Year 9 is the last NAPLAN, and the one whose numeracy test looks most like a high-school exam: 65 minutes, online and adaptive, a calculator section then a non-calculator section, on the Australian Curriculum Year 9 strand: solving linear equations, expanding and factorising, index laws and scientific notation, Pythagoras and the first trigonometry, gradient and intercept of a line, percentages and simple interest, ratio and scale, area and volume of circles and cylinders, angle sums, similar figures, two-step probability and means from tables. This practice test has 30 questions in the same two sections, with the answer and a one-line reason for each and a printable PDF. Allow 45 minutes, no help, then mark it together.
Download the Year 9 NAPLAN numeracy practice test as a PDF (30 questions, answer key with explanations, A4, free). The same 30 questions are below.
The Year 9 NAPLAN numeracy practice test
Time: 45 minutes. Questions 1 to 22: calculator allowed. Questions 23 to 30: no calculator. Choose one answer for each question.
1. Solve 5x − 7 = 2x + 8
A. x = 3 · B. x = 5 · C. x = 1 · D. x = 15
2. Expand 3(2x − 4)
A. 6x − 4 · B. 5x − 7 · C. 6x − 12 · D. 6x + 12
3. Factorise 8x + 12 fully
A. 2(4x + 12) · B. 4(2x + 3) · C. 8(x + 4) · D. 4(2x + 12)
4. Simplify x⁵ × x³
A. x¹⁵ · B. 2x⁸ · C. x² · D. x⁸
5. (2³)² = ?
A. 12 · B. 36 · C. 64 · D. 32
6. 3.6 × 10⁴ written as an ordinary number is
A. 3 600 · B. 36 000 · C. 360 000 · D. 0.00036
7. A right-angled triangle has shorter sides 6 cm and 8 cm. The hypotenuse is
A. 14 cm · B. 7 cm · C. 10 cm · D. 100 cm
8. A right-angled triangle has hypotenuse 13 cm and one side 5 cm. The other side is
A. 8 cm · B. 12 cm · C. 18 cm · D. √194 cm
9. The gradient of the line through (1, 2) and (3, 8) is
A. 2 · B. 1/3 · C. 6 · D. 3
10. The y-intercept of y = 4x − 7 is
A. 4 · B. 7 · C. 0 · D. −7
11. Increase $250 by 12%
A. $262 · B. $300 · C. $280 · D. $238
12. Simple interest on $2 000 at 5% per year for 3 years is
A. $100 · B. $300 · C. $2 300 · D. $30
13. Divide $180 in the ratio 2 : 7
A. $20 and $160 · B. $60 and $120 · C. $40 and $140 · D. $90 and $90
14. On a map with scale 1 : 50 000, a distance of 4 cm represents
A. 20 km · B. 2 km · C. 200 m · D. 0.2 km
15. The area of a circle with radius 5 cm (use π ≈ 3.14) is about
A. 31.4 cm² · B. 15.7 cm² · C. 25 cm² · D. 78.5 cm²
16. A cylinder has radius 3 cm and height 10 cm. Its volume is about
A. 94 cm³ · B. 283 cm³ · C. 188 cm³ · D. 942 cm³
17. The interior angles of a hexagon add to
A. 540° · B. 360° · C. 720° · D. 1 080°
18. Two triangles are similar. Sides 4 cm and 6 cm in the small one correspond to 10 cm and ? cm in the large one.
A. 12 cm · B. 8 cm · C. 15 cm · D. 10 cm
19. Two fair coins are tossed. The probability of two heads is
A. 1/2 · B. 1/4 · C. 1/3 · D. 3/4
20. Scores in a quiz: 2 (3 students), 3 (5 students), 4 (2 students). The mean score is
A. 3 · B. 9.7 · C. 2.9 · D. 3.5
21. In a right-angled triangle the side opposite angle θ is 3 and the side adjacent is 4. tan θ =
A. 1.33 · B. 0.6 · C. 0.8 · D. 0.75
22. 90 km/h is the same as
A. 90 m/s · B. 324 m/s · C. 25 m/s · D. 15 m/s
23. (−3)² = ?
A. −9 · B. 6 · C. 9 · D. −6
24. 2 to the power of −1 (2^−1) = ?
A. −2 · B. 1/2 · C. −1/2 · D. 2
25. Solve x/4 = 6
A. x = 1.5 · B. x = 10 · C. x = 2 · D. x = 24
26. Simplify 12a²b ÷ 4ab
A. 3ab · B. 3a · C. 3b · D. 8a
27. 20% of 45 = ?
A. 90 · B. 4.5 · C. 9 · D. 25
28. √144 = ?
A. 72 · B. 12 · C. 14 · D. 11
29. Which fraction equals 0.375?
A. 3/4 · B. 37/100 · C. 5/8 · D. 3/8
30. Expand and simplify (x + 3)(x + 2)
A. x² + 6 · B. x² + 5x + 6 · C. x² + 6x + 5 · D. 2x + 5
Answers, with the reason
| No. | Answer | Why |
|---|---|---|
| 1 | B x = 5 | 3x = 15, so x = 5. |
| 2 | C 6x − 12 | 3 × 2x = 6x and 3 × −4 = −12. |
| 3 | B 4(2x + 3) | The highest common factor is 4. |
| 4 | D x⁸ | Same base, add the indices: 5 + 3 = 8. |
| 5 | C 64 | 2⁶ = 64. |
| 6 | B 36 000 | Move the decimal point 4 places: 36 000. |
| 7 | C 10 cm | 6² + 8² = 100, √100 = 10. |
| 8 | B 12 cm | 13² − 5² = 144, √144 = 12. |
| 9 | D 3 | Rise 6 over run 2 = 3. |
| 10 | D −7 | The constant term: −7. |
| 11 | C $280 | 12% of 250 is 30; 250 + 30 = 280. |
| 12 | B $300 | 2 000 × 0.05 × 3 = 300. |
| 13 | C $40 and $140 | 9 parts = 180, one part = 20; 2 parts = 40, 7 parts = 140. |
| 14 | B 2 km | 4 × 50 000 cm = 200 000 cm = 2 km. |
| 15 | D 78.5 cm² | π × 5² = 3.14 × 25 = 78.5. |
| 16 | B 283 cm³ | π × 3² × 10 = 90π ≈ 283. |
| 17 | C 720° | (6 − 2) × 180° = 720°. |
| 18 | C 15 cm | Scale factor 10 ÷ 4 = 2.5; 6 × 2.5 = 15. |
| 19 | B 1/4 | HH, HT, TH, TT: one of four. |
| 20 | C 2.9 | (6 + 15 + 8) ÷ 10 = 2.9. |
| 21 | D 0.75 | tan = opposite ÷ adjacent = 3/4. |
| 22 | C 25 m/s | 90 000 m ÷ 3 600 s = 25 m/s. |
| 23 | C 9 | Negative × negative = 9. |
| 24 | B 1/2 | A negative index is a reciprocal: 1/2. |
| 25 | D x = 24 | Multiply both sides by 4. |
| 26 | B 3a | 12 ÷ 4 = 3, a² ÷ a = a, b ÷ b = 1. |
| 27 | C 9 | A fifth of 45 is 9. |
| 28 | B 12 | 12 × 12 = 144. |
| 29 | D 3/8 | 3 ÷ 8 = 0.375. |
| 30 | B x² + 5x + 6 | x² + 2x + 3x + 6. |
What the score means for a Year 9 student
| Score out of 30 | What it usually means | What to do before March |
|---|---|---|
| 26 to 30 | At or above the Year 9 strand; the adaptive test will branch this student to the reasoning items that separate Strong from Exceeding | Practise multi-step problems: similar figures, compound percentages, equations with brackets and fractions, timed |
| 20 to 25 | Solid; one or two topics missing (usually index laws, gradient, or trigonometry, which the school reaches late) | Fix those topics in four to six weeks, two classes a week |
| 13 to 19 | Gaps in the algebra chain from Year 7 and 8 (expanding, solving, negatives) that everything in Year 9 sits on | A term on the algebra chain in order, then the Year 9 topics; this is the most common Year 9 profile |
| under 13 | Working below Year 9 in numeracy | Start from the Year 7 strand; the school should already be providing support, ask what it is |
Where Year 9 students lose marks
- Algebra with signs. 5x − 7 = 2x + 8 done with one sign slip gives x = 1/3 or 5/7; the balancing steps need to be written, not done in the head.
- Index laws confused with each other. x⁵ × x³ = x¹⁵ is the classic; add for multiply, multiply for a power of a power.
- Pythagoras the wrong way round. Finding a shorter side means subtracting, and 13² − 5² is the question that catches it.
- The non-calculator section at the end. 2^−1, (−3)², √144 and 0.375 as a fraction, after an hour of calculator work, with the clock running.
How we prepare Year 9 students for NAPLAN
Two 1-on-1 classes a week from Term 4 on the Year 9 strand in the school's order, with the Year 7 and 8 algebra chain repaired first where it is broken, then the two-section format and timed practice in February. Year 9 numeracy is the level Year 10 maths pathways are chosen on, so the standard we teach to is Exceeding. The first 30-minute class is free; bring this test, marked. Details on the NAPLAN tutoring online page; the Year 7 test is here.
Questions parents ask
1How many questions are in the Year 9 NAPLAN numeracy test?
2Where are the official NAPLAN past papers?
3Is this the real NAPLAN 2027 test?
4My child scored under 20. Is that bad?
See how we teach this, 1-on-1 online →
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