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Free NSW Maths Practice Test

Free Year 6 Maths Test NSW Full-Year Practice Exam & Answers

Take this free Year 6 Maths practice test covering multiplication, short division, fractions, percentages, factors and multiples, measurement, perimeter, coordinates and probability.

The complete 26-question exam is displayed directly below. Do your working on paper, enter your final answers online, then check your score and worked solutions.

Multiplication Short Division Fractions HCF & LCM Percentages Perimeter Area Coordinates Probability
Year 6 Maths NSW Syllabus Guide Free NSW Maths Resources
✕ This is a non-calculator Year 6 practice exam. Use pen and paper for your calculations. The question paper starts immediately below.
Questions 26
Total marks 70
Suggested time 75 minutes
Calculator Not permitted

Section A – Multiple Choice

Questions 1–12 · 12 marks · Choose the best answer.

1. Calculate 4,728 + 2,596.
1 mark
Answer & explanation
4,728 + 2,596 = 7,324.
2. Calculate 8,000 − 3,457.
1 mark
Answer & explanation
8,000 − 3,457 = 4,543.
3. Calculate 8 × 7.
1 mark
Answer
56
4. Calculate 95 ÷ 6. Give the answer with a remainder.
1 mark
Answer & explanation
6 × 15 = 90.
95 − 90 = 5.
Answer: 15 remainder 5.
5. Which number is a factor of 36?
1 mark
Answer & explanation
36 ÷ 9 = 4 with no remainder.
Therefore 9 is a factor of 36.
6. Which is the prime factorisation of 18?
1 mark
Answer
18 = 2 × 3 × 3.
7. Simplify 12/18.
1 mark
Answer & explanation
Divide numerator and denominator by 6:
12/18 = 2/3.
8. Calculate 1/2 + 1/4.
1 mark
Answer & explanation
1/2 = 2/4.
2/4 + 1/4 = 3/4.
9. Find 25% of 80.
1 mark
Answer
25% = 1/4.
80 ÷ 4 = 20.
10. Convert 3 metres to centimetres.
1 mark
Answer
1 m = 100 cm.
3 m = 300 cm.
11. In which quadrant is the point (−4, 3)?
1 mark
Answer
Negative x and positive y means Quadrant II.
12. A bag contains 4 red, 3 blue and 3 green counters. What is the probability of choosing a blue counter?
1 mark
Answer
There are 10 counters altogether and 3 are blue.
Probability = 3/10.

Section B – Short Answer

Questions 13–22 · 40 marks · Show your working on paper.

13. Written multiplication
4 marks

a) 46 × 7

b) 38 × 24

c) 246 × 35

Answers & worked solutions

a) 46 × 7 = 322

b) 38 × 24 = 912

c) 246 × 35
= 246 × 30 + 246 × 5
= 7,380 + 1,230
= 8,610

14. Short division
4 marks

a) 864 ÷ 6

b) 1,275 ÷ 5

c) Calculate 1,387 ÷ 6. Give your answer as a quotient and remainder.

Answers

a) 144

b) 255

c) 6 × 231 = 1,386.
1,387 − 1,386 = 1.
231 remainder 1

15. Factors, HCF, LCM and prime factorisation
4 marks

a) List all the positive factors of 18.

b) Find the HCF of 18 and 30.

c) Find the LCM of 6 and 8.

d) Express 60 as a product of prime factors.

Answers & explanations

a) 1, 2, 3, 6, 9, 18

b) HCF = 6

c) LCM = 24

d) 60 = 2 × 2 × 3 × 5
= 2² × 3 × 5

16. Adding and subtracting fractions
5 marks

a) Simplify 18/24.

b) Calculate 2/3 + 5/12.
You may use the LCM method or another correct fraction method.

c) Calculate 7/8 − 1/3.

Answers & worked solutions

a) 18/24 = 3/4

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

c) LCM of 8 and 3 = 24.
7/8 = 21/24
1/3 = 8/24
21/24 − 8/24 = 13/24

17. Multiplying and dividing fractions
4 marks

a) Calculate 3/5 × 10/9.

b) Calculate 4/7 ÷ 2/3.

Answers & worked solutions

a) 3/5 × 10/9 = 30/45 = 2/3

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

18. Percentages
4 marks

a) Find 38% of 200.

b) Find 70% of 360.

Answers & worked solutions

a) 38% of 200 = 38/100 × 200 = 76

b) 70% of 360 = 7/10 × 360 = 252

19. Order of operations
3 marks

a) 18 − 3 × 4 + 6

b) 42 ÷ 6 + 5 × 3

c) 5 × (7 − 3) + 4

Answers

a) 18 − 12 + 6 = 12

b) 7 + 15 = 22

c) 5 × 4 + 4 = 24

20. Measurement conversions
4 marks

a) 4,500 mm = ? cm

b) 7 m = ? cm

c) 4 L = ? mL

d) 3,000 m = ? km

Answers

a) 450 cm

b) 700 cm

c) 4,000 mL

d) 3 km

21. Composite perimeter
4 marks
L-shaped composite figure An L-shaped figure has a top side of 10 centimetres, a left side of 8 centimetres, an upper right vertical side of 3 centimetres and an inward horizontal side of 4 centimetres. 10 cm 3 cm 4 cm 8 cm ? ?

a) Find the missing vertical length.

b) Find the missing bottom horizontal length.

c) Find the perimeter of the complete L-shaped figure.

Answers & worked solution

a) 8 − 3 = 5 cm

b) 10 − 4 = 6 cm

c) Perimeter = 10 + 3 + 4 + 5 + 6 + 8 = 36 cm

22. Area of common shapes
4 marks

a) Find the area of a rectangle measuring 8 cm by 5 cm.

b) Find the area of a square with side length 6 cm.

c) Find the area of a triangle with base 10 cm and perpendicular height 7 cm.

Answers & worked solutions

a) 8 × 5 = 40 cm²

b) 6 × 6 = 36 cm²

c) ½ × 10 × 7 = 35 cm²

Section C – Problem Solving & Year 7 Readiness

Questions 23–26 · 18 marks · Use several skills together.

23. Fractions in a class
5 marks

A Year 6 class has 48 students.

3/8 of the students choose an art activity.

a) How many students choose art?

b) How many students remain after the art students are counted?

Of the remaining students, 2/5 choose a sports activity.

c) How many of the remaining students choose sport?

Answers & worked solutions

a) 3/8 × 48 = 3 × 6 = 18 students

b) 48 − 18 = 30 students

c) 2/5 × 30 = 2 × 6 = 12 students

24. Fencing a school play area
5 marks

A rectangular school play area measures 18 m by 12 m. A rectangular entrance recess measuring 4 m wide and 3 m deep is cut into one side.

Rectangular school play area with entrance recess A rectangle is 18 metres wide and 12 metres high. A 4-metre wide and 3-metre deep rectangular recess is cut into the top side. 18 m 12 m 4 m 3 m deep Entrance recess

a) What would the perimeter be if the play area were a normal 18 m by 12 m rectangle without the recess?

b) Find the perimeter after the 3 m deep recess is added.

c) A 2 m section is left open for a gate. How many metres of fencing are required?

d) Fencing costs $6 per metre. Find the total fencing cost.

Answers & worked solutions

a) 2 × (18 + 12) = 60 m

b) The recess adds two extra 3 m sides.
60 + 3 + 3 = 66 m

c) 66 − 2 = 64 m

d) 64 × $6 = $384

25. Cartesian plane
4 marks
Four-quadrant Cartesian plane Point A is at minus four comma three, point B is at three comma minus two, and point C is at zero comma four. x y A B C −4 3 3 4 −2

a) Write the coordinates of point A.

b) In which quadrant is point B?

c) Write the coordinates of point C.

d) A new point D is 5 units to the right of A and has the same y-coordinate. Find D.

Answers

a) A = (−4, 3)

b) B = (3, −2), so it lies in Quadrant IV.

c) C = (0, 4).

d) −4 + 5 = 1.
D = (1, 3).

26. Probability and reasoning
4 marks

A bag contains:

  • 5 red counters
  • 3 blue counters
  • 2 green counters

a) Find the probability of selecting a blue counter.

b) Find the probability of selecting a counter that is not red.

c) Is red or blue more likely to be selected? Explain your reasoning on paper.

Write your explanation on paper. You will self-mark this 2-mark response after submitting.
Answers & model reasoning

a) P(blue) = 3/10

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

c) Red is more likely. There are 5 red counters but only 3 blue counters. Therefore:
P(red) = 5/10
P(blue) = 3/10
Since 5/10 > 3/10, red is more likely.

68 marks are checked automatically. Question 26(c) contains 2 reasoning marks that you self-mark after comparing your response with the model answer.

Your Year 6 Maths Test Result

0 / 70
0 %

Automatically checked 0/68
Reasoning self-mark 0/2
Final score 0/70

Topic Breakdown

Number Operations & Division 0/21
Fractions 0/16
Percentages 0/5
Measurement & Geometry 0/18
Coordinates & Probability 0/10
Your priority revision topic will appear here.

Self-mark Question 26(c)

Compare your explanation with the model response shown underneath Question 26.

Probability reasoning
Is red or blue more likely to be selected, and why?

This score is a practice diagnostic rather than a school grade. Individual schools may assess different Stage 3 skills and use different assessment formats.

What does this Year 6 Maths test assess?

This Year 6 Maths practice exam is designed to test important upper-primary mathematical foundations before students move into Year 7.

The strongest emphasis is placed on written multiplication, short division, factors and multiples, fraction operations, percentages and measurement because weaknesses in these areas can make secondary-school mathematics considerably harder.

This is a broad practice exam, not an official statewide Year 6 exam.

NSW Mathematics is stage-based and schools can sequence Stage 3 learning differently. Students preparing for a particular school test should also follow their school's current assessment notification.

For a broader explanation of Year 6 content, see the Year 6 Maths NSW Syllabus Guide .

Why is this Year 6 Maths test non-calculator?

A calculator can produce the correct numerical answer without showing whether the student actually understands multiplication, division or fraction processes.

For this practice assessment, students are therefore asked to calculate without a calculator. This makes weaknesses in multiplication facts, written multiplication, short division and number operations easier to identify.

For a real school test: always follow the calculator instructions supplied by the student's school.

Common Year 6 Maths gaps this test can identify

Fraction operations

A student may understand individual fractions but struggle when they need to add or subtract unlike denominators or choose between the rules for multiplication and division.

Division

Short division can expose weak multiplication recall, place-value confusion or difficulty interpreting remainders.

Multi-digit multiplication

Students can know their basic multiplication facts but still struggle when several written steps and place values must be coordinated.

Factors, multiples, HCF and LCM

Students may confuse factors with multiples or know how to find an LCM without understanding when it is useful. Fraction addition is one place where this distinction matters.

Composite perimeter

Composite figures require more than adding the numbers printed on a diagram. Students may first have to calculate an unknown side length before finding the complete perimeter.

Revise the Year 6 Maths topics you missed

Use the topic breakdown above to revise the weakest area before repeating the entire exam.

Multiplication Practice Strengthen multiplication facts and written multiplication. Division Practice Review division and build stronger number fluency. Basics of Fractions Equivalent fractions, simplification and fraction foundations. Adding & Subtracting Fractions Common denominators, LCM and worked examples. Multiplying & Dividing Fractions Practise all four fraction operations. Percentages Made Easy Percentage calculations and worked examples. BODMAS Review order of operations. Geometry Formulae Review perimeter and basic area. Number Plane Guide Coordinates and four-quadrant practice. Probability Guide Favourable outcomes, total outcomes and probability. Maths Practice Tests by Topic Choose an individual skill for further practice. NSW Maths Resource Hub Browse free maths resources across year levels.

Is the student ready for Year 7 Maths?

Year 7 introduces considerably more mathematical content, so Year 6 number foundations become important.

Before high school, students should ideally be increasingly confident with:

  • addition and subtraction
  • multiplication facts
  • multi-digit multiplication
  • short division
  • all four fraction operations
  • basic percentages
  • probability
  • perimeter and composite figures
  • calculating unknown side lengths

Students ready to look ahead can visit the Year 7 Maths NSW Syllabus Guide and then attempt the Free Year 7 Maths Test NSW .

Official NSW Mathematics references

Aussie Math Tutor NSW is an independent education resource. For official curriculum information, refer directly to:

Did this Year 6 Maths test identify learning gaps?

A low score does not necessarily mean every Year 6 topic needs to be retaught. A fraction problem may begin with weak multiplication or LCM, while a division problem may begin with missing multiplication facts.

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 foundation step by step.

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Year 6 Maths Test – Frequently Asked Questions

Is this Year 6 Maths test free?

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

Is the complete exam visible on this page?

Yes. All 26 questions are displayed directly on the webpage. There is no Start Test button and no login requirement.

Can students use a calculator?

This particular AMT Year 6 practice test is non-calculator. For an actual school assessment, follow the instructions supplied by the student's school.

What topics are included?

The exam includes addition, subtraction, multiplication, short division, factors and multiples, HCF and LCM, prime factorisation, fraction operations, percentages, BODMAS, measurement conversions, perimeter, area, coordinates and probability.

How long should the Year 6 practice exam take?

Approximately 75 minutes is suggested for this broad AMT practice assessment. Real school assessments can vary in length and topic coverage.

What are common Year 6 Maths difficulties?

Difficulty varies by student, but fraction operations, division, multi-digit multiplication, factors and multiples, HCF and LCM, percentages and composite perimeter problems can reveal important learning gaps.

How can this test help prepare for Year 7?

The exam checks many of the number skills students rely on when high-school mathematics introduces more algebra, negative numbers, indices, equations and advanced fraction work.

Are worked answers included?

Yes. After the student submits the test, answer explanations and worked solutions become available underneath the questions.

Resource transparency: This is independently developed 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, NESA, the NSW Department of Education or an individual school's exam paper.
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