Free Practice Questions for Matemática B (Prova 735)

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.

Exam Review

Key Facts: Matemática B (Prova 735) Exam

735

National exam code for Matemática B

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 B (735) 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 mathematical models for citizenship (elections, apportionment, interest), statistics, analytic geometry, functions and rates of change, geometric patterns, probability, synthetic geometry and inaccessible distances.

Sample Matemática B (Prova 735) Practice Questions

Try these sample questions to review concepts for the Matemática B (Prova 735) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1An architectural blueprint of an art gallery is drawn at a scale of 1:50. If an exhibition hall has a length of 14 cm on the blueprint, what is the actual length of the hall in meters?

A.2.8 m

B.14.0 m

C.28.0 m

D.7.0 m

Explanation: At a scale of 1:50, each centimeter on the plan corresponds to 50 cm in reality. Multiplying 14 cm by 50 gives 700 cm, which equals 7.0 meters (700 / 100 = 7.0 m).

2A rectangular canvas is constructed according to the golden ratio phi = (1 + sqrt(5))/2 ≈ 1.618. If the shorter side of the canvas measures 50 cm, what is the length of the longer side, rounded to the nearest tenth of a centimeter?

A.30.9 cm

B.75.0 cm

C.90.5 cm

D.80.9 cm

Explanation: In a golden rectangle, the ratio of the longer side to the shorter side is phi ≈ 1.618034. Multiplying the shorter side by phi yields 50 * 1.618034 = 80.9017 cm, which rounds to 80.9 cm.

3Two similar bronze sculpture models have volumes of 250 cm³ and 2000 cm³ respectively. If the height of the smaller sculpture is 15 cm, what is the height of the larger sculpture?

A.60 cm

B.120 cm

C.30 cm

D.24 cm

Explanation: The volume ratio between similar solids is k³ = 2000 / 250 = 8. The linear scale factor is k = cbrt(8) = 2. Therefore, the height of the larger sculpture is 15 * 2 = 30 cm.

4The golden ratio phi satisfies the quadratic relationship phi² - phi - 1 = 0. Which of the following expressions is mathematically equivalent to 1/phi?

A.phi + 1

B.2 - phi

C.phi / 2

D.phi - 1

Explanation: Dividing the equation phi² - phi - 1 = 0 by phi yields phi - 1 - 1/phi = 0, which rearranges directly to 1/phi = phi - 1 (approximately 0.618).

5A graphic designer creates a modular poster grid. A photograph with an area of 48 cm² on a mock-up is enlarged so that each linear dimension is multiplied by a scale factor of k = 2.5. What is the area of the photograph on the final enlarged poster?

A.120 cm²

B.240 cm²

C.300 cm²

D.360 cm²

Explanation: When linear dimensions are multiplied by a scale factor k, the area scales by k². Here k² = 2.5² = 6.25, so the enlarged area is 48 * 6.25 = 300 cm².

6In a golden rectangle ABCD with length x and width y where x/y = phi = (1 + sqrt(5))/2, a square of side length y is cut off from one end. What is the aspect ratio (longer side divided by shorter side) of the remaining smaller rectangle?

A.sqrt(5)

B.phi²

C.phi - 1

D.phi

Explanation: The remaining rectangle has dimensions y and x - y. Since x = phi * y, the shorter side is y(phi - 1). The aspect ratio is y / (y(phi - 1)) = 1 / (phi - 1). Because 1/phi = phi - 1, it follows that 1 / (phi - 1) = phi, proving the remaining rectangle is also a golden rectangle.

7On an urban design master plan drawn at a scale of 1:2500, a proposed pedestrian avenue has a length of 16 cm. What is the true real-world length of the avenue in meters?

A.250 m

B.40 m

C.400 m

D.4000 m

Explanation: The real length is 16 cm * 2500 = 40,000 cm. Converting centimeters to meters gives 40,000 / 100 = 400 meters.

8A ceramic tile design is based on a regular pentagon. In any regular pentagon, what is the exact ratio of the length of a diagonal d to the length of a side s?

A.sqrt(2)

B.sqrt(3)

C.(1 + sqrt(3))/2

D.(1 + sqrt(5))/2

Explanation: In any regular pentagon, the diagonals intersect in golden sections and each diagonal forms an isosceles golden triangle with two adjacent sides, making the diagonal-to-side ratio exactly phi = (1 + sqrt(5))/2 ≈ 1.618.

9A model of a museum pavilion is built with a scale factor of 1:40. The floor area of the central exhibition room in the miniature model is 350 cm². What is the actual floor area of the exhibition room in square meters (m²)?

A.14 m²

B.140 m²

C.560 m²

D.56 m²

Explanation: The area scale factor is 40² = 1600. The actual area is 350 cm² * 1600 = 560,000 cm². Converting square centimeters to square meters (1 m² = 10,000 cm²) gives 560,000 / 10,000 = 56 m².

10In Le Corbusier's Modulor proportioning system, architectural dimensions are derived from a human baseline measure m0 = 113 cm. If successive ascending dimensions follow the geometric progression mn = m0 * phi^n where phi ≈ 1.618034, what is the value of m2 rounded to the nearest whole centimeter?

A.183 cm

B.226 cm

C.296 cm

D.366 cm

Explanation: For n = 2, m2 = 113 * phi². Since phi² = phi + 1 ≈ 2.618034, we calculate 113 * 2.618034 = 295.8378 cm, which rounds to 296 cm.

About the Matemática B (Prova 735) Exam

The Exame Final Nacional de Matemática B (prova 735) 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 Matemática B (Matemática Aplicada às Artes Visuais) for the 10th and 11th grades (Despacho n.º 702/2023). No formula sheet is provided; a graphing calculator with statistical regressions (linear, quadratic and cubic) 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 mathematical models for citizenship (elections, apportionment, interest), statistics, analytic geometry, functions and rates of change, geometric patterns, probability, synthetic geometry and inaccessible distances. 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 Matemática B (Matemática Aplicada às Artes Visuais) for the 10th and 11th grades (Despacho n.º 702/2023). No formula sheet is provided; a graphing calculator with statistical regressions (linear, quadratic and cubic) 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.

Official sources

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.

~26% of this bank

Geometry, patterns and art

Scales, similarity, golden ratio, isometries, friezes, tilings and volumes.

~26% of this bank

Statistics and probability

Univariate and bivariate data, Laplace's rule and conditional probability.

~14% of this bank

Rates of change and optimization

Average and instantaneous rates of change and optimization of polynomial models.

~12% of this bank

Inaccessible distances

Trigonometry of right and oblique triangles.

~9% of this bank

Models for citizenship

Electoral methods, D'Hondt and Sainte-Laguë apportionment, simple and compound interest.

~8% of this bank

Functions

Polynomial functions up to degree 3, inverse functions and modelling.

~5% of this bank

Analytic geometry

Distances, circles, spheres and planes in the plane and in space.

Preparing for the Matemática B (Prova 735) 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 Matemática B (Matemática Aplicada às Artes Visuais) for the 10th and 11th grades (Despacho n.º 702/2023). No formula sheet is provided; a graphing calculator with statistical regressions (linear, quadratic and cubic) 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 B (Prova 735): Suggested Study Strategy

1Remember that when length scale factor is k, the area scale factor is k² and the volume scale factor is k³.

2Master the golden ratio properties: phi = (1 + sqrt(5))/2 ≈ 1.618034, satisfying phi² = phi + 1 and 1/phi = phi - 1.

3Use the Law of Cosines (a² = b² + c² - 2bc*cos(A)) when two sides and the included angle are given, and the Law of Sines (a/sin(A) = b/sin(B)) when an opposite angle-side pair is known.

4For optimization problems, set the first derivative f'(x) = 0, find critical points, and test endpoints or second derivative signs to confirm maximum or minimum values.

5In bivariate statistics, verify whether the correlation coefficient r is close to 1 or -1 before using the linear regression line for extrapolation, and remember that regression lines always pass through the mean centroid (mean(x), mean(y)).

6For electoral and apportionment problems, organize the D'Hondt or Sainte-Laguë quotients in a table and rank them carefully; ties and close quotients are common traps.

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?

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).

Is a formula sheet provided?

No. The 2026 Informação-Prova states that the Matemática B exam does not include a formula sheet, and that a graphing calculator with statistical capabilities (linear, quadratic or cubic regressions) may be required.

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.

Free Practice Questions for Matemática B (Prova 735)

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

Portugal National Secondary Examination — Alemão (Prova 501)

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

Portugal National Secondary Examination — Desenho A (Prova 706)

Portugal National Secondary Examination — Economia A (Prova 712)

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

Portugal National Secondary Examination — Filosofia (Prova 714)