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100+ Free Castilla y León PAU Mathematics II Practice Questions

Castilla y León PAU Mathematics II (Matemáticas II 2º Bachillerato) practice questions are available now; exam metadata is being verified.

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Key Facts: Castilla y León PAU Mathematics II Exam

90 min

Exam Time Limit

Comisión Organizadora PAU CYL

0–10

Grading Scale

Junta de Castilla y León

4.0

Min. Access Phase Score

Comisión Organizadora PAU CYL

EUR 91.54

Base Registration Fee

Junta de Castilla y León

5 Blocks

Curriculum Blocks

2º Bachillerato Mathematics II Syllabus

The Castilla y León PAU Mathematics II exam (Matemáticas II) is organized by the public universities of Castilla y León (USAL, UVA, UBU, ULE) and the Consejería de Educación de la Junta de Castilla y León for 2nd Bachillerato Science and Technology students. The exam lasts 90 minutes and is marked 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 with detailed worked calculations created to help students master the official Castilla y León curriculum.

Sample Castilla y León PAU Mathematics II Practice Questions

Try these sample questions to test your Castilla y León 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 = [[4, 2], [3, 5]].
A.14
B.26
C.6
D.11
Explanation: For a 2x2 matrix [[a, b], [c, d]], the determinant is det(A) = ad - bc. Here, det(A) = (4)(5) - (2)(3) = 20 - 6 = 14.
2Given matrices A = [[1, 3], [-2, 4]] and B = [[5, -1], [2, 0]], what is the matrix sum A + B?
A.[[5, -3], [-4, 0]]
B.[[6, 2], [0, 4]]
C.[[6, 4], [0, 4]]
D.[[4, 2], [0, 4]]
Explanation: Matrix addition is performed component-wise: A + B = [[1+5, 3+(-1)], [-2+2, 4+0]] = [[6, 2], [0, 4]].
3Given matrix A = [[2, -1], [0, 3]], calculate 3A - 2I, where I is the 2x2 identity matrix.
A.[[4, -3], [0, 9]]
B.[[6, -3], [0, 7]]
C.[[4, -3], [0, 7]]
D.[[4, -1], [0, 7]]
Explanation: Compute 3A = [[6, -3], [0, 9]] and 2I = [[2, 0], [0, 2]]. Subtracting yields 3A - 2I = [[6-2, -3-0], [0-0, 9-2]] = [[4, -3], [0, 7]].
4Calculate the matrix product A * B for A = [[2, 1], [0, 3]] and B = [[1, 4], [2, 5]].
A.[[2, 4], [0, 15]]
B.[[4, 11], [6, 15]]
C.[[3, 13], [6, 15]]
D.[[4, 13], [6, 15]]
Explanation: Row-by-column product: c11 = 2(1)+1(2) = 4, c12 = 2(4)+1(5) = 13, c21 = 0(1)+3(2) = 6, c22 = 0(4)+3(5) = 15. Thus A * B = [[4, 13], [6, 15]].
5If det(A) = 7 for a 3x3 square matrix A, what is the determinant of its transpose, det(A^T)?
A.7
B.-7
C.1/7
D.21
Explanation: By determinant properties, transposing a matrix does not change its determinant: det(A^T) = det(A) = 7.
6For a 3x3 square matrix A with det(A) = 3, what is the value of det(2A)?
A.6
B.24
C.12
D.18
Explanation: For an n x n matrix, det(k A) = k^n * det(A). Here n = 3 and k = 2, so det(2A) = 2^3 * det(A) = 8 * 3 = 24.
7Evaluate the determinant of the 3x3 matrix A = [[1, 0, 2], [2, -1, 3], [4, 1, 0]] using Sarrus' Rule or cofactor expansion.
A.-3
B.15
C.9
D.5
Explanation: Expanding along row 1: det(A) = 1*((-1)(0) - 3(1)) - 0 + 2*(2(1) - (-1)(4)) = 1*(-3) + 2*(2 + 4) = -3 + 12 = 9.
8For what values of the real parameter k is the matrix A = [[k, 1], [4, k]] singular (non-invertible)?
A.k = 2 or k = -2
B.k = 4 or k = -4
C.k = 0 only
D.k = 1 or k = -1
Explanation: A matrix is singular when its determinant is zero: det(A) = k^2 - 4 = 0, which implies k^2 = 4, so k = 2 or k = -2.
9Find 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: For A = [[a, b], [c, d]], A^-1 = (1/det(A)) [[d, -b], [-c, a]]. Here det(A) = (2)(3) - (5)(1) = 1. Thus 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], [3, 4]].
A.[[1, 2], [3, 4]]
B.[[11, 14], [3, 4]]
C.[[-1, -2], [3, 4]]
D.[[-1, -2], [-3, -4]]
Explanation: Since det(A) = 1, A is invertible with A^-1 = [[1, -2], [0, 1]]. Then X = A^-1 * B = [[1, -2], [0, 1]] * [[5, 6], [3, 4]] = [[1(5)-2(3), 1(6)-2(4)], [0+3, 0+4]] = [[-1, -2], [3, 4]].

About the Castilla y León PAU Mathematics II Practice Questions

Verified exam format metadata for Castilla y León PAU Mathematics II (Matemáticas II 2º Bachillerato) is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.