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100+ Free Balearic Islands PAU Mathematics II Practice Questions

Balearic Islands PAU Mathematics II Examination (Matemàtiques II / Matemáticas II 2º Bachillerato UIB 2026) practice questions are available now; exam metadata is being verified.

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Key Facts: Balearic Islands PAU Mathematics II Exam

90 Min

Total duration of the PAU Math II examination

UIB PAU Regulations

0–10

Grading scale for PAU Mathematics II paper

Balearic Islands PAU Commission

4.0 / 10

Minimum grade required in Access Phase

UIB Admissions Office

4 Major Blocks

Linear Algebra, Calculus, 3D Geometry, Probability

2º Bachillerato Mathematics II Syllabus

100

Practice questions provided in this test bank

OpenExamPrep

Balearic Islands PAU Mathematics II (UIB 2026) assesses 2º Bachillerato students on matrices, linear systems, calculus, 3D geometry, and probability in a 90-minute session.

Sample Balearic Islands PAU Mathematics II Practice Questions

Try these sample questions to test your Balearic Islands PAU Mathematics II exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Calculate the determinant of the 2x2 matrix A = [[3, -2], [4, 5]].
A.23
B.7
C.15
D.-7
Explanation: The determinant of a 2x2 matrix [[a, b], [c, d]] is computed as ad - bc. For A = [[3, -2], [4, 5]], det(A) = (3)(5) - (-2)(4) = 15 - (-8) = 23.
2Calculate the determinant of the 3x3 matrix A = [[1, 2, 0], [3, -1, 4], [0, 2, 1]].
A.-9
B.-15
C.5
D.15
Explanation: Expanding det(A) along the first row: 1*((-1)(1) - (4)(2)) - 2*((3)(1) - (4)(0)) + 0 = 1*(-1 - 8) - 2*(3 - 0) = -9 - 6 = -15.
3Compute the product matrix A * B where A = [[2, 1], [0, 3]] and B = [[1, -1], [4, 2]]. What is the element in row 1, column 1 of A * B?
A.2
B.10
C.6
D.4
Explanation: The (1,1) entry of A * B is the dot product of row 1 of A and column 1 of B: (2)(1) + (1)(4) = 2 + 4 = 6.
4Find the inverse of matrix A = [[4, 2], [1, 1]]. What is the top-left entry (row 1, column 1) of A^(-1)?
A.1.0
B.-1.0
C.2.0
D.0.5
Explanation: The determinant of A is det(A) = 4(1) - 2(1) = 2. The formula for a 2x2 inverse is (1/det(A)) * [[d, -b], [-c, a]]. Thus A^(-1) = (1/2) * [[1, -2], [-1, 4]] = [[0.5, -1], [-0.5, 2]]. The (1,1) entry is 0.5.
5Determine the rank of the matrix A = [[1, 2, 3], [2, 4, 6], [0, 0, 0]].
A.1
B.0
C.2
D.3
Explanation: The second row is 2 times the first row (linearly dependent), and the third row consists entirely of zeros. Thus, there is only 1 linearly independent row, so rank(A) = 1.
6Let A be a 3x3 matrix with det(A) = 5. What is det(2A)?
A.10
B.40
C.20
D.30
Explanation: For an n x n matrix A and scalar k, det(kA) = (k^n) * det(A). Here n = 3 and k = 2, so det(2A) = (2^3) * 5 = 8 * 5 = 40.
7If A is a square matrix with det(A) = -7, what is the determinant of its transpose, det(A^T)?
A.7
B.1/7
C.-7
D.-1/7
Explanation: A fundamental property of determinants states that det(A^T) = det(A). Therefore, det(A^T) = -7.
8Solve the matrix equation 2X + A = B for matrix X, given A = [[1, 3], [0, 2]] and B = [[5, 1], [4, 8]]. What is the top-left entry of X?
A.1
B.3
C.4
D.2
Explanation: Isolating X gives 2X = B - A, so X = (1/2)(B - A). Computing B - A = [[5-1, 1-3], [4-0, 8-2]] = [[4, -2], [4, 6]]. Dividing by 2 gives X = [[2, -1], [2, 3]]. The top-left entry is 2.
9Find the value of the parameter k for which the matrix A = [[1, 0, k], [2, 1, 1], [0, 1, 3]] is non-invertible.
A.k = -1
B.k = 1
C.k = -2
D.k = 2
Explanation: A matrix is non-invertible if and only if its determinant is zero. Expanding det(A) along the first row: 1*(3 - 1) + k*(2 - 0) = 2 + 2k. Setting 2 + 2k = 0 yields k = -1.
10If A is a 3x3 matrix with det(A) = 4, evaluate det(3 * A^(-1)).
A.0.75
B.6.75
C.12.0
D.2.25
Explanation: Using properties of determinants: det(k * A^(-1)) = (k^3) * (1 / det(A)). Here n = 3, k = 3, det(A) = 4. Thus det(3 * A^(-1)) = (3^3) * (1/4) = 27 / 4 = 6.75.

About the Balearic Islands PAU Mathematics II Practice Questions

Verified exam format metadata for Balearic Islands PAU Mathematics II Examination (Matemàtiques II / Matemáticas II 2º Bachillerato UIB 2026) is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.