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Key Facts: Extremadura PAU Applied Mathematics for Social Sciences II Exam

EUR 78.26

Ordinary registration fee for PAU

Universidad de Extremadura (UEx)

90 Mins

Official examination duration

Comisión Organizadora de la PAU de Extremadura

Min 4.0

Minimum Access Phase score required to combine with Bachillerato GPA

UEx / Junta de Extremadura

3 Units

Main thematic curriculum blocks

2º Bachillerato LOMLOE Applied Mathematics Curriculum

100

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Master Extremadura PAU Applied Mathematics for Social Sciences II with 100 realistic practice questions and fully worked step-by-step quantitative solutions.

Sample Extremadura PAU Applied Mathematics for Social Sciences II Practice Questions

Try these sample questions to review concepts for the Extremadura 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 matrices A = [[2, -1], [3, 4]] and B = [[1, 5], [-2, 0]], calculate the matrix C = 2A - B.
A.[[3, -7], [8, 8]]
B.[[1, -7], [8, 8]]
C.[[3, 3], [4, 8]]
D.[[3, -7], [4, 4]]
Explanation: To compute C = 2A - B: 2A = 2 * [[2, -1], [3, 4]] = [[4, -2], [6, 8]]. Then C = [[4, -2], [6, 8]] - [[1, 5], [-2, 0]] = [[4-1, -2-5], [6-(-2), 8-0]] = [[3, -7], [8, 8]].
2Compute the determinant of the 2x2 matrix A = [[5, -2], [3, 4]].
A.14
B.26
C.-26
D.20
Explanation: For a 2x2 matrix [[a, b], [c, d]], det(A) = a*d - b*c. Here, det(A) = (5)(4) - (-2)(3) = 20 - (-6) = 20 + 6 = 26.
3Given matrices A = [[1, 2], [3, 0]] and B = [[4, 1], [-1, 2]], calculate the product matrix AB.
A.[[2, 3], [12, 5]]
B.[[6, 5], [12, 3]]
C.[[2, 5], [12, 3]]
D.[[4, 2], [-3, 0]]
Explanation: Matrix multiplication AB: Row 1 * Col 1: 1(4) + 2(-1) = 4 - 2 = 2. Row 1 * Col 2: 1(1) + 2(2) = 1 + 4 = 5. Row 2 * Col 1: 3(4) + 0(-1) = 12 + 0 = 12. Row 2 * Col 2: 3(1) + 0(2) = 3 + 0 = 3. Thus, AB = [[2, 5], [12, 3]].
4If matrix A has dimensions 3x2 and matrix B has dimensions 2x4, what are the dimensions of the transposed product matrix (AB)^T?
A.3x4
B.2x2
C.3x2
D.4x3
Explanation: The product AB has dimensions (3x2) * (2x4) = 3x4. Transposing a 3x4 matrix swaps its rows and columns, giving dimensions 4x3.
5Calculate the trace of the 3x3 matrix A = [[4, -1, 3], [2, 7, 0], [1, 5, -2]].
A.9
B.13
C.7
D.11
Explanation: The trace of a square matrix is the sum of its main diagonal elements: Trace(A) = 4 + 7 + (-2) = 9.
6If matrix A is a 3x3 matrix with determinant det(A) = 5, what is the value of det(2A)?
A.10
B.40
C.15
D.125
Explanation: For an n x n matrix A and scalar k, det(kA) = k^n * det(A). Here n = 3 and k = 2, so det(2A) = 2^3 * det(A) = 8 * 5 = 40.
7Find the inverse of the matrix A = [[3, 1], [5, 2]].
A.[[2, 1], [5, 3]]
B.[[-2, 1], [5, -3]]
C.[[2, -1], [-5, 3]]
D.[[3, -5], [-1, 2]]
Explanation: For A = [[a, b], [c, d]], det(A) = ad - bc = 3(2) - 1(5) = 6 - 5 = 1. The inverse is A^-1 = (1/det(A)) * [[d, -b], [-c, a]] = [[2, -1], [-5, 3]].
8Solve the system of linear equations: 2x + 3y = 12 and 4x - y = 10. What is the value of x?
A.1
B.2
C.4
D.3
Explanation: From the second equation, y = 4x - 10. Substitute into the first equation: 2x + 3(4x - 10) = 12 => 2x + 12x - 30 = 12 => 14x = 42 => x = 3. (Then y = 4(3) - 10 = 2).
9Determine whether the point (3, 2) belongs to the feasible region defined by constraints: x >= 0, y >= 0, x + y <= 6, and 2x + y <= 8.
A.Yes, (3, 2) satisfies all constraints and is a feasible point
B.No, it violates x + y <= 6
C.No, it violates 2x + y <= 8
D.No, it violates non-negativity constraints
Explanation: Check constraints for x = 3, y = 2: 1) x >= 0, y >= 0 -> 3 >= 0, 2 >= 0 (True) 2) x + y = 3 + 2 = 5 <= 6 (True) 3) 2x + y = 2(3) + 2 = 6 + 2 = 8 <= 8 (True). Since all inequalities hold, (3, 2) is a valid feasible point.
10Solve the matrix equation AX = B for X, where A = [[1, 2], [0, 1]] and B = [[5, 6], [3, 4]].
A.[[1, 2], [3, 4]]
B.[[-1, -2], [3, 4]]
C.[[5, 6], [1, 2]]
D.[[-1, 2], [-3, 4]]
Explanation: Since det(A) = 1, A^-1 = [[1, -2], [0, 1]]. Multiply on the left: X = A^-1 * B = [[1, -2], [0, 1]] * [[5, 6], [3, 4]]. Row 1: [1*5 - 2*3, 1*6 - 2*4] = [5 - 6, 6 - 8] = [-1, -2]. Row 2: [0*5 + 1*3, 0*6 + 1*4] = [3, 4]. Thus X = [[-1, -2], [3, 4]].

About the Extremadura PAU Applied Mathematics for Social Sciences II Exam

The Extremadura PAU Applied Mathematics for Social Sciences II exam assesses mathematical skills in 2º Bachillerato (Humanities & Social Sciences track). Key areas include matrix operations, systems of linear equations, linear programming optimization, differential calculus, economic marginal analysis, integration, area calculation, probability theory, and inferential statistics (confidence intervals and sample sizes).

Exam sponsor: Comisión Organizadora de la PAU de Extremadura (Universidad de Extremadura - UEx / Consejería de Educación de la Junta de Extremadura). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

90-minute written examination (applied mathematical problems, linear programming, statistics; 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 78.26 ordinary registration fee for PAU (50% discount EUR 39.13 for general large family; full exemption for special large family, disability, or terrorism victims).

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.

30%

Algebra & Linear Programming

Matrix algebra, determinants, inverse matrices, systems of linear equations, Rouché-Capelli theorem, system of linear inequalities, feasible region vertices, and objective function optimization.

35%

Analysis & Calculus

Limits, continuity, derivatives, marginal profit/cost/revenue functions, monotonicity, extrema, optimization, indefinite and definite integrals, and area under/between curves.

35%

Probability & Statistics

Combinatorics, probability tree diagrams, conditional probability, total probability theorem, Bayes' theorem, normal distribution, sampling distributions, confidence intervals for mean/proportion, and sample size calculations.

Preparing for the Extremadura 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 (applied mathematical problems, linear programming, statistics; local questions are an English-language MCQ study adaptation)
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 78.26 ordinary registration fee for PAU (50% discount EUR 39.13 for general large family; full exemption for special large family, disability, or terrorism victims). Official sources

Using Our Practice Resources

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

1Practice setting up and evaluating linear programming feasible regions by finding exact intersection vertices.
2Master matrix inversion formulas A⁻¹ = (1/det(A)) * adj(A) and matrix equations AX + B = C.
3Analyze continuity at piecewise boundaries and find parameters for derivative differentiability.
4Solve economic optimization problems by setting marginal revenue equal to marginal cost.
5Calculate 95% and 99% confidence intervals for means and proportions and determine required sample sizes for specified margins of error.

Frequently Asked Questions

What is the registration fee for the PAU exam in Extremadura?

EUR 78.26 ordinary registration fee for PAU (50% discount EUR 39.13 for general large family; full exemption for special large family, disability, or terrorism victims).

What passing score is required on the PAU Applied Mathematics for Social Sciences II exam in Extremadura?

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).

What is the duration and format of the PAU Applied Mathematics for Social Sciences II exam in Extremadura?

90-minute written examination (applied mathematical problems, linear programming, statistics; local questions are an English-language MCQ study adaptation)

Which body organizes the PAU exam in Extremadura?

Comisión Organizadora de la PAU de Extremadura (Universidad de Extremadura - UEx / Consejería de Educación de la Junta de Extremadura)