Free Year 9 Pythagoras' theorem Practice | Skillo

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.

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What is tested: Pythagoras' theorem

  • ✓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

Sample questions

Question 1 — Easy

Tom and Kofi are printing posters for a community event. Tom's printer produces 96 pages in 8 minutes. Kofi's printer produces 135 pages in 9 minutes. How many more pages per minute does the faster printer produce?

A) 3 pages per minute
B) 6 pages per minute
C) 15 pages per minute
D) 27 pages per minute

Answer: Tom's printer: 96 ÷ 8 = 12 pages per minute. Kofi's printer: 135 ÷ 9 = 15 pages per minute. The difference is 15 − 12 = 3 pages per minute. Option B results from subtracting minutes (9 − 8 = 1) and adding it to an incorrectly estimated rate. Option C is Kofi's rate alone without subtracting Tom's. Option D is the raw difference in page counts (135 − 96 − 12) or a similar arithmetic error.

Question 2 — Medium

Anika is installing a television aerial on her roof in Perth. She positions a support wire from the top of the aerial down to a point on the roof. The aerial is 8 m tall and the support wire reaches a point 6 m away along the roof from the base of the aerial, forming a right-angled triangle. Using Pythagoras theorem, what is the length of the support wire?

A) 10 m
B) 7 m
C) 14 m
D) 11 m

Answer: The support wire is the hypotenuse, so its length = square root of (8² + 6²) = square root of (64 + 36) = square root of 100 = 10 m. Option A adds the two known sides (8 + 6 = 14). Option B halves the sum of the two sides. Option D is an incorrect estimate that does not follow from applying the formula correctly.

Question 3 — Hard

A 4.5 m ladder leans against a vertical wall. The base of the ladder is placed 1.8 m from the wall on level ground. How high up the wall does the ladder reach? Give your answer to the nearest centimetre.

A) 4.04 m
B) 4.86 m
C) 4.13 m
D) 3.96 m

Answer: Using Pythagoras: height² = 4.5² − 1.8² = 20.25 − 3.24 = 17.01. Height = √17.01 ≈ 4.124 m. Wait — checking option A: √17.01 ≈ 4.125 m ≈ 4.13 m. Correct answer is A.

How to use Skillo for Year 9 Numeracy

  1. Select Year 9 and Numeracy on the home screen
  2. Use Quick Practice — questions on pythagoras' theorem will appear as part of the session
  3. Check the Skill Breakdown on your profile to track your accuracy on pythagoras' theorem specifically
  4. 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.

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