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

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

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

90 min

Exam Time Limit

Distrito Único Andaluz

0–10

Grading Scale

Junta de Andalucía

4.0

Min. Access Phase Score

Comisión Interuniversitaria

EUR 58.70

Base Registration Fee

Junta de Andalucía

5 Blocks

Curriculum Content Areas

2º Bachillerato MACS II Syllabus

The Andalusia PAU Applied Mathematics for Social Sciences II exam (Matemáticas Aplicadas a las Ciencias Sociales II) is administered by the Distrito Único Andaluz and Comisión Interuniversitaria de Andalucía for students completing 2nd Bachillerato. The exam lasts 90 minutes and is graded on a 0–10 scale (minimum 4.0 required in the Access Phase). Note that local questions on this platform are an English-language MCQ study adaptation created to help students master the underlying 2nd Bachillerato curriculum with step-by-step calculations.

Sample Andalusia PAU Applied Mathematics for Social Sciences II Practice Questions

Try these sample questions to test your Andalusia 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.

1Given the 2x2 matrix A = [[2, 1], [4, 3]], what is the determinant of matrix A?
A.2
B.10
C.-2
D.6
Explanation: The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. For matrix A = [[2, 1], [4, 3]], det(A) = (2 * 3) - (1 * 4) = 6 - 4 = 2.
2If matrix A has dimensions 3x2 and matrix B has dimensions 2x4, what are the dimensions of the product matrix A * B?
A.2x2
B.3x4
C.4x3
D.3x2
Explanation: Matrix multiplication A * B is defined when the number of columns in A (2) equals the number of rows in B (2). The resulting matrix product has the number of rows of A (3) and the number of columns of B (4), giving dimensions 3x4.
3What is the transpose matrix A^T of matrix A = [[1, 5, -2], [0, 4, 3]]?
A.[[1, 0], [5, 4], [-2, 3]]
B.[[0, 1], [4, 5], [3, -2]]
C.[[1, 5, -2], [0, 4, 3]]
D.[[-2, 3], [5, 4], [1, 0]]
Explanation: The transpose of a matrix is formed by swapping its rows and columns. The 2x3 matrix A becomes a 3x2 matrix A^T where row 1 [1, 5, -2] becomes column 1 and row 2 [0, 4, 3] becomes column 2, yielding [[1, 0], [5, 4], [-2, 3]].
4A square matrix A is invertible (regular) if and only if which condition is met?
A.det(A) = 0
B.det(A) != 0
C.A is a symmetric matrix
D.All elements of A are positive
Explanation: A square matrix A is invertible (non-singular) if and only if its determinant is non-zero (det(A) != 0). If det(A) = 0, the matrix is singular and does not possess a inverse matrix.
5Given matrices A = [[3, 1], [0, 2]] and B = [[1, 4], [2, 1]], compute the matrix 2A - B.
A.[[5, -2], [-2, 3]]
B.[[5, -2], [2, 3]]
C.[[7, 6], [2, 5]]
D.[[4, -3], [-2, 1]]
Explanation: First, scalar multiply 2A = [[6, 2], [0, 4]]. Next, subtract B: 2A - B = [[6 - 1, 2 - 4], [0 - 2, 4 - 1]] = [[5, -2], [-2, 3]].
6Which matrix represents the 3x3 identity matrix I_3?
A.[[1, 0, 0], [0, 1, 0], [0, 0, 1]]
B.[[1, 1, 1], [1, 1, 1], [1, 1, 1]]
C.[[0, 0, 1], [0, 1, 0], [1, 0, 0]]
D.[[0, 1, 1], [1, 0, 1], [1, 1, 0]]
Explanation: The identity matrix of order 3 is a square 3x3 matrix with ones along its main diagonal (top-left to bottom-right) and zeros in all other entries.
7According to the Rouché-Frobenius theorem, a system of linear equations AX = B is consistent (has at least one solution) if and only if:
A.rank(A) = rank(A|B)
B.rank(A) < rank(A|B)
C.rank(A) = number of variables + 1
D.det(A) = 0
Explanation: The Rouché-Frobenius theorem states that a system of linear equations is consistent (compatible) if and only if the rank of the coefficient matrix A equals the rank of the augmented matrix (A|B).
8In a linear system with n variables, if rank(A) = rank(A|B) = n, how is the system classified under Rouché-Frobenius?
A.Inconsistent (no solution)
B.Consistent determined (unique solution)
C.Consistent undetermined (infinitely many solutions)
D.Homogeneous trivial system
Explanation: When rank(A) = rank(A|B) = n (where n is the number of unknown variables), the system is consistent determined (compatible determinado) and has exactly one unique solution.
9Calculate the inverse matrix A^-1 for A = [[1, 2], [3, 4]].
A.[[-2, 1], [1.5, -0.5]]
B.[[-2, -1], [-1.5, -0.5]]
C.[[4, -2], [-3, 1]]
D.[[2, -1], [-1.5, 0.5]]
Explanation: det(A) = (1*4) - (2*3) = 4 - 6 = -2. Using A^-1 = (1/det(A)) * [[d, -b], [-c, a]], A^-1 = (-1/2) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].
10Solve the matrix equation A * X = B for X, where A = [[2, 0], [0, 3]] and B = [[4, 6], [8, 12]].
A.[[2, 3], [8/3, 4]]
B.[[8, 18], [24, 36]]
C.[[2, 3], [4, 4]]
D.[[1/2, 2], [3, 4]]
Explanation: Multiply both sides by A^-1 on the left: X = A^-1 * B. A^-1 = [[1/2, 0], [0, 1/3]]. Thus X = [[1/2, 0], [0, 1/3]] * [[4, 6], [8, 12]] = [[(1/2)*4, (1/2)*6], [(1/3)*8, (1/3)*12]] = [[2, 3], [8/3, 4]].

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

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