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Exam Review

Key Facts: UNAM Licenciatura Exam

120

Four-option multiple-choice questions on the UNAM licenciatura selection exam

UNAM DGAE, Instructivo Licenciatura 2026

3 hours

Maximum effective time to answer the 120 questions

UNAM DGAE, Instructivo Licenciatura 2026

MXN 490

Fee for the 2026 selection exam and applicant identification

UNAM DGAE, Instructivo Licenciatura 2026

7.0

Minimum bachillerato average required to enroll after being selected

UNAM DGAE, Instructivo Licenciatura 2026

10

Filosofía questions, included only in the Área 4 (Humanidades y Artes) exam

UNAM, Guía para preparar el examen de selección (Área 4)

UNAM's licenciatura entrance exam has 120 four-option questions in up to 3 hours, with a subject mix set by the applicant's knowledge area; places go to the highest scores for each program.

Sample UNAM Licenciatura Practice Questions

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

1Solve for x in the linear equation: 5(2x - 3) - 4(x + 2) = 7.
A.x = 7/3
B.x = 5
C.x = 3
D.x = -8/3
Explanation: Expanding both terms yields 10x - 15 - 4x - 8 = 7. Combining like terms gives 6x - 23 = 7. Adding 23 to both sides results in 6x = 30, which simplifies to x = 5.
2What is the solution to the system of linear equations: 3x + 2y = 16 x - y = 2?
A.x = 2, y = 4
B.x = 2, y = 5
C.x = 6, y = 4
D.x = 4, y = 2
Explanation: From the second equation, x = y + 2. Substituting into the first: 3(y + 2) + 2y = 16, so 5y + 6 = 16 and y = 2. Then x = 2 + 2 = 4. Check: 3(4) + 2(2) = 16 and 4 - 2 = 2.
3Factor the quadratic expression: x² - 5x - 24.
A.(x - 8)(x + 3)
B.(x + 8)(x - 3)
C.(x - 6)(x + 4)
D.(x + 6)(x - 4)
Explanation: We need two numbers that multiply to -24 and add to -5. The numbers -8 and +3 satisfy (-8)(3) = -24 and -8 + 3 = -5. Thus, the factored form is (x - 8)(x + 3).
4What are the roots of the quadratic equation: 3x² - 10x + 3 = 0?
A.x = -3 and x = -1/3
B.x = 9 and x = 1
C.x = 3 and x = 1/3
D.x = 3 and x = -1/3
Explanation: Using the quadratic formula x = [-b ± sqrt(b² - 4ac)] / (2a) with a = 3, b = -10, c = 3: the discriminant is (-10)² - 4(3)(3) = 100 - 36 = 64, whose square root is 8. Thus x = (10 ± 8) / 6, giving x = 18/6 = 3 and x = 2/6 = 1/3. Equivalently, 3x² - 10x + 3 = (3x - 1)(x - 3).
5Simplify the expression: (2a³b²)⁴ / (4a⁶b⁵).
A.2a⁶b³
B.4ab
C.4a⁶b³
D.(1/2)a⁶b³
Explanation: Expanding the numerator: (2a³b²)⁴ = 2⁴ * (a³)⁴ * (b²)⁴ = 16a¹²b⁸, because a power of a power multiplies the exponents. Dividing by the denominator: (16a¹²b⁸) / (4a⁶b⁵) = (16/4) * a¹²⁻⁶ * b⁸⁻⁵ = 4a⁶b³.
6Simplify the rational algebraic expression for all values where it is defined: (x² - 9) / (x² - 2x - 15).
A.(x - 3) / (x - 5)
B.(x + 3) / (x - 5)
C.(x - 3) / (x + 5)
D.(x + 3) / (x + 5)
Explanation: The numerator is a difference of squares: x² - 9 = (x - 3)(x + 3). The denominator factors into (x - 5)(x + 3). Canceling the common factor (x + 3) yields (x - 3) / (x - 5).
7Solve the linear inequality for real x: 3x - 5 <= 5x + 7.
A.x <= -6
B.x >= 6
C.x >= -1
D.x >= -6
Explanation: Subtracting 3x from both sides gives -5 <= 2x + 7. Subtracting 7 from both sides yields -12 <= 2x. Dividing both sides by the positive number 2 preserves the inequality direction, resulting in -6 <= x, which is equivalently written as x >= -6.
8What is the equation of the line passing through the points P(2, -1) and Q(4, 5) in slope-intercept form?
A.y = 3x + 5
B.y = 3x - 7
C.y = 2x - 5
D.y = (1/3)x - 5/3
Explanation: The slope is m = (y₂ - y₁) / (x₂ - x₁) = (5 - (-1)) / (4 - 2) = 6 / 2 = 3. Using point-slope form with (2, -1): y - (-1) = 3(x - 2) => y + 1 = 3x - 6 => y = 3x - 7. Check with Q: 3(4) - 7 = 5.
9What is the distance between the points A(-3, 2) and B(5, -4) in the Cartesian plane?
A.14
B.8
C.2*sqrt(7)
D.10
Explanation: Using the distance formula d = sqrt[(x₂ - x₁)² + (y₂ - y₁)²]: d = sqrt[(5 - (-3))² + (-4 - 2)²] = sqrt[8² + (-6)²] = sqrt[64 + 36] = sqrt[100] = 10.
10Which of the following lines is perpendicular to the line with equation 3x - 4y + 8 = 0?
A.3x + 4y - 6 = 0
B.4x + 3y - 6 = 0
C.4x - 3y + 2 = 0
D.3x - 4y - 5 = 0
Explanation: Rewriting 3x - 4y + 8 = 0 in slope-intercept form gives 4y = 3x + 8, so m₁ = 3/4. Two non-vertical lines are perpendicular if and only if m₁ * m₂ = -1, meaning m₂ = -4/3. For 4x + 3y - 6 = 0, 3y = -4x + 6 => y = (-4/3)x + 2, which has slope -4/3.

About the UNAM Licenciatura Exam

Independent UNAM licenciatura admission practice by OpenExamPrep. The Concurso de Selección para Ingreso a Licenciatura is UNAM's competitive undergraduate entrance exam, run by the Dirección General de Administración Escolar. Every applicant answers 120 four-option multiple-choice questions in up to 3 hours; the subject mix depends on the knowledge area of the chosen degree, and only Área 4 (Humanidades y Artes) includes Filosofía. Places go to the applicants with the most correct answers for each program. The official exam is written in Spanish. This bank is an English-language MCQ study adaptation, not an official translation or a simulation of the exam: Spanish-language items keep their Spanish sentences, and the questions mirror the official subject mix averaged across the four areas.

Exam sponsor: Universidad Nacional Autónoma de México (UNAM) — Dirección General de Administración Escolar (DGAE). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

120 four-option questions in every area. Área 1: Español 18, Matemáticas 26, Física 16, Química 10, Biología 10, Historia Universal 10, Historia de México 10, Literatura 10, Geografía 10. Área 2: Matemáticas 24, Física 12, Química 13, Biología 13, other subjects as in Área 1. Área 3: Matemáticas 24, Física 10, Historia Universal 14, Historia de México 14, other subjects 10 each plus Español 18. Área 4: Matemáticas 22, Física 10, Filosofía 10, other subjects 10 each plus Español 18.

Time Limit

Up to 3 hours

Passing Score

No fixed pass mark: places are assigned in descending order of aciertos (correct answers out of 120) until each program is full, and a bachillerato average of at least 7.0 is required

Exam / Certification Fees

MXN 490 (2026 Concurso de Selección)

Exam sponsor website

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

Official sources

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.

18-22%

Matemáticas

22-26 questions depending on the area: algebra, equations, analytic geometry, trigonometry, functions; calculus only in Áreas 1 and 2

15%

Español

18 questions: language functions, reading comprehension, grammar, syntax, orthography, accentuation, and punctuation

8-13%

Física

10-16 questions: kinematics, dynamics, energy, fluids, heat, waves, electricity, and optics

8-11%

Química

10-13 questions: atomic structure, periodic table, bonding, stoichiometry, solutions, acids and bases; carbon chemistry only in Área 2

8-11%

Biología

10-13 questions: cells, metabolism, genetics, evolution, and ecology

8-12%

Historia Universal

10-14 questions: Enlightenment and revolutions, industrialization, imperialism, world wars, Cold War

8-12%

Historia de México

10-14 questions: Mesoamerica, New Spain, Independence, Reform, Porfiriato, Revolution, 20th century

8%

Literatura

10 questions: genres, figures of speech, versification, drama, and literary movements

8%

Geografía

10 questions: coordinates and map scale, tectonics, atmosphere and climate, and the geography of Mexico

Área 4 only (10 questions)

Filosofía

Logic and argument types, ethics and moral norms, and the disciplines of philosophy

Preparing for the UNAM Licenciatura Exam

What You Need to Know

  • Passing score: No fixed pass mark: places are assigned in descending order of aciertos (correct answers out of 120) until each program is full, and a bachillerato average of at least 7.0 is required
  • Assessment: 120 four-option questions in every area. Área 1: Español 18, Matemáticas 26, Física 16, Química 10, Biología 10, Historia Universal 10, Historia de México 10, Literatura 10, Geografía 10. Área 2: Matemáticas 24, Física 12, Química 13, Biología 13, other subjects as in Área 1. Área 3: Matemáticas 24, Física 10, Historia Universal 14, Historia de México 14, other subjects 10 each plus Español 18. Área 4: Matemáticas 22, Física 10, Filosofía 10, other subjects 10 each plus Español 18.
  • Time limit: Up to 3 hours
  • Exam / certification fees: MXN 490 (2026 Concurso de Selección) 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

UNAM Licenciatura: Suggested Study Strategy

1Download the official DGAE study guide for your area, because the number of questions per subject changes from Área 1 to Área 4.
2Practice arithmetic and algebra by hand, since calculators are not allowed during the exam.
3Give Español steady attention: its 18 questions are the same in every area and cover accentuation, punctuation, grammar and reading.
4If you apply to Área 1 or 2, include limits, derivatives and integrals; if you apply to Área 4, prepare the 10 Filosofía questions on logic and ethics.
5Take timed 120-question practice sessions to build the pace needed to finish within 3 hours.

Frequently Asked Questions

What is the UNAM licenciatura admission exam?

It is the selection exam of UNAM's Concurso de Selección para Ingreso a Licenciatura, run by the Dirección General de Administración Escolar (DGAE). Applicants who do not have pase reglamentado take it to compete for a place in a specific degree program, campus and study system (escolarizado or SUAyED).

How many questions are on the UNAM exam and how long is it?

The exam has 120 multiple-choice questions with four answer options, and applicants have up to 3 hours to answer them. Calculators, phones and other electronic devices are not allowed. Your score is the number of correct answers (aciertos).

Does the exam change by knowledge area?

Yes. Everyone answers 120 questions, but the number per subject depends on the area of the chosen degree. For example, Área 1 has 26 Matemáticas and 16 Física questions, Área 3 has 14 questions each of Historia Universal and Historia de México, and only Área 4 includes 10 Filosofía questions. Español always has 18 questions.

What score do I need to get into UNAM?

There is no fixed passing score. Places for each program are filled in descending order of aciertos, so the cutoff depends on that year's demand and places. You must also finish bachillerato with an average of at least 7.0.

Is the UNAM exam online or in person?

In 2026 the exam was taken online from home using UNAM's secure browser with webcam and microphone. After reviewing that process, UNAM announced on 4 September 2026 that, until secure online conditions are guaranteed, entrance exams will be taken in person on preloaded electronic devices at venues around the country. Check the next DGAE call for the exact format.

Is the exam in Spanish, and why is this practice bank in English?

The official exam is in Spanish, and applicants whose first language is not Spanish must pass a CEPE Spanish exam to enroll. OpenExamPrep publishes this bank as an English-language MCQ study adaptation for learners who prepare in English. It is not an official translation or a simulation of the exam; Spanish grammar, spelling and reading items keep their Spanish sentences so the tested skill is preserved.