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100+ Free Basque PAU Applied Math Social Sci Practice Questions

Basque Country PAU Applied Mathematics for Social Sciences II Examination — UPV/EHU (2º Bachillerato 2026) practice questions are available now; exam metadata is being verified.

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2026 Statistics

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 test your Basque PAU Applied Math Social Sci exam readiness. 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 Practice Questions

Verified exam format metadata for Basque Country PAU Applied Mathematics for Social Sciences II Examination — UPV/EHU (2º Bachillerato 2026) is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.