100+ Free EFOMM Practice Questions

Prepare for the Processo Seletivo de Admissão às Escolas de Formação de Oficiais da Marinha Mercante (EFOMM) exam with instant access — no signup required.

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2026 Statistics

Key Facts: EFOMM Exam

Total Questions

EFOMM Edital

50%

Min Subject Score

DPC / Marinha

2 Days (8h)

Total Duration

CIAGA / CIABA

R$ 110

Registration Fee

Marinha do Brasil

The EFOMM entrance exam spans 80 questions over two 4-hour days covering Portuguese (20), English (20), Mathematics (20), and Physics (20) plus an essay; this bank provides 100 English-language practice questions across all blueprint subjects.

Sample EFOMM Practice Questions

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

1The roots of the polynomial equation x³ − 12x² + 44x − 48 = 0 form an arithmetic progression. What is the product of the two largest roots?

A.24

B.8

C.12

D.44

Explanation: By Girard's relations the three roots sum to 12 and multiply to 48. Writing them as an arithmetic progression with middle term r₂ gives 3r₂ = 12, so r₂ = 4. The remaining pair must multiply to 48/4 = 12 and sum to 8, giving 2 and 6. The roots are therefore 2, 4 and 6, and the product of the two largest is 4 × 6 = 24.

2What is the sum of all solutions of the trigonometric equation cos(2x) + 3·sin(x) − 2 = 0 lying in the interval [0, 2π]?

A.3π/2

B.π

C.2π

D.5π/2

Explanation: Substituting cos(2x) = 1 − 2·sin²(x) turns the equation into 2·sin²(x) − 3·sin(x) + 1 = 0, which factors as (2·sin(x) − 1)(sin(x) − 1) = 0. This gives sin(x) = 1/2, so x = π/6 or 5π/6, and sin(x) = 1, so x = π/2. Summing the three roots gives π/6 + 5π/6 + π/2 = 3π/2.

3Let z = (1 + i√3)⁶, where i is the imaginary unit. What is the simplified algebraic form of z?

A.64

B.−64

C.64i

D.−64i

Explanation: In trigonometric form, 1 + i√3 has modulus √(1 + 3) = 2 and argument π/3. By De Moivre's theorem, z = 2⁶·[cos(6 · π/3) + i·sin(6 · π/3)] = 64·[cos(2π) + i·sin(2π)] = 64·(1 + 0i) = 64.

4What is the equation of the line tangent to the circle C: x² + y² − 4x + 6y − 12 = 0 at the point P(5, 1)?

A.3x + 4y − 19 = 0

B.4x + 3y − 23 = 0

C.3x − 4y − 11 = 0

D.4x − 3y − 17 = 0

Explanation: Completing the squares gives (x − 2)² + (y + 3)² = 25, so the centre is C(2, −3) and the radius is 5. The radius vector to P is CP = (3, 4), whose slope is 4/3, so the tangent perpendicular to it has slope −3/4. Through P(5, 1) this gives y − 1 = −(3/4)(x − 5), hence 4y − 4 = −3x + 15 and 3x + 4y − 19 = 0.

5A right circular cone of height 12 cm and base radius 5 cm is cut by a plane parallel to its base at a distance of 3 cm from the apex. What is the volume of the resulting frustum?

A.1575π/16 cm³

B.100π cm³

C.375π/4 cm³

D.1525π/16 cm³

Explanation: The whole cone has volume (1/3)π·5²·12 = 100π cm³. The small cone cut off is similar with linear ratio k = 3/12 = 1/4, so its volume ratio is k³ = 1/64 and its volume is 100π/64 = 25π/16 cm³. The frustum is the difference: 100π − 25π/16 = (1600π − 25π)/16 = 1575π/16 cm³.

6How many distinct anagrams of the letters in EFOMM begin with a consonant?

A.36

B.24

C.60

D.48

Explanation: EFOMM has 5 letters with M repeated twice, and its consonants are F, M and M. If the word starts with F, the remaining letters E, O, M, M give 4!/2! = 12 arrangements. If it starts with M, the remaining letters E, F, O, M are all distinct and give 4! = 24 arrangements. The two cases are disjoint, so the total is 12 + 24 = 36.

7Let A be a 3 × 3 square matrix with det(A) = 4. What is the determinant of M = 2 · A⁻¹ · Aᵀ · A²?

A.128

B.32

C.64

D.256

Explanation: For an n × n matrix scaled by k, det(k·X) = kⁿ·det(X), and here n = 3, so the factor is 2³ = 8. By Binet's theorem the inner product satisfies det(A⁻¹·Aᵀ·A²) = (1/4) · 4 · 4² = 16. Therefore det(M) = 8 × 16 = 128.

8What is the instantaneous rate of change of the area of a circle with respect to its radius r at the moment when r = 8 cm?

A.16π cm²/cm

B.64π cm²/cm

C.8π cm²/cm

D.32π cm²/cm

Explanation: The area as a function of radius is A(r) = π·r², so the instantaneous rate of change is the derivative dA/dr = 2π·r. At r = 8 cm this gives 16π cm²/cm — which is exactly the circumference, the geometric reason a thin ring of thickness dr adds area 2πr·dr.

9In an increasing geometric progression of three real terms, the sum of the terms is 26 and their product is 216. What is the common ratio?

A.3

B.2

C.1/3

D.4

Explanation: Writing the terms as a/q, a, a·q makes the product a³ = 216, so a = 6. The sum then gives 6/q + 6 + 6q = 26, that is 3q² − 10q + 3 = 0, whose roots are q = 3 and q = 1/3. Since the progression must be strictly increasing, q = 3 and the terms are 2, 6, 18.

10What real value of x satisfies the logarithmic equation log₂(x) + log₄(x) = 6?

A.16

B.8

C.64

D.32

Explanation: Change the second logarithm to base 2: log₄(x) = log₂(x)/log₂(4) = (1/2)·log₂(x). The equation becomes (3/2)·log₂(x) = 6, so log₂(x) = 4 and x = 2⁴ = 16.

About the EFOMM Exam

The EFOMM Processo Seletivo is the national competitive selection for merchant marine officer cadets training at CIAGA (Centro de Instrução Almirante Graça Aranha in Rio de Janeiro/RJ) and CIABA (Centro de Instrução Almirante Braz de Aguiar in Belém/PA). The academic exam is administered over two consecutive days: Day 1 includes 20 questions in Portuguese, 20 in English, and an argumentative essay (Redação); Day 2 includes 20 questions in Mathematics and 20 in Physics. Every objective question offers five alternatives (A–E), and each of the four papers is worth 100 points with a 50-point minimum. Graduates earn degrees in Nautical Sciences (Ciências Náuticas) qualifying them as Deck Officers (Oficiais de Náutica) or Engine Officers (Oficiais de Máquinas). Note: the official exam is set and answered in Portuguese; this bank is an English-language MCQ study adaptation of the published syllabus, not an official translation or a substitute for essay practice.

Questions

80 scored questions

Time Limit

2 days: 4 hours per day (real exam)

Passing Score

50 of 100 points in each of the four subjects

Exam Fee

R$ 110 (Marinha do Brasil / Diretoria de Portos e Costas (DPC))

EFOMM Exam Content Outline

25%

Matemática

Trigonometry, complex numbers, analytic geometry, matrices, and functions

25%

Física

Classical mechanics, hydrostatics, thermodynamics, wave optics, and electromagnetism

25%

Língua Portuguesa

Textual analysis, period syntax, concordance, crasis, and normative grammar

25%

Língua Inglesa

Reading comprehension, grammatical structures, conditional sentences, and vocabulary

How to Pass the EFOMM Exam

What You Need to Know

Passing score: 50 of 100 points in each of the four subjects
Exam length: 80 questions
Time limit: 2 days: 4 hours per day (real exam)
Exam fee: R$ 110

Keys to Passing

Work through all 100 available questions
Review every answer and explanation
Track weak areas and revisit them
Use our AI tutor for tough concepts

EFOMM Study Tips from Top Performers

1Practice multi-step physics problems in mechanics, hydrostatics, and wave optics that mirror the CIAGA/CIABA question style

2Master analytic geometry, trigonometry, and complex number operations under timed conditions

3Sharpen English reading skills, grammar analysis, and preposition/verb collocations

4Solve past official EFOMM test papers from 2018-2025 to develop strong pacing

Frequently Asked Questions

What is the structure of the EFOMM entrance examination?

The EFOMM written exam takes place over two consecutive days. Day 1 tests Portuguese (20 questions), English (20 questions), and Redação (essay). Day 2 tests Mathematics (20 questions) and Physics (20 questions), with each day allocated 4 hours.

What are the passing criteria for EFOMM?

Each of the four objective papers is marked out of 100 points, and a candidate must reach at least 50 points in Portuguese, English, Mathematics and Physics to stay in the competition. The Redação is a separate 100-point dissertative-argumentative essay of 20 to 30 lines assessed on cohesion, coherence, clarity, grammatical accuracy and textual structure.

What officer qualifications does EFOMM confer?

EFOMM graduates receive bachelor's degrees in Nautical Sciences and are commissioned as Second Lieutenants in the Merchant Marine Reserve (2º Tenente da Reserva da Marinha), qualifying as 2º Oficial de Náutica or 2º Oficial de Máquinas.

What is the registration fee for EFOMM?

The registration fee is R$ 110, payable via bank slip or official payment voucher, with exemption available for eligible CadÚnico participants and marrow donors.