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100+ Free PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL Practice Questions

Canary Islands PAU Applied Mathematics for Social Sciences II / Matemáticas Aplicadas a las Ciencias Sociales II 2º Bachillerato ULPGC & ULL 2026 practice questions are available now; exam metadata is being verified.

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Key Facts: PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL Exam

90 min

Exam duration

COPAU Canary Islands Official Guidelines

0–10

Grading scale

COPAU Regulations

4.0 / 10

Minimum Access Phase mark required to combine with Bachillerato GPA

Gobierno de Canarias / COPAU

EUR 76.12

Base registration fee for Access Phase

Gobierno de Canarias 2026

2º Bach

Target education level (Social Sciences track)

Canary Islands LOMLOE Curriculum

100

Practice questions in this OpenExamPrep question bank

OpenExamPrep

The 2026 Canary 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 — Canary Islands / ULPGC & ULL Practice Questions

Try these sample questions to test your PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL 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], [3, 4]] and B = [[1, 5], [-2, 0]], compute the matrix C = 2A - 3B.
A.[[1, -17], [12, 8]]
B.[[1, 13], [0, 8]]
C.[[-1, -17], [12, 4]]
D.[[1, -17], [4, 8]]
Explanation: We compute 2A = [[4, -2], [6, 8]] and 3B = [[3, 15], [-6, 0]]. Subtracting element by element gives 2A - 3B = [[4-3, -2-15], [6-(-6), 8-0]] = [[1, -17], [12, 8]].
2Given the matrices A = [[1, 2], [3, 0]] and B = [[-1, 4], [2, 1]], compute the product A · B.
A.[[3, 6], [-3, 12]]
B.[[-3, 6], [3, 12]]
C.[[3, 8], [-3, 0]]
D.[[-1, 8], [6, 0]]
Explanation: Multiplying row by column: Row 1: (1)(-1)+(2)(2)=3, (1)(4)+(2)(1)=6. Row 2: (3)(-1)+(0)(2)=-3, (3)(4)+(0)(1)=12. The product A · B is [[3, 6], [-3, 12]].
3Compute the determinant of the matrix A = [[4, -3], [2, 5]].
A.26
B.14
C.-26
D.20
Explanation: The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. For A, det(A) = (4)(5) - (-3)(2) = 20 - (-6) = 20 + 6 = 26.
4Which of the following properties about the transpose of square matrices A and B is correct?
A.(A · B)^T = B^T · A^T
B.(A + B)^T = A^T - B^T
C.(A · B)^T = A^T · B^T
D.det(A^T) = -det(A)
Explanation: The fundamental property of the transpose of a product of two matrices states that (A · B)^T = B^T · A^T, reversing the order of multiplication.
5Find the inverse matrix of A = [[3, 2], [1, 1]].
A.[[1, 2], [1, 3]]
B.[[1, -2], [-1, 3]]
C.[[3, -2], [-1, 1]]
D.[[-1, 2], [1, -3]]
Explanation: The determinant is det(A) = 3(1) - 2(1) = 1. The inverse of [[a, b], [c, d]] is (1/det(A)) * [[d, -b], [-c, a]]. Therefore, A^(-1) = [[1, -2], [-1, 3]].
6What is the rank of the matrix A = [[1, 2, 3], [2, 4, 6], [0, 0, 0]]?
A.0
B.1
C.2
D.3
Explanation: Row 2 is twice row 1 (F2 = 2F1), and row 3 is null. There is only 1 linearly independent row, so the rank of the matrix is 1.
7Compute the determinant of the 3x3 matrix A = [[1, 0, 2], [2, 1, 3], [0, 4, 1]] using Sarrus' rule or cofactor expansion.
A.11
B.5
C.0
D.-5
Explanation: Expanding along the first column: det(A) = 1 · (1·1 - 3·4) - 2 · (0·1 - 2·4) + 0 = 1(1 - 12) - 2(-8) = -11 + 16 = 5.
8Solve the system of linear equations: 2x + y = 7, x - y = 2.
A.x = 2, y = 3
B.x = 1, y = 5
C.x = 4, y = -1
D.x = 3, y = 1
Explanation: Adding both equations cancels y: 3x = 9 => x = 3. Substituting x = 3 into the second equation: 3 - y = 2 => y = 1. The solution is (3, 1).
9Identify which point belongs to the feasible region defined by x >= 0, y >= 0, x + y <= 6, 2x + y <= 8.
A.(3, 3)
B.(2, 3)
C.(5, 2)
D.(-1, 4)
Explanation: For (2, 3): 2 >= 0, 3 >= 0; 2 + 3 = 5 <= 6; 2(2) + 3 = 7 <= 8. It satisfies all the constraints of the feasible region.
10Evaluate the objective function z = 3x + 4y at the vertex (x, y) = (4, 5).
A.23
B.35
C.32
D.40
Explanation: Substituting the vertex values into the objective function: z = 3(4) + 4(5) = 12 + 20 = 32.

About the PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL Practice Questions

Verified exam format metadata for Canary Islands PAU Applied Mathematics for Social Sciences II / Matemáticas Aplicadas a las Ciencias Sociales II 2º Bachillerato ULPGC & ULL 2026 is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.