Free Year 9 Pythagoras' theorem Practice | Skillo
Skillo provides free Year 9 NAPLAN Pythagoras' theorem practice (AC9M8M06) for Australian students. No signup, no email, no credit card. Practice questions aligned with the ACARA Australian Curriculum v9.0 strand. Open and start in 10 seconds.
Year 9 students sitting their final NAPLAN need to be confident with pythagoras' theorem. Use Pythagoras' theorem to solve problems involving the side lengths of right-angled triangles. Skillo has targeted practice questions for this exact skill, mapped to the Australian Curriculum v9.0, free and ready to go.
No account needed. No email. No credit card.
What does the Year 9 NAPLAN Pythagoras' theorem test cover?
- Use Pythagoras' theorem to solve problems involving the side lengths of right-angled triangles.
- Questions may include word problems set in real Australian contexts
- Both calculator and non-calculator question types are covered
Try a sample Pythagoras' theorem question
Question 1 — Easy
A block of land in Canberra is in the shape of a right-angled triangle. The two shorter sides measure 24 metres and 10 metres. What is the length of the hypotenuse?
Answer: Using Pythagoras: hypotenuse² = 24² + 10² = 576 + 100 = 676. √676 = 26 m.
Question 2 — Medium
Zac is driving from Sydney to Canberra. His car travels 336 km on 42 litres of fuel. Anika's car travels 325 km on 25 litres of fuel. Which car is more fuel efficient, and what is its rate in kilometres per litre?
Answer: Option D is correct — Zac's car: 336 ÷ 42 = 8 km per litre. Anika's car: 325 ÷ 25 = 13 km per litre. Anika's car travels more kilometres per litre, making it the more fuel efficient vehicle at 13 km per litre.
Question 3 — Hard
In a right-angled triangle, the side opposite an angle θ is 5 cm and the hypotenuse is 10 cm. What is the size of angle θ?
Answer: sin θ = opposite ÷ hypotenuse = 5 ÷ 10 = 0.5. Since sin 30° = 0.5, angle θ = 30°.
How should my child prepare for Year 9 NAPLAN Pythagoras' theorem?
- Select Year 9 and Numeracy on the home screen
- Use Quick Practice — questions on pythagoras' theorem will appear as part of the session
- Check the Skill Breakdown on your profile to track your accuracy on pythagoras' theorem specifically
- Review explanations after each question to understand the reasoning behind correct answers
Skillo is free, requires no email or account details, and is built specifically for Australian students. Every question is mapped to the Australian Curriculum v9.0 and filtered by skill so your child practises exactly what they need.
Common questions about NAPLAN Pythagoras' theorem
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Is Skillo really free?
Yes. Skillo is completely free for all Australian students — no subscription, no credit card, no hidden paywall. No free trial that converts to paid.
Does my child need an account?
No. Skillo doesn't require an account to practise. Open any page and start immediately — no email, no registration.
Does Skillo collect any personal information?
No. Skillo is built to require zero personal information. No name, no email, no date of birth is collected from students.
Is Skillo affiliated with NAPLAN?
Skillo's NAPLAN-style practice is authored independently. NAPLAN® is a registered trademark of ACARA. Skillo is not affiliated with, endorsed by, or sponsored by ACARA.
No account needed. No email. No credit card.
About this practice
Skillo's NAPLAN-style practice is authored independently. NAPLAN® is a registered trademark of ACARA. Skillo is not affiliated with, endorsed by, or sponsored by ACARA.