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100+ Free PAU Applied Math ACS II (Galicia) Practice Questions

Galicia PAU Applied Mathematics for Social Sciences II / Matemáticas Aplicadas a las Ciencias Sociales II Exam practice questions are available now; exam metadata is being verified.

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2026 Statistics

Key Facts: PAU Applied Math ACS II (Galicia) Exam

90 min

Exam Duration

CIUG Regulations

0–10

Grading Scale

Xunta de Galicia / CIUG

4.0 / 10

Min. Access Phase Mark

PAU Access Rules

60 / 40

GPA / PAU Weighting

Spanish Education Ministry & CIUG

EUR 63.67

Ordinary Registration Fee

CIUG Official Tariff

The Galicia PAU Applied Mathematics for Social Sciences II exam (Matemáticas Aplicadas a las Ciencias Sociales II 2º Bachillerato) is administered by CIUG (Comisión Interuniversitaria de Galicia). Lasting 90 minutes, it tests linear algebra & matrix equations, linear programming, real analysis & optimization, probability & Bayes' theorem, and inferential statistics. This 100-question practice set offers a comprehensive English MCQ adaptation of the official 2026 CIUG syllabus.

Sample PAU Applied Math ACS II (Galicia) Practice Questions

Try these sample questions to test your PAU Applied Math ACS II (Galicia) 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 = [[3, -1], [2, 4]] and B = [[1, 4], [-3, 2]], compute matrix C = 3A - 2B.
A.[[7, -11], [12, 8]]
B.[[7, 5], [0, 8]]
C.[[7, -11], [0, 8]]
D.[[11, -11], [12, 16]]
Explanation: Multiply matrix A by 3 to obtain 3A = [[9, -3], [6, 12]] and matrix B by 2 to obtain 2B = [[2, 8], [-6, 4]]. Subtracting 2B from 3A entry by entry yields C = [[9-2, -3-8], [6-(-6), 12-4]] = [[7, -11], [12, 8]].
2Calculate the matrix product A * B for A = [[1, 2], [-1, 3]] and B = [[2, 0], [1, -2]].
A.[[4, -4], [1, -6]]
B.[[2, 0], [-1, -6]]
C.[[4, 0], [1, -6]]
D.[[3, -4], [2, -6]]
Explanation: Compute entry (1,1) as 1(2) + 2(1) = 4, entry (1,2) as 1(0) + 2(-2) = -4, entry (2,1) as -1(2) + 3(1) = 1, and entry (2,2) as -1(0) + 3(-2) = -6. The product matrix is [[4, -4], [1, -6]].
3For the matrix A = [[4, -2, 5], [1, 3, 0], [-1, 2, 6]], calculate the sum of the trace of A and the trace of its transpose A^T.
A.26
B.13
C.0
D.39
Explanation: The trace of a square matrix is the sum of its main diagonal elements: Trace(A) = 4 + 3 + 6 = 13. Since taking the transpose does not change diagonal entries, Trace(A^T) = Trace(A) = 13. The total sum is 13 + 13 = 26.
4Given matrix A = [[2, 1], [0, 2]] and matrix B = [[x, y], [0, x]], under what conditions on real numbers x and y does AB = BA hold?
A.For all real numbers x and y
B.Only when x = 0
C.Only when y = 0
D.Only when x = y
Explanation: Multiplying AB gives [[2x, 2y + x], [0, 2x]]. Multiplying BA gives [[2x, x + 2y], [0, 2x]]. Comparing corresponding entries shows 2y + x = x + 2y for all real x and y, so AB = BA holds universally for these matrices.
5Find all real values of k for which the matrix A = [[k-1, 4], [2, k+1]] has a determinant equal to zero.
A.k = 3 and k = -3
B.k = 9 and k = -9
C.k = 1 and k = -1
D.k = 5 and k = -5
Explanation: The determinant is calculated as (k-1)(k+1) - (4)(2) = k^2 - 1 - 8 = k^2 - 9. Setting k^2 - 9 = 0 gives k^2 = 9, so k = 3 or k = -3.
6Calculate the determinant of the 3x3 matrix A = [[1, 0, 2], [2, 1, 1], [0, 3, -1]].
A.8
B.-8
C.4
D.12
Explanation: Using cofactor expansion along the first row: det(A) = 1*(1*(-1) - 3*1) - 0 + 2*(2*3 - 0*1) = 1*(-4) + 2*(6) = -4 + 12 = 8.
7Find the inverse matrix A^(-1) of the matrix A = [[3, 1], [5, 2]].
A.[[2, -1], [-5, 3]]
B.[[-2, 1], [5, -3]]
C.[[3, -1], [-5, 2]]
D.[[2, 1], [5, 3]]
Explanation: The determinant det(A) = (3)(2) - (1)(5) = 6 - 5 = 1. The inverse is (1/det(A)) * [[d, -b], [-c, a]] = [[2, -1], [-5, 3]].
8If A is a 3x3 matrix with det(A) = 4, calculate det(2 * A^(-1) * A^T).
A.8
B.4
C.16
D.2
Explanation: Using properties of determinants for an n x n matrix with n = 3: det(2 * A^(-1) * A^T) = 2^3 * det(A^(-1)) * det(A^T) = 8 * (1/4) * 4 = 8.
9Given matrix A = [[1, 1], [0, 1]], calculate the matrix power A^10.
A.[[1, 10], [0, 1]]
B.[[1, 1], [0, 1]]
C.[[1, 1024], [0, 1]]
D.[[10, 10], [0, 10]]
Explanation: Computing powers: A^2 = [[1, 2], [0, 1]], A^3 = [[1, 3], [0, 1]], and by induction A^n = [[1, n], [0, 1]]. For n = 10, A^10 = [[1, 10], [0, 1]].
10If the matrix A = [[2, x+1], [5, 3]] is symmetric, find the value of x.
A.4
B.5
C.3
D.2
Explanation: A matrix is symmetric if A = A^T, which requires corresponding off-diagonal elements to be equal: x + 1 = 5, yielding x = 4.

About the PAU Applied Math ACS II (Galicia) Practice Questions

Verified exam format metadata for Galicia PAU Applied Mathematics for Social Sciences II / Matemáticas Aplicadas a las Ciencias Sociales II Exam is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.