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100+ Free COLMIL Examen Intelectual Practice Questions

Prepare for the Colegio Militar del Ejército 'Cnl. Gualberto Villarroel' Examen Intelectual (Bolivia) exam with instant access — no signup required.

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2026 Statistics

Key Facts: COLMIL Examen Intelectual Exam

51/100

Intellectual Minimum

COLMIL Prospecto de Admisión

50% of General Average

Weighting

COLMIL Prospecto de Admisión

5 Subject Modules

Tested Subjects

COLMIL Prospecto de Admisión

Spanish

Delivery Language

Ejército de Bolivia

17–22 years

Age Requirement

COLMIL Admission Guidelines

This 100-question practice test is an English-language study adaptation for the Bolivian Army's Colegio Militar del Ejército (COLMIL) intellectual admission exam. It covers mathematics, physics, language and literature, Bolivian history, and national geography. The official intellectual evaluation requires a minimum score of 51/100 and accounts for 50% of the overall admission ranking.

Sample COLMIL Examen Intelectual Practice Questions

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

1What is the complete factorization of the algebraic expression 4x^2 - 12x + 9?
A.(2x - 3)^2
B.(2x + 3)(2x - 3)
C.(4x - 3)(x - 3)
D.(2x + 3)^2
Explanation: The polynomial 4x^2 - 12x + 9 is a perfect square trinomial of the form (a - b)^2 = a^2 - 2ab + b^2, where a = 2x and b = 3. Expanding (2x - 3)^2 yields (2x)^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9.
2If a military patrol marches at a constant speed of 5 km/h and another motorized unit departs from the same point 2 hours later at 15 km/h along the same route, after how many hours from the departure of the motorized unit will it reach the patrol?
A.1.0 hour
B.1.5 hours
C.2.0 hours
D.2.5 hours
Explanation: In the initial 2 hours, the patrol covers 5 km/h * 2 h = 10 km. The relative speed at which the motorized unit closes the distance is 15 km/h - 5 km/h = 10 km/h. The time required is 10 km / 10 km/h = 1.0 hour.
3What is the solution pair (x, y) for the linear system: 3x + 2y = 19 and 2x - y = 8?
A.x = 5, y = 2
B.x = 4, y = 3.5
C.x = 6, y = 0.5
D.x = 3, y = 5
Explanation: From the second equation, y = 2x - 8. Substituting into the first gives 3x + 2(2x - 8) = 19, which simplifies to 7x - 16 = 19, so 7x = 35 and x = 5. Substituting back gives y = 2(5) - 8 = 2.
4An artillery observation post on a hill 120 meters above level ground observes a target under an angle of depression of 30 degrees. What is the direct line-of-sight distance (slant range) from the post to the target?
A.240 m
B.120*sqrt(3) m (approx. 207.8 m)
C.240*sqrt(3) m (approx. 415.7 m)
D.180 m
Explanation: In a right triangle where the vertical opposite side is h = 120 m and the angle of depression is 30 degrees, sin(30 deg) = opposite / hypotenuse = 120 / d. Since sin(30 deg) = 0.5, d = 120 / 0.5 = 240 m.
5What is the value of x that satisfies the logarithmic equation log_2(x + 6) - log_2(x - 1) = 3?
A.x = 2
B.x = 3
C.x = 4
D.x = 5
Explanation: Using quotient property of logarithms: log_2((x + 6)/(x - 1)) = 3. Converting to exponential form yields (x + 6)/(x - 1) = 2^3 = 8. Thus x + 6 = 8(x - 1) = 8x - 8, which gives 14 = 7x, hence x = 2.
6Simplify the expression: (27^(2/3) * 16^(-1/2)) / 8^(1/3).
A.9/8
B.9/4
C.3/4
D.27/16
Explanation: First, evaluate each term: 27^(2/3) = (cbrt(27))^2 = 3^2 = 9. Next, 16^(-1/2) = 1 / sqrt(16) = 1/4. In the denominator, 8^(1/3) = cbrt(8) = 2. The expression becomes (9 * 1/4) / 2 = (9/4) / 2 = 9/8.
7What are the real roots of the quadratic equation 2x^2 - 5x - 3 = 0?
A.x = 3 and x = -1/2
B.x = -3 and x = 1/2
C.x = 2 and x = -3/2
D.x = 1 and x = -3
Explanation: Factoring the quadratic: 2x^2 - 6x + x - 3 = 2x(x - 3) + 1(x - 3) = (2x + 1)(x - 3) = 0. Setting each factor to zero gives 2x + 1 = 0 => x = -1/2, and x - 3 = 0 => x = 3.
8Which of the following expressions is identically equal to (sin(x) / (1 + cos(x))) + ((1 + cos(x)) / sin(x)) for all valid angles x?
A.2 * csc(x)
B.2 * sec(x)
C.2 * tan(x)
D.2 * cot(x)
Explanation: Finding a common denominator: (sin^2(x) + (1 + cos(x))^2) / (sin(x)(1 + cos(x))) = (sin^2(x) + 1 + 2cos(x) + cos^2(x)) / (sin(x)(1 + cos(x))). Since sin^2(x) + cos^2(x) = 1, numerator becomes 2 + 2cos(x) = 2(1 + cos(x)). Cancelling (1 + cos(x)) leaves 2 / sin(x) = 2 * csc(x).
9What is the equation of the line perpendicular to 2x - 3y + 6 = 0 that passes through the point (4, -1)?
A.3x + 2y - 10 = 0
B.3x - 2y - 14 = 0
C.2x + 3y - 5 = 0
D.-3x + 2y + 14 = 0
Explanation: The given line 2x - 3y + 6 = 0 has slope m1 = 2/3. A perpendicular line has slope m2 = -3/2. Using point-slope formula with (4, -1): y - (-1) = (-3/2)(x - 4) => 2(y + 1) = -3(x - 4) => 2y + 2 = -3x + 12 => 3x + 2y - 10 = 0.
10In triangle ABC, side a = 7 cm, side b = 8 cm, and the included angle C = 60 degrees. What is the length of side c?
A.sqrt(57) cm (approx. 7.55 cm)
B.sqrt(113) cm (approx. 10.63 cm)
C.sqrt(65) cm (approx. 8.06 cm)
D.sqrt(97) cm (approx. 9.85 cm)
Explanation: Applying the Law of Cosines: c^2 = a^2 + b^2 - 2ab*cos(C) = 7^2 + 8^2 - 2(7)(8)*cos(60 deg) = 49 + 64 - 112*(0.5) = 113 - 56 = 57. Thus c = sqrt(57) cm.

About the COLMIL Examen Intelectual Exam

Prepare for the Bolivian Army Military Academy (COLMIL) intellectual admission exam with 100 free practice questions covering mathematics, physics, language, Bolivian history, and geography. Note: English-language study adaptation for the official Bolivian assessment.

Assessment

Question count not published by the exam provider

Time Limit

Not published as a single fixed duration; administered in subject sessions

Passing Score

At least 51/100 on the intellectual evaluation; contributes 50% to the general admission average

Exam Fee

Published prospect fee and medical/laboratory costs per annual admission directive (Colegio Militar del Ejército 'Cnl. Gualberto Villarroel')

COLMIL Examen Intelectual Exam Content Outline

Practice bank: 20%

Matemática

Algebraic factoring, equations, systems of linear equations, quadratic formulas, logarithms, and trigonometry.

Practice bank: 20%

Física

Vectors, linear and projectile kinematics, Newton's laws, mechanical energy, power, and hydrostatics.

Practice bank: 20%

Lenguaje y Literatura

Spanish orthography, accentuation, sentence syntax, textual comprehension, and classic Bolivian authors.

Practice bank: 20%

Historia de Bolivia

From Tiwanaku and colonial Charcas through the 1825 independence, Pacific War, Chaco War, and 1952 Revolution.

Practice bank: 20%

Geografía de Bolivia

The three physiographic regions, drainage basins, international borders, mining reserves, and national parks.

How to Pass the COLMIL Examen Intelectual Exam

What You Need to Know

  • Passing score: At least 51/100 on the intellectual evaluation; contributes 50% to the general admission average
  • Assessment: Question count not published by the exam provider
  • Time limit: Not published as a single fixed duration; administered in subject sessions
  • Exam fee: Published prospect fee and medical/laboratory costs per annual admission directive

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

COLMIL Examen Intelectual Study Tips from Top Performers

1Practice solving algebra, trigonometry, and physics problems by hand with worked numerical solutions.
2Review key dates, commanders, and treaties of Bolivian military history, especially the Battle of Aroma, Ingavi, Alto de la Alianza, and the defenses of Boquerón and Villamontes.
3Memorize Bolivia's hydrographic network, including the main tributaries of the Amazon, Del Plata, and Endorheic basins, as well as key mineral deposits like lithium in Uyuni and iron in El Mutún.
4Reinforce Spanish grammatical rules, orthography, and the major works of authors such as Augusto Céspedes, Alcides Arguedas, and Nataniel Aguirre.

Frequently Asked Questions

What are the eligibility requirements for COLMIL admission?

Applicants must be Bolivian by birth, single with no children, aged 17 to 22, hold a high school diploma (Bachiller), and have clean police and judicial records.

How is the final COLMIL admission list determined?

Admission is granted strictly by ranked merit average based on the intellectual examination (50%), physical fitness evaluation, and satisfactory completion of medical and psychological stages.