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

Aragón 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 (Aragón) Exam

90 min

Exam Duration

UNIZAR PAU Commission

0–10

Grading Scale

Gobierno de Aragón

4.0 / 10

Min. Access Phase Mark

PAU Regulations

60 / 40

GPA / PAU Weighting

Spanish University Access Regulations

The Aragón PAU Applied Mathematics for Social Sciences II exam (Matemáticas Aplicadas a las Ciencias Sociales II 2º Bachillerato) is administered by UNIZAR / PAU Organising Commission of Aragón. Lasting 90 minutes, it tests linear algebra & matrix equations, linear programming, real analysis & optimization, and probability & inferential statistics. This 100-question practice set offers an English MCQ adaptation of the official 2026 UNIZAR syllabus.

Sample PAU Applied Math ACS II (Aragón) Practice Questions

Try these sample questions to test your PAU Applied Math ACS II (Aragón) 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 = [[2, -1], [3, 4]] and B = [[1, 5], [-2, 0]], calculate the matrix C = 2A - 3B.
A.[[1, -17], [12, 8]]
B.[[1, -17], [0, 8]]
C.[[7, 13], [0, 8]]
D.[[1, 13], [12, 8]]
Explanation: Compute 2A = [[4, -2], [6, 8]] and 3B = [[3, 15], [-6, 0]]. Subtracting 3B from 2A yields C = [[4-3, -2-15], [6-(-6), 8-0]] = [[1, -17], [12, 8]].
2If matrix A has dimensions 2 x 3 and matrix B has dimensions 3 x 4, what are the dimensions of the product matrix C = A * B?
A.4 x 2
B.2 x 4
C.The product A * B is undefined.
D.3 x 3
Explanation: Matrix multiplication is defined when the number of columns of the first matrix (3) equals the number of rows of the second matrix (3). The resulting product matrix C has the number of rows of A (2) and the number of columns of B (4), so its dimensions are 2 x 4.
3Calculate the matrix product A * B for A = [[1, 2], [0, -1]] and B = [[3, 1], [4, 2]].
A.[[3, 2], [0, -2]]
B.[[7, 3], [-4, -2]]
C.[[11, 5], [4, 2]]
D.[[11, 5], [-4, -2]]
Explanation: Perform row-by-column multiplication: c11 = 1*3 + 2*4 = 11; c12 = 1*1 + 2*2 = 5; c21 = 0*3 + (-1)*4 = -4; c22 = 0*1 + (-1)*2 = -2. Thus A * B = [[11, 5], [-4, -2]].
4Which of the following identities is true for any two invertible square matrices A and B of the same size?
A.(A * B)^T = A^T * B^T
B.(A + B)^T = A^T * B^T
C.det(A + B) = det(A) + det(B)
D.(A * B)^T = B^T * A^T
Explanation: The transpose of a product of matrices reverses the order of multiplication: (A * B)^T = B^T * A^T.
5For what value of k is the matrix A = [[k, 4], [2, k-2]] singular (non-invertible)?
A.k = -2 and k = 0
B.k = -4 and k = 2
C.k = 4 and k = -2
D.k = 2 and k = 4
Explanation: A matrix is singular if its determinant equals 0. det(A) = k*(k - 2) - 4*2 = k^2 - 2k - 8 = 0. Factoring gives (k - 4)(k + 2) = 0, so k = 4 or k = -2.
6Calculate the determinant of the 3x3 matrix A = [[1, 0, 2], [3, -1, 1], [2, 1, 4]].
A.-5
B.-3
C.3
D.5
Explanation: Expanding along the first row: det(A) = 1 * det([[-1, 1], [1, 4]]) - 0 + 2 * det([[3, -1], [2, 1]]) = 1*(-5) + 2*(5) = -5 + 10 = 5.
7If A is a 3 x 3 matrix with det(A) = 4, what is the value of det(2 * A^(-1))?
A.2
B.1/2
C.8
D.1
Explanation: For an n x n matrix, det(k M) = k^n * det(M). Here n = 3, so det(2 A^(-1)) = 2^3 * det(A^(-1)). Since det(A^(-1)) = 1 / det(A) = 1/4, we have det(2 A^(-1)) = 8 * (1/4) = 2.
8Find the inverse of the 2x2 matrix A = [[3, 5], [1, 2]].
A.[[1/3, 1/5], [1, 1/2]]
B.[[2, -5], [-1, 3]]
C.[[-2, 5], [1, -3]]
D.[[3, -5], [-1, 2]]
Explanation: For A = [[a, b], [c, d]], det(A) = ad - bc = 3*2 - 5*1 = 1. The inverse is A^(-1) = (1/det(A)) * [[d, -b], [-c, a]] = [[2, -5], [-1, 3]].
9If matrix A is invertible and A * X = B, how is the unknown matrix X isolated?
A.X = A^(-1) * B
B.X = A * B^(-1)
C.X = B * A^(-1)
D.X = B / A
Explanation: To isolate X when A is multiplied on the left (A * X = B), left-multiply both sides by A^(-1): A^(-1) * (A * X) = A^(-1) * B => I * X = A^(-1) * B => X = A^(-1) * B. Order matters in matrix multiplication!
10Solve the matrix equation [[2, 1], [5, 3]] * X = [[4, 2], [1, 0]].
A.[[11, 6], [26, 14]]
B.[[11, 6], [-18, -10]]
C.[[-11, -6], [26, 14]]
D.[[4, -2], [-1, 6]]
Explanation: Multiplying on the left by A^(-1) = [[3, -1], [-5, 2]] gives X = A^(-1) * B = [[3, -1], [-5, 2]] * [[4, 2], [1, 0]] = [[11, 6], [-18, -10]].

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

Verified exam format metadata for Aragón 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.