100+ Free ADFA Maths Practice Questions

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Key Facts: ADFA Maths Exam

Questions

ADF Assessment

20 mins

Time Limit

44s per question

No Calculator

Allowed

Scratch paper only

Exam Fee

ADF Recruitment

6 months

Retake Wait Time

ADF Careers

3 years

Score Validity

ADF Careers

The ADFA Officer Entry Mathematics Test is a 20-minute, calculator-free exam consisting of 27 multiple-choice questions. It evaluates Year 11-12 mathematical ability. Achieving a competitive score is necessary to unlock highly technical officer specialisations including aviation/pilot, engineering, and intelligence streams in the Australian Defence Force.

Sample ADFA Maths Practice Questions

Try these sample questions to test your ADFA Maths exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate 0.12 ÷ 0.03 without using a calculator.

A.0.4

B.4

C.0.04

D.40

Explanation: Dividing by decimals is simplified by shifting the decimal point. Shifting both numbers two places to the right gives 12 ÷ 3 = 4.

2Calculate the sum of the fractions: 2/3 + 1/4.

A.5/12

B.11/12

C.1/2

D.3/7

Explanation: To add fractions, find the lowest common denominator, which is 12. Convert 2/3 to 8/12 and 1/4 to 3/12, then add to get 11/12.

3What is 15% of 80?

A.10

B.8

C.12

D.15

Explanation: To find 15% of 80, calculate 10% which is 8, and 5% which is 4. Summing these values gives 8 + 4 = 12.

4Convert the fraction 5/8 into a decimal.

A.0.75

B.0.825

C.0.58

D.0.625

Explanation: Dividing 5 by 8 yields 0.625. Knowing that 1/8 = 0.125, we can multiply 0.125 by 5 to get 0.625.

5Simplify the ratio 24:36 to its simplest form.

A.4:6

B.3:4

C.2:3

D.1:2

Explanation: Find the highest common factor of 24 and 36, which is 12. Dividing both terms by 12 yields 2:3.

6Evaluate the product of the mixed numbers: 1 1/2 × 2 2/3.

A.4

B.3 1/3

C.4 1/2

D.3 2/3

Explanation: Convert the mixed numbers to improper fractions: 1 1/2 = 3/2 and 2 2/3 = 8/3. Multiplying them gives (3/2) × (8/3) = 24/6 = 4.

7Calculate: 5.4 - 1.85.

A.4.55

B.4.65

C.3.55

D.3.65

Explanation: Align the decimal points, adding a placeholder zero: 5.40 - 1.85. Subtracting gives 3.55.

8A coat price is increased from $80 to $100. Calculate the percentage increase.

A.20%

B.25%

C.30%

D.15%

Explanation: The amount of increase is $100 - $80 = $20. The percentage increase is ($20 / $80) × 100% = 25%.

9Divide $150 in the ratio 2:3:5. What is the largest share?

A.$90

B.$75

C.$50

D.$60

Explanation: The total number of parts is 2 + 3 + 5 = 10. Each part is worth $150 / 10 = $15. The largest share is 5 parts, which is 5 × $15 = $75.

10Determine the Highest Common Factor (HCF) of 48 and 72.

A.8

B.24

C.12

D.16

Explanation: The prime factors are 48 = 2^4 × 3 and 72 = 2^3 × 3^2. The HCF is 2^3 × 3 = 24, which is the largest integer that divides both numbers without a remainder.

About the ADFA Maths Exam

Mathematics assessment for ADFA officer entry. The exam covers Year 11 and 12 mathematics concepts including algebra, geometry, and trigonometry to determine role eligibility.

Questions

27 scored questions

Time Limit

20 minutes

Passing Score

Varies by Role

Exam Fee

$0 (Australian Defence Force (ADF))

ADFA Maths Exam Content Outline

25%

Arithmetic & Foundations

Fractions, decimals, percentages, ratios, and basic calculation skills under time pressure.

30%

Algebra & Indices

Factorisation, expanding terms, index laws, linear/quadratic equations, and formula rearrangement.

20%

Geometry

Perimeter, area, volume, circle theorems, and coordinate geometry.

25%

Trigonometry

Pythagoras' Theorem, basic trigonometric ratios, special angles, and non-right triangle equations.

How to Pass the ADFA Maths Exam

What You Need to Know

Passing score: Varies by Role
Exam length: 27 questions
Time limit: 20 minutes
Exam fee: $0

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

ADFA Maths Study Tips from Top Performers

1Practice mental arithmetic daily - solve fractions, percentages, and decimals without using a calculator.

2Master basic algebra operations, including expanding brackets, factorising quadratics, and laws of indices.

3Memorize exact values for common trigonometric angles (30°, 45°, 60°) for sine, cosine, and tangent.

4Focus on speed and time management - you only have 44 seconds per question, so skip difficult ones and return to them later.

5Review circle geometry theorems and coordinate geometry formulas (distance, midpoint, perpendicular gradients).

Frequently Asked Questions

What is the format of the ADFA Officer Entry Mathematics Test?

The test consists of 27 multiple-choice questions. You have exactly 20 minutes to complete the test, meaning you must average approximately 44 seconds per question. It is completed under supervised conditions during your ADF recruitment process.

Can I use a calculator on the ADFA Maths Test?

No, calculators are strictly prohibited. You will be provided with pencils, an eraser, and scratch paper to perform all calculations by hand. It is essential to practice mental math and fraction arithmetic beforehand.

What is the passing score for the ADFA Maths Test?

The ADF does not publish a single 'passing' score. Instead, your raw score determines your eligibility for different officer occupations. Technical fields like engineering, aviation/pilot, and intelligence require significantly higher scores.

What topics are covered on the ADFA Mathematics Test?

The exam assesses mathematical skills up to a Year 11-12 secondary level in Australia. The four main domains are Arithmetic & Foundations (25%), Algebra & Indices (30%), Geometry (20%), and Trigonometry (25%).

How long are my ADF aptitude test results valid?

Aptitude and mathematical ability test results are generally valid for three years. If you wish to retake the test to qualify for a different role, you must wait at least 6 months before your next attempt.