100+ Free EMI PSA Practice Questions

Prepare for the Escuela Militar de Ingeniería 'Mcal. Antonio José de Sucre' Prueba de Suficiencia Académica (Bolivia) exam with instant access — no signup required.

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2026 Statistics

Key Facts: EMI PSA Exam

5.1 / 10 (51%)

Passing Score

Reglamento RAC-01

Bs 100

Registration Fee

EMI Portal RIPRE

Math, Physics, Chemistry

Core Subjects

EMI Admission Regulations

Escuela Militar de Ingeniería

Administering Body

EMI Portal Oficial

Spanish

Official Language

EMI Directives

This 100-question practice test is an English-language study adaptation for the Escuela Militar de Ingeniería (EMI) Prueba de Suficiencia Académica (PSA). It covers core secondary STEM disciplines: Mathematics/Algebra (35%), Physics (35%), and Chemistry (30%). The official exam costs Bs 100 and requires a minimum passing grade of 5.1 out of 10.

Sample EMI PSA Practice Questions

Try these sample questions to test your EMI PSA 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 algebraic factorization of the expression 8x^3 - 27y^3?

A.(2x - 3y)(4x^2 + 6xy + 9y^2)

B.(2x - 3y)(4x^2 - 6xy + 9y^2)

C.(2x - 3y)^3

D.(2x + 3y)(4x^2 - 6xy + 9y^2)

Explanation: This is a difference of two cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2). With a = 2x and b = 3y, expanding yields (2x - 3y)((2x)^2 + (2x)(3y) + (3y)^2) = (2x - 3y)(4x^2 + 6xy + 9y^2).

2Simplify (x^2 + x - 12) / (x^2 - 16), retaining the original restrictions x != 4 and x != -4.

A.(x - 3) / (x - 4)

B.(x + 3) / (x - 4)

C.(x - 3) / (x + 4)

D.(x + 4) / (x - 4)

Explanation: Factor the numerator as (x + 4)(x - 3) and the denominator as (x + 4)(x - 4). Canceling the common factor x + 4 gives (x - 3)/(x - 4), while the original restrictions x != -4 and x != 4 remain.

3Solve for x in the rational equation: (3 / (x - 1)) + (2 / (x + 1)) = 4 / (x^2 - 1).

A.x = 3/5

B.x = 5/3

C.x = 1

D.x = -1

Explanation: Multiply both sides by the common denominator (x^2 - 1) = (x - 1)(x + 1): 3(x + 1) + 2(x - 1) = 4 => 3x + 3 + 2x - 2 = 4 => 5x + 1 = 4 => 5x = 3 => x = 3/5.

4What is the sum and product of the roots of the quadratic equation 4x^2 - 12x + 5 = 0?

A.Sum = 3, Product = 5/4

B.Sum = -3, Product = 5/4

C.Sum = 3, Product = -5/4

D.Sum = 12, Product = 5

Explanation: By Vieta's formulas for ax^2 + bx + c = 0: Sum of roots S = -b / a = -(-12) / 4 = 3. Product of roots P = c / a = 5 / 4.

5An engineering laboratory purchases 4 oscilloscopes and 6 multimeters for Bs 9,400. Later, they buy 3 oscilloscopes and 2 multimeters of the same models for Bs 5,800. What is the individual price of one oscilloscope?

A.Bs 1,600

B.Bs 500

C.Bs 1,200

D.Bs 1,800

Explanation: Let x be the price of an oscilloscope and y be the price of a multimeter: (1) 4x + 6y = 9400 => 2x + 3y = 4700; (2) 3x + 2y = 5800. Multiplying (1) by 2 and (2) by 3: 4x + 6y = 9400 and 9x + 6y = 17400. Subtracting gives 5x = 8000 => x = Bs 1,600. (y = Bs 500).

6Solve for x: 9^(x+1) - 28 * 3^x + 3 = 0.

A.x = -2 and x = 1

B.x = 0 and x = 2

C.x = -1 and x = 2

D.x = 1 and x = 3

Explanation: Rewrite 9^(x+1) as 9 * (3^x)^2. Let u = 3^x (u > 0): 9u^2 - 28u + 3 = 0. Factoring: (9u - 1)(u - 3) = 0 => u = 1/9 or u = 3. Since u = 3^x: 3^x = 1/9 = 3^(-2) => x = -2; and 3^x = 3^1 => x = 1.

7If log_10(2) = a and log_10(3) = b, express log_10(75) in terms of a and b.

A.2 - 2a + b

B.2 + a - 2b

C.1 - a + 2b

D.2 - a + b

Explanation: Note that 75 = 3 * 25 = 3 * (100 / 4) = 3 * 100 / 2^2. Thus log_10(75) = log_10(3) + log_10(100) - log_10(2^2) = b + 2 - 2*log_10(2) = 2 - 2a + b.

8Simplify the expression: (1 - tan^2(x)) / (1 + tan^2(x)).

A.cos(2x)

B.sin(2x)

C.tan(2x)

D.sec(2x)

Explanation: Since 1 + tan^2(x) = sec^2(x) = 1 / cos^2(x), and 1 - tan^2(x) = 1 - sin^2(x)/cos^2(x) = (cos^2(x) - sin^2(x)) / cos^2(x). Dividing gives cos^2(x) - sin^2(x) = cos(2x).

9Find all solutions to cos(2x) = cos(x) for x in the interval [0, 2*pi).

A.0, 2*pi/3, and 4*pi/3

B.pi/3, pi, and 5*pi/3

C.0, pi/2, and 3*pi/2

D.pi/6, 5*pi/6, and 3*pi/2

Explanation: cos(2x) - cos(x) = 0 => (2*cos^2(x) - 1) - cos(x) = 0 => 2*cos^2(x) - cos(x) - 1 = 0. Factoring: (2*cos(x) + 1)(cos(x) - 1) = 0. Thus cos(x) = 1 => x = 0; cos(x) = -1/2 => x = 2*pi/3 and x = 4*pi/3.

10What is the equation of the line tangent to the circle x^2 + y^2 = 25 at the point P(3, 4)?

A.3x + 4y - 25 = 0

B.4x - 3y = 0

C.3x - 4y + 7 = 0

D.4x + 3y - 24 = 0

Explanation: For a circle centered at the origin x^2 + y^2 = r^2, the tangent line at (x1, y1) is given by x*x1 + y*y1 = r^2. Substituting (3, 4) gives 3x + 4y = 25 => 3x + 4y - 25 = 0.

About the EMI PSA Exam

Prepare for the Bolivian Military School of Engineering (EMI) PSA admission exam with 100 free practice questions on mathematics, physics, and chemistry. Note: English-language study adaptation.

Assessment

Question count not published by the exam provider

Time Limit

Approximately 1 to 3 hours depending on the applicable evaluation modality

Passing Score

5.1 / 10 (51%) minimum passing score per RAC-01 regulation

Exam Fee

Bs 100 for the direct Prueba de Suficiencia Académica (PSA) (Escuela Militar de Ingeniería 'Mcal. Antonio José de Sucre')

EMI PSA Exam Content Outline

Practice bank: 35%

Matemáticas y Álgebra

Polynomial factoring, rational equations, logarithms, trigonometry, and conic analytic geometry.

Practice bank: 35%

Física

Vectors, kinematics, Newton's laws, static equilibrium, work-energy, hydrostatics, and thermodynamics.

Practice bank: 30%

Química

Quantum numbers, nomenclature, mass stoichiometry, gas laws, solutions, and acid-base pH.

How to Pass the EMI PSA Exam

What You Need to Know

Passing score: 5.1 / 10 (51%) minimum passing score per RAC-01 regulation
Assessment: Question count not published by the exam provider
Time limit: Approximately 1 to 3 hours depending on the applicable evaluation modality
Exam fee: Bs 100 for the direct Prueba de Suficiencia Académica (PSA)

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

EMI PSA Study Tips from Top Performers

1Solve physics and chemistry stoichiometry problems by hand using dimensional analysis and standard SI units.

2Review the laws of exponents and logarithms, quadratic factoring, and trigonometric angle transformation identities.

3Practice multi-step static equilibrium and thermodynamic work calculations.

4Familiarize yourself with basic laboratory solution molarity, dilution, and gas law computations.

Frequently Asked Questions

Who is eligible to take the EMI PSA?

High school graduates (Bachilleres) who present their national identity card, secondary education credentials, and complete the Bs 100 registration fee.

What careers are offered at EMI?

EMI offers accredited engineering programs including Civil, Petroleum and Gas, Systems, Mechatronics, Industrial, Commercial, Environmental, and Agro-industrial Engineering.