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Key Facts: Angola Military Technical Institute (ISTM) Exam Exam

ISTM / FAA

Military Polytechnic / Defense Institution

Forças Armadas Angolanas

13 / 20

Minimum Secondary-School Average to Apply

Comunicado FAA — Recrutamento Especial 2026/2027

Math, Physics & Chem

Core STEM Examination Subjects

Despacho de Abertura do ISTM

Portuguese

Official Examination Language

CRA Article 19

Free English-language MCQ study adaptation for Angola's Portuguese-language Concurso de Admissão ao Instituto Superior Técnico Militar (ISTM/FAA), covering higher secondary Mathematics, Physics, Chemistry, and technical reasoning. It is not an official translation or laboratory practical substitute.

Sample Angola Military Technical Institute (ISTM) Exam Practice Questions

Try these sample questions to review concepts for the Angola Military Technical Institute (ISTM) Exam exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the derivative with respect to x of the function f(x) = x³ · e^(2x)?
A.f'(x) = 6x² · e^(2x)
B.f'(x) = x³ · e^(2x) + 3x²
C.f'(x) = x² · e^(2x) · (3 + 2x)
D.f'(x) = 3x² · e^(2x)
Explanation: Using the product rule (u · v)' = u'v + uv': u = x³ → u' = 3x²; v = e^(2x) → v' = 2e^(2x). Then f'(x) = 3x²e^(2x) + 2x³e^(2x) = x²e^(2x)(3 + 2x).
2Evaluate the definite integral: ∫ (from 0 to 2) (3x² - 4x + 1) dx.
A.8
B.2
C.0
D.4
Explanation: Antiderivative F(x) = [x³ - 2x² + x] evaluated from 0 to 2: F(2) = (2³ - 2(2²) + 2) = (8 - 8 + 2) = 2. F(0) = 0. Thus the integral equals 2 - 0 = 2.
3What is the determinant of the 3×3 matrix A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]]?
A.24
B.11
C.0
D.60
Explanation: For an upper triangular matrix, the determinant is the product of its diagonal entries: det(A) = 1 × 4 × 6 = 24.
4Solve the first-order separable differential equation dy/dx = 2x · y for y > 0 with initial condition y(0) = 3.
A.y(x) = e^(x²) + 2
B.y(x) = 3 · e^(2x)
C.y(x) = 3x² + 3
D.y(x) = 3 · e^(x²)
Explanation: Separating variables: dy / y = 2x dx. Integrating both sides: ln(y) = x² + C → y = A · e^(x²). Using y(0) = 3: 3 = A · e⁰ → A = 3. Thus y(x) = 3e^(x²).
5What is the modulus |z| and argument θ of the complex number z = 1 + i√3?
A.|z| = 2 and θ = π/6 (30°)
B.|z| = √2 and θ = π/4 (45°)
C.|z| = 2 and θ = π/3 (60°)
D.|z| = 4 and θ = π/6 (30°)
Explanation: Modulus |z| = √(1² + (√3)²) = √(1 + 3) = √4 = 2. The argument is θ = arctan(√3 / 1) = 60° = π/3 radians.
6What is the equation of the ellipse centered at (0, 0) with major axis of length 10 along the x-axis and minor axis of length 6 along the y-axis?
A.x² / 10 + y² / 6 = 1
B.x² / 25 + y² / 9 = 1
C.x² / 100 + y² / 36 = 1
D.x² / 9 + y² / 25 = 1
Explanation: The semi-major axis is a = 10/2 = 5 (so a² = 25) and semi-minor axis is b = 6/2 = 3 (so b² = 9). The standard equation is x²/a² + y²/b² = 1 → x²/25 + y²/9 = 1.
7Calculate the eigenvalues of the 2×2 matrix A = [[3, 1], [0, 2]].
A.λ₁ = 3 and λ₂ = 2
B.λ₁ = 1 and λ₂ = 5
C.λ₁ = 6 and λ₂ = 0
D.λ₁ = -3 and λ₂ = -2
Explanation: For a triangular matrix, the eigenvalues are simply the entries along the main diagonal: det(A - λI) = (3 - λ)(2 - λ) - 0 = 0 → λ₁ = 3 and λ₂ = 2.
8Using L'Hôpital's rule, evaluate the limit: lim (x → 0) [ (e^(3x) - 1) / sin(2x) ].
A.1
B.0
C.3
D.3/2 (or 1.5)
Explanation: Direct substitution gives 0/0. Applying L'Hôpital's rule by differentiating numerator and denominator: lim (x → 0) [ 3e^(3x) / (2cos(2x)) ] = (3 · 1) / (2 · 1) = 3/2.
9What is the cross product u × v of vectors u = (1, 0, 0) and v = (0, 1, 0)?
A.(1, 1, 0)
B.(0, 0, 0)
C.(0, 0, 1)
D.(0, 0, -1)
Explanation: The cross product of standard unit basis vectors î × ĵ is the k̂ unit vector along the z-axis: (1, 0, 0) × (0, 1, 0) = (0, 0, 1).
10What is the general solution of the second-order homogeneous differential equation y'' + 9y = 0?
A.y(x) = C₁ · cos(3x) + C₂ · sin(3x)
B.y(x) = C₁ · e^(3x) + C₂ · e^(-3x)
C.y(x) = C₁ · cos(9x) + C₂ · sin(9x)
D.y(x) = (C₁ + C₂x) · e^(3x)
Explanation: The characteristic equation is r² + 9 = 0 → r² = -9 → r = ±3i. Complex conjugate roots r = 0 ± 3i yield sinusoidal general solutions y(x) = C₁ cos(3x) + C₂ sin(3x).

About the Angola Military Technical Institute (ISTM) Exam Exam

The Concurso de Admissão ao ISTM is the competitive entrance examination for military engineering and military medicine officer cadet training in Angola, testing advanced mathematics, physics, chemistry, and technical problem-solving.

Exam sponsor: Instituto Superior Técnico Militar (ISTM) / EMGFAA. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

The Concurso de Admissão ao ISTM is the polytechnic higher education entrance examination of the Forças Armadas Angolanas (FAA). ISTM prepares military engineer officers (Mechanical, Electrotechnical, Computer/Informatics, and Construction & Fortifications Engineering) and military health officers (Medicine and Nursing). The rigorous admission process selects candidates based on performance in written STEM tests and physical/medical assessments.

Time Limit

90 to 120 minutes per written subject test

Passing Score

Competitive ranking within available course vacancies on the 0-20 scale plus medical/physical clearance; application requires a secondary-school certificate average of at least 13/20 (2026/2027 special recruitment)

Exam / Certification Fees

No application fee charged for official FAA recruitment applications

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.

not-published

Matemática

Algebra, trigonometry, coordinate geometry, matrices, determinants, functions, and calculus

not-published

Física

Mechanics, kinematics, work and energy, fluid mechanics, thermodynamics, and electricity

not-published

Química Geral e Tecnológica

Atomic structure, chemical bonding, stoichiometry, solutions, electrochemistry, and organic chemistry

not-published

Raciocínio Técnico-Científico e Ciências Militares

Technical logic, algorithmic thinking, materials properties, and military engineering concepts

Preparing for the Angola Military Technical Institute (ISTM) Exam Exam

What You Need to Know

  • Passing score: Competitive ranking within available course vacancies on the 0-20 scale plus medical/physical clearance; application requires a secondary-school certificate average of at least 13/20 (2026/2027 special recruitment)
  • Assessment: The Concurso de Admissão ao ISTM is the polytechnic higher education entrance examination of the Forças Armadas Angolanas (FAA). ISTM prepares military engineer officers (Mechanical, Electrotechnical, Computer/Informatics, and Construction & Fortifications Engineering) and military health officers (Medicine and Nursing). The rigorous admission process selects candidates based on performance in written STEM tests and physical/medical assessments.
  • Time limit: 90 to 120 minutes per written subject test
  • Exam / certification fees: No application fee charged for official FAA recruitment applications 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

Angola Military Technical Institute (ISTM) Exam: Suggested Study Strategy

1Practice solving complex algebraic manipulations, trigonometry proofs, logarithmic equations, and limits without a calculator
2Deepen your understanding of Newtonian mechanics, vector decomposition, kinetic/potential energy, and basic circuit analysis (Ohm's and Kirchhoff's laws)
3Review stoichiometry, molar concentration, redox balancing, and acid-base equilibrium in chemistry
4Work through past entrance examination problems and timed STEM problem sets
5Maintain a strong physical fitness regimen to meet the military physical entrance criteria

Frequently Asked Questions

What is the Instituto Superior Técnico Militar (ISTM) in Angola?

ISTM is the military polytechnic and higher educational institution of the Forças Armadas Angolanas, located in Luanda, dedicated to educating and training military engineer officers and military medical officers for all branches of the armed forces.

What courses and degrees are offered at ISTM?

ISTM offers engineering degree programs in Mechanical Engineering, Electrotechnical Engineering, Computer (Informatics) Engineering, and Construction and Fortifications Engineering, alongside degree programs in Military Medicine and Nursing (Enfermagem).

What subjects are tested on the ISTM Entrance Examination?

For engineering tracks, candidates are tested on Mathematics, Physics, and Chemistry. For the health track (Medicine and Nursing), candidates are tested on Biology, Physics, and Chemistry.

Is this question bank an official ISTM examination?

No. The official ISTM entrance exams are written in Portuguese by the ISTM academic board under EMGFAA. This bank is an English-language study adaptation to help candidates master the required STEM fundamentals and technical concepts.