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Free Practice Questions for Heroico Colegio Militar

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Exam Review

Key Facts: Heroico Colegio Militar Exam

100

Examen cultural questions

SEDENA Convocatoria 2026

2 hours

Examen cultural time

SEDENA Convocatoria 2026

60 / 100

Minimum passing score

SEDENA Convocatoria 2026

$0 MXN

Admission exam fee

SEDENA Convocatoria 2026

4

Temario subjects

SEDENA HCM Temarios 2026

18–20

Civilian age range (years)

SEDENA Convocatoria 2026

The 2026 HCM examen cultural has 100 questions, a 2-hour limit and a 60/100 minimum, and SEDENA charges no fee. For both licenciaturas the temario covers four subjects: Spanish, algebra (Baldor I–VI), contemporary world history and Mexican geography. The English diagnostic taken the same day is separate. This free bank offers independent English-language practice on those four subjects; it does not simulate the Spanish-language exam.

Sample Heroico Colegio Militar Practice Questions

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

1Simplify by removing the grouping symbols and reducing like terms: 3x - [2y - (4x + 3y) + 5x]
A.2x - y
B.4x - y
C.2x + y
D.-6x - 5y
Explanation: Work from the innermost sign outward. -(4x + 3y) becomes -4x - 3y, so the bracket is 2y - 4x - 3y + 5x = x - y. The minus sign in front of the bracket changes the sign of every term inside it: 3x - (x - y) = 3x - x + y = 2x + y.
2Divide the monomials: (-24a^5 b^3 c) ÷ (6a^2 b)
A.4a^3 b^2 c
B.-4a^3 b^2 c
C.-18a^3 b^2 c
D.-4a^7 b^4 c
Explanation: Divide the coefficients and apply the law of signs: -24 ÷ 6 = -4, because unlike signs give a negative quotient. Then subtract the exponents of equal bases: a^(5-2) = a^3 and b^(3-1) = b^2. The letter c appears only in the dividend, so it passes to the quotient unchanged: -4a^3 b^2 c.
3Expand the cube of a binomial: (3x - 2y)^3
A.27x^3 - 18x^2 y + 12xy^2 - 8y^3
B.27x^3 - 36x^2 y + 54xy^2 - 8y^3
C.9x^3 - 54x^2 y + 36xy^2 - 6y^3
D.27x^3 - 54x^2 y + 36xy^2 - 8y^3
Explanation: Use (a - b)^3 = a^3 - 3a^2 b + 3ab^2 - b^3 with a = 3x and b = 2y: (3x)^3 - 3(3x)^2(2y) + 3(3x)(2y)^2 - (2y)^3 = 27x^3 - 3(9x^2)(2y) + 3(3x)(4y^2) - 8y^3 = 27x^3 - 54x^2 y + 36xy^2 - 8y^3. The signs alternate because the second term of the binomial is negative.
4Multiply the binomials: (3x - 2)(2x + 5)
A.6x^2 + 11x - 10
B.6x^2 - 11x - 10
C.6x^2 + 19x - 10
D.6x^2 - 10
Explanation: Multiply each term of the first factor by each term of the second: 3x · 2x = 6x^2, 3x · 5 = 15x, -2 · 2x = -4x and -2 · 5 = -10. Reducing the like terms 15x - 4x = 11x gives 6x^2 + 11x - 10.
5Find the product using notable products: (2x - 3y)(2x + 3y)(4x^2 + 9y^2)
A.16x^4 + 81y^4
B.16x^4 - 72x^2 y^2 + 81y^4
C.16x^4 - 81y^4
D.8x^4 - 18y^4
Explanation: The first two factors are a sum times a difference, so (2x - 3y)(2x + 3y) = 4x^2 - 9y^2. That result multiplied by 4x^2 + 9y^2 is again a sum times a difference: (4x^2)^2 - (9y^2)^2 = 16x^4 - 81y^4.
6Write the notable quotient directly: (8a^3 + 27b^3) ÷ (2a + 3b)
A.4a^2 + 6ab + 9b^2
B.4a^2 - 6ab + 9b^2
C.4a^2 + 12ab + 9b^2
D.2a^2 - 6ab + 3b^2
Explanation: 8a^3 + 27b^3 is a sum of cubes, (2a)^3 + (3b)^3, and a sum of cubes divided by the sum of its cube roots is exact. The quotient is the square of the first root, minus the product of the roots, plus the square of the second root: (2a)^2 - (2a)(3b) + (3b)^2 = 4a^2 - 6ab + 9b^2. Check: (2a + 3b)(4a^2 - 6ab + 9b^2) = 8a^3 + 27b^3.
7Add the polynomials: (3a^2 - 5ab + 2b^2) + (-a^2 + 7ab - 4b^2) + (2a^2 - ab + b^2)
A.4a^2 + 3ab - b^2
B.6a^2 + ab - b^2
C.4a^2 + ab + 7b^2
D.4a^2 + ab - b^2
Explanation: Group like terms and add their coefficients with their signs: for a^2, 3 - 1 + 2 = 4; for ab, -5 + 7 - 1 = 1; for b^2, 2 - 4 + 1 = -1. The sum is 4a^2 + ab - b^2.
8From 5x^3 - 2x^2 + 7 subtract 3x^3 + 4x^2 - x - 2.
A.2x^3 - 6x^2 + x + 9
B.2x^3 + 2x^2 - x + 5
C.-2x^3 + 6x^2 - x - 9
D.2x^3 - 6x^2 - x + 5
Explanation: 'From A subtract B' means A - B. Change the sign of every term of the subtrahend and add: 5x^3 - 2x^2 + 7 - 3x^3 - 4x^2 + x + 2. Reducing like terms gives 2x^3 - 6x^2 + x + 9.
9Subtract -4m^2 + 3mn - n^2 from 2m^2 - mn + 5n^2.
A.-2m^2 + 2mn + 4n^2
B.-6m^2 + 4mn - 6n^2
C.6m^2 - 4mn + 6n^2
D.6m^2 + 2mn + 6n^2
Explanation: The polynomial after 'from' is the minuend: (2m^2 - mn + 5n^2) - (-4m^2 + 3mn - n^2). Changing the signs of the subtrahend gives 2m^2 - mn + 5n^2 + 4m^2 - 3mn + n^2 = 6m^2 - 4mn + 6n^2.
10Simplify: -{-3a + [2a - (a - 4) + 3] - 5}
A.-2a + 2
B.2a - 2
C.2a + 6
D.4a - 2
Explanation: Start inside: -(a - 4) = -a + 4, so the bracket is 2a - a + 4 + 3 = a + 7. The braces then contain -3a + a + 7 - 5 = -2a + 2. The minus sign before the braces changes every sign: -(-2a + 2) = 2a - 2.

About the Heroico Colegio Militar Exam

The Heroico Colegio Militar (HCM) trains officers for the Mexican Army's arms and services (Licenciatura en Administración Militar) and for the Guardia Nacional (Licenciatura en Seguridad Pública). Civilian applicants go through SEDENA's annual admission process, whose academic stage is the examen cultural: 100 questions in 2 hours, with 60 of 100 points as the minimum. For both licenciaturas, SEDENA's 2026 temario lists four subjects, each tied to specific textbook chapters: Español (Zarzar Charur, Taller de Lectura y Redacción 1), Álgebra (Baldor, chapters I–VI), Historia (Rodríguez Arvizu, Historia Universal, chapter 6) and Geografía (Tamayo, Geografía Moderna de México). The official exam is in Spanish. This independent OpenExamPrep bank is an English-language MCQ study adaptation of those topics, keeping Spanish terms and sentences where the grammar and spelling skill requires them; it is not an official translation or a simulation of the exam.

Exam sponsor: Secretaría de la Defensa Nacional (SEDENA) — Dirección General de Educación Militar y Rectoría de la UDEFA y G.N.. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Examen cultural: 100 questions in 2 hours, taken in Spanish on SEDENA's automated evaluation system at the Centro Integral de Evaluación, Campo Militar No. 1-A, Mexico City. The same day includes a 1-hour English diagnostic and a 1-hour-40-minute psychological exam (4 hours 40 minutes in total). Earlier and later stages: document validation and somatometry, a physical capacity exam (land and water tests), a comprehensive medical exam, and a confirmatory medical and toxicology exam.

Time Limit

2 hours (examen cultural)

Passing Score

60/100 (grade 6.0); admission then depends on ranking within SEDENA's quota

Exam / Certification Fees

$0 MXN (no cost)

Exam sponsor website

Reported exam pass rate: Not published. SEDENA does not publish pass rates or applicant-to-admission ratios. 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

Español

Communication process, language functions, basic syntax, accentuation and punctuation (Taller de Lectura y Redacción 1).

Not published

Álgebra

Addition, subtraction, grouping symbols, multiplication, division, and notable products and quotients (Baldor I–VI).

Not published

Historia

Cold War, international organizations, recent events and the 21st century (Historia Universal, chapter 6).

Not published

Geografía

Position, extent, political division, maps, orogenic units, coastlines and islands of Mexico (Tamayo).

Preparing for the Heroico Colegio Militar Exam

What You Need to Know

  • Passing score: 60/100 (grade 6.0); admission then depends on ranking within SEDENA's quota
  • Assessment: Examen cultural: 100 questions in 2 hours, taken in Spanish on SEDENA's automated evaluation system at the Centro Integral de Evaluación, Campo Militar No. 1-A, Mexico City. The same day includes a 1-hour English diagnostic and a 1-hour-40-minute psychological exam (4 hours 40 minutes in total). Earlier and later stages: document validation and somatometry, a physical capacity exam (land and water tests), a comprehensive medical exam, and a confirmatory medical and toxicology exam.
  • Time limit: 2 hours (examen cultural)
  • Exam / certification fees: $0 MXN (no cost) 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

Heroico Colegio Militar: Suggested Study Strategy

1Download the 2026 temario for your licenciatura and study the exact chapters it lists; SEDENA's sample questions cite those books.
2Practise Baldor chapters I–VI by hand, including long division of polynomials and notable products and quotients, because calculators are prohibited.
3Memorize the RAE accentuation rules for agudas, llanas, esdrújulas, hiatus, monosyllables and the tilde diacrítica.
4Learn Mexico's extreme points, coastal states, main islands and orogenic units, and practise converting map scales.
5Build a Cold War timeline from 1945 to 1991 and a table of the founding dates and purposes of major international organizations.
6Train for the physical capacity exam at the same time: it includes a 5-metre decision jump, a 25-metre freestyle swim and a 1,200-metre run.

Frequently Asked Questions

What is the Heroico Colegio Militar examen cultural?

It is the academic stage of SEDENA's admission process for the Heroico Colegio Militar. According to the 2026 convocatoria, it has 100 questions scored from 0 to 100, lasts 2 hours, and requires at least 60 points (a 6.0 grade).

Which subjects does the 2026 HCM temario cover?

For both the Licenciatura en Administración Militar and the Licenciatura en Seguridad Pública, the temario lists Español (Taller de Lectura y Redacción 1), Álgebra (Baldor, chapters I–VI), Historia (Historia Universal, chapter 6 on the contemporary world) and Geografía (Geografía Moderna de México). SEDENA does not publish how many questions come from each subject.

Is English part of the examen cultural?

No. The 2026 convocatoria schedules a separate 1-hour English diagnostic on the same day as the 2-hour examen cultural and the psychological exam. Graduates must also show 60% English proficiency before receiving their degree. This bank does not cover the English diagnostic.

What are the other stages of the admission process?

Candidates go through document validation and somatometry (height and weight), a physical capacity exam with land and water tests, the examen cultural with the English diagnostic and psychological exam, a comprehensive medical exam, and a confirmatory medical and toxicology exam. Passing every stage does not guarantee admission; places go to the highest-ranked candidates within SEDENA's quota.

How much does it cost to apply?

Nothing. The 2026 convocatoria states that the convocatoria and the admission exams have no cost and warns applicants about fraudsters who ask for payment in exchange for admission.

Where is the examen cultural taken?

At the Centro Integral de Evaluación inside Campo Militar No. 1-A in Mexico City, on SEDENA's automated evaluation system. Phones, calculators, watches and other devices are not allowed.

What language is the official exam in, and how does this bank differ?

The official exam is in Spanish, and SEDENA's sample questions cite the textbooks listed in the temario. This independent OpenExamPrep bank is an English-language multiple-choice study adaptation of the same topics. It keeps Spanish words and sentences in grammar and spelling items, but it is not an official translation or a simulation of the exam.

Do candidates for the intensive officer courses take the same exam?

No. The intensive officer courses at the HCM for serving sergeants (CIFOA, Military Police and Guardia Nacional courses) have their own 2026 temarios covering military law, human rights and branch-specific subjects. This bank covers the civilian licenciatura temario only.