Free NSW Maths Resource

Free Year 7 Maths Test NSW Full-Year Practice Exam & Answers

Test your Year 7 maths skills with a free 75-mark practice exam covering fractions, decimals, percentages, negative numbers, algebra, indices, equations, number plane, geometry, measurement, statistics and probability.

The complete question paper is displayed directly on this page. Use pen and paper for your working, enter your final answers, then check your result and review the worked solutions.

Fractions Decimals Percentages Negative Numbers Like Terms Indices Equations Number Plane Geometry Probability

Year 7 Maths NSW Syllabus Guide Free NSW Maths Resources

↓ Your Year 7 Maths question paper starts immediately below. No sign-up, no Start Test button and no timer.

Questions 27

Total marks 75

Suggested time 90 minutes

Working Use paper

Section A – Multiple Choice

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

1. Evaluate −7 + 12 − 9.

1 mark

A. −16 B. −4 C. 4 D. 14

Answer & explanation

−7 + 12 = 5.
5 − 9 = −4.

2. Find the highest common factor (HCF) of 18 and 30.

1 mark

A. 3 B. 6 C. 9 D. 12

Answer & explanation

Factors of 18 include 1, 2, 3, 6, 9 and 18.
Factors of 30 include 1, 2, 3, 5, 6, 10, 15 and 30.
The highest common factor is 6.

3. Which fraction has the greatest value?

1 mark

A. 3/5 B. 5/8 C. 2/3 D. 7/12

Answer & explanation

3/5 = 0.6
5/8 = 0.625
2/3 ≈ 0.667
7/12 ≈ 0.583

The greatest is 2/3.

4. Write 0.35 as a percentage.

1 mark

A. 3.5% B. 35% C. 350% D. 0.35%

Answer & explanation

0.35 × 100 = 35%.

5. Simplify the ratio 12 : 18.

1 mark

A. 3 : 4 B. 4 : 5 C. 2 : 3 D. 6 : 7

Answer & explanation

Divide both parts by 6:
12 : 18 = 2 : 3.

6. Simplify 4x + 3 + 5x − 7.

1 mark

A. 9x − 4 B. 9x + 10 C. 20x − 4 D. 9x

Answer & explanation

4x + 5x = 9x.
3 − 7 = −4.
Therefore: 9x − 4.

7. Simplify a³ × a².

1 mark

A. a⁶ B. a⁵ C. 2a⁵ D. a

Answer & explanation

When powers with the same base are multiplied, add the indices.
a³ × a² = a⁵.

8. Solve x + 9 = 17.

1 mark

A. 6 B. 7 C. 8 D. 26

Answer & explanation

x = 17 − 9
x = 8.

9. The point (−3, 2) lies in which quadrant?

1 mark

A. Quadrant I B. Quadrant II C. Quadrant III D. Quadrant IV

Answer & explanation

x is negative and y is positive.
The point lies in Quadrant II.

10. Two parallel lines are cut by a transversal. One alternate angle is 68°. Find the other alternate angle.

1 mark

A. 22° B. 68° C. 112° D. 180°

Answer & explanation

Alternate angles between parallel lines are equal.
Therefore the angle is 68°.

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

A. 16 cm² B. 24 cm² C. 32 cm² D. 64 cm²

Answer & solution

Area = ½(a + b)h
= ½(6 + 10)(4)
= 32 cm².

12. A survey records each student's favourite sport. What type of data is being collected?

1 mark

A. Categorical data B. Continuous numerical data C. Discrete numerical data D. Measurement data only

Answer & explanation

Favourite sport describes a category rather than a numerical measurement.
The answer is categorical data.

13. A bag contains 3 red, 2 blue and 5 green counters. What is the probability of randomly selecting a blue counter?

1 mark

A. 1/10 B. 2/5 C. 1/2 D. 1/5

Answer & explanation

Total counters = 10.
Blue counters = 2.
Probability = 2/10 = 1/5.

14. A rectangular prism measures 4 cm × 3 cm × 5 cm. Find its volume.

1 mark

A. 12 cm³ B. 20 cm³ C. 60 cm³ D. 120 cm³

Answer & solution

Volume = length × width × height
= 4 × 3 × 5
= 60 cm³.

15. Which decimal is equal to 3/8?

1 mark

A. 0.30 B. 0.375 C. 0.625 D. 0.83

Answer & explanation

3 ÷ 8 = 0.375.

Section B – Short Answer

Questions 16–24 · 40 marks · Use paper for working and enter your final answers.

16. Integers, factors and indices

5 marks

a) Evaluate −12 + 7.

Answer

b) Evaluate 9 − (−6).

Answer

c) Find the LCM of 8 and 12.

LCM

d) Find the HCF of 24 and 36.

HCF

e) Simplify 3² × 3⁴ as a single power.

Single power

Answers & worked solutions

a) −5

b) 9 − (−6) = 9 + 6 = 15

c) Multiples of 8: 8, 16, 24...
Multiples of 12: 12, 24...
LCM = 24

d) HCF(24,36) = 12

e) When multiplying powers with the same base, add the indices:
3² × 3⁴ = 3⁶

17. Fraction operations

6 marks

a) Simplify 18/24.

Simplified fraction

b) Calculate 2/3 + 5/12.

Answer

c) Calculate 7/8 − 1/3.

Answer

d) Calculate 3/5 × 10/9.

Answer

e) Calculate 4/7 ÷ 2/3.

Answer

Answers & worked solutions

a) 18/24 = 3/4

b) 2/3 = 8/12
8/12 + 5/12 = 13/12 = 1 1/12

c) 7/8 = 21/24
1/3 = 8/24
21/24 − 8/24 = 13/24

d) 3/5 × 10/9 = 30/45 = 2/3

e) 4/7 ÷ 2/3 = 4/7 × 3/2 = 12/14 = 6/7

18. Fractions, decimals and percentages

5 marks

a) Write 0.375 as a fraction in simplest form.

Fraction

b) Write 7/20 as a decimal.

Decimal

c) Write 0.62 as a percentage.

Percentage

d) Write 35% as a decimal.

Decimal

e) Find 18% of 250.

Answer

Answers & worked solutions

a) 0.375 = 375/1000 = 3/8

b) 7 ÷ 20 = 0.35

c) 0.62 × 100 = 62%

d) 35 ÷ 100 = 0.35

e) 0.18 × 250 = 45

19. Algebra and like terms

4 marks

a) Simplify: 6x + 2 + 4x − 9

Simplified expression

b) If a = 4 and b = 5, evaluate 3a + 2b.

Value

c) Expand: 2(y + 6)

Expanded expression

Answers & worked solutions

a) 6x + 4x = 10x
2 − 9 = −7
10x − 7

b) 3(4) + 2(5) = 12 + 10 = 22

c) 2 × y + 2 × 6 = 2y + 12

20. Solve the equations

4 marks

a) y − 6 = 13

y =

b) 5m = 35

m =

c) 3x + 4 = 22

x =

Answers & worked solutions

a) y = 13 + 6 = 19

b) m = 35 ÷ 5 = 7

c) 3x + 4 = 22
3x = 18
x = 6

21. Number plane and simple linear relationships

3 marks

a) Write the coordinates of point A.

x-coordinate

y-coordinate

b) In which quadrant is point B?

c) A straight-line pattern contains the points (−2, −1), (0, 1) and (2, 3). If the pattern continues, what is y when x = 4?

y =

Answers & explanation

a) A = (−3, 2)

b) B has positive x and negative y, so it lies in Quadrant IV.

c) The pattern follows y = x + 1.
When x = 4, y = 5.

22. Parallel lines and angle relationships

4 marks

a) What relationship describes angles a and b?

b) Find angle b.

b (degrees)

c) Angles a and c are co-interior angles. Find angle c.

c (degrees)

Answers & worked solutions

a) a and b are alternate angles.

b) Alternate angles are equal: b = 68°.

c) Co-interior angles add to 180°:
c = 180 − 68 = 112°.

23. Area of quadrilaterals

5 marks

Find the area of each shape.

a) Trapezium

Area (cm²)

b) Rhombus

Area (cm²)

c) Kite

Area (cm²)

d) Parallelogram

Area (cm²)

Answers & worked solutions

a) Trapezium:
½(8 + 14)(5) = 55 cm²

b) Rhombus:
½ × 10 × 6 = 30 cm²

c) Kite:
½ × 12 × 8 = 48 cm²

d) Parallelogram:
base × perpendicular height
9 × 4 = 36 cm²

24. Statistics and probability

4 marks

a) A survey records students' eye colour. What type of data is this?

b) Find the mean of: 4, 6, 7, 7, 9, 12

Mean

c) Find the median of: 4, 6, 7, 7, 9, 12

Median

d) A bag contains 3 red, 2 blue and 5 green counters. Find P(not green).

Probability

Answers & explanations

a) Eye colour is categorical data.

b) Total = 45.
45 ÷ 6 = 7.5

c) The middle two values are 7 and 7.
Median = 7

d) Not green = red or blue = 3 + 2 = 5 outcomes.
P(not green) = 5/10 = 1/2

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 of the students travel by bus.
25% of the students walk.
The remaining students travel by car.

a) How many students travel by bus?

Students

b) How many students walk?

Students

c) How many students travel by car?

Students

d) What fraction of the class either travels by bus or walks? Give your answer in simplest form.

Fraction

e) The number of students walking increases by 50% the following month. How many students would then be walking?

Students

Answers & worked solutions

a) 3/8 × 32 = 12 students

b) 25% of 32 = 0.25 × 32 = 8 students

c) 32 − 12 − 8 = 12 students

d) Bus or walk = 12 + 8 = 20.
20/32 = 5/8

e) 50% of 8 = 4.
New total = 8 + 4 = 12 students

26. School garden area

7 marks

A school garden is shaped like a trapezium. Inside it is a rectangular herb bed.

a) Find the area of the entire trapezium garden.

Area (m²)

b) Find the area of the rectangular herb bed.

Area (m²)

c) The rest of the garden will be planted with grass. Find the area that will be grass.

Grass area (m²)

d) One bag of grass seed covers 8 m². What is the minimum number of whole bags required?

Bags

Answers & worked solutions

a) Area of trapezium = ½(14 + 8)(6)
= ½(22)(6) = 66 m²

b) Herb bed = 5 × 4 = 20 m²

c) Grass = 66 − 20 = 46 m²

d) 46 ÷ 8 = 5.75.
You cannot buy 0.75 of a bag, so at least 6 bags are required.

27. Year 7 revision survey

6 marks

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

Revision method	Students
Practice questions	16
Videos	10
Written notes	8
Group study	6

a) A student is chosen at random. Find the probability that the student prefers practice questions.

Probability

b) What percentage of the class prefers videos?

Percentage

c) Write the ratio written notes : group study in simplest form.

Ratio

d) How many more students prefer practice questions than group study?

Difference

e) Explain on paper why the preferences of one class should not automatically be assumed to represent every Year 7 student in NSW.

Write your reasoning on paper. You will self-mark this 2-mark response after checking the test.

Answers & model reasoning

a) 16/40 = 2/5 = 0.4

b) 10/40 × 100 = 25%

c) 8 : 6 = 4 : 3

d) 16 − 6 = 10 students

e) A strong response recognises that the survey only used one class. That group may not be representative of all Year 7 students in different schools, locations or learning environments. A larger and more varied sample would provide stronger evidence.

73 marks are checked automatically. Question 27(e) contains 2 reasoning marks that you self-mark after comparing your answer with the model response.

Your Year 7 Maths Test Result

0 / 75

0 %

Automatically checked 0/73

Reasoning self-mark 0/2

Final score 0/75

Topic breakdown

Number, Fractions & Percentages 0/28

Algebra & Indices 0/12

Geometry & Measurement 0/19

Graphs, Data & Probability 0/16

Your priority revision topic will appear here.

Self-mark Question 27(e)

Compare your written explanation with the model answer underneath Question 27.

Question 27(e)
Why should one class not be treated as representative of every Year 7 student in NSW?

This result is a practice diagnostic rather than a school grade. Schools can use different topics, marking criteria and assessment formats.

What does this Year 7 Maths test assess?

This full-year Year 7 Maths practice test samples a broad collection of skills commonly developed during NSW Stage 4. It includes number and algebra, measurement and geometry, statistics, probability and introductory Cartesian-plane work.

The paper gives particular attention to fractions, decimals, percentages, negative numbers, like terms and geometry because these are areas where foundational gaps can become particularly visible when students move from primary school into Year 7.

This is a full-year practice test, not a universal school exam.

Individual NSW schools can organise Stage 4 topics differently. A student may therefore encounter some questions here before or after those topics appear in their own school program.

If you want to see how Year 7 topics can fit together, read the Year 7 Maths NSW Syllabus Guide .

Common Year 7 Maths mistakes this test is designed to identify

Adding and subtracting fractions

A student may understand individual fractions but become confused when denominators are different. The important first step is recognising that addition and subtraction require compatible denominators.

Factors, multiples and LCM

Knowing multiplication tables is not the same as understanding how factors and multiples are used. A student may know the tables accurately but still not recognise why an LCM is useful when adding fractions.

Fraction, decimal and percentage conversions

Students can make mistakes when the same quantity appears in different forms. For example: 1/4 = 0.25 = 25%.

Like terms in algebra

Students need to recognise that 3x and 5x are like terms, while 3x and 5y are not. Simply adding every number and letter visible in an expression does not produce a valid simplification.

Negative numbers

Sign errors can quickly affect later algebra and coordinate work. Expressions such as 7 − (−3) need to be interpreted carefully rather than treating both minus signs as ordinary subtraction.

Corresponding and alternate angles

Geometry can become difficult because students first need to recognise the visual relationship in the diagram. The arithmetic is often simple once the correct angle rule has been identified.

Trapeziums, rhombuses and kites

Less familiar quadrilaterals can cause difficulty because students need to identify the correct measurements and formula before calculating the area.

Revise the Year 7 Maths topics you missed

Use your topic breakdown above to revise the area causing the difficulty rather than repeating the entire test immediately.

Basics of Fractions Equivalent fractions, simplification and fraction foundations. Adding & Subtracting Fractions LCM, common denominators and worked examples. Multiplying & Dividing Fractions Learn the different rules for fraction multiplication and division. Fractions ↔ Decimals Practise moving confidently between fractions and decimals. Percentages Made Easy Percentage conversions and calculations for NSW students. Algebra Made Easy Pronumerals, expressions, like terms and algebra foundations. Year 7 Algebra Substitution Replace pronumerals with values and evaluate expressions. Simple Linear Equations One-step and introductory multi-step equations. Indices Made Easier Powers, roots and the introductory index laws. Number Plane Guide Coordinates, quadrants and introductory Cartesian-plane work. Triangles & Quadrilaterals Review shapes, angles and geometrical relationships. Geometry Formulae Review area and measurement formulas for common shapes. Year 7 Probability Probability, chance experiments and complementary events. NSW Maths Resource Hub Browse free maths resources across Years 1–10.

How long is a Year 7 Maths test in NSW?

There is no single NSW-wide Year 7 examination length, question count or marks total. Schools may use topic tests, common assessment tasks, projects, investigations, semester examinations or yearly examinations.

A school assessment can therefore be much shorter and more topic-specific than this page. This AMT test uses 27 questions, 75 marks and approximately 90 minutes because it is designed as a broad full-year practice assessment.

Preparing for an actual school exam?

Follow the school's assessment notification for the examinable topics, calculator rules, time allowance and permitted reference material.

Official NSW Mathematics references

This is an independent practice resource. For official and current NSW Mathematics information, use the NSW Curriculum and Department of Education resources.

NSW Mathematics K–10 Course Overview Official NSW Curriculum information for Mathematics 7–10. NSW Stage 4 Sample Scope & Sequences Department of Education examples for Stage 4 programming.

Is the student ready for Year 8 Maths?

The most useful Year 7 foundations to strengthen before Year 8 include fraction operations, negative numbers, percentages, like terms, basic equations, index laws and geometry.

Students who are comfortable with most of this test can continue with the Year 8 Maths NSW Syllabus Guide and later attempt the Free Year 8 Maths Test NSW .

Did the Year 7 Maths test identify learning gaps?

A low score in one topic does not always mean the current topic itself is the starting problem. For example, difficulty adding fractions may come from an earlier misunderstanding of multiples and LCM.

Aussie Math Tutor NSW provides personalised maths support around Telopea and nearby areas, as well as online tutoring, with lessons designed to identify where the difficulty begins and rebuild the skill step by step.

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Year 7 Maths Test – Frequently Asked Questions

Is the complete Year 7 Maths test on this page?

Yes. All 27 questions are displayed directly on the page. Students can use pen and paper for working and enter their final answers online.

Is this Year 7 Maths test free?

Yes. The test, automatic answer checking, topic breakdown and worked solutions are free to use.

Is this an official NSW Year 7 Maths exam?

No. It is an independent Aussie Math Tutor NSW practice test. Individual schools determine their own assessment structure and topic sequencing within the NSW curriculum.

What topics are included in this Year 7 Maths test?

The test includes integers, factors and multiples, fractions, decimals, percentages, ratios, algebra, like terms, indices, equations, number plane, geometry, area, measurement, statistics and probability.

What are some difficult Year 7 Maths topics?

Difficulty varies by student, but fraction operations, conversions between fractions, decimals and percentages, negative numbers, like terms, parallel-line angles and area of less familiar quadrilaterals can expose important gaps.

How long should this practice test take?

Approximately 90 minutes is suggested because this is a broad full-year assessment. Actual school tests may be shorter or may cover only selected topics.

Can students use a calculator?

A calculator can be used for this practice assessment. For an actual school test, follow the calculator instructions supplied by the student's school.

What should a student do after completing the test?

Use the topic breakdown to identify the weakest area, review the related learning resource and then attempt similar questions again without looking at the worked solution.

Resource transparency: This is independently created Aussie Math Tutor NSW practice material. AI-assisted drafting was used during development, followed by educational review and editing. The questions are original practice questions and are not copied from Cambridge, ICE-EM, NESA, the NSW Department of Education or an individual school's examination paper.

Free exam papers

Free Year 7 Maths Test NSW Full-Year Practice Exam & Answers

Section A – Multiple Choice

Section B – Short Answer

Section C – Problem Solving & Reasoning

Your Year 7 Maths Test Result

Topic breakdown

Self-mark Question 27(e)

What does this Year 7 Maths test assess?

Common Year 7 Maths mistakes this test is designed to identify

Adding and subtracting fractions

Factors, multiples and LCM

Fraction, decimal and percentage conversions

Like terms in algebra

Negative numbers

Corresponding and alternate angles

Trapeziums, rhombuses and kites

Revise the Year 7 Maths topics you missed

How long is a Year 7 Maths test in NSW?

Official NSW Mathematics references

Is the student ready for Year 8 Maths?

Did the Year 7 Maths test identify learning gaps?

Year 7 Maths Test – Frequently Asked Questions

Choose a suitable time for your free assessment.

Book Your Free Assessment

Free Year 7 Maths Test NSW Full-Year Practice Exam & Answers

Section A – Multiple Choice

Section B – Short Answer

Section C – Problem Solving & Reasoning

Your Year 7 Maths Test Result

Topic breakdown

Self-mark Question 27(e)

What does this Year 7 Maths test assess?

Common Year 7 Maths mistakes this test is designed to identify

Adding and subtracting fractions

Factors, multiples and LCM

Fraction, decimal and percentage conversions

Like terms in algebra

Negative numbers

Corresponding and alternate angles

Trapeziums, rhombuses and kites

Revise the Year 7 Maths topics you missed

How long is a Year 7 Maths test in NSW?

Official NSW Mathematics references

Is the student ready for Year 8 Maths?

Did the Year 7 Maths test identify learning gaps?

Year 7 Maths Test – Frequently Asked Questions

Book Your Free Assessment

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