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Free Practice Questions for PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL

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Exam Review

Key Facts: PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL Exam

90 min

Exam duration

COPAU Canary Islands Official Guidelines

0–10

Grading scale

COPAU Regulations

4.0 / 10

Minimum Access Phase mark required to combine with Bachillerato GPA

Gobierno de Canarias / COPAU

EUR 76.12

Base registration fee for Access Phase

Gobierno de Canarias 2026

2º Bach

Target education level (Social Sciences track)

Canary Islands LOMLOE Curriculum

100

Practice questions in this OpenExamPrep question bank

OpenExamPrep

The 2026 Canary Islands PAU Math CCSS II exam tests 2º Bachillerato students on matrix operations, linear programming, applied calculus, probability, and statistical inference over a 90-minute session.

Sample PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL Practice Questions

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

1Given the matrices A = [[2, -1], [3, 4]] and B = [[1, 5], [-2, 0]], compute the matrix C = 2A - 3B.
A.[[1, -17], [12, 8]]
B.[[1, 13], [0, 8]]
C.[[-1, -17], [12, 4]]
D.[[1, -17], [4, 8]]
Explanation: We compute 2A = [[4, -2], [6, 8]] and 3B = [[3, 15], [-6, 0]]. Subtracting element by element gives 2A - 3B = [[4-3, -2-15], [6-(-6), 8-0]] = [[1, -17], [12, 8]].
2Given the matrices A = [[1, 2], [3, 0]] and B = [[-1, 4], [2, 1]], compute the product A · B.
A.[[3, 6], [-3, 12]]
B.[[-3, 6], [3, 12]]
C.[[3, 8], [-3, 0]]
D.[[-1, 8], [6, 0]]
Explanation: Multiplying row by column: Row 1: (1)(-1)+(2)(2)=3, (1)(4)+(2)(1)=6. Row 2: (3)(-1)+(0)(2)=-3, (3)(4)+(0)(1)=12. The product A · B is [[3, 6], [-3, 12]].
3Compute the determinant of the matrix A = [[4, -3], [2, 5]].
A.26
B.14
C.-26
D.20
Explanation: The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. For A, det(A) = (4)(5) - (-3)(2) = 20 - (-6) = 20 + 6 = 26.
4Which of the following properties about the transpose of square matrices A and B is correct?
A.(A · B)^T = B^T · A^T
B.(A + B)^T = A^T - B^T
C.(A · B)^T = A^T · B^T
D.det(A^T) = -det(A)
Explanation: The fundamental property of the transpose of a product of two matrices states that (A · B)^T = B^T · A^T, reversing the order of multiplication.
5Find the inverse matrix of A = [[3, 2], [1, 1]].
A.[[1, 2], [1, 3]]
B.[[1, -2], [-1, 3]]
C.[[3, -2], [-1, 1]]
D.[[-1, 2], [1, -3]]
Explanation: The determinant is det(A) = 3(1) - 2(1) = 1. The inverse of [[a, b], [c, d]] is (1/det(A)) * [[d, -b], [-c, a]]. Therefore, A^(-1) = [[1, -2], [-1, 3]].
6What is the rank of the matrix A = [[1, 2, 3], [2, 4, 6], [0, 0, 0]]?
A.0
B.1
C.2
D.3
Explanation: Row 2 is twice row 1 (F2 = 2F1), and row 3 is null. There is only 1 linearly independent row, so the rank of the matrix is 1.
7Compute the determinant of the 3x3 matrix A = [[1, 0, 2], [2, 1, 3], [0, 4, 1]] using Sarrus' rule or cofactor expansion.
A.11
B.5
C.0
D.-5
Explanation: Expanding along the first column: det(A) = 1 · (1·1 - 3·4) - 2 · (0·1 - 2·4) + 0 = 1(1 - 12) - 2(-8) = -11 + 16 = 5.
8Solve the system of linear equations: 2x + y = 7, x - y = 2.
A.x = 2, y = 3
B.x = 1, y = 5
C.x = 4, y = -1
D.x = 3, y = 1
Explanation: Adding both equations cancels y: 3x = 9 => x = 3. Substituting x = 3 into the second equation: 3 - y = 2 => y = 1. The solution is (3, 1).
9Identify which point belongs to the feasible region defined by x >= 0, y >= 0, x + y <= 6, 2x + y <= 8.
A.(3, 3)
B.(2, 3)
C.(5, 2)
D.(-1, 4)
Explanation: For (2, 3): 2 >= 0, 3 >= 0; 2 + 3 = 5 <= 6; 2(2) + 3 = 7 <= 8. It satisfies all the constraints of the feasible region.
10Evaluate the objective function z = 3x + 4y at the vertex (x, y) = (4, 5).
A.23
B.35
C.32
D.40
Explanation: Substituting the vertex values into the objective function: z = 3(4) + 4(5) = 12 + 20 = 32.

About the PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL Exam

The Canary Islands PAU Applied Mathematics for Social Sciences II exam (Matemáticas Aplicadas a las Ciencias Sociales II) is the standardized university entrance examination administered across the Canary Islands by ULPGC and ULL under the COPAU commission. It evaluates core skills in matrix algebra, linear programming, calculus applied to economics and social sciences, probability theory, and statistical inference.

Exam sponsor: Canary Islands PAU Organising Commission (COPAU) / ULPGC & ULL. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

The exam consists of 4 main problem-solving blocks evaluated over 90 minutes (1.5 hours). Students complete questions covering matrices & systems of linear equations, linear programming, differential and integral calculus, and probability & inferential statistics under LOMLOE regulations.

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 76.12 base registration fee for PAU Access Phase (set by Gobierno de Canarias / COPAU).

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%

Algebra & Matrices

Matrix operations, determinants, inverse matrices, systems of linear equations, Gauss elimination, and Rouché-Capelli theorem.

20%

Linear Programming

System of inequalities, convex feasible region construction, vertex evaluation, objective function maximization/minimization, and social science applications.

30%

Mathematical Analysis

Limits, continuity, derivatives, curve sketching, business profit/cost optimization, definite integrals, and area computations.

25%

Probability & Inferential Statistics

Events, conditional probability, Bayes' theorem, normal distributions, sample statistics, and confidence intervals for means and proportions.

Preparing for the PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL 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: The exam consists of 4 main problem-solving blocks evaluated over 90 minutes (1.5 hours). Students complete questions covering matrices & systems of linear equations, linear programming, differential and integral calculus, and probability & inferential statistics under LOMLOE regulations.
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 76.12 base registration fee for PAU Access Phase (set by Gobierno de Canarias / COPAU). 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

PAU Applied Mathematics for Social Sciences II — Canary Islands / ULPGC & ULL: Suggested Study Strategy

1Practice computing matrix inverses using determinants and adjugate matrices, and solve parameterized 3x3 linear systems.
2Master sketching linear programming constraints accurately and checking vertex coordinates in the objective function.
3Review derivative optimization problems for marginal cost, marginal revenue, and maximum profit P(x) = R(x) - C(x).
4Master standard normal z-score calculations Z = (X - mu)/sigma and standard normal table lookups.
5Memorize confidence interval formulas for population mean x̄ ± z_(alpha/2) * (sigma / sqrt(n)) and proportion p̂ ± z_(alpha/2) * sqrt(p̂(1-p̂)/n).

Frequently Asked Questions

Is this practice bank in the same format as the real Canary Islands PAU exam?

No, and it is important to know the difference. The official Canary Islands PAU paper is a 90-minute examination sat in Spanish and built around multi-part written problems that must be solved and justified in full. Under the 2026 PAU design rules agreed by COPAU and the CRUE, open and semi-constructed responses must account for at least 70% of every paper, so the real exam contains no multiple-choice section. This bank is an English-language multiple-choice study adaptation of the same official 2º Bachillerato syllabus — not an official translation, not a past paper, and not a simulation of the exam format. Use it to drill the underlying knowledge and reasoning quickly, then practise writing out complete, justified solutions and showing every step of your working separately, because that is what the examiners actually mark.

What is the PAU Applied Mathematics for Social Sciences II exam in the Canary Islands?

It is the official university entrance exam (Pruebas de Acceso a la Universidad - PAU) organized by the Canary Islands PAU Organising Commission (COPAU) and administered by ULPGC and ULL for 2º Bachillerato Social Sciences students.

What is the passing score for the PAU Access Phase?

The exam is graded on a 0 to 10 scale. A minimum grade of 4.0 is required in the Access Phase to calculate the final university access mark (60% Bachillerato GPA + 40% PAU Access Phase, requiring a total of 5.0 or higher).

How long is the PAU Math CCSS II examination?

The examination duration is 90 minutes (1.5 hours).

What standard calculator is permitted in the Canary Islands PAU exam?

Standard non-programmable scientific calculators without graphic display, symbolic algebraic computation (CAS), or communication capabilities are permitted.

What main topic areas are assessed?

The exam assesses four core blocks: Algebra & Linear Programming, Differential & Integral Calculus, and Probability & Inferential Statistics.

In what language is the Canary Islands PAU exam offered?

The examination paper is provided in Spanish.