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Exam Review

Key Facts: Basque PAU Applied Math Social Sci Exam

90 Min

Official examination time limit at UPV/EHU

UPV/EHU PAU Regulations 2026

0–10

Grading scale

UPV/EHU Regulations

4.0 / 10

Minimum grade required in Access Phase to blend with Bachillerato GPA

Spanish University Access Decree

4 Modules

Curricular blocks: Matrices, Linear Programming, Calculus, Statistics

Basque Government Department of Education Syllabus

EUR 86.33

Ordinary registration fee (Access Phase)

UPV/EHU Fee Schedule 2026

100

Original MCQ practice items in OpenExamPrep study bank

OpenExamPrep

Basque Country PAU Applied Mathematics for Social Sciences II (UPV/EHU 2026) is a 90-minute university entrance exam assessing 2º Bachillerato syllabus domains.

Sample Basque PAU Applied Math Social Sci Practice Questions

Try these sample questions to review concepts for the Basque PAU Applied Math Social Sci exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Given the matrices A = [[2, -1], [4, 3]] and B = [[1, 5], [-2, 0]], what is the result of the linear combination 2A - 3B?
A.[[1, -17], [2, 9]]
B.[[1, 13], [2, 6]]
C.[[-1, -17], [14, 3]]
D.[[1, -17], [14, 6]]
Explanation: Compute 2A = [[4, -2], [8, 6]] and 3B = [[3, 15], [-6, 0]]. Subtracting component-wise yields [[4-3, -2-15], [8-(-6), 6-0]] = [[1, -17], [14, 6]].
2Matrix A has dimension 3 x 2 and matrix B has dimension 2 x 4. What are the dimensions of the product matrix A · B?
A.2 x 2
B.4 x 3
C.3 x 4
D.Matrix multiplication is undefined for these dimensions.
Explanation: Matrix multiplication A · B is valid because the number of columns in A (2) equals the number of rows in B (2). The outer dimensions give the size of the product matrix: 3 rows by 4 columns (3 x 4).
3Which of the following matrix algebra properties is FALSE in general for square matrices A and B of order n?
A.(A + B)^T = A^T + B^T
B.(A · B)^T = B^T · A^T
C.A · B = B · A
D.(A^T)^T = A
Explanation: Matrix multiplication is generally non-commutative (A · B ≠ B · A). The other three identities are standard theorems of matrix algebra.
4What is the determinant of the 2 x 2 matrix A = [[4, 7], [2, 5]]?
A.34
B.-6
C.27
D.6
Explanation: The determinant of a 2 x 2 matrix [[a, b], [c, d]] is computed as ad - bc. For matrix A, det(A) = (4)(5) - (7)(2) = 20 - 14 = 6.
5What is the inverse of the matrix A = [[2, 1], [5, 3]]?
A.[[3, -1], [-5, 2]]
B.[[3, 1], [5, 2]]
C.[[-2, 5], [1, -3]]
D.[[1/2, 1], [1/5, 1/3]]
Explanation: First calculate det(A) = (2)(3) - (1)(5) = 1. For a 2 x 2 matrix, A^-1 = (1/det(A)) * [[d, -b], [-c, a]]. Substituting yields [[3, -1], [-5, 2]].
6What is the determinant of the 3 x 3 matrix A = [[1, 2, 0], [0, 3, 1], [2, 1, 4]]?
A.11
B.15
C.7
D.9
Explanation: Expanding along the first row: det(A) = 1*(3*4 - 1*1) - 2*(0*4 - 1*2) + 0 = 1*(12 - 1) - 2*(-2) = 11 + 4 = 15.
7For what value of the parameter k is the matrix A = [[1, 0, k], [2, 1, 3], [0, 2, 1]] singular (non-invertible)?
A.k = -5/4
B.k = 5
C.k = 5/4
D.k = 4/5
Explanation: A matrix is singular when det(A) = 0. Expanding along row 1: det(A) = 1*(1*1 - 3*2) - 0 + k*(2*2 - 1*0) = 1*(-5) + 4k = -5 + 4k. Setting -5 + 4k = 0 gives k = 5/4.
8Given invertible square matrix A and matrix B, how is the unknown matrix X isolated in the matrix equation A · X = B?
A.X = B · A^-1
B.X = B / A
C.X = A · B^-1
D.X = A^-1 · B
Explanation: Multiplying both sides on the left by A^-1 yields A^-1 · (A · X) = A^-1 · B => (A^-1 · A) · X = A^-1 · B => X = A^-1 · B. Left-multiplication is mandatory because matrix multiplication is non-commutative.
9Solve for the matrix X in the matrix equation X · A + B = C, assuming matrix A is invertible.
A.X = (C - B) · A^-1
B.X = A^-1 · (C - B)
C.X = (B - C) · A^-1
D.X = C · A^-1 - B
Explanation: First isolate X · A by subtracting B from both sides: X · A = C - B. Then right-multiply both sides by A^-1 to get X = (C - B) · A^-1.
10According to the Rouché-Capelli theorem, what is the classification of a system of 3 linear equations in 3 unknowns if rank(A) = 2 and rank(A|B) = 2?
A.Consistent determined (unique solution)
B.Inconsistent (no solution)
C.Consistent undetermined (infinitely many solutions depending on 1 parameter)
D.Consistent undetermined (infinitely many solutions depending on 2 parameters)
Explanation: Since rank(A) = rank(A|B) = 2, the system is consistent. Because the rank (2) is strictly less than the number of unknowns (n = 3), it has infinitely many solutions depending on n - rank = 3 - 2 = 1 free parameter.

About the Basque PAU Applied Math Social Sci Exam

The Basque Country PAU Applied Mathematics for Social Sciences II examination (Matemáticas Aplicadas a las Ciencias Sociales II) is the official standardized university entrance examination administered by the Universidad del País Vasco / Euskal Herriko Unibertsitatea (UPV/EHU). It evaluates 2º de Bachillerato students (Humanities and Social Sciences track) in matrix algebra, systems of linear equations, two-variable linear programming, differential and integral calculus, marginal business optimization, probability theory, sampling distributions, and statistical confidence intervals.

Exam sponsor: PAU Organising Commission of the Basque Country / UPV/EHU. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written 90-minute standardized exam. Local practice items are an English-language MCQ study adaptation of the official open/semi-constructed Basque Country 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 86.33 ordinary registration fee (UPV/EHU 2026 PAU)

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%

Matrices & Systems of Linear Equations

Matrix algebra operations, determinants, inverse matrix calculations, Gaussian elimination, Rouché-Capelli theorem, Cramer's rule, and Leontief input-output models.

25%

Linear Programming

Formulation of 2-variable linear inequality constraints, bounded and unbounded feasible regions, vertex corner point evaluation, objective function optimization, and social science applications.

25%

Differential & Integral Calculus

Limits, continuity, piecewise functions, derivatives, marginal revenue/cost analysis, curve behavior, local extrema, applied business profit optimization, definite integrals, and area under curves.

25%

Probability & Inferential Statistics

Combinatorics, conditional probability, total probability theorem, Bayes' theorem, standard normal distribution (Z-scores), sampling distributions, confidence intervals, margin of error, and sample size determination.

Preparing for the Basque PAU Applied Math Social Sci 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: Written 90-minute standardized exam. Local practice items are an English-language MCQ study adaptation of the official open/semi-constructed Basque Country PAU paper, not an official translation or format simulation.
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 86.33 ordinary registration fee (UPV/EHU 2026 PAU) 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

Basque PAU Applied Math Social Sci: Suggested Study Strategy

1Master calculating matrix inverses and solving parameterized linear systems using Rouché-Capelli theorem and Cramer's Rule.
2Practice drawing linear programming feasible regions precisely and evaluating objective functions at all corner vertices.
3Review derivative rules, curve sketching, and applied economic optimization (maximizing profit P(x) = R(x) - C(x)).
4Understand definite integrals and calculating exact areas bounded between curves and axes.
5Memorize confidence interval formulas for population means x̄ ± z_(α/2)*(σ/√n) and proportions p̂ ± z_(α/2)*√(p̂(1-p̂)/n).

Frequently Asked Questions

What is the format and duration of the PAU Applied Math CCSS II exam in the Basque Country?

The exam lasts 90 minutes (1.5 hours) and is organized by UPV/EHU. It consists of practical problem-solving questions across matrices & linear systems, linear programming, differential & integral calculus, and probability/statistics.

What standard of calculator is permitted during the UPV/EHU PAU exam?

Scientific non-programmable calculators without graphic displays, symbolic algebraic capability (CAS), or wireless communications are permitted.

In which languages can students take the PAU exam in Euskadi?

Students have the official right to sit the examination in Basque (Euskara) or Spanish (Castellano).

How is the final PAU admission score calculated?

The overall admission grade combines Bachillerato GPA (60%) and the PAU Access Phase grade (40%), provided a minimum score of 4.0 is obtained on the Access Phase exam.

What is the registration fee for the PAU exam at UPV/EHU in 2026?

The standard ordinary registration fee for the PAU Access Phase at UPV/EHU is EUR 86.33.

Are these 100 practice questions official UPV/EHU exam papers?

No. These 100 practice questions are an independent English-language MCQ study adaptation designed by OpenExamPrep to help students master core mathematical concepts from the 2º Bachillerato syllabus.