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

La Rioja 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 (La Rioja) Exam

90 min

Exam Duration

UR PAU Commission

0–10

Grading Scale

Gobierno de La Rioja

EUR 55.43

Base Registration Fee

UR 2026 Rate

4.0 / 10

Min. Access Phase Mark

PAU Regulations

60 / 40

GPA / PAU Weighting

Spanish University Access Regulations

The La Rioja PAU Applied Mathematics for Social Sciences II exam (Matemáticas Aplicadas a las Ciencias Sociales II 2º Bachillerato) is administered by Universidad de La Rioja (UR) / Comisión Organizadora de la PAU de La Rioja. 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 UR syllabus.

Sample PAU Applied Math ACS II (La Rioja) Practice Questions

Try these sample questions to test your PAU Applied Math ACS II (La Rioja) 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, -2], [1, 5]] and B = [[2, 4], [-1, 3]], calculate C = 3A - 2B.
A.[[5, -14], [5, 9]]
B.[[5, -14], [1, 9]]
C.[[13, 2], [1, 21]]
D.[[5, 2], [5, 9]]
Explanation: Compute 3A = [[9, -6], [3, 15]] and 2B = [[4, 8], [-2, 6]]. Subtracting 2B from 3A gives C = [[9-4, -6-8], [3-(-2), 15-6]] = [[5, -14], [5, 9]].
2If matrix A has dimensions 3 x 2 and matrix B has dimensions 2 x 4, what are the dimensions of matrix product C = A * B?
A.2 x 2
B.3 x 4
C.4 x 3
D.The product is undefined.
Explanation: The product of a (m x n) matrix and an (n x p) matrix is an (m x p) matrix. Here, m = 3, n = 2, and p = 4, so C has dimensions 3 x 4.
3Calculate the determinant of matrix A = [[4, 7], [2, 5]].
A.6
B.-6
C.34
D.13
Explanation: For a 2x2 matrix [[a, b], [c, d]], the determinant is ad - bc. Thus, det(A) = (4)(5) - (7)(2) = 20 - 14 = 6.
4Find the product matrix A * B for A = [[2, 1], [0, 3]] and B = [[1, 4], [2, -1]].
A.[[4, 7], [6, -3]]
B.[[2, 4], [0, -3]]
C.[[4, 7], [6, 3]]
D.[[3, 5], [2, 2]]
Explanation: Element (1,1) = 2(1)+1(2) = 4; (1,2) = 2(4)+1(-1) = 7; (2,1) = 0(1)+3(2) = 6; (2,2) = 0(4)+3(-1) = -3. So A*B = [[4, 7], [6, -3]].
5Compute the determinant of the 3x3 matrix A = [[1, 2, 0], [0, 3, 1], [2, 1, 4]].
A.13
B.11
C.15
D.7
Explanation: Expanding det(A) along row 1: 1 * det([[3, 1], [1, 4]]) - 2 * det([[0, 1], [2, 4]]) + 0 = 1(12 - 1) - 2(0 - 2) = 11 - 2(-2) = 11 + 4 = 15.
6Which matrix identity is always true for invertible matrices A and B of the same size?
A.(A * B)^(-1) = B^(-1) * A^(-1)
B.(A * B)^(-1) = A^(-1) * B^(-1)
C.(A + B)^(-1) = A^(-1) + B^(-1)
D.det(A + B) = det(A) + det(B)
Explanation: The inverse of a matrix product reverses the multiplication order: (AB)^(-1) = B^(-1)A^(-1).
7Find the transpose matrix A^T for A = [[1, 5, 9], [2, 6, 0]].
A.[[1, 2], [5, 6], [9, 0]]
B.[[2, 6, 0], [1, 5, 9]]
C.[[9, 5, 1], [0, 6, 2]]
D.[[1, 6], [5, 0], [9, 2]]
Explanation: The transpose A^T converts rows into columns. Row 1 [1, 5, 9] becomes column 1, and Row 2 [2, 6, 0] becomes column 2, yielding a 3x2 matrix [[1, 2], [5, 6], [9, 0]].
8Solve the matrix equation X + [[2, -1], [4, 3]] = [[5, 2], [1, 7]].
A.[[3, 3], [-3, 4]]
B.[[7, 1], [5, 10]]
C.[[3, 1], [-3, 4]]
D.[[3, 3], [3, 4]]
Explanation: Subtract A from B: X = [[5-2, 2-(-1)], [1-4, 7-3]] = [[3, 3], [-3, 4]].
9Calculate the inverse matrix A^(-1) for A = [[2, 5], [1, 3]].
A.[[3, -5], [-1, 2]]
B.[[-3, 5], [1, -2]]
C.[[3, 1], [5, 2]]
D.[[2, -5], [-1, 3]]
Explanation: det(A) = 2(3) - 5(1) = 6 - 5 = 1. The inverse formula for [[a, b], [c, d]] is (1/det)[[d, -b], [-c, a]]. So A^(-1) = [[3, -5], [-1, 2]].
10Solve the matrix equation A * X = B for X, where A = [[1, 2], [0, 1]] and B = [[5, 6], [2, 3]].
A.[[1, 0], [2, 3]]
B.[[5, 6], [2, 3]]
C.[[9, 12], [2, 3]]
D.[[1, 1], [2, 3]]
Explanation: Compute A^(-1) = [[1, -2], [0, 1]]. Then X = A^(-1)B = [[1, -2], [0, 1]] * [[5, 6], [2, 3]] = [[1(5)-2(2), 1(6)-2(3)], [0(5)+1(2), 0(6)+1(3)]] = [[1, 0], [2, 3]].

About the PAU Applied Math ACS II (La Rioja) Practice Questions

Verified exam format metadata for La Rioja 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.