Free Practice Questions for Cuba University Entrance Math Exam

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Exam pass rate: 52.7% in Mathematics in the sitting reported by Cubadebate, the weakest of the three subjects

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Key Facts: Cuba University Entrance Math Exam Exam

3 compulsory subjects

Applicants to the Curso Diurno sit Matemática, Español and Historia de Cuba

Resolución 129/2018 del MES, Artículo 2

60 of 100 points

Minimum mark for a paper to count as passed and enter the first allocation round

Resolución 129/2018 del MES, Artículo 3

52.7% passed Mathematics

Mathematics is the weakest of the three papers, against 92.1% in Spanish and 76.4% in History

Cubadebate, resultados de los exámenes de ingreso

96,305 places

Higher-education places offered for the 2026-2027 course across day, encuentros and distance modes

Granma, 25 March 2026, MES press conference

Suspended for 2026-2027

MES cancelled the June 2026 sittings over the energy crisis and allocated places on academic index

Mesa Redonda, 19 May 2026; Radio Rebelde, 20 May 2026

2 sittings per year

Each cycle has a Convocatoria Ordinaria and a Convocatoria Especial for justified absences

Universidad de La Habana, Nota Informativa sobre el Proceso de Ingreso

Cuba's national university entrance Mathematics exam is a Spanish-language written paper of multi-part development exercises scored 0–100, with 60 points setting priority in the first round of degree allocation. It covers algebra, functions, systems, trigonometry and geometry. MES suspended the exams for the 2026-2027 cycle because of the energy crisis without abolishing them. This 100-question English MCQ bank adapts the syllabus for structured study.

Sample Cuba University Entrance Math Exam Practice Questions

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

1Which of the following represents the simplified form of the radical expression sqrt(75) - sqrt(27) + sqrt(12)?

A.4*sqrt(3)

B.3*sqrt(3)

C.2*sqrt(3)

D.6*sqrt(3)

Explanation: Factoring each radicand into prime factors gives sqrt(75) = sqrt(25*3) = 5*sqrt(3), sqrt(27) = sqrt(9*3) = 3*sqrt(3), and sqrt(12) = sqrt(4*3) = 2*sqrt(3). Combining like terms yields 5*sqrt(3) - 3*sqrt(3) + 2*sqrt(3) = 4*sqrt(3).

2What is the result of rationalizing the denominator of the expression 6 / (sqrt(5) - sqrt(2))?

A.2*(sqrt(5) + sqrt(2))

B.3*(sqrt(5) + sqrt(2))

C.6*(sqrt(5) + sqrt(2))

D.2*(sqrt(5) - sqrt(2))

Explanation: Multiply numerator and denominator by the conjugate (sqrt(5) + sqrt(2)). The denominator becomes (sqrt(5))^2 - (sqrt(2))^2 = 5 - 2 = 3. Dividing the numerator 6*(sqrt(5) + sqrt(2)) by 3 gives 2*(sqrt(5) + sqrt(2)).

3What is the complete real solution set for the absolute value equation |2x - 5| = 9?

A.x = 7 and x = -2

B.x = 7 and x = 2

C.x = -7 and x = 2

D.x = 14 and x = -4

Explanation: The equation |2x - 5| = 9 splits into two linear cases: 2x - 5 = 9, which yields 2x = 14 so x = 7; and 2x - 5 = -9, which yields 2x = -4 so x = -2. Both solutions satisfy the original equation.

4What is the solution set of the linear inequality (3x - 4) / 2 <= (x + 2) / 3?

A.(-infinity, 16/7]

B.[16/7, infinity)

C.(-infinity, 8/7]

D.(-infinity, 16/5]

Explanation: Multiplying both sides by 6 (the least common multiple of 2 and 3) preserves the inequality direction: 3*(3x - 4) <= 2*(x + 2), leading to 9x - 12 <= 2x + 4. Subtracting 2x and adding 12 gives 7x <= 16, hence x <= 16/7, which corresponds to the interval (-infinity, 16/7].

5What is the completely factored form over the real numbers of the polynomial P(x) = x^3 - 4x^2 - x + 4?

A.(x - 4)(x - 1)(x + 1)

B.(x + 4)(x - 1)(x + 1)

C.(x - 4)(x - 1)^2

D.(x - 2)(x + 2)(x - 1)

Explanation: Grouping terms yields x^2(x - 4) - 1(x - 4) = (x - 4)(x^2 - 1). Factoring the difference of squares x^2 - 1 gives (x - 4)(x - 1)(x + 1).

6What is the solution set for the fractional equation x / (x - 2) - 2 / (x + 2) = 8 / (x^2 - 4)?

A.Empty set (no real solution)

B.x = 2

C.x = -2

D.x = 2 and x = -2

Explanation: The common denominator is (x - 2)(x + 2) = x^2 - 4 with domain restrictions x != 2 and x != -2. Multiplying by the common denominator yields x(x + 2) - 2(x - 2) = 8, which simplifies to x^2 + 2x - 2x + 4 = 8, so x^2 + 4 = 8, giving x^2 = 4 and x = +/-2. Because both values violate the domain restrictions, they are extraneous, and the solution set is empty.

7What is the real solution to the irrational equation sqrt(2x + 3) - x = 0?

A.x = 3

B.x = -1

C.x = 3 and x = -1

D.x = 1

Explanation: Isolating the radical gives sqrt(2x + 3) = x, which requires x >= 0. Squaring both sides produces 2x + 3 = x^2, or x^2 - 2x - 3 = 0. Factoring gives (x - 3)(x + 1) = 0, so candidate roots are x = 3 and x = -1. Checking in the original equation: for x = 3, sqrt(6 + 3) - 3 = 3 - 3 = 0 (valid); for x = -1, sqrt(-2 + 3) - (-1) = 1 + 1 = 2 != 0 (extraneous). Thus x = 3 is the only solution.

8What is the real solution to the exponential equation 2^(x + 2) + 2^x = 20?

A.x = 2

B.x = 1

C.x = 3

D.x = 4

Explanation: Rewrite 2^(x + 2) as 2^x * 2^2 = 4 * 2^x. Then 4 * 2^x + 2^x = 20, which simplifies to 5 * 2^x = 20. Dividing by 5 yields 2^x = 4 = 2^2, so x = 2.

9What is the solution set of the logarithmic equation log2(x + 3) + log2(x - 1) = 5?

A.x = 5

B.x = -7

C.x = 5 and x = -7

D.x = 7

Explanation: The domain requires x + 3 > 0 and x - 1 > 0, so x > 1. Applying logarithm properties gives log2((x + 3)(x - 1)) = 5, so (x + 3)(x - 1) = 2^5 = 32. Expanding gives x^2 + 2x - 3 = 32, or x^2 + 2x - 35 = 0. Factoring yields (x + 7)(x - 5) = 0, giving x = 5 and x = -7. Since x = -7 violates the domain restriction x > 1, x = 5 is the unique solution.

10What is the solution set for the quadratic inequality x^2 - 3x - 10 <= 0?

A.[-2, 5]

B.(-infinity, -2] U [5, infinity)

C.[-5, 2]

D.(-2, 5)

Explanation: Factoring the quadratic gives (x - 5)(x + 2) <= 0. The roots of the corresponding equation are x = -2 and x = 5. Since the parabola opens upward (leading coefficient positive), the quadratic is less than or equal to zero between the roots, which gives the closed interval [-2, 5].

About the Cuba University Entrance Math Exam Exam

The Examen de Ingreso a la Educación Superior en Matemática is Cuba's national university entrance examination in Mathematics, administered by the Ministerio de Educación Superior (MES) in coordination with the Ministerio de Educación (MINED) and required of applicants to the Curso Diurno under Resolución 129/2018. It assesses competencies developed across the three-year pre-university cycle (grades 10, 11 and 12): numerical domains and algebraic manipulation, function analysis, systems of equations and practical word problems, trigonometric identities and equations, and plane and spatial Euclidean geometry. The paper is written entirely in Spanish and scored 0–100, with 60 points the threshold for the first round of career allocation. IMPORTANT 2026 STATUS: on 19 May 2026 the MES announced that the entrance exams would not be held for the 2026-2027 admission cycle because of the national energy crisis, and that places would be allocated on accumulated academic index instead; the ministry stated the following day that the exams remain its preferred mechanism, and no decision has been published abolishing them permanently. This 100-question practice bank is an English-language multiple-choice study adaptation of the same syllabus, not an official translation and not a simulation of the exam's written-development format.

Exam sponsor: Ministerio de Educación Superior (MES). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Administered on the same day and hour across every Cuban province in a single morning session beginning at 09:00. The paper comprises multi-part problem exercises covering algebraic manipulation, functions, systems and word problems, trigonometry, and plane and solid Euclidean geometry, with the full working shown by hand.

Time Limit

Single morning session from 09:00; official duration not published by MES

Passing Score

60 / 100

Exam / Certification Fees

Free (no examination or registration fee; university education in Cuba is free)

Exam sponsor website

Reported exam pass rate: 52.7% in Mathematics in the sitting reported by Cubadebate, the weakest of the three subjects. Mathematics is consistently the hardest of the three papers: in the sitting reported by Cubadebate, 52.7% passed Mathematics against 92.1% in Spanish and 76.4% in History, and only 50.4% of the 21,942 candidates passed all three. In 2024-2025, 51.5% of the 18,402 candidates presented passed. Since 2023 reaching 60 points is no longer required to obtain a place: it determines priority in the first round of career allocation, while candidates who fail or do not sit receive remaining vacancies in later rounds. This describes exam candidates, not OpenExamPrep users or results from using our resources. 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.

24 practice questions

Dominios Numéricos y Trabajo Algebraico (Numerical Domains and Algebra)

Properties of real numbers, radicals, fractional exponents, absolute value equations and inequalities, polynomial factorization, algebraic fraction simplification, exponential, logarithmic, and irrational equations.

16 practice questions

Funciones y sus Propiedades (Functions and Graphs)

Linear, quadratic, exponential, logarithmic, and trigonometric functions: domain, range, zeroes, monotonicity, intervals of sign, graphical transformations, symmetry, asymptotes, and extrema.

15 practice questions

Sistemas de Ecuaciones y Problemas Prácticos (Systems and Applications)

Linear and non-linear systems in two and three variables, matrix elimination, applied word problems (motion, mixture, rate of work, geometry, economics), and domain restrictions.

20 practice questions

Trigonometría (Trigonometry)

Trigonometric ratios, fundamental Pythagorean identities, reduction to first quadrant, sum and difference formulas, double angles, trigonometric equations, sine and cosine laws, and oblique triangle solving.

25 practice questions

Geometría Plana y del Espacio (Plane and Solid Geometry)

Angle relations, triangle congruence and similarity, Thales and Pythagoras theorems, quadrilateral properties, circles, arcs, chords, tangents, inscribed angles, polygon areas, and surface areas and volumes of prisms, pyramids, cylinders, cones, and spheres.

Preparing for the Cuba University Entrance Math Exam Exam

What You Need to Know

Passing score: 60 / 100
Assessment: Administered on the same day and hour across every Cuban province in a single morning session beginning at 09:00. The paper comprises multi-part problem exercises covering algebraic manipulation, functions, systems and word problems, trigonometry, and plane and solid Euclidean geometry, with the full working shown by hand.
Time limit: Single morning session from 09:00; official duration not published by MES
Exam / certification fees: Free (no examination or registration fee; university education in Cuba is free) 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

Cuba University Entrance Math Exam: Suggested Study Strategy

1Master exact longhand arithmetic: the paper is marked on the procedure you write out, so practise factoring, radical simplification and exact trigonometric values without relying on a calculator.

2Memorize exact trigonometric values (0, 30, 45, 60, 90 degrees) and fundamental identities: Pythagorean relations, angle addition, and double-angle formulas appear consistently.

3Check solutions against domain constraints: irrational equations, logarithmic equations, and rational expressions often yield extraneous roots that must be tested against the original domain.

4Structure geometric proofs logically: state known theorems (e.g. angle subtended by a diameter is 90°, opposite angles of a cyclic quadrilateral sum to 180°, Thales' theorem) step-by-step.

5Practice word problem translation: assign variables clearly, set up system equations, and verify that final values are physically realistic.

Frequently Asked Questions

What is the Examen de Ingreso de Matemática in Cuba?

It is the national standardized university entrance examination in Mathematics administered across Cuba by the Ministerio de Educación Superior (MES) for pre-university graduates seeking admission to higher education institutions.

Will the entrance exams be held for the 2026-2027 course?

No. On 19 May 2026 the ministers of Education and Higher Education announced that the exams scheduled for 5, 9 and 12 June 2026 would not take place because of the energy crisis, and that places would be allocated on students' accumulated academic index. MES said the day after that entrance exams remain the best mechanism for ordering access, and has published no decision abolishing them, so the syllabus remains the reference for future sittings.

What is the passing score and how does it affect university placement?

The examination is graded from 0 to 100 points. Scoring 60 points or above allows the candidate to enter the first round of university major allocations based on academic ranking. Those who score below 60 or do not sit may receive unfilled vacancies in subsequent allocation phases.

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

MES publishes neither a fixed item count nor an official duration. The paper is a set of multi-part development exercises (preguntas de desarrollo con incisos) sat in a single morning session that starts at 09:00 on the same day and hour in every province.

Why is this practice bank in English when the official exam is in Spanish?

The official Cuban examination is administered exclusively in Spanish. This practice bank provides an English-language MCQ study adaptation for international learners and bilingual candidates, testing the identical mathematical concepts, formulas, and theorems.

What happens if an applicant misses or fails the ordinary sitting?

MES schedules a Convocatoria Especial for applicants who missed the ordinary sitting for extremely justified reasons. Applicants who fail are not excluded: since 2023 they receive places in the second and later rounds of allocation, and they may ask the Comisión de Ingreso Provincial to sit again the following year.