Free Practice Questions for ACADEMIL Admission

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Key Facts: ACADEMIL Admission Exam

4 subjects

Academic subjects confirmed in 2026 results

FP-UNA ACADEMIL admission results

Spanish

Official academic assessment language

Army-linked admission prospectus and FP-UNA papers

100 practice MCQs

Independent study bank size

OpenExamPrep practice bank

3 branches

Army, Navy and Air Force officer training

Fuerza Aérea Paraguaya ACADEMIL page

Study the four academic subject areas with independent English explanations. The official academic assessment is in Spanish, and the detailed outline available through the Army is historical.

Sample ACADEMIL Admission Practice Questions

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

1A rectangular plot has length 5 m greater than its width and area 14 m^2. Which value is its width, after rejecting the inadmissible root of the resulting quadratic equation?

A.2 m

B.7 m

C.-7 m

D.9 m

Explanation: If the width is x, the length is x + 5, so x(x + 5) = 14. Factoring x^2 + 5x - 14 gives (x + 7)(x - 2) = 0, with roots -7 and 2. A physical width must be positive, leaving 2 m; the length is then 7 m.

2Four notebooks and three pens cost Gs. 31,000; two notebooks and five pens cost Gs. 26,000. With the same unit prices, what do five notebooks and two pens cost?

A.Gs. 30,500

B.Gs. 33,500

C.Gs. 35,500

D.Gs. 37,000

Explanation: Let n and p be notebook and pen prices. Subtracting 4n + 3p = 31,000 from twice 2n + 5p = 26,000 gives 7p = 21,000, so p = 3,000 and n = 5,500. Thus 5n + 2p = Gs. 33,500.

3In an arithmetic progression, the first term is a_1 = 5 and the common difference is d = 4. What is the 15th term (a_15)?

A.61

B.65

C.57

D.69

Explanation: The n-th term of an arithmetic progression is given by a_n = a_1 + (n - 1)d. For n = 15, a_15 = 5 + (15 - 1)(4) = 5 + 14(4) = 5 + 56 = 61.

4What is the sum of the first 20 terms of an arithmetic progression where a_1 = 3 and the 20th term is a_20 = 79?

A.820

B.800

C.840

D.790

Explanation: The sum of the first n terms of an arithmetic progression is S_n = (n / 2) * (a_1 + a_n). Here S_20 = (20 / 2) * (3 + 79) = 10 * 82 = 820.

5For common logarithms (base 10), solve log(x) + log(x + 9) = 1 over the real numbers.

A.10

B.-10

C.1

D.9

Explanation: The arguments require x > 0. Combining logarithms gives x(x + 9) = 10, or (x - 1)(x + 10) = 0. Only x = 1 satisfies the domain; log(1) + log(10) = 0 + 1.

6What is the exact value of sin(105 degrees)?

A.(sqrt(6) + sqrt(2)) / 4

B.(sqrt(6) - sqrt(2)) / 4

C.(sqrt(3) + 1) / 2

D.(sqrt(2) + 1) / 4

Explanation: Split 105 degrees into the standard angles 60 and 45 degrees. The addition identity gives sin(60 + 45) = sin(60)cos(45) + cos(60)sin(45) = (sqrt(6) + sqrt(2))/4. Sines of angles cannot simply be added.

7In triangle ABC, side a = 8 cm, side b = 6 cm, and the included angle C = 60 degrees. What is the length of side c?

A.2*sqrt(13) cm

B.2*sqrt(15) cm

C.10 cm

D.2*sqrt(37) cm

Explanation: By the Law of Cosines, c^2 = a^2 + b^2 - 2ab*cos(C) = 8^2 + 6^2 - 2(8)(6)*cos(60 deg) = 64 + 36 - 96*(0.5) = 100 - 48 = 52. Thus c = sqrt(52) = 2*sqrt(13) cm.

8An upright cylindrical container has internal radius 4 cm and internal height 10 cm. It is half full of water. What additional volume raises it to three-quarters full?

A.40*pi cm^3

B.80*pi cm^3

C.120*pi cm^3

D.160*pi cm^3

Explanation: The full capacity is pi * 4^2 * 10 = 160*pi cm^3. The required increase is 3/4 - 1/2 = 1/4 of that capacity. Therefore the additional water volume is 40*pi cm^3.

9A solid metal sphere has surface area 144*pi cm^2. It is melted and recast as a solid cylinder of radius 3 cm, with no loss or change in volume. What is the cylinder's height?

A.32 cm

B.16 cm

C.24 cm

D.96 cm

Explanation: From 4*pi*r^2 = 144*pi, the sphere's radius is 6 cm and its volume is (4/3)*pi*6^3 = 288*pi cm^3. The cylinder has volume pi*3^2*h = 9*pi*h. Equating the volumes gives h = 288/9 = 32 cm.

10Factor the polynomial 6x^2 + 11x - 10 completely into linear binomial factors.

A.(2x + 5)(3x - 2)

B.(2x - 5)(3x + 2)

C.(6x - 5)(x + 2)

D.(3x + 5)(2x - 2)

Explanation: To factor 6x^2 + 11x - 10, find two numbers that multiply to 6 * (-10) = -60 and add to 11. These numbers are 15 and -4. Rewriting as 6x^2 + 15x - 4x - 10 gives 3x(2x + 5) - 2(2x + 5) = (2x + 5)(3x - 2).

About the ACADEMIL Admission Exam

Independent practice for ACADEMIL admission with 100 English-language MCQs on mathematics, general physics, Paraguayan social studies and Spanish communication. This is an English-language MCQ study adaptation, not an official translation or format simulation. Spanish passages and terms are retained where they are the tested skill. It does not replace Spanish-language study, any written-response preparation or medical, psychological and physical selection preparation.

Exam sponsor: ACADEMIL / Fuerzas Armadas del Paraguay; FP-UNA academic examination services. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Four Spanish-language written academic papers, plus medical, physical and psychological selection stages described in the Army-linked prospectus. Exact 2026 item types and stage rules remain unverified.

Time Limit

not-published

Passing Score

not-published

Exam / Certification Fees

not-published

Exam sponsor website

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

Official sources

Ejército del Paraguay — Cómo formar parte · Source checked 2026-10-09Official recruitment page linking the ACADEMIL prospectus. The linked document is dated 2019–2020, not 2026.
ACADEMIL 2019–2020 admission prospectus linked by the Army · Source checked 2026-10-09Historical detailed subject outline and selection stages; older fees, timings and marks must not be treated as current.
FP-UNA — ACADEMIL academic admission results · Source checked 2026-10-092026 results confirm an active competition and the four academic subjects. FP-UNA describes preparing, administering and grading the academic examinations.
Fuerza Aérea Paraguaya — ACADEMIL officers · Source checked 2026-10-09Official joint officer-training route and undated admission requirements; not a complete dated 2026 call.
Constitución Nacional — Biblioteca y Archivo Central del Congreso · Source checked 2026-10-09Primary text for constitutional civics, including Articles 1, 5, 129, 140, 173 and 238.

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 questions

Mathematics

Arithmetic, algebra, progressions, geometry and trigonometry.

25 questions

General Physics

Mechanics, statics, work, energy, power and hydrostatics.

25 questions

Social Studies

National history, geography and constitutional civics.

25 questions

Communication

Spanish grammar, orthography, vocabulary and passage analysis.

Preparing for the ACADEMIL Admission Exam

What You Need to Know

Passing score: not-published
Assessment: Four Spanish-language written academic papers, plus medical, physical and psychological selection stages described in the Army-linked prospectus. Exact 2026 item types and stage rules remain unverified.
Time limit: not-published
Exam / certification fees: not-published Official sources

Using Our Practice Resources

Work through all 100 available questions
Review every answer and explanation
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ACADEMIL Admission: Suggested Study Strategy

1Solve arithmetic and algebra problems with units and domain restrictions.

2Draw force diagrams before applying Newton's laws or torque equilibrium.

3Build a timeline separating the independence movement, Triple Alliance War and Chaco War.

4Practice Spanish reading and grammar in Spanish as well as reviewing these English explanations.

5Consult the current admission call for eligibility and physical or medical requirements.

Frequently Asked Questions

Is ACADEMIL admission active in 2026?

Yes. FP-UNA publishes 2026 admission results for Comunicación, Física, Estudios Sociales and Matemática. ACADEMIL trains officers for Paraguay's Army, Navy and Air Force.

What official format and language should I prepare for?

The academic assessment consists of written Spanish-language papers. The available historical prospectus also describes medical, physical and psychological selection stages. A current question count, precise item-type mix, timing, fee and pass threshold were not verified. No mandatory assignment, oral examination or case-study component was verified; this does not establish their absence from a future call.

How current is the topic information?

The 2026 results confirm the four subjects. Detailed topic selection here uses the Army-linked 2019–2020 prospectus, whose subject papers carried equal points. Current subtopic weights were not verified. Check the current prospectus for changes; this bank is not complete syllabus coverage.

Is this an official translation or test simulation?

No. It is independent English-language MCQ study practice. Spanish remains integral to the communication questions. Use official-language materials and separate preparation for any written responses and the practical selection stages.