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100+ Free PAU Applied Mathematics for Social Sciences II — Balearic Islands / UIB Practice Questions

Balearic Islands PAU Applied Mathematics for Social Sciences II / Matemàtiques Aplicades a les Ciències Socials II 2º Bachillerato UIB 2026 practice questions are available now; exam metadata is being verified.

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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 test your PAU Applied Mathematics for Social Sciences II — Balearic Islands / UIB exam readiness. 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 Practice Questions

Verified exam format metadata for Balearic Islands PAU Applied Mathematics for Social Sciences II / Matemàtiques Aplicades a les Ciències Socials II 2º Bachillerato UIB 2026 is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.