Free Year 9 Trigonometric ratios Practice | Skillo

Year 9 students sitting their final NAPLAN need to be confident with trigonometric ratios. Recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity. 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: Trigonometric ratios

  • ✓Recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity.
  • ✓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 is painting a triangular mural on a wall. The triangle has a base of 14 m and a height of 6 m. Use the formula for the area of a triangle to find its area.

A) 84 m²
B) 48 m²
C) 20 m²
D) 42 m²

Answer: The area of a triangle is A = ½ × base × height = ½ × 14 × 6 = 42 m². Option A forgets the ½ and gives base × height. Option C adds the base and height. Option D uses an incorrect calculation of ½ × base × height with a different height.

Question 2 — Medium

Luca is saving to buy a drone. He has $320 and saves an additional $55 per week. The drone costs $760. After how many complete weeks of saving will Luca be able to buy the drone?

A) 7 weeks
B) 6 weeks
C) 9 weeks
D) 8 weeks

Answer: Amount still needed = $760 − $320 = $440. Weeks needed = $440 ÷ $55 = 8 weeks exactly. After 8 complete weeks, Luca has exactly $760.

Question 3 — Hard

Zac is tiling a bathroom floor that measures 3.6 m by 2.4 m. He uses square tiles with a side length of 30 cm. Tiles are sold in boxes of 20. How many boxes does Zac need to buy?

A) 4 boxes
B) 7 boxes
C) 6 boxes
D) 5 boxes

Answer: Floor area = 3.6 × 2.4 = 8.64 m² = 86 400 cm². Tile area = 30 × 30 = 900 cm². Number of tiles = 86 400 ÷ 900 = 96 tiles. Boxes needed = 96 ÷ 20 = 4.8, so 5 boxes must be purchased.

How to use Skillo for Year 9 Numeracy

  1. Select Year 9 and Numeracy on the home screen
  2. Use Quick Practice — questions on trigonometric ratios will appear as part of the session
  3. Check the Skill Breakdown on your profile to track your accuracy on trigonometric ratios 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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No account needed. No email. No credit card.