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Free Practice Questions for Andalusia PAU Applied Mathematics for Social Sciences II

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Key Facts: Andalusia PAU Applied Mathematics for Social Sciences 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 Content Areas

2º Bachillerato MACS II Syllabus

The Andalusia PAU Applied Mathematics for Social Sciences II exam (Matemáticas Aplicadas a las Ciencias Sociales II) is administered by the Distrito Único Andaluz and Comisión Interuniversitaria de Andalucía for students completing 2nd Bachillerato. The exam lasts 90 minutes and is graded 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 created to help students master the underlying 2nd Bachillerato curriculum with step-by-step calculations.

Sample Andalusia PAU Applied Mathematics for Social Sciences II Practice Questions

Try these sample questions to review concepts for the Andalusia PAU Applied Mathematics for Social Sciences II exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Given the 2x2 matrix A = [[2, 1], [4, 3]], what is the determinant of matrix A?
A.2
B.10
C.-2
D.6
Explanation: The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. For matrix A = [[2, 1], [4, 3]], det(A) = (2 * 3) - (1 * 4) = 6 - 4 = 2.
2If matrix A has dimensions 3x2 and matrix B has dimensions 2x4, what are the dimensions of the product matrix A * B?
A.2x2
B.3x4
C.4x3
D.3x2
Explanation: Matrix multiplication A * B is defined when the number of columns in A (2) equals the number of rows in B (2). The resulting matrix product has the number of rows of A (3) and the number of columns of B (4), giving dimensions 3x4.
3What is the transpose matrix A^T of matrix A = [[1, 5, -2], [0, 4, 3]]?
A.[[1, 0], [5, 4], [-2, 3]]
B.[[0, 1], [4, 5], [3, -2]]
C.[[1, 5, -2], [0, 4, 3]]
D.[[-2, 3], [5, 4], [1, 0]]
Explanation: The transpose of a matrix is formed by swapping its rows and columns. The 2x3 matrix A becomes a 3x2 matrix A^T where row 1 [1, 5, -2] becomes column 1 and row 2 [0, 4, 3] becomes column 2, yielding [[1, 0], [5, 4], [-2, 3]].
4A square matrix A is invertible (regular) if and only if which condition is met?
A.det(A) = 0
B.det(A) != 0
C.A is a symmetric matrix
D.All elements of A are positive
Explanation: A square matrix A is invertible (non-singular) if and only if its determinant is non-zero (det(A) != 0). If det(A) = 0, the matrix is singular and does not possess a inverse matrix.
5Given matrices A = [[3, 1], [0, 2]] and B = [[1, 4], [2, 1]], compute the matrix 2A - B.
A.[[5, -2], [-2, 3]]
B.[[5, -2], [2, 3]]
C.[[7, 6], [2, 5]]
D.[[4, -3], [-2, 1]]
Explanation: First, scalar multiply 2A = [[6, 2], [0, 4]]. Next, subtract B: 2A - B = [[6 - 1, 2 - 4], [0 - 2, 4 - 1]] = [[5, -2], [-2, 3]].
6Which matrix represents the 3x3 identity matrix I_3?
A.[[1, 0, 0], [0, 1, 0], [0, 0, 1]]
B.[[1, 1, 1], [1, 1, 1], [1, 1, 1]]
C.[[0, 0, 1], [0, 1, 0], [1, 0, 0]]
D.[[0, 1, 1], [1, 0, 1], [1, 1, 0]]
Explanation: The identity matrix of order 3 is a square 3x3 matrix with ones along its main diagonal (top-left to bottom-right) and zeros in all other entries.
7According to the Rouché-Frobenius theorem, a system of linear equations AX = B is consistent (has at least one solution) if and only if:
A.rank(A) = rank(A|B)
B.rank(A) < rank(A|B)
C.rank(A) = number of variables + 1
D.det(A) = 0
Explanation: The Rouché-Frobenius theorem states that a system of linear equations is consistent (compatible) if and only if the rank of the coefficient matrix A equals the rank of the augmented matrix (A|B).
8In a linear system with n variables, if rank(A) = rank(A|B) = n, how is the system classified under Rouché-Frobenius?
A.Inconsistent (no solution)
B.Consistent determined (unique solution)
C.Consistent undetermined (infinitely many solutions)
D.Homogeneous trivial system
Explanation: When rank(A) = rank(A|B) = n (where n is the number of unknown variables), the system is consistent determined (compatible determinado) and has exactly one unique solution.
9Calculate the inverse matrix A^-1 for A = [[1, 2], [3, 4]].
A.[[-2, 1], [1.5, -0.5]]
B.[[-2, -1], [-1.5, -0.5]]
C.[[4, -2], [-3, 1]]
D.[[2, -1], [-1.5, 0.5]]
Explanation: det(A) = (1*4) - (2*3) = 4 - 6 = -2. Using A^-1 = (1/det(A)) * [[d, -b], [-c, a]], A^-1 = (-1/2) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].
10Solve the matrix equation A * X = B for X, where A = [[2, 0], [0, 3]] and B = [[4, 6], [8, 12]].
A.[[2, 3], [8/3, 4]]
B.[[8, 18], [24, 36]]
C.[[2, 3], [4, 4]]
D.[[1/2, 2], [3, 4]]
Explanation: Multiply both sides by A^-1 on the left: X = A^-1 * B. A^-1 = [[1/2, 0], [0, 1/3]]. Thus X = [[1/2, 0], [0, 1/3]] * [[4, 6], [8, 12]] = [[(1/2)*4, (1/2)*6], [(1/3)*8, (1/3)*12]] = [[2, 3], [8/3, 4]].

About the Andalusia PAU Applied Mathematics for Social Sciences II Exam

The Andalusia PAU Applied Mathematics for Social Sciences II exam (Matemáticas Aplicadas a las Ciencias Sociales II) evaluates secondary school graduates across Andalusia on core mathematical methods used in social sciences, business, economics, and humanities. Key content includes matrices and systems of linear equations, linear programming optimization, calculus of functions, optimization, probability theory, probability distributions (binomial and normal), and statistical inference (confidence intervals and sample size determination). Please note: The official PAU exam features written problem-solving questions in Spanish; the 100 questions provided here are an English-language multiple-choice study adaptation designed for self-assessment and core concept mastery.

Exam sponsor: Distrito Único Andaluz / Comisión Interuniversitaria de Andalucía. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

90-minute written examination (traditionally open-ended problem solving; local questions are an English-language MCQ study adaptation)

Time Limit

90 minutes (1.5 hours)

Passing Score

Marked on a 0–10 scale. Minimum 4.0 required in Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU >= 5.0 to pass).

Exam / Certification Fees

EUR 58.70 base registration fee for PAU Access Phase (or ~14.70 € per subject in voluntary admission phase) set by Junta de Andalucía.

Exam sponsor website

Reported exam pass rate: High (~85-95% PAU overall pass rate in Andalusia). This describes exam candidates, not OpenExamPrep users or results from using our resources. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

25%

Matrices and Systems of Linear Equations

Matrix algebra, operations (addition, scalar multiplication, matrix product), matrix transpose, determinant calculation for 2x2 and 3x3 matrices, inverse matrix via adjugate or Gauss-Jordan methods, matrix equations of the form AX + B = C, systems of linear equations, Gauss elimination method, and Rouché-Frobenius theorem for system classification and parameter analysis.

20%

Linear Programming

Formulation of two-variable linear programming problems from economic and social scenarios, construction of system of linear inequality constraints, determination of the feasible region and its vertices (corner points), objective function visualization via level curves, and application of the fundamental theorem of linear programming to find maximum/minimum solutions.

15%

Limits, Continuity, and Functions

Concept of limit of a function, algebraic calculation of limits, resolution of indeterminate forms (0/0, infinity/infinity, 1^infinity), definition and analysis of continuity, points of discontinuity (removable, jump, essential), piecewise-defined functions, and vertical and horizontal asymptotes.

20%

Calculus, Derivatives, and Optimization

Concept of derivative as instantaneous rate of change, differentiation rules for polynomial, rational, exponential, and logarithmic functions, equation of the tangent line to a curve, analysis of monotonicity (increasing/decreasing intervals), determination of relative/local extrema (maxima and minima), concavity and inflection points, and real-world optimization problems in economic and social contexts.

20%

Probability, Distributions, and Inferential Statistics

Random experiments, sample space, events and operations, axioms of probability, conditional probability, independence of events, total probability theorem, Bayes' theorem, discrete probability distributions (Binomial distribution B(n,p)), continuous probability distributions (Standard Normal distribution N(0,1) and N(mu, sigma)), central limit theorem, sampling distributions, confidence intervals for a population proportion and mean, and sample size calculations.

Preparing for the Andalusia PAU Applied Mathematics for Social Sciences II Exam

What You Need to Know

  • Passing score: Marked on a 0–10 scale. Minimum 4.0 required in Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU >= 5.0 to pass).
  • Assessment: 90-minute written examination (traditionally open-ended problem solving; local questions are an English-language MCQ study adaptation)
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 58.70 base registration fee for PAU Access Phase (or ~14.70 € per subject in voluntary admission phase) set by Junta de Andalucía. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Andalusia PAU Applied Mathematics for Social Sciences II: Suggested Study Strategy

1Practice matrix arithmetic step-by-step, ensuring accuracy in matrix multiplication and calculating inverse matrices via det(A) and adj(A).
2Master linear programming: carefully plot constraint boundary lines, identify the feasible region shaded area, find exact vertex coordinates, and test vertices in the objective function.
3Review limits and derivative rules for piecewise functions, ensuring you test left- and right-hand limits at boundary points to check for continuity and differentiability.
4Solve optimization word problems by setting up single-variable objective functions, finding first derivatives, solving f'(x)=0, and verifying max/min with second derivatives.
5Drill Z-score calculations for normal distributions, Bayes' theorem tree diagrams, and standard error formulas for confidence intervals (Z_{alpha/2} * sigma / sqrt(n) or Z_{alpha/2} * sqrt(p(1-p)/n)).

Frequently Asked Questions

What is the format of the official Andalusia PAU Applied Mathematics II exam?

The official Andalusia PAU Applied Mathematics for Social Sciences II exam is a 90-minute written examination administered in Spanish, consisting of open-ended practical mathematical problems. Note that the 100 questions available on this site are an English-language multiple-choice practice adaptation developed to help students test their calculation skills and theoretical understanding of the official curriculum.

What is the passing score for Andalusia PAU Applied Mathematics II?

The exam is graded on a 0–10 scale. In the Access Phase (Fase de Acceso), a minimum score of 4.0 is required to average with the Bachillerato GPA (which counts for 60% of the final university access score, while PAU counts for 40%, requiring a total average of >= 5.0).

What is the fee for taking the PAU exam in Andalusia?

The base registration fee for the PAU Access Phase in Andalusia is set by the Junta de Andalucía at EUR 58.70 (or approximately EUR 14.70 per subject in the voluntary admission phase), with fee waivers or reductions for large families (familia numerosa) or specific categories.

Who sets the curriculum for the Andalusia PAU Applied Mathematics II test?

The curriculum and exam criteria are established by the Distrito Único Andaluz and the Comisión Interuniversitaria de Andalucía based on the official 2nd Bachillerato syllabus for Applied Mathematics for Social Sciences II.

Why are the practice questions here in English and in multiple-choice format?

These questions serve as an English-language MCQ study adaptation designed for international students, bilingual program candidates, and revision learners seeking to master the calculations and concepts required for the Andalusian curriculum.