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100+ Free Andalusia PAU Mathematics II Practice Questions

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

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Key Facts: Andalusia PAU Mathematics II Exam

90 min

Exam Time Limit

Distrito Único Andaluz

0–10

Grading Scale

Junta de Andalucía

4.0

Min. Access Phase Score

Comisión Interuniversitaria

EUR 58.70

Base Registration Fee

Junta de Andalucía

5 Blocks

Curriculum Blocks

2º Bachillerato Mathematics II Syllabus

The Andalusia PAU Mathematics II exam (Matemáticas II) is administered by the Distrito Único Andaluz and Comisión Interuniversitaria de Andalucía 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 Andalusian curriculum.

Sample Andalusia PAU Mathematics II Practice Questions

Try these sample questions to test your Andalusia 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.

1For the matrix A = [[2, 1], [4, 3]], what is the determinant det(A)?
A.2
B.10
C.-2
D.6
Explanation: For a 2x2 matrix [[a, b], [c, d]], the determinant is computed as ad - bc. Here det(A) = (2)(3) - (1)(4) = 6 - 4 = 2.
2Given A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 5]], what is the matrix sum A + B?
A.[[3, 2], [4, 9]]
B.[[2, 0], [3, 20]]
C.[[3, 2], [4, 20]]
D.[[1, 2], [4, 9]]
Explanation: Matrix addition is performed entrywise: A + B = [[1+2, 2+0], [3+1, 4+5]] = [[3, 2], [4, 9]].
3What is the transpose of the matrix M = [[1, 5, 9], [2, 6, 0]]?
A.[[1, 2], [5, 6], [9, 0]]
B.[[9, 5, 1], [0, 6, 2]]
C.[[2, 6, 0], [1, 5, 9]]
D.[[1, 6, 9], [2, 5, 0]]
Explanation: The transpose M^T is formed by swapping rows and columns. The 2x3 matrix becomes a 3x2 matrix where column 1 is [1, 5, 9]^T and column 2 is [2, 6, 0]^T.
4If det(A) = 5 for a 3x3 matrix A, what is det(2A)?
A.40
B.10
C.30
D.25
Explanation: For an n x n matrix, det(k A) = k^n det(A). For n = 3 and k = 2, det(2A) = 2^3 det(A) = 8 * 5 = 40.
5For what value of k is the 2x2 matrix [[k, 3], [2, 6]] singular (non-invertible)?
A.1
B.0
C.4
D.9
Explanation: A matrix is singular if its determinant equals 0. Setting det = (k)(6) - (3)(2) = 6k - 6 = 0 yields 6k = 6, so k = 1.
6What is the inverse of the 2x2 matrix A = [[1, 2], [0, 1]]?
A.[[1, -2], [0, 1]]
B.[[-1, -2], [0, -1]]
C.[[1, 0], [2, 1]]
D.[[1, 1/2], [0, 1]]
Explanation: For A = [[a, b], [c, d]] with det(A) = ad - bc = 1 - 0 = 1, A^-1 = (1/det)[[d, -b], [-c, a]] = [[1, -2], [0, 1]].
7According to the Rouché-Capelli theorem, a system of 3 linear equations in 3 unknowns is compatible determined (unique solution) if and only if:
A.rank(A) = rank(A|B) = 3
B.rank(A) = rank(A|B) = 2
C.rank(A) < rank(A|B)
D.rank(A) = 3 and rank(A|B) = 4
Explanation: By Rouché-Capelli, the system is compatible if rank(A) = rank(A|B). If this common rank equals the number of unknowns (n = 3), the system has a unique solution (compatible determined).
8What is the derivative of f(x) = x^3 - 4x^2 + 7x - 12?
A.3x^2 - 8x + 7
B.3x^2 - 4x + 7
C.x^2 - 8x + 7
D.3x^2 - 8x
Explanation: Applying the power rule d/dx(x^n) = n x^(n-1) term-by-term: f'(x) = 3x^2 - 4(2x) + 7(1) - 0 = 3x^2 - 8x + 7.
9What is the derivative of g(x) = e^(2x)?
A.2 e^(2x)
B.e^(2x)
C.2x e^(2x-1)
D.1/2 e^(2x)
Explanation: By the chain rule, d/dx(e^(u(x))) = e^(u(x)) * u'(x). Here u(x) = 2x, so u'(x) = 2, giving g'(x) = 2 e^(2x).
10What is the limit lim (x -> 0) [sin(3x) / x]?
A.3
B.1
C.0
D.Undefined
Explanation: Using the standard limit lim (u->0) [sin(u)/u] = 1, rewrite as 3 * [sin(3x) / (3x)]. As x -> 0, 3x -> 0, so the limit is 3 * 1 = 3 (or apply L'Hôpital: lim cos(3x)*3 / 1 = 3).

About the Andalusia PAU Mathematics II Practice Questions

Verified exam format metadata for Andalusia 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.