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100+ Free PAU Matemáticas II (Extremadura) Practice Questions

Extremadura PAU Mathematics II Exam — Matemáticas II 2º Bachillerato UEx 2026 practice questions are available now; exam metadata is being verified.

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Key Facts: PAU Matemáticas II (Extremadura) Exam

UEx / Junta

Comisión Organizadora de la PAU de Extremadura

Universidad de Extremadura

90 Mins

Official examination duration

PAU Extremadura Regulations

Min 4.0

Minimum Access Phase mark to combine with Bachillerato GPA

UEx Admission Guidelines

5 Blocks

Syllabus blocks covering algebra, calculus, geometry, and probability

LOMLOE 2º Bachillerato Mathematics II Curriculum

100

Practice questions available in this OpenExamPrep bank

OpenExamPrep

The Extremadura PAU Mathematics II exam tests advanced secondary mathematical problem solving, rigorous algebraic manipulation, spatial geometry, and probabilistic reasoning.

Sample PAU Matemáticas II (Extremadura) Practice Questions

Try these sample questions to test your PAU Matemáticas II (Extremadura) 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], [-1, 3]] and B = [[0, -2], [4, 1]], compute the matrix result of 2A - 3B.
A.[[4, 8], [-14, 3]]
B.[[4, -4], [10, 3]]
C.[[2, 3], [-5, 2]]
D.[[4, 8], [10, 9]]
Explanation: Compute scalar multiples: 2A = [[4, 2], [-2, 6]] and 3B = [[0, -6], [12, 3]]. Subtracting component-wise yields 2A - 3B = [[4-0, 2-(-6)], [-2-12, 6-3]] = [[4, 8], [-14, 3]].
2Calculate the determinant of the upper triangular 3x3 matrix A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]].
A.15
B.24
C.0
D.12
Explanation: For any triangular matrix (upper or lower), the determinant is the product of its main diagonal entries: det(A) = 1 * 4 * 6 = 24.
3Find the inverse of the 2x2 matrix A = [[3, 1], [5, 2]].
A.[[2, -1], [-5, 3]]
B.[[3, -5], [-1, 2]]
C.[[-2, 1], [5, -3]]
D.[[1/3, 1], [1/5, 1/2]]
Explanation: The determinant of A is det(A) = 3*2 - 1*5 = 6 - 5 = 1. The inverse formula for a 2x2 matrix [[a, b], [c, d]] is (1/det(A)) * [[d, -b], [-c, a]]. Thus A^-1 = [[2, -1], [-5, 3]].
4Solve the linear system 2x + 3y = 8 and x - y = -1 using Cramer's rule. What is the value of x?
A.x = 2
B.x = -1
C.x = 1
D.x = 3
Explanation: The main determinant is D = |[2, 3], [1, -1]| = -2 - 3 = -5. Replacing the first column with constants yields Dx = |[8, 3], [-1, -1]| = -8 - (-3) = -5. By Cramer's rule, x = Dx / D = -5 / -5 = 1.
5Determine the rank of the matrix M = [[1, 2, 3], [2, 4, 6], [0, 1, 1]].
A.1
B.3
C.2
D.0
Explanation: Row 2 is exactly twice Row 1 (R2 = 2*R1), making R2 linearly dependent. Row 1 [1, 2, 3] and Row 3 [0, 1, 1] are linearly independent because no scalar multiple of [0, 1, 1] gives [1, 2, 3]. Therefore, the maximum number of linearly independent rows is 2, so rank(M) = 2.
6If matrix A has dimensions 2x3 and matrix B has dimensions 3x4, what are the dimensions of the product matrix C = A * B?
A.3x3
B.4x2
C.2x3
D.2x4
Explanation: Matrix multiplication of an (m x n) matrix and an (n x p) matrix produces an (m x p) matrix. Here m = 2, n = 3, and p = 4, so C has dimensions 2x4.
7For what values of the real parameter k is the matrix A = [[k, 1, 1], [1, k, 1], [1, 1, k]] singular (det(A) = 0)?
A.k = 1 and k = -2
B.k = -1 and k = 2
C.k = 0 and k = 3
D.k = 1 and k = 2
Explanation: Computing the determinant det(A) = k(k^2 - 1) - 1(k - 1) + 1(1 - k) = k^3 - 3k + 2. Factoring the polynomial yields (k - 1)^2 * (k + 2) = 0. The roots are k = 1 and k = -2.
8Consider the system with parameter a: x + y + z = 1, x + ay + z = 1, x + y + az = a. For a = 1, how many solutions does the system possess?
A.Unique solution
B.No solution
C.Infinitely many solutions with 2 degrees of freedom
D.Infinitely many solutions with 1 degree of freedom
Explanation: Substituting a = 1 reduces all three equations to x + y + z = 1. This represents a single plane in R^3. The rank of the coefficient matrix and augmented matrix are both 1. With n = 3 variables, the number of free parameters is 3 - 1 = 2 degrees of freedom.
9Given the matrix equation A * X + B = C where A is an invertible square matrix, solve for the matrix X.
A.X = (C - B) * A^-1
B.X = A^-1 * (C - B)
C.X = A^-1 * C - B
D.X = (C - A^-1) * B
Explanation: Subtract B from both sides: A * X = C - B. Left-multiply both sides by A^-1: A^-1 * (A * X) = A^-1 * (C - B) => X = A^-1 * (C - B). Left-multiplication is mandatory because matrix multiplication is non-commutative.
10Using Cramer's rule on the system x + y + z = 6, 2x - y + z = 3, and x + 2y - z = 2, find the value of z.
A.z = 1
B.z = 2
C.z = 3
D.z = 4
Explanation: Determinant D = |[1, 1, 1], [2, -1, 1], [1, 2, -1]| = 1(1 - 2) - 1(-2 - 1) + 1(4 + 1) = -1 + 3 + 5 = 7. Dz = |[1, 1, 6], [2, -1, 3], [1, 2, 2]| = 1(-2 - 6) - 1(4 - 3) + 6(4 + 1) = -8 - 1 + 30 = 21. Thus z = Dz / D = 21 / 7 = 3.

About the PAU Matemáticas II (Extremadura) Practice Questions

Verified exam format metadata for Extremadura PAU Mathematics II Exam — Matemáticas II 2º Bachillerato UEx 2026 is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.