PracticeVideosBlogFlashcardsEspañol
All Practice Exams

Free Practice Questions for Matemática Aplicada às Ciências Sociais (Prova 835)

Exam-style questions and explanations by OpenExamPrep.

✓ No registration✓ No credit card
100+ Questions
100% Free

Loading practice questions...

Same family resources

Explore More Portugal National Secondary Education Final Examinations (Exames Nacionais do Ensino Secundário — EduQA)

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

Portugal National Secondary Examination — Alemão (Prova 501)

Practice Questions

Portugal National Secondary Examination — Biologia e Geologia (Prova 702)

Practice Questions

Portugal National Secondary Examination — Desenho A (Prova 706)

Practice Questions

Portugal National Secondary Examination — Economia A (Prova 712)

Practice Questions

Portugal National Secondary Examination — Espanhol (Provas 547/847)

Practice Questions

Portugal National Secondary Examination — Filosofia (Prova 714)

Practice Questions
Exam Review

Key Facts: Matemática Aplicada às Ciências Sociais (Prova 835) Exam

835

National exam code for Matemática Aplicada às Ciências Sociais

EduQA Informação-Prova 2026

150 minutes

Duration: 150 minutes (+ 30 minutes tolerance)

EduQA Informação-Prova 2026

0–200

Scoring scale; admission minimums are set by institutions (never below 95)

JNE/DGES Guia Geral de Exames 2026

€0 / €3

Free for on-time students in compulsory education; €3 per exam in other cases

JNE/DGES Guia Geral de Exames 2026

EduQA

Exam papers prepared by EduQA, I. P. (successor to IAVE)

Decreto-Lei n.º 105/2025

Portugal's Exame Nacional de Matemática Aplicada às Ciências Sociais (835) is an 11th-grade national exam prepared by EduQA (formerly IAVE): 150 minutes (+ 30 minutes tolerance), scored 0–200. This free bank offers 100 English-language multiple-choice questions on decision methods (elections and apportionment), statistics, financial models and salaries, graphs, population models, probability, the normal model and introductory statistical inference.

Sample Matemática Aplicada às Ciências Sociais (Prova 835) Practice Questions

Try these sample questions to review concepts for the Matemática Aplicada às Ciências Sociais (Prova 835) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A connected graph G represents a public transit network with five stations. The degrees of the vertices are deg(A) = 4, deg(B) = 4, deg(C) = 2, deg(D) = 2, and deg(E) = 4. Does an Eulerian circuit exist in this graph, and why?
A.No, because all vertices must have an odd degree to form an Eulerian circuit
B.No, an Eulerian circuit requires exactly two vertices with odd degrees
C.Yes, because the graph is connected and every vertex has an even degree
D.Yes, but only if the graph contains at least six vertices
Explanation: According to Euler's theorem, an undirected connected graph contains an Eulerian circuit if and only if every vertex has an even degree. Here, all vertex degrees are 4, 4, 2, 2, and 4, which are all even positive integers. Therefore, an Eulerian circuit exists that traverses every edge exactly once and returns to the starting vertex.
2A connected communication network has 6 terminals whose connection degrees are 2, 3, 4, 3, 2, and 4. According to the Handshaking Lemma, how many transmission links (edges) exist in this network?
A.18 links
B.9 links
C.8 links
D.12 links
Explanation: The Handshaking Lemma states that the sum of the degrees of all vertices in an undirected graph equals twice the number of edges: sum(deg(v)) = 2|E|. Summing the degrees gives 2 + 3 + 4 + 3 + 2 + 4 = 18. Dividing by 2 yields |E| = 18 / 2 = 9 edges.
3A street-sweeping vehicle must traverse every road in a residential quarter exactly once without repeating any road. The street intersections have degrees: deg(V1) = 3, deg(V2) = 4, deg(V3) = 2, deg(V4) = 3, and deg(V5) = 4. Which of the following statements is mathematically correct regarding the vehicle's route?
A.The vehicle can start and end at any vertex because the graph is connected
B.No route exists, because some vertices have odd degree
C.An Eulerian path exists and must start at V1 and end at V4 (or vice versa)
D.An Eulerian circuit exists that allows the vehicle to start and end at V2
Explanation: Euler's path theorem establishes that a connected graph has an open Eulerian path if and only if it has exactly two vertices of odd degree. In this network, exactly two vertices have odd degrees: V1 (degree 3) and V4 (degree 3). Any valid Eulerian path must necessarily originate at one of these two odd-degree vertices and terminate at the other.
4A civil engineering team is connecting 5 regional water tanks into a single network using Kruskal's algorithm to minimize piping costs. Which rule governs the termination of Kruskal's algorithm and the number of pipelines chosen?
A.It stops after selecting 5 pipelines so that every tank has a redundant loop
B.It adds pipelines in alphabetical order of the tanks
C.It selects pipelines in descending order of cost until all tanks have degree 2
D.It stops after selecting exactly 4 pipelines without creating any cycle
Explanation: A minimum spanning tree on n vertices always contains exactly n - 1 edges. For n = 5 water tanks, the tree must contain exactly 5 - 1 = 4 edges. Kruskal's algorithm iteratively selects the available edge of minimum weight that does not form a cycle, terminating as soon as 4 edges are chosen.
5Consider five fiber-optic hubs (A, B, C, D, E) with available link installation costs: CD = 1, AB = 2, AC = 2, BC = 3, BE = 3, DE = 4, EA = 5, and BD = 6. Using Kruskal's algorithm, what is the total minimum cost to interconnect all five hubs?
A.10
B.11
C.7
D.8
Explanation: Sort edges in ascending order of cost: CD (1), AB (2), AC (2), BC (3), BE (3), DE (4), EA (5), BD (6). Step 1: select CD (cost 1). Step 2: select AB (cost 2). Step 3: select AC (cost 2). Step 4: next is BC (cost 3), but A-B-C forms a cycle, so reject BC. Step 5: select BE (cost 3), which connects E without forming a cycle. Now 4 edges are selected on 5 vertices: total cost = 1 + 2 + 2 + 3 = 8.
6What is the fundamental difference between an Eulerian path and a Hamiltonian path in graph theory?
A.Both paths must return to their starting vertex, but Hamiltonian paths only apply to trees
B.An Eulerian path visits every edge exactly once, whereas a Hamiltonian path visits every vertex exactly once
C.An Eulerian path visits every vertex exactly once, whereas a Hamiltonian path visits every edge exactly once
D.An Eulerian path applies only to directed networks, whereas a Hamiltonian path applies only to planar graphs
Explanation: By definition, an Eulerian path traverses every edge of the graph exactly once. In contrast, a Hamiltonian path visits every vertex of the graph exactly once. A path returning to its starting vertex becomes an Eulerian circuit or a Hamiltonian cycle, respectively.
7A distribution truck must visit four towns A, B, C, and D before returning to A. The pairwise road distances are: AB = 10 km, AC = 15 km, AD = 20 km, BC = 35 km, BD = 25 km, and CD = 30 km. Using the Nearest Neighbor algorithm starting at town A, what is the total travel distance of the completed tour?
A.90 km via A -> B -> C -> D -> A
B.70 km via A -> C -> D -> B -> A
C.80 km via A -> B -> D -> C -> A
D.65 km via A -> D -> B -> C -> A
Explanation: Starting at A, the nearest unvisited town is B (10 km). From B, remaining unvisited towns are C (35 km) and D (25 km); the nearest is D (25 km). From D, the only remaining unvisited town is C (30 km). Finally, the truck returns from C back to A (15 km). Total distance = 10 + 25 + 30 + 15 = 80 km.
8Five sales offices (A, B, C, D, E) are fully interconnected with travel costs: AB = 4, CD = 5, BC = 7, DE = 8, EA = 9, BD = 10, AC = 11, AD = 12, BE = 13, and CE = 14. Applying the Sorted Edges (Cheapest Link) algorithm, what is the total cost of the Hamiltonian tour?
A.38
B.36
C.29
D.33
Explanation: Sorted Edges algorithm selects edges in increasing order of weight without creating a vertex degree > 2 or a premature sub-circuit: 1) Select AB (4). 2) Select CD (5). 3) Select BC (7); now path is A-B-C-D. 4) Select DE (8); now path is A-B-C-D-E (no vertex exceeds degree 2). 5) Select EA (9) to close the 5-vertex circuit. Total weight = 4 + 5 + 7 + 8 + 9 = 33.
9In a logistical bipartite network K_{3,4}, three distribution centers supply four retail outlets, with every distribution center connected to every outlet, but no connections between centers or between outlets. What is the chromatic number χ(G) of this graph?
A.2
B.3
C.4
D.7
Explanation: A graph is bipartite if its vertices can be partitioned into two disjoint sets such that no two vertices within the same set share an edge. By definition, any bipartite graph containing at least one edge can be properly colored with exactly 2 colors (one color for each partition). Thus, the chromatic number of K_{3,4} is 2.
10The Welsh-Powell algorithm is employed to color the vertices of a conflict graph for radio frequency allocation. What is the systematic initial step of this algorithm?
A.Select a random vertex and assign it a color based on the number of odd cycles
B.List all vertices in descending order of their degrees
C.List the edges in ascending order of their weights
D.Colour first the vertex with the smallest degree
Explanation: The Welsh-Powell algorithm begins by ordering all vertices of the graph in non-increasing (descending) order of their degrees. It then assigns Color 1 to the first uncolored vertex and greedily to all subsequent non-adjacent vertices in the list, repeating the process with successive colors until all vertices are colored.

About the Matemática Aplicada às Ciências Sociais (Prova 835) Exam

The Exame Final Nacional de Matemática Aplicada às Ciências Sociais (prova 835) is an 11th-grade national secondary exam in Portugal. Since the 2025 reorganization of the Ministry of Education (Decreto-Lei n.º 105/2025), exam papers are prepared by EduQA — Instituto de Educação, Qualidade e Avaliação, I. P., which succeeded IAVE, and the exams are organized and graded under the Júri Nacional de Exames. Written exam on the Aprendizagens Essenciais of MACS for the 10th and 11th grades, with a formula sheet. A graphing calculator with statistical capabilities (linear, exponential, logarithmic and logistic regressions) is used. The paper combines selection items (such as multiple choice) and constructed-response items, scored out of 200 points; answers are written on answer sheets that are later digitized. The exam covers decision methods (elections and apportionment), statistics, financial models and salaries, graphs, population models, probability, the normal model and introductory statistical inference. It counts towards the subject's final grade and can be used as an admission exam (prova de ingresso) for higher education where a course requires it. This bank is an independent English-language multiple-choice study adaptation with 100 original practice questions. It is not affiliated with EduQA or the JNE and does not reproduce the official paper or its constructed-response tasks.

Exam sponsor: EduQA, I. P. (exam papers; successor to IAVE since 2025) with the Júri Nacional de Exames (JNE). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written exam on the Aprendizagens Essenciais of MACS for the 10th and 11th grades, with a formula sheet. A graphing calculator with statistical capabilities (linear, exponential, logarithmic and logistic regressions) is used. The paper combines selection items (such as multiple choice) and constructed-response items, scored out of 200 points; answers are written on answer sheets that are later digitized.

Time Limit

150 minutes (+ 30 minutes tolerance)

Passing Score

Scored 0–200; counts 25% of the subject grade for internal students; admission-exam minimums are set by institutions (never below 95/200)

Exam / Certification Fees

€0 for on-time students in compulsory education; €3 per exam in other cases; €25 + €3 per exam if registering late

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.

~18% of this bank

Statistics

Sampling, univariate and bivariate data, correlation and regression.

~16% of this bank

Probability

Laplace's rule, conditional probability and finite probability models.

~14% of this bank

Graphs

Euler and Hamilton graphs, trees and colouring.

~13% of this bank

Electoral methods

Plurality, runoff, Borda, Condorcet, approval and Arrow's theorem.

~12% of this bank

Apportionment and fair division

Hamilton, Jefferson, Adams, Webster and D'Hondt; divider–chooser and sealed bids.

~11% of this bank

Financial models and salaries

Interest, credit, TAN/TAEG and net salary.

~10% of this bank

Population models

Linear, exponential, logarithmic and logistic growth.

~6% of this bank

Normal model and inference

The normal distribution, confidence intervals and margin of error.

Preparing for the Matemática Aplicada às Ciências Sociais (Prova 835) Exam

What You Need to Know

  • Passing score: Scored 0–200; counts 25% of the subject grade for internal students; admission-exam minimums are set by institutions (never below 95/200)
  • Assessment: Written exam on the Aprendizagens Essenciais of MACS for the 10th and 11th grades, with a formula sheet. A graphing calculator with statistical capabilities (linear, exponential, logarithmic and logistic regressions) is used. The paper combines selection items (such as multiple choice) and constructed-response items, scored out of 200 points; answers are written on answer sheets that are later digitized.
  • Time limit: 150 minutes (+ 30 minutes tolerance)
  • Exam / certification fees: €0 for on-time students in compulsory education; €3 per exam in other cases; €25 + €3 per exam if registering late 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

Matemática Aplicada às Ciências Sociais (Prova 835): Suggested Study Strategy

1Master the precise criteria for Euler circuits (all vertices have even degree) and Euler paths (exactly two vertices have odd degree).
2For graph coloring, use the Welsh-Powell algorithm systematically by listing vertices in descending order of degrees.
3In voting methods, distinguish clearly between Borda points assignment, plurality ranking, and pairwise Condorcet matrix comparisons.
4Understand the difference between quota methods (Hamilton) and divisor methods (Jefferson, Adams, Webster), and know which paradoxes affect each.
5Ensure fluency with graphing calculator functions for bivariate linear regression (finding slope a, intercept b, and correlation coefficient r).
6In probability, always verify whether events are independent before multiplying individual probabilities, and use tree diagrams for multi-stage processes.
7In financial math, distinguish clearly between nominal rates and effective annual rates (TAE), and remember how loan payments are partitioned into interest and principal amortization.
8For logistic growth models, identify the carrying capacity K and remember that maximum growth rate occurs at P = K/2.

Frequently Asked Questions

Who prepares and grades the exam?

Since the 2025 reorganization (Decreto-Lei n.º 105/2025), exam papers are prepared by EduQA — Instituto de Educação, Qualidade e Avaliação, I. P., which succeeded IAVE. The exams are run in schools and graded under the Júri Nacional de Exames (JNE).

How is the exam structured?

Written exam on the Aprendizagens Essenciais of MACS for the 10th and 11th grades, with a formula sheet. A graphing calculator with statistical capabilities (linear, exponential, logarithmic and logistic regressions) is used. The paper combines selection items (such as multiple choice) and constructed-response items, scored out of 200 points; answers are written on answer sheets that are later digitized.

Is there a pass mark?

No single pass mark: the exam is scored 0–200. For internal students it counts for 25% of the final subject grade (CFD = 0.75 × internal grade + 0.25 × exam); for external candidates the exam grade is the subject grade, so at least 95/200 is needed. When used as an admission exam (prova de ingresso), each higher-education institution sets the minimum, never below 95/200.

How much does it cost?

Free for students in compulsory education who register on time and for internal students in the 1st phase; €3 per exam for 2nd-phase grade improvement, for external candidates (autopropostos) outside compulsory education and for external grade improvement; late registration costs €25 plus €3 per exam (JNE/DGES Guia Geral de Exames 2026).

Which calculator features are needed?

The 2026 Informação-Prova refers to a graphing calculator with statistical capabilities, including linear, exponential, logarithmic and logistic regressions; the exam includes a formula sheet.

How does this practice bank relate to the official exam?

This bank is an independent English-language multiple-choice study adaptation with 100 original practice questions. It is not affiliated with EduQA or the JNE and does not reproduce the official paper or its constructed-response tasks. Use it to review content and concepts alongside official Informação-Prova documents and past papers.