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Key Facts: Geometria Descritiva A (Prova 708) Exam

708

National exam code for Geometria Descritiva A

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 Geometria Descritiva A (708) 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 Monge's double orthogonal projection (points, lines, planes, intersections, parallelism and perpendicularity, auxiliary methods), solids, sections, shadows and axonometry.

Sample Geometria Descritiva A (Prova 708) Practice Questions

Try these sample questions to review concepts for the Geometria Descritiva A (Prova 708) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In Monge's double orthogonal projection method, which coordinate determines the distance of a point to the horizontal projection plane (PHP)?

A.Azimuth

B.Cota

C.Abcissa

D.Afastamento

Explanation: In Portuguese descriptive geometry, the cota (z-coordinate) measures the directed perpendicular distance from a point to the horizontal projection plane (PHP). When the cota is positive, the point lies above the PHP, projecting above the ground line (Linha de Terra) on the frontal plane.

2A point P has coordinates (2, 4, 5), representing (abcissa, afastamento, cota) in centimeters. In which dihedral angle (diedro) is point P situated?

A.First dihedral (1º Diedro)

B.Fourth dihedral (4º Diedro)

C.Second dihedral (2º Diedro)

D.Third dihedral (3º Diedro)

Explanation: In the Monge projection system, a point belongs to the first dihedral (1º Diedro) when both its afastamento (y > 0) and its cota (z > 0) are strictly positive. Since point P has an afastamento of +4 and a cota of +5, it lies in the first dihedral.

3When the horizontal projection plane (PHP) is rotated into coincidence with the frontal projection plane (PFP) around the ground line (Linha de Terra), where does the horizontal projection of a point with positive afastamento appear?

A.Coincident with the ground line (Linha de Terra)

B.Below the ground line (Linha de Terra)

C.Above the ground line (Linha de Terra)

D.Infinitely far to the left of the origin

Explanation: By Monge's convention, the anterior horizontal semi-plane rotates downward around the x-axis to merge into coincidence with the inferior frontal semi-plane. Consequently, any point with positive afastamento (located in front of the PFP) has its horizontal projection displayed below the ground line.

4A point Q is defined with coordinates (0, -3, 6). Where are the horizontal projection Q1 and frontal projection Q2 located relative to the ground line (x-axis)?

A.Both Q1 and Q2 are located above the ground line

B.Q1 is below the ground line and Q2 is below the ground line

C.Q1 is on the ground line and Q2 is above the ground line

D.Q1 is below the ground line and Q2 is above the ground line

Explanation: Point Q has negative afastamento (-3) and positive cota (+6), placing it in the second dihedral. Because negative afastamento rotates upward above the ground line and positive cota projects upward, both Q1 and Q2 appear above the ground line in the drawing (épura).

5Which condition must a point satisfy to belong to the first-and-third dihedral bisector plane (plano bissetor dos diedros ímpares, β13)?

A.Its abcissa must equal the sum of its afastamento and cota

B.Its cota must equal zero regardless of its afastamento

C.Its afastamento and cota must have opposite signs with equal absolute values (afastamento = -cota)

D.Its afastamento and cota must be equal in both sign and magnitude (afastamento = cota)

Explanation: The β13 bisector plane bisects the first and third dihedrals at a 45-degree angle. Every point on β13 possesses an afastamento equal to its cota (y = z), meaning both values have identical numerical magnitudes and the same algebraic sign.

6What is the defining characteristic of the projections of a point located on the second-and-fourth bisector plane (β24)?

A.Its horizontal and frontal projections coincide into a single point (P1 ≡ P2)

B.Its horizontal and frontal projections are symmetrical relative to the ground line

C.Its horizontal projection is at double the distance from the ground line compared to its frontal projection

D.Its frontal projection always lies directly on the ground line

Explanation: Points on the β24 plane satisfy afastamento = -cota. When the PHP is rotated onto the PFP, a point with afastamento y and cota -y projects to the exact same position relative to the ground line, making the horizontal projection P1 and frontal projection P2 strictly coincident.

7If a point R lies on the anterior semi-plane of the horizontal projection plane (semiplano horizontal anterior), what are its coordinates?

A.afastamento > 0 and cota = 0

B.afastamento = 0 and cota > 0

C.afastamento < 0 and cota = 0

D.afastamento = 0 and cota < 0

Explanation: Any point situated on the horizontal projection plane has a cota of zero. The anterior portion corresponds to the space in front of the frontal plane, where afastamento is strictly positive. Therefore, a point on the anterior horizontal semi-plane has afastamento > 0 and cota = 0.

8A point M has coordinates (-1, -5, -4). In which dihedral does point M lie?

A.First dihedral (1º Diedro)

B.Second dihedral (2º Diedro)

C.Fourth dihedral (4º Diedro)

D.Third dihedral (3º Diedro)

Explanation: The third dihedral is defined by the region behind the frontal projection plane (negative afastamento) and below the horizontal projection plane (negative cota). Since point M has afastamento -5 and cota -4, both coordinates are negative, placing it firmly in the third dihedral.

9Point A has coordinates (3, 6, 2). In which octant (octante) of space is point A located?

A.8th Octant (8º Octante)

B.2nd Octant (2º Octante)

C.4th Octant (4º Octante)

D.1st Octant (1º Octante)

Explanation: The first dihedral is subdivided by the bisector plane β13 into the 1st and 2nd octants. The 1st octant comprises points below β13, where afastamento is strictly greater than cota (y > z > 0). Since point A has afastamento 6 and cota 2 (6 > 2 > 0), it is located in the 1st octant.

10Which octant contains point B with coordinates (1, -2, 5)?

A.2nd Octant (2º Octante)

B.3rd Octant (3º Octante)

C.4th Octant (4º Octante)

D.6th Octant (6º Octante)

Explanation: Point B has negative afastamento (-2) and positive cota (+5), placing it in the second dihedral. In the second dihedral, the bisector β24 separates the 3rd octant (where cota > |afastamento|) from the 4th octant (where |afastamento| > cota). Here, cota (5) > |-2| (2), meaning point B lies in the 3rd octant.

About the Geometria Descritiva A (Prova 708) Exam

The Exame Final Nacional de Geometria Descritiva A (prova 708) 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. Exam on the Aprendizagens Essenciais of Geometria Descritiva A for the 10th and 11th grades, consisting of problems of descriptive representation solved exclusively by graphic means. Blocks: dihedral (Monge) representation — elementary entities with membership and intersections, plane figures and solids, shadows, sections and truncation, and intersection of a line with a solid — and axonometric representation (clinogonal or orthogonal) of shapes made of juxtaposed solids. The exam covers Monge's double orthogonal projection (points, lines, planes, intersections, parallelism and perpendicularity, auxiliary methods), solids, sections, shadows and axonometry. 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

Exam on the Aprendizagens Essenciais of Geometria Descritiva A for the 10th and 11th grades, consisting of problems of descriptive representation solved exclusively by graphic means. Blocks: dihedral (Monge) representation — elementary entities with membership and intersections, plane figures and solids, shadows, sections and truncation, and intersection of a line with a solid — and axonometric representation (clinogonal or orthogonal) of shapes made of juxtaposed solids.

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.

~20% of this bank

Lines and traces

Types of lines, traces, true size and dihedral position.

~20% of this bank

Planes

Types of planes, traces and characteristic lines.

~18% of this bank

Projections and points

Coordinates, dihedrals, octants and bisector planes.

~15% of this bank

Solids, shadows and axonometry

Solids, sections, shadows and axonometric representation.

~15% of this bank

Intersections and perpendicularity

Intersections of lines and planes, parallelism and perpendicularity.

~12% of this bank

Auxiliary methods

Rebatimento, counter-rebatimento and true size.

Preparing for the Geometria Descritiva A (Prova 708) 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: Exam on the Aprendizagens Essenciais of Geometria Descritiva A for the 10th and 11th grades, consisting of problems of descriptive representation solved exclusively by graphic means. Blocks: dihedral (Monge) representation — elementary entities with membership and intersections, plane figures and solids, shadows, sections and truncation, and intersection of a line with a solid — and axonometric representation (clinogonal or orthogonal) of shapes made of juxtaposed solids.
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

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Geometria Descritiva A (Prova 708): Suggested Study Strategy

1Master Cartesian coordinate conventions: positive afastamento lies in front of PFP (projecting below the x-axis), while positive cota lies above PHP (projecting above the x-axis).

2Memorize the defining projection characteristics of notable lines and planes, especially topo planes (fα oblique, hα perpendicular to x) and vertical planes (hα oblique, fα perpendicular to x).

3Remember the fundamental theorem of perpendicularity: a line is perpendicular to a plane if and only if its horizontal projection is perpendicular to the horizontal trace of the plane (r1 ⊥ hα) and its frontal projection is perpendicular to the frontal trace (r2 ⊥ fα).

4Practice rebatimento constructions to determine true size (VG) of plane figures by setting the trace as the hinge (charneira) and applying the rebatimento right triangle.

5Understand the intersection of a line with a plane by systematically applying an auxiliary projecting plane (plano de topo or plano vertical) containing the given line.

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).

Are written answers required?

No. Items are solved exclusively by graphic construction; captions or reports are neither requested nor considered.

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 Geometria Descritiva A (Prova 708)

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