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Exam Review

Key Facts: Balearic Islands PAU Mathematics II Exam

90 Min

Total duration of the PAU Math II examination

UIB PAU Regulations

0–10

Grading scale for PAU Mathematics II paper

Balearic Islands PAU Commission

4.0 / 10

Minimum grade required in Access Phase

UIB Admissions Office

4 Major Blocks

Linear Algebra, Calculus, 3D Geometry, Probability

2º Bachillerato Mathematics II Syllabus

100

Practice questions provided in this test bank

OpenExamPrep

Balearic Islands PAU Mathematics II (UIB 2026) assesses 2º Bachillerato students on matrices, linear systems, calculus, 3D geometry, and probability in a 90-minute session.

Sample Balearic Islands PAU Mathematics II Practice Questions

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

1Calculate the determinant of the 2x2 matrix A = [[3, -2], [4, 5]].
A.23
B.7
C.15
D.-7
Explanation: The determinant of a 2x2 matrix [[a, b], [c, d]] is computed as ad - bc. For A = [[3, -2], [4, 5]], det(A) = (3)(5) - (-2)(4) = 15 - (-8) = 23.
2Calculate the determinant of the 3x3 matrix A = [[1, 2, 0], [3, -1, 4], [0, 2, 1]].
A.-9
B.-15
C.5
D.15
Explanation: Expanding det(A) along the first row: 1*((-1)(1) - (4)(2)) - 2*((3)(1) - (4)(0)) + 0 = 1*(-1 - 8) - 2*(3 - 0) = -9 - 6 = -15.
3Compute the product matrix A * B where A = [[2, 1], [0, 3]] and B = [[1, -1], [4, 2]]. What is the element in row 1, column 1 of A * B?
A.2
B.10
C.6
D.4
Explanation: The (1,1) entry of A * B is the dot product of row 1 of A and column 1 of B: (2)(1) + (1)(4) = 2 + 4 = 6.
4Find the inverse of matrix A = [[4, 2], [1, 1]]. What is the top-left entry (row 1, column 1) of A^(-1)?
A.1.0
B.-1.0
C.2.0
D.0.5
Explanation: The determinant of A is det(A) = 4(1) - 2(1) = 2. The formula for a 2x2 inverse is (1/det(A)) * [[d, -b], [-c, a]]. Thus A^(-1) = (1/2) * [[1, -2], [-1, 4]] = [[0.5, -1], [-0.5, 2]]. The (1,1) entry is 0.5.
5Determine the rank of the matrix A = [[1, 2, 3], [2, 4, 6], [0, 0, 0]].
A.1
B.0
C.2
D.3
Explanation: The second row is 2 times the first row (linearly dependent), and the third row consists entirely of zeros. Thus, there is only 1 linearly independent row, so rank(A) = 1.
6Let A be a 3x3 matrix with det(A) = 5. What is det(2A)?
A.10
B.40
C.20
D.30
Explanation: For an n x n matrix A and scalar k, det(kA) = (k^n) * det(A). Here n = 3 and k = 2, so det(2A) = (2^3) * 5 = 8 * 5 = 40.
7If A is a square matrix with det(A) = -7, what is the determinant of its transpose, det(A^T)?
A.7
B.1/7
C.-7
D.-1/7
Explanation: A fundamental property of determinants states that det(A^T) = det(A). Therefore, det(A^T) = -7.
8Solve the matrix equation 2X + A = B for matrix X, given A = [[1, 3], [0, 2]] and B = [[5, 1], [4, 8]]. What is the top-left entry of X?
A.1
B.3
C.4
D.2
Explanation: Isolating X gives 2X = B - A, so X = (1/2)(B - A). Computing B - A = [[5-1, 1-3], [4-0, 8-2]] = [[4, -2], [4, 6]]. Dividing by 2 gives X = [[2, -1], [2, 3]]. The top-left entry is 2.
9Find the value of the parameter k for which the matrix A = [[1, 0, k], [2, 1, 1], [0, 1, 3]] is non-invertible.
A.k = -1
B.k = 1
C.k = -2
D.k = 2
Explanation: A matrix is non-invertible if and only if its determinant is zero. Expanding det(A) along the first row: 1*(3 - 1) + k*(2 - 0) = 2 + 2k. Setting 2 + 2k = 0 yields k = -1.
10If A is a 3x3 matrix with det(A) = 4, evaluate det(3 * A^(-1)).
A.0.75
B.6.75
C.12.0
D.2.25
Explanation: Using properties of determinants: det(k * A^(-1)) = (k^3) * (1 / det(A)). Here n = 3, k = 3, det(A) = 4. Thus det(3 * A^(-1)) = (3^3) * (1/4) = 27 / 4 = 6.75.

About the Balearic Islands PAU Mathematics II Exam

The PAU Mathematics II (Matemàtiques II / Matemáticas II) exam is the official entrance assessment administered by the University of the Balearic Islands (UIB) for students completing 2º Bachillerato in the Science and Technology track. It tests advanced competence in matrices, system classification, differential and integral calculus, 3D analytic geometry, and probability distributions.

Exam sponsor: PAU Organising Commission of the Balearic Islands / UIB. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

The PAU Mathematics II exam in the Balearic Islands (UIB) is a 90-minute paper divided into compulsory topic blocks covering Linear Algebra, Calculus & Analysis, 3D Geometry, and Probability. Local practice items are an English-language MCQ study adaptation of the official open/semi-constructed Balearic Islands PAU paper, not an official translation or format simulation.

Time Limit

90 minutes (1.5 hours)

Passing Score

Marked on a 0–10 scale. Minimum 4.0 required in Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU >= 5.0 to pass).

Exam / Certification Fees

EUR 69.21 ordinary registration fee (Access Phase); EUR 13.85 per additional Admission Phase subject paper (UIB 2026)

Exam sponsor website

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

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.

25%

Linear Algebra & Matrices

Matrix operations, determinants, inverse matrices, matrix equations, rank, and parametric linear systems (Rouché-Fröbenius theorem).

35%

Mathematical Analysis & Calculus

Limits, continuity, L'Hôpital's rule, derivatives, function analysis, optimization, antiderivatives, integration techniques, definite integrals, and area computation.

20%

3D Analytical Geometry

Vectors, dot/cross products, lines and planes equations, relative positions, angles, distances, and symmetric points.

20%

Probability & Random Variables

Conditional probability, Bayes' theorem, discrete/continuous random variables, Binomial and Normal distributions, and normal approximations.

Preparing for the Balearic Islands PAU Mathematics II Exam

What You Need to Know

  • Passing score: Marked on a 0–10 scale. Minimum 4.0 required in Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU >= 5.0 to pass).
  • Assessment: The PAU Mathematics II exam in the Balearic Islands (UIB) is a 90-minute paper divided into compulsory topic blocks covering Linear Algebra, Calculus & Analysis, 3D Geometry, and Probability. Local practice items are an English-language MCQ study adaptation of the official open/semi-constructed Balearic Islands PAU paper, not an official translation or format simulation.
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 69.21 ordinary registration fee (Access Phase); EUR 13.85 per additional Admission Phase subject paper (UIB 2026) Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
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Balearic Islands PAU Mathematics II: Suggested Study Strategy

1Master parametric matrix system classification using Rouché-Fröbenius theorem and Cramer's Rule for degenerate cases.
2Practice integral calculus techniques, specifically integration by parts, partial fractions, and calculating exact areas bounded by curves.
3Be confident in 3D geometry formulas for distance between skew lines, point-to-plane distance, and plane equations.
4Review Bayes' theorem, total probability law, and standard normal distribution Z-table conversions.
5Ensure all calculation steps are written clearly with exact fractional or rounded decimal answers where required.

Frequently Asked Questions

Are these official Balearic Islands PAU exam questions?

Local practice items are an English-language MCQ study adaptation of the official open/semi-constructed Balearic Islands PAU paper, not an official translation or format simulation. Use official UIB past papers and subject matrices for open-response, listening, graphic, and performance practice.

What is the structure of the PAU Mathematics II exam in the Balearic Islands?

The exam is a 90-minute test consisting of questions spanning Linear Algebra, Calculus, 3D Analytical Geometry, and Probability.

What passing score is required on the PAU Math II exam?

The paper is scored out of 10 points. If taken in the compulsory Access Phase, a minimum mark of 4.0 is required to calculate the university entry grade (CAU = 0.6 * Bachillerato + 0.4 * PAU).

Are non-programmable calculators allowed on the UIB PAU Math II exam?

Yes, non-programmable scientific calculators without graphic representation, symbolic algebra, or matrix computation features are permitted according to UIB guidelines.

What languages are available for the exam paper?

In the Balearic Islands, students receive exam papers in Catalan (ca) and Spanish (es).

How much is the exam registration fee for UIB 2026?

The ordinary fee for the Access Phase is EUR 69.21, plus EUR 13.85 per additional subject paper in the Specific Phase.