarely checked until it is too late to fix cheaply.

Rearranging without thinking about it: Making x the subject, clearing fractions, handling a negative sign through a bracket. Year 11 does this inside every other question, so a student still working it out consciously is spending their attention on the wrong layer.
Moving between a graph and its equation: Reading a gradient off a line, knowing what changing a coefficient does to a curve. This is the language the senior courses are taught in.
Indices and surds handled exactly: Senior maths asks for exact answers far more often than Year 10 does. Reaching for a decimal is a habit worth breaking before it costs marks.
Setting working out so someone can follow it: In Year 10 the answer is usually enough. From Year 11 the method carries marks of its own, and the habit of showing it has to be built somewhere.

How to use these papers in Year 10

Not as revision for a test you are about to sit. Use them to find which of the assumed skills are actually there, ideally in the holidays before Year 11 rather than in the first weeks of it.

A wrong answer here is cheap. The same gap found in Year 12 is tangled up with two years of work built on top of it, and costs a term instead of an afternoon.

Work under time even now. The habit is harder to build later, when the content is also new.

Common questions

Does Year 10 maths count towards the HSC?: No, it is not assessed. It matters because Year 11 assumes it from the first week — the algebra especially — and a gap costs an afternoon to fix now against a term later.
Which Year 10 topics matter most for senior maths?: Rearranging equations, working with indices and surds exactly, and reading between a graph and its equation. Those three carry more weight in Year 11 than anything else on the Year 10 course.
Should I choose Advanced or Standard?: That is a school and family decision, but a useful test is whether algebra currently feels like a tool or a task. If it still takes conscious effort, spend a term making it automatic before deciding — the choice is easier from a position of fluency.

10 full papers for Year 10 Maths

Complete practice exams with a model answer for every part, and your own marks saved question by question so you can see where they went.

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