Aussie Math Tutor NSW Free Tutor Assessment
Free NSW Maths Diagnostic

Free Year 7 Maths Test NSW

A clearer picture. A practical learning plan.

Discover what is going well and what to practise next. Complete the test at your own pace, review worked answers, and receive a free revision plan based on the questions you attempt.

Number & fractions · Algebra · Geometry · Data & probability

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27questions
75total marks
90 minsuggested time
73auto-marked
Freelearning plan
Welcome back. Your previous Year 7 answers or learning-plan progress were found in this browser.
Year 7 Diagnostic
Use paper for working. Calculator permitted.
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Before you begin

Allow about 90 minutes for the full test, or return later on this browser. Use paper for working; a calculator is permitted. This samples Year 7 / Stage 4 skills, and your school may teach topics in a different order.

You can leave an answer blank, or mark it “Not yet taught”. Neither is treated as evidence of a misconception. You need at least 8 attempted answer parts for a preliminary learning plan; a completed test gives a broader picture.

Use / for fractions, a space for mixed numbers (for example 2 1/3), and ^ for powers (for example 2^4). Give simplest form where requested. Measurement answers may include the stated units. Automatic marks assess final answers only; they do not award method marks for your paper working.

Answers and plan progress are saved on this device when browser storage is available. Avoid entering names or personal information in the written response.

Section A – Multiple Choice

Questions 1–15 · 15 marks · Select the best answer.

1. Evaluate −7 + 12 − 9.
1 mark
2. Find the highest common factor (HCF) of 18 and 30.
1 mark
3. Which fraction has the greatest value?
1 mark
4. Write 0.35 as a percentage.
1 mark
5. Simplify the ratio 12 : 18.
1 mark
6. Simplify 4x + 3 + 5x − 7.
1 mark
7. Simplify a³ × a².
1 mark
8. Solve x + 9 = 17.
1 mark
9. The point (−3, 2) lies in which quadrant?
1 mark
10. Two parallel lines are cut by a transversal. One alternate angle is 68°. Find the other alternate angle.
1 mark
11. A trapezium has parallel sides of 6 cm and 10 cm and a perpendicular height of 4 cm. What is its area?
1 mark
12. A survey records each student's favourite sport. What type of data is being collected?
1 mark
13. A bag contains 3 red, 2 blue and 5 green counters. What is the probability of randomly selecting a blue counter?
1 mark
14. A rectangular prism measures 4 cm × 3 cm × 5 cm. Find its volume.
1 mark
15. Which decimal is equal to 3/8?
1 mark

Section B – Short Answer

Questions 16–24 · 40 marks · Show your working on paper and enter your final answers.

16. Integers, factors and indices
5 marks
17. Fraction operations
6 marks
18. Fractions, decimals and percentages
5 marks
19. Algebra and like terms
4 marks
20. Solve the equations
4 marks
21. Number plane and simple linear relationships
3 marks
22. Parallel lines and angle relationships
4 marks
23. Area of quadrilaterals
5 marks
TrapeziumParallel sides 8 cm and 14 cm; perpendicular height 5 cm.
8 cm14 cm5 cm
RhombusThe full diagonals measure 10 cm and 6 cm.
10 cm6 cm
KiteThe full diagonals measure 12 cm and 8 cm.
12 cm8 cm
ParallelogramBase 9 cm; perpendicular height 4 cm.
9 cm4 cm
24. Statistics and probability
4 marks

Section C – Problem Solving & Reasoning

Questions 25–27 · 20 marks · Apply several Year 7 skills within each problem.

25. How students travel to school
7 marks

A Year 7 class has 32 students. 3/8 travel by bus, 25% walk, and the remaining students travel by car.

26. School garden area
7 marks

A school garden is a trapezium with parallel sides 14 m and 8 m and perpendicular height 6 m. Inside it is a rectangular herb bed measuring 5 m × 4 m.

27. Year 7 revision survey
6 marks

A class of 40 Year 7 students is asked which revision method they prefer.

Revision methodStudents
Practice questions16
Videos10
Written notes8
Group study6

After you submit the test, a model response and a 0–2 self-mark selector will appear.

Finished? Get your result and learning plan.

We will mark 73 points automatically, summarise your attempted answers, and build a recommended study sequence. You can then self-mark the final 2 reasoning marks.

This is a practice diagnostic, not a school grade. NSW schools may teach Stage 4 topics in different sequences.

Year 7 Maths Personalised Learning Plan

Aussie Math Tutor NSW · aussiemathtutor.com.au

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Diagnostic result

Your Year 7 Maths Diagnostic

Self-mark Question 27(e) — 2 marks

Model response: One class is only a small sample and may not represent students from different schools, locations or learning environments. A larger and more varied sample would provide stronger evidence.


1. Your skill snapshot

Results describe the questions attempted, not mastery of an entire topic. Unanswered and not-yet-taught parts are shown separately.

2. Your next priorities

Only skills with incorrect attempted answers become revision priorities. Prerequisites are suggested checks, not assumed gaps.

3. Your personalised study plan

Start whenever you like. Sessions are used instead of weekdays so the plan works for any student. Aim for about 15–25 focused minutes per session.

Optional personalised support

Want help turning these results into improvement?

✓ Discuss your results
✓ Agree on practical next steps
✓ Face-to-face near Telopea or online across NSW

No obligation. The free learning plan above remains available whether or not you choose tutoring.

4. Check Your Improvement

Use the fresh check questions in your plan after revision. Repeating this same test can help review methods, but remembering answers is not evidence of new learning.

Practise by topic

Use the links in your priority cards. Many Aussie Math Tutor NSW topic pages include worked examples and interactive practice.

Browse all free maths practice

Retake the diagnostic later

Your current result and learning-plan progress stay saved in this browser until you clear them. When ready, clear the answers and try the assessment again.

Worked Solutions

Review these after completing the assessment. Focus especially on the questions linked to your top learning priorities.