Year 9 maths questions with worked answers, and how NAPLAN numeracy works

The daily Year 9 Maths paper has 8 original questions worth 25 to 35 marks. It practises the skills Year 9 builds on and NAPLAN numeracy leans on: fractions, decimals and percentages, ratio, money and units, expressions and equations, straight-line graphs, sequences, area and perimeter, angles, averages and probability. It has no index laws, factorising, Pythagoras or trigonometry, so practise those with the questions below.

Year 9 NAPLAN numeracy

• When: NAPLAN runs from 11 to 23 March in 2026 and from 10 to 22 March in 2027.
• Format: online and tailored, so the next set of questions gets easier or harder depending on your answers. Questions are multiple choice, typed answers, and drag-and-drop or hot-spot items.
• Calculator: in Years 7 and 9 there is a short non-calculator section on arithmetic; an online calculator is available for the rest of the test.
• What it covers: number, algebra, measurement, space, statistics and probability.
• Results: four proficiency levels: Exceeding, Strong, Developing, and Needs additional support.

From ACARA's NAPLAN numeracy and key dates pages, checked 7 November 2026. Your school's own Year 9 maths exams follow your state's curriculum: Stage 5 of the NSW Mathematics K to 10 Syllabus (2022), Level 9 of Victoria's Mathematics Version 2.0, or Year 9 of the Australian Curriculum elsewhere.

Year 9 maths questions with answers

We wrote these for this page. Questions 1 and 6 suit the non-calculator section; use a calculator for the rest.

1. Index laws and scientific notation

Question: Simplify (2x³)² × x⁴ ÷ x⁵, then write 0.00045 in scientific notation. Answer: (2x³)² = 4x⁶. Multiplying adds powers and dividing subtracts them: 4x^{6 + 4 − 5} = 4x⁵. Move the decimal point 4 places right to get 4.5 × 10⁻⁴. The Scientific Notation Calculator converts both ways.

2. Expanding and factorising

Question: Expand (x + 5)(x − 3), then factorise 6x² + 9x. Answer: multiply each term by each term: x² − 3x + 5x − 15 = x² + 2x − 15. For 6x² + 9x, the highest common factor is 3x, so it is 3x(2x + 3). Expand it back to check. Try expanding brackets in our Algebra course, then press Mark.

3. The equation of a line

Question: Find the equation of the line through (1, 4) and (3, 10). Answer: gradient m = (10 − 4) ÷ (3 − 1) = 3. Substitute (1, 4) into y = 3x + c: 4 = 3 + c, so c = 1 and the line is y = 3x + 1. Plot it in the Linear Graph tool.

4. Pythagoras and trigonometry

Question: A right-angled triangle has shorter sides of 12 cm and 9 cm. Find the hypotenuse and the angle opposite the 9 cm side. Answer: c² = 12² + 9² = 144 + 81 = 225, so c = 15 cm. tan θ = opposite ÷ adjacent = 9 ÷ 12 = 0.75, so θ ≈ 36.9°.

5. Volume and surface area of a cylinder

Question: A cylinder has radius 3 cm and height 10 cm. Find its volume and total surface area. Answer: V = πr²h = π × 9 × 10 = 90π ≈ 282.7 cm³. The surface area is two circles plus the curved side: 2πr² + 2πrh = 18π + 60π = 78π ≈ 245.0 cm².

6. Two-step probability

Question: Two fair six-sided dice are rolled. What is the probability that the total is 7? Answer: there are 6 × 6 = 36 equally likely outcomes, and 6 of them total 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1). So P(7) = 6/36 = 1/6. A two-way table of all 36 outcomes makes it easy to see.

Use the daily paper as a practice test

1. Open today's Year 9 Maths paper and work to the suggested time, about 30 to 40 minutes.
2. Do the arithmetic questions without a calculator, as in NAPLAN's first section.
3. Mark it and note the topics you lost marks on.
4. Practise index laws, factorising, Pythagoras and trigonometry with the questions on this page, because the paper doesn't cover them.

Common Year 9 maths mistakes

• Multiplying powers instead of adding them: x³ × x⁴ is x⁷, not x¹².
• Forgetting the middle term when expanding (x + 5)(x − 3).
• Swapping rise and run in the gradient. It is change in y over change in x.
• Adding the squares wrongly when finding a shorter side. For a shorter side, subtract: a² = c² − b².
• Using the diameter instead of the radius in πr².

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