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100+ Free PAU Mathematics II (Aragón) Practice Questions

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

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Key Facts: PAU Mathematics II (Aragón) Exam

90 min

Exam Time Limit

UNIZAR PAU Commission

0–10

Grading Scale

Gobierno de Aragón

4.0

Min. Access Phase Mark

Spanish PAU Regulations

EUR 75.00

Ordinary Registration Fee

UNIZAR PAU inscription page 2026

3 Blocks

Curriculum Blocks

2º Bachillerato Mathematics II

The Aragón PAU Mathematics II exam (Matemáticas II) is administered by UNIZAR and the PAU Organising Commission of Aragón for 2nd Bachillerato Science track students. Running 90 minutes, it evaluates linear algebra, differential and integral calculus, and 3D analytical geometry on a 0–10 grading scale. Questions on this platform provide an English MCQ study adaptation with full step-by-step mathematical derivations.

Sample PAU Mathematics II (Aragón) Practice Questions

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

1What is the determinant of the 2x2 matrix A = [[3, -1], [5, 2]]?
A.1
B.-11
C.11
D.6
Explanation: For a 2x2 matrix [[a, b], [c, d]], the determinant is ad - bc. Here det(A) = (3)(2) - (-1)(5) = 6 - (-5) = 6 + 5 = 11.
2Given matrices A = [[1, 4], [-2, 3]] and B = [[3, -1], [5, 0]], what is the matrix sum A + B?
A.[[4, 3], [3, 3]]
B.[[3, -4], [-10, 0]]
C.[[4, 5], [3, 3]]
D.[[2, 5], [-7, 3]]
Explanation: Matrix addition is performed entrywise: A + B = [[1+3, 4+(-1)], [-2+5, 3+0]] = [[4, 3], [3, 3]].
3Given A = [[2, 0], [1, 3]] and B = [[1, -1], [4, 2]], compute the linear combination 3A - 2B.
A.[[5, -2], [-5, 5]]
B.[[4, 2], [5, 5]]
C.[[4, -2], [11, 13]]
D.[[4, 2], [-5, 5]]
Explanation: Compute 3A = [[6, 0], [3, 9]] and 2B = [[2, -2], [8, 4]]. Then 3A - 2B = [[6-2, 0-(-2)], [3-8, 9-4]] = [[4, 2], [-5, 5]].
4For matrices A = [[1, 2], [3, 0]] and B = [[2, -1], [1, 4]], what is the matrix product A * B?
A.[[7, 4], [-3, 6]]
B.[[2, -2], [3, 0]]
C.[[4, 7], [6, -3]]
D.[[4, 7], [6, 0]]
Explanation: Row-column multiplication: top-left = 1(2)+2(1)=4; top-right = 1(-1)+2(4)=7; bottom-left = 3(2)+0(1)=6; bottom-right = 3(-1)+0(4)=-3. Thus A*B = [[4, 7], [6, -3]].
5If A = [[1, 2], [0, 5]], what is the transpose matrix A^T?
A.[[1, 0], [2, 5]]
B.[[5, 2], [0, 1]]
C.[[1, -2], [0, 5]]
D.[[5, 0], [2, 1]]
Explanation: The transpose of a matrix swaps its rows and columns. The first row (1, 2) becomes the first column, and the second row (0, 5) becomes the second column, yielding [[1, 0], [2, 5]].
6Solve the matrix equation A X = B for column vector X, where A = [[1, 2], [3, 5]] and B = [[1], [2]].
A.[[1], [-1]]
B.[[3], [1]]
C.[[-5], [2]]
D.[[-1], [1]]
Explanation: det(A) = 1(5) - 2(3) = -1. A^-1 = (1/-1) [[5, -2], [-3, 1]] = [[-5, 2], [3, -1]]. Then X = A^-1 B = [[-5(1) + 2(2)], [3(1) - 1(2)]] = [[-1], [1]].
7If the matrix A = [[2, x - 1], [3, 5]] is symmetric, what is the value of x?
A.-2
B.3
C.2
D.4
Explanation: A matrix is symmetric if A^T = A, meaning off-diagonal elements are equal: a_12 = a_21. Here x - 1 = 3 => x = 4.
8Given A = [[1, 0], [2, 1]], find the matrix power A^5.
A.[[1, 0], [2, 1]]
B.[[5, 0], [10, 5]]
C.[[1, 0], [32, 1]]
D.[[1, 0], [10, 1]]
Explanation: A^2 = [[1, 0], [4, 1]], A^3 = [[1, 0], [6, 1]], and by induction A^n = [[1, 0], [2n, 1]]. For n = 5, A^5 = [[1, 0], [10, 1]].
9Using Sarrus' rule, calculate the determinant of the 3x3 matrix A = [[1, 0, 2], [2, -1, 1], [0, 3, 1]].
A.11
B.14
C.8
D.-8
Explanation: det(A) = 1(-1)(1) + 0(1)(0) + 2(2)(3) - [0(-1)(2) + 3(1)(1) + 1(2)(0)] = (-1 + 0 + 12) - (0 + 3 + 0) = 11 - 3 = 8.
10If A is a 3x3 matrix with determinant det(A) = 5, what is the determinant of the matrix 2A?
A.30
B.40
C.20
D.10
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 * 5 = 40.

About the PAU Mathematics II (Aragón) Practice Questions

Verified exam format metadata for Aragón 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.