120+ Free ICAS Mathematics Practice Questions

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Key Facts: ICAS Mathematics Exam

Years 2-12 (Australia)

Australian year levels; mappings vary by country

ICAS Assessments Mathematics

5 strands

Full framework strands; exact coverage and depth vary by paper

ICAS Mathematics Assessment Framework

Online

Multiple-choice and written questions under supervision

ICAS Assessments Mathematics

No own calculator

An on-screen calculator is provided when a question needs one

ICAS Assessments Mathematics

No pass mark

Results use percentiles and levels up to High Distinction

ICAS FAQs for parents

Janison

Owns and operates the ICAS Assessments platform

ICAS Assessments

120

Original practice questions in this bank

OpenExamPrep

ICAS Mathematics is an annual supervised online competition using multiple-choice and written questions. Introductory has 30 questions in 35 minutes; Papers A–C have 40 in 45 minutes; Papers D–J have 40 in 60 minutes. Country-specific paper mappings vary, and there is no pass mark.

Sample ICAS Mathematics Practice Questions

Try these sample questions to test your ICAS Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 120+ question experience with AI tutoring.

1A baker packs 156 muffins into boxes that each hold 12 muffins. How many full boxes can the baker make, and how many muffins are left over?

A.13 boxes with 0 left over

B.12 boxes with 12 left over

C.13 boxes with 6 left over

D.14 boxes with 0 left over

Explanation: Dividing 156 by 12 gives exactly 13 with no remainder, since 12 x 13 = 156. So 13 full boxes are made with nothing left over.

2What is the value of the digit 7 in the number 473 286?

A.7000

B.70 000

C.700

D.7

Explanation: In 473 286 the digit 7 sits in the ten-thousands place. Its place value is therefore 7 x 10 000 = 70 000.

3Which of these calculations gives the largest answer?

A.48 + 27

B.9 x 8

C.120 - 47

D.144 divided by 2

Explanation: Evaluating each: 48 + 27 = 75, 9 x 8 = 72, 120 - 47 = 73, and 144 divided by 2 = 72. The largest result is 75 from 48 + 27.

4A shop sells pencils at 3 for $1.20. At the same rate, how much do 8 pencils cost?

A.$2.40

B.$3.20

C.$3.60

D.$4.00

Explanation: Each pencil costs $1.20 divided by 3 = $0.40. Eight pencils therefore cost 8 x $0.40 = $3.20.

5What is 3/4 of 60?

A.15

B.20

C.45

D.80

Explanation: One quarter of 60 is 15, so three quarters is 3 x 15 = 45. Alternatively, 60 x 3 divided by 4 = 180 divided by 4 = 45.

6A jacket originally priced at $80 is reduced by 25% in a sale. What is the sale price?

A.$55

B.$60

C.$65

D.$75

Explanation: A 25% reduction on $80 is 0.25 x $80 = $20 off. The sale price is $80 - $20 = $60.

7Which fraction is equivalent to 0.375?

A.3/8

B.3/5

C.1/4

D.5/16

Explanation: 0.375 = 375/1000, which simplifies by dividing top and bottom by 125 to give 3/8. Indeed 3 divided by 8 = 0.375.

8What is the value of 2 to the power of 5 (2^5)?

A.10

B.16

C.32

D.64

Explanation: 2^5 means 2 multiplied by itself five times: 2 x 2 x 2 x 2 x 2 = 32.

9Which of the following is a prime number?

A.51

B.57

C.59

D.63

Explanation: 59 has no factors other than 1 and itself, so it is prime. The others are composite: 51 = 3 x 17, 57 = 3 x 19, and 63 = 7 x 9.

10Using the order of operations, what is the value of 6 + 4 x (10 - 7)?

A.18

B.30

C.21

D.42

Explanation: Brackets first: 10 - 7 = 3. Then multiplication: 4 x 3 = 12. Finally addition: 6 + 12 = 18.

About the ICAS Mathematics Exam

ICAS Mathematics is Janison's annual international school mathematics competition. In Australia it is offered for Years 2–12; paper mappings and availability differ in other countries. The supervised online assessment uses multiple-choice and written questions across five skill areas. This question bank is an original practice set, not a released ICAS paper.

Assessment

ICAS Mathematics is a family of 11 supervised online papers (Intro and A–J), not one universal test. Paper-to-year mapping varies by country, and each paper has its own framework coverage; for example, Intro does not assess the formal Algebra or Space and Geometry strands.

Time Limit

35 minutes for Introductory; 45 minutes for Papers A–C; 60 minutes for Papers D–J

Passing Score

No fixed pass mark. Students receive a percentile and a result level (Participation, Merit, Credit, Distinction or High Distinction), with Medals for top performers.

Exam Fee

Current 2026 Australian entry fees start at AUD 21.95 per subject; confirm the country- and school-specific price. (Janison Solutions Pty Limited (ICAS Assessments))

ICAS Mathematics Exam Content Outline

24 local practice questions

Number and Arithmetic

Problems on place value, the four operations, fractions, decimals, percentages, ratio, factors, primes, indices, integers and multi-step money and rate calculations.

24 local practice questions

Algebra and Patterns

Number and shape patterns, sequences, function rules, missing numbers, simplifying and expanding expressions, substitution and solving linear equations.

24 local practice questions

Measures and Units

Length, perimeter, area, volume, surface area, mass, capacity, time, elapsed time, speed, rates and map scale, including unit conversions and composite shapes.

24 local practice questions

Space and Geometry

Angles, triangles and polygons, parallel and perpendicular lines, symmetry, nets, transformations, coordinate geometry and Pythagoras' theorem.

24 local practice questions

Chance and Data

Reading and comparing graphs and tables, mean, median, mode and range, single and compound probability, complementary events and expected frequency.

How to Pass the ICAS Mathematics Exam

What You Need to Know

Passing score: No fixed pass mark. Students receive a percentile and a result level (Participation, Merit, Credit, Distinction or High Distinction), with Medals for top performers.
Assessment: ICAS Mathematics is a family of 11 supervised online papers (Intro and A–J), not one universal test. Paper-to-year mapping varies by country, and each paper has its own framework coverage; for example, Intro does not assess the formal Algebra or Space and Geometry strands.
Time limit: 35 minutes for Introductory; 45 minutes for Papers A–C; 60 minutes for Papers D–J
Exam fee: Current 2026 Australian entry fees start at AUD 21.95 per subject; confirm the country- and school-specific price.

Keys to Passing

Work through all 120 available questions
Review every answer and explanation
Track weak areas and revisit them
Use our AI tutor for tough concepts

ICAS Mathematics Study Tips from Top Performers

1Practise reading multi-step word problems carefully, underlining what is asked before choosing an operation or strategy.

2Use the official framework for your exact paper before studying; do not assume every paper assesses all five framework strands.

3Since questions get harder through the paper, answer the easier early questions confidently before spending time on the toughest ones.

4Learn to estimate and check answers; eliminating unreasonable options is powerful in a multiple-choice problem-solving test.

5Practise calculating without a calculator so you are quick with mental and written arithmetic when the on-screen calculator is not offered.

6Review every wrong answer to understand the reasoning error, since ICAS rewards higher-order thinking over memorised procedures.

Frequently Asked Questions

Who sits ICAS Mathematics?

ICAS Mathematics is an international school competition. In Australia it is offered for Years 2–12, while other countries use different year labels and may not offer every paper. Students should use the current country-to-paper table rather than assume the Australian mapping applies everywhere.

What does ICAS Mathematics assess?

The full ICAS Mathematics framework spans Number and Arithmetic, Algebra and Patterns, Measures and Units, Space and Geometry, and Chance and Data. Individual papers assess different subsets and levels; Intro, for example, does not include formal Algebra or Space and Geometry.

Is ICAS Mathematics all multiple-choice?

No. Janison's current product description says ICAS assessments include multiple-choice and written questions. The assessment is delivered online under supervision; do not assume unsupported interaction types beyond the current official description.

Is there a pass mark for ICAS Mathematics?

No. ICAS Mathematics has no fixed pass mark. Each student receives a percentile and a result level such as Participation, Merit, Credit, Distinction or High Distinction, and top performers can receive a Medal.

Can students use a calculator in ICAS Mathematics?

Students may not use their own calculator. The online ICAS system provides an on-screen calculator when a question requires one, so practice should build mental and written calculation skills.

Are these official ICAS questions?

No. These are original practice questions written to align with the ICAS Mathematics framework strands and format. They do not copy released ICAS papers or official sample items.