100+ Free Romanian BAC Math Practice Questions

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Question 1

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Find the term containing x⁴ in the expansion of (x + 2)⁶.

240x⁴

120x⁴

60x⁴

15x⁴

to track

2026 Statistics

Key Facts: Romanian BAC Math Exam

The Romanian Bacalaureat Mathematics paper (Proba E.c) is a 3-hour written exam covering algebra, calculus, matrices, trigonometry, and (for M_mate-info) algebraic structures; a grade ≥ 5/10 is required to pass.

Sample Romanian BAC Math Practice Questions

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

1The arithmetic mean of two positive numbers is 6.5 and their product is 36. What is the larger of the two numbers?

A.9

B.12

C.4

D.8

Explanation: Let the two numbers be a and b. Then a+b = 13 and ab = 36. They satisfy t² − 13t + 36 = 0. Discriminant = 169 − 144 = 25, so t = (13 ± 5)/2. Thus t = 9 or t = 4. The larger number is 9.

2Three numbers form an arithmetic progression with common difference d = 3. If the middle term is 7, what is the product of all three terms?

A.280

B.240

C.210

D.160

Explanation: The three terms of an AP with middle term 7 and common difference 3 are: 7−3=4, 7, and 7+3=10. Their product is 4 × 7 × 10 = 280.

3Find the real number x such that x, 8, and 2x+1 are consecutive terms of an arithmetic progression.

A.5

B.3

C.7

D.−1

Explanation: For three numbers to be consecutive terms of an AP, the middle term equals the average of the first and third: 8 = (x + 2x+1)/2. Multiplying both sides by 2: 16 = 3x+1, so 3x = 15, thus x = 5. Verification: the terms are 5, 8, 11 — equal common difference 3 ✓.

4The first term of a geometric progression is 2 and the common ratio is 3. What is the sum of the first 4 terms?

A.80

B.78

C.82

D.76

Explanation: The sum of the first n terms of a geometric progression is Sₙ = a₁(rⁿ − 1)/(r − 1). With a₁ = 2, r = 3, n = 4: S₄ = 2(3⁴ − 1)/(3 − 1) = 2(81 − 1)/2 = 2 × 80/2 = 80. Alternatively: 2 + 6 + 18 + 54 = 80.

5Solve the equation log₅(x) + log₅(x − 4) = 1 for real x.

A.x = 5

B.x = 4

C.x = 1

D.x = 6

Explanation: Using the logarithm product rule: log₅(x(x−4)) = 1, so x(x−4) = 5. This gives x² − 4x − 5 = 0, which factors as (x−5)(x+1) = 0, so x = 5 or x = −1. Since the arguments of logarithms must be positive (x > 0 and x > 4), we need x > 4. Only x = 5 satisfies this. Verification: log₅(5) + log₅(1) = 1 + 0 = 1 ✓.

6Solve the equation log₅(x²) = log₅(4x + 5) for real x > 0.

A.x = 5

B.x = 1

C.x = −1

D.x = 25

Explanation: Since the logarithm base 5 is one-to-one, log₅(x²) = log₅(4x+5) implies x² = 4x+5. Rearranging: x² − 4x − 5 = 0, which factors as (x−5)(x+1) = 0, giving x = 5 or x = −1. Since x > 0, the only valid solution is x = 5. Verification: log₅(25) = log₅(25) ✓.

7How many 2-digit natural numbers with distinct digits, having an odd tens digit, can be formed using digits from the set A = {1, 3, 5, 7, 8}?

A.16

B.20

C.12

D.18

Explanation: The tens digit must be odd and from A: choices are 1, 3, 5, 7 — that is 4 options. The units digit must differ from the tens digit and be from A: for each tens choice, the remaining 4 elements of A are available. So the count is 4 × 4 = 16.

8In a Cartesian coordinate system, points A(0, 5) and B(3, 4) are given. Find the coordinates of point C such that 3·OC⃗ = OA⃗ + OB⃗.

A.(1, 3)

B.(3, 1)

C.(1, 2)

D.(2, 1)

Explanation: OA⃗ = (0, 5) and OB⃗ = (3, 4). Their sum is (3, 9). Dividing by 3: C = (1, 3). So the coordinates of C are (1, 3).

9Given the matrix A = [[2, 1], [3, 4]], which of the following equals det(A)?

A.5

B.11

C.−5

D.8

Explanation: For a 2×2 matrix A = [[a, b], [c, d]], det(A) = ad − bc. Here det(A) = 2·4 − 1·3 = 8 − 3 = 5.

10For what values of a is the matrix A(a) = [[1, a], [2, a+1]] invertible?

A.a ≠ −1

B.a ≠ 1

C.a ≠ 0

D.all real a

Explanation: A matrix is invertible if and only if its determinant is non-zero. det(A) = 1·(a+1) − a·2 = a+1 − 2a = 1 − a. Setting det(A) = 0 gives 1 − a = 0, so a = 1. Therefore A(a) is invertible for all a ≠ 1.

About the Romanian BAC Math Exam

The Romanian Bacalaureat (Examenul Național de Bacalaureat) is the national secondary-school-leaving certificate required for university admission in Romania. Mathematics is tested in Proba E.c (the compulsory profile paper) for graduates of the real profile. Four differentiated programs exist: M_mate-info (mathematics-informatics, the most rigorous), M_șt-nat (natural sciences), M_tehnologic, and M_pedagogic. The M_mate-info program covers algebra, complex numbers, combinatorics, matrices and systems, trigonometry and analytic geometry, limits and continuity, derivatives and function study, definite integrals, and algebraic structures (groups, rings, fields). The written paper carries 90 points across 10 compulsory problems, plus 10 points awarded automatically, yielding a grade out of 10. A grade of at least 5.00 is required to pass each paper. The 2026 Bacalaureat main session is held in June–July 2026, with an autumn resit in August.

Questions

100 scored questions

Time Limit

180 minutes (3 hours) for the written mathematics paper.

Passing Score

5.00/10.00 on each written paper; overall Bacalaureat average ≥ 6.00 with no paper below 5.00.

Exam Fee

Free — the Bacalaureat is a state-funded national examination for Romanian high school graduates. (Centrul Național pentru Curriculum și Evaluare (CNCE), Ministerul Educației al României)

Romanian BAC Math Exam Content Outline

15%

Algebra & Real Numbers

Powers, radicals, logarithms, equations, inequalities, arithmetic and geometric progressions.

15%

Functions & Equations

Quadratic, exponential, logarithmic, trigonometric functions; injectivity, surjectivity, inverse and composite functions.

Complex Numbers

Algebraic and trigonometric form, modulus, argument, de Moivre's theorem, roots of unity.

10%

Combinatorics & Probability

Permutations, arrangements, combinations, binomial theorem, basic probability calculations.

15%

Matrices, Determinants & Systems

Matrix operations, determinants, Cramer's rule, invertibility, systems of linear equations.

12%

Trigonometry & Analytic Geometry

Identities, addition formulas, law of sines/cosines, vectors, dot product, lines and distances.

10%

Limits & Continuity

Limits of sequences and functions, L'Hôpital, Darboux theorem, asymptotes.

10%

Derivatives & Function Study

Chain rule, Rolle and Lagrange theorems, monotonicity, extrema, concavity, graphing.

10%

Integrals

Antiderivatives, integration by parts, substitution, Leibniz–Newton formula, area between curves.

Algebraic Structures

Binary operations, groups, subgroups, rings, fields, morphisms (M_mate-info profile only).

How to Pass the Romanian BAC Math Exam

What You Need to Know

Passing score: 5.00/10.00 on each written paper; overall Bacalaureat average ≥ 6.00 with no paper below 5.00.
Exam length: 100 questions
Time limit: 180 minutes (3 hours) for the written mathematics paper.
Exam fee: Free — the Bacalaureat is a state-funded national examination for Romanian high school graduates.

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

Romanian BAC Math Study Tips from Top Performers

1Download official past papers (subiecte.edu.ro) from at least the last 5 years and solve all 10 problems per paper under timed conditions — the exam structure is very consistent.

2Master the standard derivatives and integrals table by heart: ln(x), eˣ, sin/cos, arctan, arcsin, and their chain-rule variants appear in almost every Subject III.

3For Subject II (matrices/systems), practise computing determinants by cofactor expansion and Cramer's rule until it is automatic; checking det(A)=0 to identify non-invertibility is a recurring 5-point subproblem.

4Study function analysis systematically: domain → monotonicity (first derivative) → extrema → concavity (second derivative) → asymptotes → graph; this framework covers the entire Subject III Part 1.

5Review the binomial theorem and know C(n,k) values for n ≤ 10; Subject I combinatorics problems are typically straightforward counting questions worth easy points.

6Use the 2026 national simulation paper (Simulare BAC 24 Martie 2026) as a full mock exam — it reflects the exact current format including the algebraic structures problem in Subject II.

Frequently Asked Questions

What is the Romanian Bacalaureat Mathematics exam?

The Romanian Bacalaureat Mathematics exam (Proba E.c) is the compulsory written mathematics paper of the national Bacalaureat examination, required for university admission. It is a 3-hour paper graded on a scale of 1 to 10, with a passing score of 5.00.

What mathematics programs (profiles) are there?

Four programs exist: M_mate-info (mathematics-informatics, the most advanced, includes algebraic structures), M_șt-nat (natural sciences), M_tehnologic (technological), and M_pedagogic (pedagogical). The choice depends on the student's high school profile.

What topics are covered in the M_mate-info program?

M_mate-info covers real numbers and algebra, functions and equations, complex numbers, combinatorics and the binomial theorem, matrices and determinants, systems of linear equations, trigonometry, analytic geometry and vectors, limits and continuity, derivatives, integrals, and algebraic structures (groups, rings, fields).

How is the Bacalaureat Mathematics paper structured?

The written paper has three mandatory sections: Subject I (6 problems, 5 points each = 30 points), Subject II (2 multi-part problems, 15 points each = 30 points), and Subject III (2 multi-part problems, 15 points each = 30 points). Ten points are awarded automatically, giving 100 points total, converted to a grade /10.

What is the passing score for the Romanian Bacalaureat?

Each written paper requires a grade of at least 5.00/10.00. The overall Bacalaureat diploma requires an average grade of at least 6.00 across all papers, with no individual paper below 5.00.

When is the Romanian Bacalaureat 2026 held?

The 2026 Bacalaureat main session is held in June–July 2026. A national simulation is typically held in March 2026. An autumn resit session takes place in August 2026 for candidates who did not pass the summer session.