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Key Facts: PAU Applied Mathematics for Social Sciences II — Balearic Islands / UIB Exam

90 min

Exam duration

UIB PAU Official Guidelines

0–10

Grading scale

UIB PAU Regulations

4.0 / 10

Minimum Access Phase mark to average with Bachillerato GPA

UIB Access Regulations

EUR 69.21

Ordinary registration fee (Access Phase)

UIB Fee Schedule 2026

2º Bach

Target education level (Social Sciences track)

Balearic Islands Curriculum

100

Practice questions in this OpenExamPrep question bank

OpenExamPrep

The 2026 Balearic Islands PAU Math CCSS II exam tests 2º Bachillerato students on matrix operations, linear programming, applied calculus, probability, and statistical inference over a 90-minute session.

Sample PAU Applied Mathematics for Social Sciences II — Balearic Islands / UIB Practice Questions

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

1Given matrices A = [[1, 3], [-2, 4]] and B = [[2, -1], [0, 5]], calculate the matrix C = A + 2B.
A.[[5, 1], [-2, 14]]
B.[[3, 2], [-2, 9]]
C.[[5, 5], [-2, 14]]
D.[[4, 1], [-4, 14]]
Explanation: To compute C = A + 2B: 2B = 2 * [[2, -1], [0, 5]] = [[4, -2], [0, 10]]. Then C = [[1, 3], [-2, 4]] + [[4, -2], [0, 10]] = [[1+4, 3+(-2)], [-2+0, 4+10]] = [[5, 1], [-2, 14]].
2Compute the determinant of the 2x2 matrix A = [[4, -3], [2, 5]].
A.14
B.26
C.-26
D.23
Explanation: For a 2x2 matrix [[a, b], [c, d]], det(A) = ad - bc. Here det(A) = (4)(5) - (-3)(2) = 20 - (-6) = 20 + 6 = 26.
3If matrix A has dimensions 2x3 and matrix B has dimensions 3x4, what are the dimensions of the transposed product matrix (A · B)^T?
A.2x4
B.3x3
C.4x2
D.4x3
Explanation: The product matrix A · B has dimensions (2x3) · (3x4) = 2x4. Taking the transpose swaps the dimensions, so (A · B)^T has dimensions 4x2.
4Calculate the matrix product A · B for A = [[2, 1], [0, 3]] and B = [[1, 4], [2, -1]].
A.[[2, 4], [0, -3]]
B.[[4, 9], [6, -3]]
C.[[3, 5], [2, 2]]
D.[[4, 7], [6, -3]]
Explanation: Matrix multiplication row by column: Row 1: [2(1)+1(2), 2(4)+1(-1)] = [2+2, 8-1] = [4, 7]. Row 2: [0(1)+3(2), 0(4)+3(-1)] = [0+6, 0-3] = [6, -3]. Thus A · B = [[4, 7], [6, -3]].
5Solve for the scalar x if [[x, 0], [0, x]] · [[3], [-5]] = [[12], [-20]].
A.4
B.3
C.-4
D.12
Explanation: Multiplying the matrix by the vector gives [[3x], [-5x]] = [[12], [-20]]. Thus 3x = 12, which yields x = 4. Checking -5(4) = -20 verifies the solution.
6If A is a 3x3 square matrix with determinant det(A) = 5, what is the value of det(2A)?
A.10
B.40
C.30
D.20
Explanation: For an n x n square matrix A and scalar k, det(kA) = k^n * det(A). Here n = 3 and k = 2, so det(2A) = 2^3 * det(A) = 8 * 5 = 40.
7A company buys 2 desks and 3 chairs for €340, and 4 desks and 1 chair for €480. Which matrix equation A · X = B represents this linear system?
A.[[2, 4], [3, 1]] · [[d], [c]] = [[340], [480]]
B.[[2, 3], [1, 4]] · [[d], [c]] = [[480], [340]]
C.[[2, 3], [4, 1]] · [[d], [c]] = [[340], [480]]
D.[[3, 2], [1, 4]] · [[d], [c]] = [[340], [480]]
Explanation: Let d = cost of a desk, c = cost of a chair. Equation 1: 2d + 3c = 340. Equation 2: 4d + 1c = 480. In matrix form A · X = B: [[2, 3], [4, 1]] · [[d], [c]] = [[340], [480]].
8Find the inverse matrix A^(-1) for A = [[3, 2], [1, 4]].
A.[[0.4, 0.2], [0.1, 0.3]]
B.[[4, -2], [-1, 3]]
C.[[-0.3, 0.2], [0.1, -0.4]]
D.[[0.4, -0.2], [-0.1, 0.3]]
Explanation: det(A) = (3)(4) - (2)(1) = 12 - 2 = 10. For A = [[a, b], [c, d]], A^(-1) = (1/det(A)) * [[d, -b], [-c, a]]. A^(-1) = (1/10) * [[4, -2], [-1, 3]] = [[0.4, -0.2], [-0.1, 0.3]].
9Solve the system of equations in matrix form A · X = B for X, where A = [[2, 1], [5, 3]] and B = [[4], [11]].
A.[[1], [2]]
B.[[2], [1]]
C.[[3], [-2]]
D.[[0], [4]]
Explanation: det(A) = (2)(3) - (1)(5) = 6 - 5 = 1. Thus A^(-1) = [[3, -1], [-5, 2]]. X = A^(-1) · B = [[3(4) + (-1)(11)], [-5(4) + 2(11)]] = [[12 - 11], [-20 + 22]] = [[1], [2]].
10Evaluate the determinant of the 3x3 matrix A = [[1, 2, 0], [3, -1, 4], [0, 2, 1]].
A.15
B.-15
C.-7
D.9
Explanation: Expand by Row 1: det(A) = 1 * det([[-1, 4], [2, 1]]) - 2 * det([[3, 4], [0, 1]]) + 0 = 1 * ((-1)(1) - (4)(2)) - 2 * ((3)(1) - (4)(0)) = 1 * (-1 - 8) - 2 * (3 - 0) = -9 - 6 = -15.

About the PAU Applied Mathematics for Social Sciences II — Balearic Islands / UIB Exam

The Balearic Islands PAU Applied Mathematics for Social Sciences II exam (Matemàtiques Aplicades a les Ciències Socials II) is the standardized university entrance examination administered by the Universitat de les Illes Balears (UIB). It assesses competencies in matrix algebra, linear programming, differential and integral calculus applied to business and social sciences, probability theory, sampling distributions, and statistical confidence intervals.

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 exam consists of 4 main problem-solving blocks evaluated over 90 minutes (1.5 hours). Students choose designated option questions covering matrices & systems of linear equations, linear programming optimization, differential and integral calculus, and probability & inferential statistics. 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%

Algebra & Matrices

Matrix operations, determinants, inverse matrices, systems of linear equations, Gauss elimination, Rouché-Capelli theorem, and input-output matrices.

20%

Linear Programming

System of inequalities, feasible region construction, vertex evaluation, objective function optimization, and social science applications.

30%

Calculus & Functions

Limits, continuity, derivatives, curve sketching, business profit/cost optimization, definite integrals, and area computations.

25%

Probability & Statistics

Events, conditional probability, Bayes' theorem, normal and binomial distributions, sample statistics, and confidence intervals.

Preparing for the PAU Applied Mathematics for Social Sciences II — Balearic Islands / UIB 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 exam consists of 4 main problem-solving blocks evaluated over 90 minutes (1.5 hours). Students choose designated option questions covering matrices & systems of linear equations, linear programming optimization, differential and integral calculus, and probability & inferential statistics. 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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PAU Applied Mathematics for Social Sciences II — Balearic Islands / UIB: Suggested Study Strategy

1Practice computing matrix inverses and solving parameterized linear systems using Rouché-Capelli and Cramer's Rule.
2Master drawing linear programming feasible regions accurately and evaluating the objective function at every boundary vertex.
3Review derivative rules and applied economic optimization (maximizing revenue/profit P(x) = R(x) - C(x)).
4Understand standard normal distribution table lookups (Z-scores) and continuity correction when approximating binomial distributions.
5Memorize confidence interval formulas for population mean x̄ ± z_(α/2) * (σ / √n) and proportion p̂ ± z_(α/2) * √(p̂(1-p̂)/n).

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 PAU Applied Mathematics for Social Sciences II exam in the Balearic Islands?

It is the official university entrance exam (Proves d'Accés a la Universitat - PAU) administered by the Universitat de les Illes Balears (UIB) for students completing 2º Bachillerato in the Humanities and Social Sciences track.

What is the passing score for the PAU exam?

The exam is graded on a 0 to 10 scale. In the compulsory Access Phase, a minimum mark of 4.0 is required to combine with the Bachillerato GPA (weighted 60% Bachillerato + 40% PAU, needing a total >= 5.0 to pass).

How long is the PAU Math CCSS II examination?

The examination lasts 90 minutes (1.5 hours).

What standard calculator is permitted in the UIB PAU exam?

Scientific non-programmable calculators without graphic display or symbolic algebraic computation (CAS) capabilities are permitted.

What main topic areas are assessed?

The exam assesses four core areas: Algebra & Matrices, Linear Programming, Differential & Integral Calculus, and Probability & Statistics.

In what languages is the UIB PAU exam offered?

Exam papers are provided in Catalan and Spanish in accordance with official Balearic Islands educational regulations.