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100+ Free Catalonia PAU Applied Mathematics for Social Sciences Exam Practice Questions

Catalonia PAU Applied Mathematics for Social Sciences / Matemàtiques Aplicades a les Ciències Socials II Exam practice questions are available now; exam metadata is being verified.

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2026 Statistics

Key Facts: Catalonia PAU Applied Mathematics for Social Sciences Exam Exam

90 min

Exam Duration

Consell Interuniversitari de Catalunya

0–10

Grading Scale

Generalitat de Catalunya

4.0

Minimum Access Pass Mark

PAU Regulations

EUR 110.00+ access phase (EUR 41.30 exam right + EUR 68.70 access phase; plus EUR 13.80 per admission exercise, Generalitat de Catalunya 2026)

Base Access Phase Fee

Generalitat de Catalunya 2026

The Catalonia PAU Applied Mathematics for Social Sciences II exam tests 2nd Bachillerato students on matrix algebra, linear programming, calculus optimization, financial calculations, probability, and statistical confidence intervals. The exam lasts 90 minutes and is evaluated on a 0–10 scale by the Consell Interuniversitari de Catalunya. The 100 practice questions offered here form an English-language multiple-choice adaptation of the official Generalitat de Catalunya curriculum.

Sample Catalonia PAU Applied Mathematics for Social Sciences Exam Practice Questions

Try these sample questions to test your Catalonia PAU Applied Mathematics for Social Sciences Exam 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 result of 2A - 3B.
A.[[1, -17], [12, 8]]
B.[[1, -17], [0, 8]]
C.[[7, 13], [0, 8]]
D.[[1, 13], [12, 8]]
Explanation: To compute 2A - 3B, first multiply matrix A by 2 to get [[4, -2], [6, 8]] and matrix B by 3 to get [[3, 15], [-6, 0]]. Subtracting 3B from 2A yields [[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.3 x 3
B.2 x 4
C.4 x 2
D.The product is undefined
Explanation: Matrix multiplication is defined when the number of columns of the first matrix matches the number of rows of the second matrix (both are 3). The resulting product matrix takes the row dimension of the first matrix (2) and the column dimension of the second matrix (4), giving dimensions 2 x 4.
3Calculate the matrix product A * B for A = [[1, 2], [3, 4]] and B = [[2, 0], [1, -1]].
A.[[4, -2], [10, -4]]
B.[[2, 0], [3, -4]]
C.[[4, 0], [10, -4]]
D.[[3, 2], [4, 3]]
Explanation: Multiplying row by column: top-left entry is 1(2) + 2(1) = 4; top-right entry is 1(0) + 2(-1) = -2; bottom-left entry is 3(2) + 4(1) = 10; bottom-right entry is 3(0) + 4(-1) = -4. The product matrix is [[4, -2], [10, -4]].
4Calculate the determinant of the 2x2 matrix A = [[5, -2], [3, 4]].
A.14
B.26
C.-26
D.20
Explanation: For a 2x2 matrix [[a, b], [c, d]], the determinant is computed as ad - bc. Here, det(A) = (5)(4) - (-2)(3) = 20 - (-6) = 20 + 6 = 26.
5Find the determinant of the 3x3 matrix A = [[1, 2, 0], [3, -1, 4], [2, 0, 1]].
A.9
B.-11
C.5
D.0
Explanation: Expanding along the first row: det(A) = 1 * ((-1)(1) - (4)(0)) - 2 * ((3)(1) - (4)(2)) + 0 = 1(-1) - 2(3 - 8) = -1 - 2(-5) = -1 + 10 = 9.
6Determine the inverse of the matrix A = [[4, 2], [3, 2]].
A.[[1, -1], [-1.5, 2]]
B.[[2, -2], [-3, 4]]
C.[[-2, 1], [1.5, -2]]
D.[[0.25, 0.5], [0.33, 0.5]]
Explanation: The determinant of A is (4)(2) - (2)(3) = 8 - 6 = 2. The adjugate matrix is [[2, -2], [-3, 4]]. Multiplying by 1/det(A) = 1/2 gives A^-1 = [[1, -1], [-1.5, 2]].
7For what value of parameter k is the matrix A = [[k, 6], [2, 3]] singular (non-invertible)?
A.k = 4
B.k = -4
C.k = 9
D.k = 0
Explanation: A matrix is singular if its determinant equals zero. Setting det(A) = 3k - (6)(2) = 3k - 12 = 0 gives 3k = 12, so k = 4.
8Find the value of k for which the matrix A = [[1, 0, k], [2, k, 1], [0, 1, 1]] does NOT have an inverse.
A.k = 1/3
B.k = 3
C.k = -1
D.k = 0
Explanation: A matrix fails to have an inverse when its determinant is zero. Expanding along the first row: det(A) = 1(k(1) - 1(1)) - 0 + k(2(1) - k(0)) = k - 1 + 2k = 3k - 1. Setting 3k - 1 = 0 yields k = 1/3.
9Solve the matrix equation A * X = B for vector X, given A = [[3, 1], [2, 1]] and B = [[5], [4]].
A.x = 1, y = 2
B.x = 2, y = 1
C.x = 3, y = -1
D.x = 0, y = 5
Explanation: The determinant of A is (3)(1) - (1)(2) = 1. The inverse A^-1 is [[1, -1], [-2, 3]]. Multiplying X = A^-1 * B gives [[1, -1], [-2, 3]] * [[5], [4]] = [[1(5) - 1(4)], [-2(5) + 3(4)]] = [[1], [2]]. Thus x = 1 and y = 2.
10Given the matrix equation X * A + B = C, where A is an invertible matrix, solve for X.
A.X = (C - B) * A^-1
B.X = A^-1 * (C - B)
C.X = (C + B) * A^-1
D.X = C * A^-1 - B
Explanation: First subtract B from both sides to obtain X * A = C - B. Since matrix multiplication is non-commutative and X is multiplied on the right by A, post-multiply both sides by A^-1 to get X = (C - B) * A^-1.

About the Catalonia PAU Applied Mathematics for Social Sciences Exam Practice Questions

Verified exam format metadata for Catalonia PAU Applied Mathematics for Social Sciences / Matemàtiques Aplicades a les Ciències Socials II Exam is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.