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Key Facts: Catalonia PAU Applied Mathematics for Social Sciences Exam Exam

90 min

Exam Duration

Consell Interuniversitari de Catalunya

0–10

Grading Scale

Generalitat de Catalunya

4.0

Minimum Access Pass Mark

PAU Regulations

EUR 110.00+ access phase (EUR 41.30 exam right + EUR 68.70 access phase; plus EUR 13.80 per admission exercise, Generalitat de Catalunya 2026)

Base Access Phase Fee

Generalitat de Catalunya 2026

The Catalonia PAU Applied Mathematics for Social Sciences II exam tests 2nd Bachillerato students on matrix algebra, linear programming, calculus optimization, financial calculations, probability, and statistical confidence intervals. The exam lasts 90 minutes and is evaluated on a 0–10 scale by the Consell Interuniversitari de Catalunya. The 100 practice questions offered here form an English-language multiple-choice adaptation of the official Generalitat de Catalunya curriculum.

Sample Catalonia PAU Applied Mathematics for Social Sciences Exam Practice Questions

Try these sample questions to review concepts for the Catalonia PAU Applied Mathematics for Social Sciences Exam 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 result of 2A - 3B.
A.[[1, -17], [12, 8]]
B.[[1, -17], [0, 8]]
C.[[7, 13], [0, 8]]
D.[[1, 13], [12, 8]]
Explanation: To compute 2A - 3B, first multiply matrix A by 2 to get [[4, -2], [6, 8]] and matrix B by 3 to get [[3, 15], [-6, 0]]. Subtracting 3B from 2A yields [[4-3, -2-15], [6-(-6), 8-0]] = [[1, -17], [12, 8]].
2If matrix A has dimensions 2 x 3 and matrix B has dimensions 3 x 4, what are the dimensions of the product matrix C = A * B?
A.3 x 3
B.2 x 4
C.4 x 2
D.The product is undefined
Explanation: Matrix multiplication is defined when the number of columns of the first matrix matches the number of rows of the second matrix (both are 3). The resulting product matrix takes the row dimension of the first matrix (2) and the column dimension of the second matrix (4), giving dimensions 2 x 4.
3Calculate the matrix product A * B for A = [[1, 2], [3, 4]] and B = [[2, 0], [1, -1]].
A.[[4, -2], [10, -4]]
B.[[2, 0], [3, -4]]
C.[[4, 0], [10, -4]]
D.[[3, 2], [4, 3]]
Explanation: Multiplying row by column: top-left entry is 1(2) + 2(1) = 4; top-right entry is 1(0) + 2(-1) = -2; bottom-left entry is 3(2) + 4(1) = 10; bottom-right entry is 3(0) + 4(-1) = -4. The product matrix is [[4, -2], [10, -4]].
4Calculate 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]], the determinant is computed as ad - bc. Here, det(A) = (5)(4) - (-2)(3) = 20 - (-6) = 20 + 6 = 26.
5Find the determinant of the 3x3 matrix A = [[1, 2, 0], [3, -1, 4], [2, 0, 1]].
A.9
B.-11
C.5
D.0
Explanation: Expanding along the first row: det(A) = 1 * ((-1)(1) - (4)(0)) - 2 * ((3)(1) - (4)(2)) + 0 = 1(-1) - 2(3 - 8) = -1 - 2(-5) = -1 + 10 = 9.
6Determine the inverse of the matrix A = [[4, 2], [3, 2]].
A.[[1, -1], [-1.5, 2]]
B.[[2, -2], [-3, 4]]
C.[[-2, 1], [1.5, -2]]
D.[[0.25, 0.5], [0.33, 0.5]]
Explanation: The determinant of A is (4)(2) - (2)(3) = 8 - 6 = 2. The adjugate matrix is [[2, -2], [-3, 4]]. Multiplying by 1/det(A) = 1/2 gives A^-1 = [[1, -1], [-1.5, 2]].
7For what value of parameter k is the matrix A = [[k, 6], [2, 3]] singular (non-invertible)?
A.k = 4
B.k = -4
C.k = 9
D.k = 0
Explanation: A matrix is singular if its determinant equals zero. Setting det(A) = 3k - (6)(2) = 3k - 12 = 0 gives 3k = 12, so k = 4.
8Find the value of k for which the matrix A = [[1, 0, k], [2, k, 1], [0, 1, 1]] does NOT have an inverse.
A.k = 1/3
B.k = 3
C.k = -1
D.k = 0
Explanation: A matrix fails to have an inverse when its determinant is zero. Expanding along the first row: det(A) = 1(k(1) - 1(1)) - 0 + k(2(1) - k(0)) = k - 1 + 2k = 3k - 1. Setting 3k - 1 = 0 yields k = 1/3.
9Solve the matrix equation A * X = B for vector X, given A = [[3, 1], [2, 1]] and B = [[5], [4]].
A.x = 1, y = 2
B.x = 2, y = 1
C.x = 3, y = -1
D.x = 0, y = 5
Explanation: The determinant of A is (3)(1) - (1)(2) = 1. The inverse A^-1 is [[1, -1], [-2, 3]]. Multiplying X = A^-1 * B gives [[1, -1], [-2, 3]] * [[5], [4]] = [[1(5) - 1(4)], [-2(5) + 3(4)]] = [[1], [2]]. Thus x = 1 and y = 2.
10Given the matrix equation X * A + B = C, where A is an invertible matrix, solve for X.
A.X = (C - B) * A^-1
B.X = A^-1 * (C - B)
C.X = (C + B) * A^-1
D.X = C * A^-1 - B
Explanation: First subtract B from both sides to obtain X * A = C - B. Since matrix multiplication is non-commutative and X is multiplied on the right by A, post-multiply both sides by A^-1 to get X = (C - B) * A^-1.

About the Catalonia PAU Applied Mathematics for Social Sciences Exam Exam

The Catalonia PAU Applied Mathematics for Social Sciences II (Matemàtiques Aplicades a les Ciències Socials II) examination is an official upper-secondary assessment administered by the Consell Interuniversitari de Catalunya (CIC) for 2nd Bachillerato students entering university. The curriculum covers matrix algebra and systems of linear equations, two-variable linear programming optimization, differential and integral calculus applied to economics and social sciences, financial mathematics (interest rates, annuities, TAE), classical and conditional probability (Bayes' theorem), and statistical inference (normal distribution, sample distribution, confidence intervals, margin of error). Official exams consist of written problem-solving tasks in Catalan or Spanish; the 100 practice questions provided here serve as an English-language multiple-choice study adaptation to reinforce mathematical concepts and quantitative problem-solving skills.

Exam sponsor: Consell Interuniversitari de Catalunya (CIC) / Generalitat de Catalunya. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Question count not published by the exam provider

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 41.30 examination right + EUR 68.70 access phase + EUR 13.80 per admission-phase exercise (Generalitat de Catalunya, PAU 2026); 50% reduction and full exemption available for eligible groups

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.

20%

Matrix Algebra and Systems of Linear Equations

Matrix operations, determinants, inverse matrices, matrix equations, and systems of linear equations solved via Gauss elimination, Rouché-Capelli analysis, and Cramer's Rule.

20%

Linear Programming

Linear inequalities, feasible regions, vertex identification, objective function evaluation, and constrained optimization for social sciences and business management.

30%

Functions, Limits, Continuity, Derivatives, and Optimization

Domain, limits, continuity of piecewise functions, derivatives, tangent lines, monotonicity, relative extrema, inflection points, cost/revenue/profit optimization, and basic integration.

10%

Financial Mathematics

Simple and compound interest, annual percentage rate (TAE / APR), compounding frequencies, present and future values, and savings/loan annuity calculations.

20%

Probability, Normal Distribution, and Statistical Inference

Probability rules, conditional probability, Total Probability and Bayes' theorems, standard normal distribution N(0,1), sampling distributions, and confidence intervals for population mean and proportion.

Preparing for the Catalonia PAU Applied Mathematics for Social Sciences Exam 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: Question count not published by the exam provider
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 41.30 examination right + EUR 68.70 access phase + EUR 13.80 per admission-phase exercise (Generalitat de Catalunya, PAU 2026); 50% reduction and full exemption available for eligible groups 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

Catalonia PAU Applied Mathematics for Social Sciences Exam: Suggested Study Strategy

1Master matrix arithmetic, determinant computation (Sarrus rule), matrix inverses, and applying Cramer's Rule / Rouché-Capelli theorem to systems with parameters.
2Practice graphing linear inequality constraints quickly to find all boundary vertices and evaluate objective functions in linear programming problems.
3Review derivative rules (product, quotient, chain rule) and practice setting the first derivative to zero to find local maxima/minima in economic profit and cost models.
4Memorize key statistical inference formulas: standard error (sigma / sqrt(n)), critical z-values (z=1.96 for 95% confidence, z=1.645 for 90%, z=2.576 for 99%), and margin of error E = z * (sigma / sqrt(n)).
5Work through these 100 practice questions step-by-step without relying on a graphing calculator, as official PAU exams permit only non-programmable, non-graphing scientific calculators.

Frequently Asked Questions

What is the official format of the Catalonia PAU Applied Mathematics for Social Sciences II exam?

The official examination set by the Consell Interuniversitari de Catalunya consists of written multi-part mathematical problem-solving exercises in Catalan (or Spanish), requiring full algebraic steps, graphs, and numerical reasoning. The 100 practice questions in this bank are an English-language multiple-choice study adaptation designed to build mastery over calculation steps and concepts.

What passing score is required for the PAU exam in Catalonia?

The exam is graded on a 0 to 10 scale. In the compulsory Access Phase (Fase d'Accés), a minimum mark of 4.0 is required so that it can be combined with the student's Bachillerato GPA (60% Bachillerato GPA + 40% PAU Access Grade >= 5.0 to pass). High scores in the optional Admission Phase (Fase d'Admissió) offer weighted weighting factors (0.1 or 0.2) to boost the university admission score up to 14.0.

How much does the PAU exam cost in Catalonia?

The Generalitat de Catalunya, through the Consell Interuniversitari de Catalunya (CIC), sets the 2026 PAU ordinary fees at EUR 41.30 examination right, EUR 68.70 access phase, and EUR 13.80 per admission-phase exercise. A 50% reduction and a full exemption are available for eligible groups such as large families (família nombrosa general), scholarship holders, and students with a recognised disability of 33% or more.

Which key topics are covered in Catalonia PAU Applied Mathematics for Social Sciences II?

The Generalitat de Catalunya curriculum focuses on matrix operations and systems of linear equations; linear programming optimization in two variables; differential calculus (limits, continuity, derivatives, local extrema, optimization of cost/profit); financial mathematics (compound interest, TAE, annuities); probability (tree diagrams, total probability, Bayes' theorem); and statistical inference (normal distribution, sample mean distributions, confidence intervals, sample size determination).