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Exam Review

Key Facts: AFA Exam

64

Total Questions

AFA Edital

4.0 / 10.0

Min Subject Score

AFA Edital

5h 20m

Exam Duration

DIRENS

R$ 120

Registration Fee

FAB

The AFA admission exam features 64 objective questions across Portuguese, English, Mathematics, and Physics (16 each) plus an essay in one 5h20m sitting, with a 4.0/10.0 floor in every objective subject and a 5.0 Média Final; this bank provides 100 English-language practice questions across all four blueprint domains.

Sample AFA Practice Questions

Try these sample questions to review concepts for the AFA exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Consider the polynomial P(x) = x³ − 6x² + 11x − 6. Given that its roots form an arithmetic progression, what is the sum of the squares of those roots?
A.14
B.16
C.24
D.36
Explanation: By Girard's relations (Vieta's formulas), the sum of the roots is r₁ + r₂ + r₃ = 6 and the sum of the pairwise products is r₁r₂ + r₁r₃ + r₂r₃ = 11. Writing the roots as an arithmetic progression (a − r, a, a + r) gives 3a = 6, so a = 2. Testing the divisors of 6 confirms the roots are 1, 2 and 3. Their squares sum to 1 + 4 + 9 = 14, which the algebraic identity also gives directly: (r₁+r₂+r₃)² − 2(r₁r₂+r₁r₃+r₂r₃) = 6² − 2(11) = 36 − 22 = 14.
2Let f: ℝ − {1} → ℝ − {2} be the bijective function defined by f(x) = (2x + 3)/(x − 1). What is the rule that defines the inverse function f⁻¹(x)?
A.f⁻¹(x) = (x + 3)/(x − 2)
B.f⁻¹(x) = (x − 3)/(x + 2)
C.f⁻¹(x) = (2x − 1)/(x + 3)
D.f⁻¹(x) = (3x + 1)/(2x − 1)
Explanation: Set y = (2x + 3)/(x − 1) and solve for x in terms of y: y(x − 1) = 2x + 3, so yx − y = 2x + 3, giving x(y − 2) = y + 3 and x = (y + 3)/(y − 2). Swapping the variable names yields f⁻¹(x) = (x + 3)/(x − 2). Note that the excluded value 2 in the codomain of f becomes the excluded value in the domain of f⁻¹, which is a useful sanity check.
3Over the real numbers, the solution set of the logarithmic inequality log_(1/2)(x² − 5x + 7) ≥ 0 is which interval?
A.[2, 3]
B.(2, 3)
C.(−∞, 2] ∪ [3, +∞)
D.[1, 4]
Explanation: Because the base 1/2 lies between 0 and 1, the logarithmic function is decreasing, so removing the logarithm reverses the inequality: x² − 5x + 7 ≤ (1/2)⁰ = 1, that is x² − 5x + 6 ≤ 0. The roots of x² − 5x + 6 = 0 are 2 and 3, and the upward-opening parabola is non-positive exactly on the closed interval [2, 3]. The existence condition x² − 5x + 7 > 0 holds for every real x because its discriminant is 25 − 28 = −3 < 0.
4What is the sum of all solutions of the trigonometric equation sin(2x) = cos(x) on the closed interval [0, π]?
A.3π/2
B.π
C.4π/3
D.2π
Explanation: Apply the double-angle identity sin(2x) = 2·sin(x)·cos(x), giving 2·sin(x)·cos(x) − cos(x) = 0, which factors as cos(x)·(2·sin(x) − 1) = 0. The first factor gives cos(x) = 0, so x = π/2. The second gives sin(x) = 1/2, so x = π/6 or x = 5π/6. All three lie in [0, π], and their sum is π/6 + 3π/6 + 5π/6 = 9π/6 = 3π/2.
5Given the complex number z = 1 + i√3, what is the value of z¹²?
A.4096
B.4096i
C.−4096
D.2048
Explanation: The modulus is |z| = √(1² + (√3)²) = √4 = 2, and the principal argument is θ = arctan(√3/1) = π/3. By De Moivre's theorem, z¹² = 2¹²·[cos(12 · π/3) + i·sin(12 · π/3)] = 4096·[cos(4π) + i·sin(4π)] = 4096·(1 + 0i) = 4096.
6In the Cartesian plane, what is the distance between the point P(2, −1) and the line r with general equation 3x − 4y + 5 = 0?
A.3
B.4
C.5
D.15
Explanation: The distance from a point P(x₀, y₀) to a line Ax + By + C = 0 is d = |A·x₀ + B·y₀ + C| / √(A² + B²). Substituting gives d = |3(2) − 4(−1) + 5| / √(3² + (−4)²) = |6 + 4 + 5| / √25 = 15/5 = 3.
7The equation 9x² + 25y² = 225 represents an ellipse in the Cartesian plane. What is the eccentricity of that ellipse?
A.0.8
B.0.6
C.0.75
D.1.25
Explanation: Dividing through by 225 gives the canonical form x²/25 + y²/9 = 1. Since 25 > 9, the semi-major axis is a = 5 along the x-axis and the semi-minor axis is b = 3. The fundamental relation a² = b² + c² gives 25 = 9 + c², so c = 4. The eccentricity is e = c/a = 4/5 = 0.8.
8A right circular cone has a base radius of 6 cm and a height of 8 cm. What is the total surface area of this cone?
A.96π cm²
B.60π cm²
C.84π cm²
D.120π cm²
Explanation: The slant height g follows from the Pythagorean theorem: g² = r² + h² = 36 + 64 = 100, so g = 10 cm. The base area is A_b = π·r² = 36π cm² and the lateral area is A_l = π·r·g = π·6·10 = 60π cm². The total surface area is therefore 36π + 60π = 96π cm².
9How many distinct anagrams can be formed from the letters of the Portuguese word AVIAÇÃO, ignoring the accent and cedilla marks?
A.840
B.5040
C.2520
D.420
Explanation: Once the diacritics are ignored, AVIAÇÃO is the 7-letter string A, V, I, A, C, A, O, in which the letter A occurs three times and every other letter occurs once. The number of permutations with repetition is 7!/3! = (7 × 6 × 5 × 4 × 3!)/3! = 7 × 6 × 5 × 4 = 840.
10Let A be a 3 × 3 square matrix with det(A) = 4. What is the determinant of the matrix 2A⁻¹?
A.2
B.1/2
C.8
D.1/8
Explanation: Two determinant properties are needed. First, det(k·M) = kⁿ·det(M) for an n × n matrix, and here n = 3, so det(2A⁻¹) = 2³·det(A⁻¹). Second, det(A⁻¹) = 1/det(A) = 1/4. Combining them gives det(2A⁻¹) = 8 · (1/4) = 2.

About the AFA Exam

The AFA Concurso de Admissão is the annual competitive entrance examination for the Academia da Força Aérea (AFA) in Pirassununga/SP, Brazil, selecting officer cadets for Aviator (CFOAV), Quartermaster (CFOINT), and Infantry (CFOINF) careers in the Brazilian Air Force (Força Aérea Brasileira). The written examination consists of 64 multiple-choice questions (16 each in Portuguese, English, Mathematics, and Physics) plus an argumentative essay (Redação), completed in a single 5h20m session. Every question has four alternatives (A–D). Candidates need at least 4.0 out of 10.0 in each objective subject, 5.0 in the essay, and a Média Final of at least 5.0. Note: the official exam is written and answered in Portuguese; this practice bank is an English-language MCQ study adaptation of the published syllabus, not an official translation or a simulation of the essay component.

Exam sponsor: Academia da Força Aérea (AFA) / Comando da Aeronáutica (FAB). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

64 questions

Time Limit

5 hours 20 minutes (real exam)

Passing Score

Minimum 4.0/10.0 per objective subject, 5.0 in Redação, Média Final 5.0

Exam / Certification Fees

R$ 120

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

25%

Matemática

Functions, analytic geometry, trigonometry, complex numbers, and combinatorics

25%

Física

Mechanics, thermodynamics, wave optics, electrostatics, and electromagnetism

25%

Língua Portuguesa

Text analysis, syntax, punctuation, concordance, and normative grammar

25%

Língua Inglesa

Reading comprehension, modal verbs, clause structure, and vocabulary

Preparing for the AFA Exam

What You Need to Know

  • Passing score: Minimum 4.0/10.0 per objective subject, 5.0 in Redação, Média Final 5.0
  • Exam length: 64 questions
  • Time limit: 5 hours 20 minutes (real exam)
  • Exam / certification fees: R$ 120 Official sources

Using Our Practice Resources

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

AFA: Suggested Study Strategy

1Practice deep calculus-ready algebra, trigonometry, and analytic geometry problems under strict time constraints
2Master classical mechanics, thermodynamics, and circuit analysis with multi-step physical derivations
3Review Portuguese normative syntax, particularly crasis, regency, and subordinate clause classification
4Solve past official AFA papers (EA CFOAV/CFOINT/CFOINF) to calibrate speed and accuracy

Frequently Asked Questions

How many questions are on the official AFA admission exam?

The official AFA written exam consists of 64 multiple-choice questions (16 in Portuguese, 16 in English, 16 in Mathematics, and 16 in Physics) plus a dissertative-argumentative essay (Redação) completed in 5 hours and 15 minutes.

What is the passing score for the AFA exam?

Under Articles 138 and 162 of the AFA Instruções Específicas, a candidate must score at least 4.0 out of 10.0 in each objective subject (Portuguese, Physics, Mathematics, English) before the essay is even marked, at least 5.0 in the Redação, and a Média Final of at least 5.0 across all five grades.

What officer career paths does AFA prepare for?

AFA trains officers for three Brazilian Air Force career streams: Aviador (Aviation Officer), Intendente (Quartermaster Officer), and Infantaria (Infantry Officer, male candidates only).

What is the registration fee for AFA?

The registration fee is R$ 120, with fee waivers (isenção) available for candidates registered in CadÚnico or recognized bone marrow donors.