PracticeVideosBlogFlashcardsEspañol
All Practice Exams

100+ Free ITA Practice Questions

Prepare for the Concurso de Admissão ao Instituto Tecnológico de Aeronáutica (Vestibular ITA) exam with instant access — no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately
100+ Questions
100% Free

Loading practice questions...

Same family resources

Explore More Brazilian Armed Forces Admission Examinations (Concursos Militares)

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

AFA Concurso de Admissão (Academia da Força Aérea, Brazil)

Practice Questions

CPAEAM Concurso de Admissão às Escolas de Aprendizes-Marinheiros (Brazil)

Practice Questions

CPAEN Concurso de Admissão à Escola Naval (Brazil)

Practice Questions

EFOMM Processo Seletivo (Escola de Formação de Oficiais da Marinha Mercante, Brazil)

Practice Questions

ESA Concurso de Admissão (Escola de Sargentos das Armas, Brazil)

Practice Questions

EsPCEx Concurso de Admissão (Escola Preparatória de Cadetes do Exército, Brazil)

Practice Questions
2026 Statistics

Key Facts: ITA Exam

48

1st Phase MCQs

Vestibular ITA

5 of 12

Min Correct per Subject

ITA Edital

2 Phases

Exam Format

ITA São José dos Campos

R$ 195

Registration Fee

Comando da Aeronáutica

The ITA entrance competition features a 48-question 1st Phase spanning Mathematics, Physics, Chemistry, and English followed by discursive exams; this bank provides 100 English-language practice questions across all official STEM domains.

Sample ITA Practice Questions

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

1Let z = 1 + i√3. What is the smallest positive integer n for which z^n is a strictly negative real number?
A.3
B.6
C.9
D.12
Explanation: The modulus is 2 and the argument is π/3, so z^n has argument nπ/3. A strictly negative real needs an argument that is an odd multiple of π, so nπ/3 = π gives n = 3.
2What is the sum of all roots of the polynomial equation P(x) = 2x⁴ − 6x³ + 5x² − x − 7 = 0?
A.3/2
B.3
C.−3
D.5/2
Explanation: Girard's first relation gives the sum of the roots as −a₃/a₄, where a₄ = 2 and a₃ = −6, so the sum is 6/2 = 3.
3In three-dimensional Euclidean space, what is the distance from the point P(1, 2, 3) to the plane π: 2x − y + 2z − 1 = 0?
A.5/3
B.2
C.7/3
D.5/9
Explanation: The distance formula gives |2 − 2 + 6 − 1|/√(4 + 1 + 4) = 5/3.
4How many solutions does the trigonometric equation sin(2x) = cos(x) have in the closed interval [0, 2π]?
A.2
B.3
C.4
D.6
Explanation: Factoring gives cos(x)·(2sin(x) − 1) = 0. From cos(x) = 0 come x = π/2 and 3π/2; from sin(x) = 1/2 come x = π/6 and 5π/6. That is 4 solutions.
5What is the term independent of x in the expansion of the binomial (x² + 1/x)⁶?
A.6
B.15
C.20
D.1
Explanation: The general term is C(6, k)·x^(12 − 3k), which is constant when k = 4. The coefficient is then C(6, 4) = 15.
6Consider the upper triangular matrix A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]]. What is det(A)?
A.11
B.18
C.24
D.30
Explanation: The determinant of a triangular matrix is the product of its diagonal entries: 1 × 4 × 6 = 24. The entries above the diagonal never enter the calculation.
7Let P(x) = x³ + ax² + bx + c be a monic polynomial with real coefficients whose three roots form an increasing geometric progression of positive reals. Given P(0) = −8 and that the roots sum to 14, what is P(1)?
A.5
B.7
C.9
D.11
Explanation: P(0) = c = −8 means the root product is 8, so writing the roots as m/q, m, mq gives m³ = 8 and m = 2. The sum condition gives 2(q + 1/q) = 12, so a = −14, b = 4(q + 1/q) + 4 = 28 and P(1) = 1 − 14 + 28 − 8 = 7.
8In the Argand-Gauss plane let z belong to the set {z ∈ ℂ : |z − 3i| = 2}. What is the maximum value of |z − 1|?
A.√10 − 2
B.√10 + 2
C.√13 + 2
D.5
Explanation: The set is a circle of centre 3i and radius 2, and |z − 1| is the distance from the point 1 to a point on it. The centre-to-point distance is |3i − 1| = √10, so the maximum is √10 + 2.
9A line r in ℝ³ passes through A(1, −1, 2) with direction vector v = (2, 1, −1). The plane π has equation x + y + z − 6 = 0. What is the intersection point of r and π?
A.(5, 1, 0)
B.(3, 0, 1)
C.(1, −1, 2)
D.(−1, −2, 3)
Explanation: Parametrising gives (1 + 2t, −1 + t, 2 − t). Substituting into the plane equation gives 2t − 4 = 0, so t = 2 and the point is (5, 1, 0).
10What is the exact value of S = cos²(10°) + cos²(50°) + cos²(70°)?
A.1
B.3/2
C.5/4
D.7/4
Explanation: Using cos²θ = (1 + cos 2θ)/2 turns S into 3/2 + ½[cos 20° + cos 100° + cos 140°]. Those three cosines are spaced 120° apart and therefore sum to zero, leaving S = 3/2.

About the ITA Exam

The Vestibular ITA is the legendary entrance competition for the Instituto Tecnológico de Aeronáutica in São José dos Campos/SP, Brazil's foremost aeronautical and aerospace engineering university under the Brazilian Air Force command. Candidates compete for entry into military (Quadro de Oficiais Engenheiros da Ativa) or civilian reserve engineering careers. The selection consists of a 1st Phase with 48 advanced multiple-choice questions (12 Math, 12 Physics, 12 Chemistry, 12 English) in a 5-hour sitting, followed by a 2nd Phase spread over four consecutive 4-hour afternoons: 10 discursive questions each in Mathematics, Chemistry and Physics, then a Portuguese day of 15 objective questions plus a dissertative-argumentative Redação. The final average weights the 1st Phase and each of the four 2nd Phase papers at 20% apiece. Note: the official exam is set and answered in Portuguese and its decisive second phase is discursive; this bank is an English-language MCQ study adaptation of the published Programa de Matérias, not an official translation or a simulation of the discursive papers.

Questions

48 scored questions

Time Limit

5 hours (1st Phase objective exam)

Passing Score

Min 5 of 12 correct per discipline plus 1st Phase average of 5.0000

Exam Fee

R$ 195 (Comando da Aeronáutica / DCTA / ITA)

ITA Exam Content Outline

30%

Matemática

Complex numbers, polynomials, 3D geometry, trigonometry, and advanced algebra

30%

Física

Rotational mechanics, fluids, wave interference, thermodynamics, and electromagnetism

25%

Química

Molecular structure, chemical equilibrium, thermochemistry, and organic reaction mechanisms

15%

Língua Inglesa e Portuguesa

Advanced textual comprehension, syntax, vocabulary, and discursive skills

How to Pass the ITA Exam

What You Need to Know

  • Passing score: Min 5 of 12 correct per discipline plus 1st Phase average of 5.0000
  • Exam length: 48 questions
  • Time limit: 5 hours (1st Phase objective exam)
  • Exam fee: R$ 195

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

ITA Study Tips from Top Performers

1Focus on high-level mathematical theory including De Moivre's formulas, roots of unity, and coordinate geometry in 3D
2Practice Olympiad-level physics problems in non-inertial reference frames, thermodynamic cycles, and electromagnetic wave propagation
3Master chemical equilibrium calculations with non-ideal behavior, galvanic and electrolytic cells, and stereochemistry
4Solve past official Vestibular ITA exams from 2012 to 2025 to develop rapid multi-concept problem decomposition

Frequently Asked Questions

What is the examination structure of the Vestibular ITA?

The ITA examination process has three stages. The 1st Phase is a single 5-hour sitting of 48 objective multiple-choice questions, 12 each in Mathematics, Physics, Chemistry and English. Candidates meeting the cutoff thresholds advance to the 2nd Phase: four consecutive 4-hour afternoons carrying 10 discursive questions each in Mathematics, Chemistry and Physics, then 15 objective Portuguese questions plus a dissertative-argumentative Redação. A 3rd stage of health inspection follows for qualified candidates.

What engineering programs are offered at ITA?

ITA offers undergraduate engineering degrees in Aeronautical Engineering, Aerospace Engineering, Mechanical-Aeronautical Engineering, Civil-Aeronautical Engineering, Electronic Engineering, and Computer Engineering.

What are the passing criteria for the 1st Phase of ITA?

Item 4.6.2 of the Edital ITA 2027 requires three things at once: at least 5 correct answers in each 12-question block (Mathematics, Physics, Chemistry and English), a first-phase average of at least 5.0000, and a place inside the call-up limits of 490 general-competition candidates, 175 pretos e pardos, 21 indígenas or 14 quilombolas. The average itself is computed only from the 36 Mathematics, Physics and Chemistry questions — English is eliminatory but never classificatory.

What is the registration fee for the ITA entrance exam?

The registration fee is R$ 195, with fee exemptions available for low-income candidates registered in CadÚnico and verified bone marrow donors.