PracticeVideosBlogFlashcardsEspañol
All Practice Exams

100+ Free Madrid PAU Applied Mathematics for Social Sciences II Practice Questions

Madrid PAU Applied Mathematics for Social Sciences II — Matemáticas Aplicadas a las Ciencias Sociales II 2º Bachillerato Comunidad de Madrid 2026 practice questions are available now; exam metadata is being verified.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately
100+ Questions
100% Free

Loading practice questions...

Same family resources

Explore More Spain Madrid PAU (Prueba de Acceso a la Universidad)

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

Madrid PAU Art Foundations

Practice Questions

Madrid PAU Artistic Drawing II

Practice Questions

Madrid PAU Biology

Practice Questions

Madrid PAU Business and Business Model Design

Practice Questions

Madrid PAU Chemistry

Practice Questions

Madrid PAU Choir and Vocal Technique II

Practice Questions
2026 Statistics

Key Facts: Madrid PAU Applied Mathematics for Social Sciences II Exam

Madrid PAU

PAU Organising Commission of Madrid / UCM

Community of Madrid Education Department

90 Mins

Official examination duration

Madrid PAU Structure

Min 4.0

Minimum Access Phase mark to calculate admission grade

Spanish University Regulations

5 Core Blocks

Algebra & LP, Limits, Calculus, Probability, Inference

LOMLOE 2º Bach CCSS II Syllabus

100

Practice questions available in this OpenExamPrep bank

OpenExamPrep

Madrid PAU Applied Mathematics for Social Sciences II tests 2º Bachillerato students on matrix operations, linear programming, calculus applications, probability, and inferential statistics for university entry in Madrid.

Sample Madrid PAU Applied Mathematics for Social Sciences II Practice Questions

Try these sample questions to test your Madrid PAU Applied Mathematics for Social Sciences II exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Calculate the sum of matrices A = [[2, 5], [1, -3]] and B = [[4, -1], [3, 2]].
A.[[6, 4], [4, -1]]
B.[[8, -5], [3, -6]]
C.[[6, 6], [2, -5]]
D.[[2, 4], [4, 1]]
Explanation: Matrix addition is performed entrywise: A + B = [[2+4, 5+(-1)], [1+3, -3+2]] = [[6, 4], [4, -1]].
2Given A = [[3, -2], [4, 1]], evaluate the matrix 3A - 2I, where I is the 2x2 identity matrix.
A.[[7, -6], [12, 1]]
B.[[7, -6], [10, 1]]
C.[[9, -6], [12, 3]]
D.[[1, -2], [4, -1]]
Explanation: 3A = [[9, -6], [12, 3]] and 2I = [[2, 0], [0, 2]]. Subtracting elementwise gives 3A - 2I = [[9-2, -6-0], [12-0, 3-2]] = [[7, -6], [12, 1]].
3Find the product A * B of matrices A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 5]].
A.[[4, 10], [10, 20]]
B.[[2, 0], [3, 20]]
C.[[3, 10], [10, 20]]
D.[[4, 5], [6, 20]]
Explanation: Row-by-column multiplication gives: (1)(2)+(2)(1) = 4; (1)(0)+(2)(5) = 10; (3)(2)+(4)(1) = 10; (3)(0)+(4)(5) = 20. Thus A * B = [[4, 10], [10, 20]].
4What is the determinant of matrix A = [[5, -2], [3, 4]]?
A.26
B.14
C.-26
D.20
Explanation: For a 2x2 matrix [[a, b], [c, d]], det(A) = ad - bc. Here det(A) = (5)(4) - (-2)(3) = 20 + 6 = 26.
5Calculate the inverse of matrix A = [[3, 5], [1, 2]].
A.[[2, -5], [-1, 3]]
B.[[-2, 5], [1, -3]]
C.[[3, -5], [-1, 2]]
D.[[2, 1], [5, 3]]
Explanation: det(A) = (3)(2) - (5)(1) = 6 - 5 = 1. The inverse is (1/det(A)) * [[d, -b], [-c, a]] = [[2, -5], [-1, 3]].
6Compute the determinant of the 3x3 matrix A = [[1, 2, 0], [0, 3, 4], [2, 0, 1]].
A.19
B.11
C.3
D.-13
Explanation: Expanding along row 1: det(A) = 1 * (3*1 - 4*0) - 2 * (0*1 - 4*2) + 0 = 1(3) - 2(-8) = 3 + 16 = 19.
7If A is a 3x3 square matrix with det(A) = 4, what is det(3A)?
A.108
B.12
C.36
D.64
Explanation: For an n x n matrix A and scalar k, det(k A) = k^n * det(A). Here n = 3 and k = 3, so det(3A) = 3^3 * 4 = 27 * 4 = 108.
8Which identity correctly expresses the transpose of the product of two matrices A and B?
A.(A * B)^T = B^T * A^T
B.(A * B)^T = A^T * B^T
C.(A * B)^T = A * B^T
D.(A * B)^T = (A^T * B)^T
Explanation: The transpose of a matrix product reverses the order of factors: (A * B)^T = B^T * A^T.
9Solve the matrix equation A * X = B for X, where A = [[2, 1], [1, 1]] and B = [[4], [3]].
A.[[1], [2]]
B.[[2], [1]]
C.[[5], [-2]]
D.[[7], [1]]
Explanation: det(A) = 2 - 1 = 1, so A^(-1) = [[1, -1], [-1, 2]]. Then X = A^(-1) * B = [[1*4 - 1*3], [-1*4 + 2*3]] = [[1], [2]].
10Determine the rank of matrix M = [[1, 2, 3], [2, 4, 6]].
A.1
B.2
C.3
D.0
Explanation: Row 2 is exactly twice Row 1 (R2 = 2 R1). Thus, there is only 1 linearly independent row, so rank(M) = 1.

About the Madrid PAU Applied Mathematics for Social Sciences II Practice Questions

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