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Year 9 Maths sample questions

Year 9 Maths practice preview

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Year 9 Maths practice questions

This public preview page identifies the planned Year 9 Maths demo route and links it to curriculum coverage while the reviewed sample question set is being completed.

Sample-question focus

The planned public sample is for Year 9 Maths practice and will open after the demo questions are reviewed.

Skills covered

Practice number, algebra, measurement, space, statistics, probability, patterns, and problem solving.

Exercise and test mode

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Curriculum link

Compare this demo with the Year 7-9 Maths curriculum page to scan related topics, subtopics, and pathway coverage.

Sample Year 9 Maths questions

These sample questions are visible on the page before login. They show Year 9 index laws, linear graphs, trigonometry, similarity, statistics, and probability explanations before opening the demo.

Year 9 Maths Index laws hard sequence graph

1. If 3ᵃ = 27 and 3ᵇ = 9, what is 3ᵃ⁺ᵇ?

Powers of three a b 3⁵
Choices
  • 243
  • 81
  • 729
  • 36
Explanation:

Since 27 = 3³, a = 3. Since 9 = 3², b = 2. Therefore 3ᵃ⁺ᵇ = 3⁵ = 243.

Year 9 Maths Linear graphs hard break-even graph

2. A taxi fare is modelled by C = 4.20 + 1.80d, where d is the distance in kilometres. If the fare is $31.20, what is d?

Taxi fare graph d C $
Choices
  • 15 km
  • 17.3 km
  • 19.7 km
  • 27 km
Explanation:

Subtract the fixed charge: 31.20 - 4.20 = 27.00. Then divide by 1.80, giving d = 15 km.

Year 9 Maths Trigonometry hard diagram

3. From a point 42 m from the base of a building, the angle of elevation to the top is 36°. What is the building height to the nearest 0.1 m?

Angle of elevation to a building 42 m h 36°
Choices
  • 30.5 m
  • 24.7 m
  • 57.8 m
  • 34.0 m
Explanation:

Use tan(36°) = height / 42. The height is 42 × tan(36°) = 30.516..., which rounds to 30.5 m.

Year 9 Maths Similarity hard scale plan

4. Two similar rectangles have a scale factor of 3/2 from the smaller to the larger. If the smaller area is 48 cm², what is the larger area?

Similar rectangles S L 3/2
Choices
  • 108 cm²
  • 72 cm²
  • 96 cm²
  • 162 cm²
Explanation:

Areas scale by the square of the length scale factor. The area factor is (3/2)² = 9/4, so the larger area is 48 × 9/4 = 108 cm².

Year 9 Maths Statistics hard weighted score chart

5. The data values 10, 12, 12, 15, 16 and 20 have one more value x added. If the new mean is 15, what is x?

Mean with one missing value Σ x 15
Choices
  • 20
  • 15
  • 18
  • 25
Explanation:

The six known values sum to 85. Seven values with mean 15 must sum to 105, so x = 105 - 85 = 20.

Year 9 Maths Probability hard probability tree

6. A bag contains 5 blue counters and 3 red counters. Two counters are drawn without replacement. What is the probability that both are blue?

Counters without replacement B R BB
Choices
  • 5/14
  • 25/64
  • 5/8
  • 3/14
Explanation:

The probability is 5/8 for the first blue and 4/7 for the second blue after one blue is removed. So P(two blue) = 5/8 × 4/7 = 20/56 = 5/14.

For parents comparing Year 9 Maths support

Year 9 maths practice should build senior-readiness through index laws, linear modelling, trigonometry, similarity, statistics, and probability. These examples show the worked reasoning before the no-login Year 9 Maths demo.

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In progress

Year 9 Maths is available to purchase, and the public demo preview is still being prepared.

Students can use the purchased subject once subscribed; this anonymous preview will be opened after the curated public question set is ready.

Maths practice questions FAQ

Does this page include Year 9 Maths practice questions?

Not yet. The Year 9 Maths demo route is public, but the interactive sample questions will open after the reviewed public set is ready.

Can students try the demo without signing up?

No sign-up is required to view the preview status. The no-login interactive demo will be available after the sample set is completed.

How does this demo relate to curriculum coverage?

This demo is linked with the Year 7-9 Maths curriculum coverage page, where parents can compare the broader topic and pathway structure used for Skill Align practice.