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Exam Review

Key Facts: PAU Technical Drawing II (Aragón) Exam

90 min

Exam Time Limit

UNIZAR / PAU Aragón

0–10

Grading Scale (Min 4.0 for Access Phase)

Gobierno de Aragón

EUR 75.00

Ordinary Registration Fee

UNIZAR PAU inscription page 2026

4 Core Blocks

Plane, Dihedral, Axonometric, ISO Standards

2nd Bachillerato Curriculum

The Technical Drawing II exam for the Aragón PAU (Prueba de Acceso a la Universidad) features a 90-minute university entrance test administered by UNIZAR / PAU Commission of Aragón. Graded on a 0–10 scale, a minimum mark of 4.0 is required in the Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU >= 5.0 to pass). The official exam consists of practical graphic drawing tasks; this dataset provides an English-language MCQ study adaptation designed for core concept practice, rule verification, and theoretical mastery.

Sample PAU Technical Drawing II (Aragón) Practice Questions

Try these sample questions to review concepts for the PAU Technical Drawing II (Aragón) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the locus of the centers of all circles that are tangent to two given non-parallel lines?
A.The perpendicular bisector of the segment connecting their intersection point to infinity
B.The angle bisectors of the angles formed by the two lines
C.A circle concentric with the intersection point
D.A parabola whose focus is the intersection point
Explanation: The locus of points equidistant from two intersecting lines consists of the two perpendicular angle bisectors of the angles formed by those lines. Since any circle tangent to both lines must have its center at a point equidistant from both lines, the center must lie on an angle bisector.
2In plane geometry, what is the 'power' of a point P with respect to a circle of radius R and center O, where d is the distance PO?
A.Power = d / R
B.Power = d^2 + R^2
C.Power = d^2 - R^2
D.Power = (d - R)^2
Explanation: The power of a point P with respect to a circle O(R) is defined as K = d^2 - R^2, where d = PO. If P is outside the circle, K > 0 and equals the square of the length of the tangent segment from P to the circle.
3The radical axis of two non-concentric circles is defined as:
A.The line connecting the centers of the two circles
B.The locus of points having equal power with respect to both circles
C.The common tangent line passing through the midpoint between centers
D.The circle passing through the intersection points of both circles
Explanation: The radical axis (eje radical) of two non-concentric circles is the straight line containing all points that have equal power with respect to both circles. It is always perpendicular to the line of centers.
4Where is the radical center of three circles with non-collinear centers located?
A.At the circumcenter of the triangle formed by the three centers
B.Three circles with non-collinear centers do not have a radical center
C.At the centroid of the triangle formed by the three centers
D.At the intersection point of the three radical axes taken in pairs
Explanation: The radical center (centro radical) of three circles whose centers are not collinear is the unique point where the three pairwise radical axes intersect. This point has equal power with respect to all three circles.
5In plane inversion (inversión plana) with center O and positive ratio K (K > 0), what is the inverse of a straight line NOT passing through the center of inversion O?
A.A circle centered at O
B.A parabola with focus at O
C.A straight line parallel to the original line
D.A circle passing through the center of inversion O
Explanation: In plane inversion, a straight line that does not pass through the center of inversion O transforms into a circle that passes through O, with its diameter along the perpendicular line from O to the original line.
6What is the inverse of a circle that passes through the center of inversion O?
A.A circle not passing through O
B.A straight line not passing through O
C.A point at infinity only
D.An ellipse centered at O
Explanation: By the reciprocal property of geometric inversion, since a line not passing through O inverts into a circle through O, any circle passing through O inverts into a straight line not passing through O.
7Which transformation property is fundamental to plane inversion (inversión)?
A.It is conformal (preserves angles between curves)
B.It maps all straight lines to parallel straight lines
C.It preserves the area of all closed figures
D.It preserves distances between all pairs of points (isometry)
Explanation: Plane inversion is a conformal transformation (transformación conforme), meaning it preserves the magnitude of angles between intersecting curves, though it reverses their sense (orientation).
8In a homothety (homotecia) with center O and ratio k = -2, if segment AB has a length of 5 cm, what is the length and orientation of the transformed segment A'B'?
A.Length 2.5 cm, perpendicular to AB
B.Length 5 cm, rotated by 180 degrees
C.Length 10 cm, parallel to AB in the opposite direction
D.Length 10 cm, parallel to AB in the same direction
Explanation: In homothety, any segment AB transforms into a parallel segment A'B' whose length is |k| * |AB| = |-2| * 5 = 10 cm. Since k < 0 (negative ratio), A'B' is oriented in the opposite direction relative to center O.
9Homology (homología) in plane geometry is defined by which minimum set of independent elements?
A.Three non-collinear invariant points
B.Two parallel axes and a scale ratio
C.Center of homology and radius of inversion
D.Center of homology, axis of homology, and a pair of homologous points
Explanation: A central homology (homología plana) is uniquely determined by its center O, its axis e, and one pair of corresponding (homologous) points P and P' (or a vanishing line / dirección de rectas homólogas).
10In an affinity transformation (afinidad) in the plane, which property remains invariant?
A.Lengths of segments in all directions
B.Circle shapes (all circles remain circles)
C.Angles between lines
D.Parallelism between lines
Explanation: Affinity is an affine transformation. Key invariants include: straight lines remain straight lines, parallel lines remain parallel, and ratio of segments along parallel lines is preserved. Angles, lengths, and circle shapes are generally altered.

About the PAU Technical Drawing II (Aragón) Exam

The Aragón PAU Technical Drawing II (Dibujo Técnico II) exam evaluates secondary students across Aragonese high schools and university admission candidates on plane geometry, descriptive geometry (dihedral projection system), axonometric and conical perspective representation, and UNE/ISO technical normalization and dimensioning. Please note: This practice bank provides an English-language multiple-choice question (MCQ) study adaptation created to assist students in mastering theoretical fundamentals, geometric constructions, projection mechanics, and dimensioning standards required by the official 2026 UNIZAR curriculum.

Exam sponsor: PAU Organising Commission of Aragón / UNIZAR. 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 75.00 ordinary registration fee (Access Phase plus two voluntary subjects); EUR 30.93 per additional voluntary subject (UNIZAR 2026)

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%

Plane Geometry & Geometric Transformations

Concepts of tangency, power of a point, radical axis and radical center, transformations (homothety, affinity, inversion), conic sections (ellipse, parabola, hyperbola) properties, and cycloidal curves.

30%

Descriptive Geometry & Dihedral System

Dihedral (orthographic) representation of points, lines, and planes; traces; intersections; relative positions; distance calculations; auxiliary operations (plane changes, rotations, abatements); polyhedra and surface sections.

25%

Axonometric & Perspective Systems

Orthographic axonometry (isometric, dimetric, trimetric), reduction coefficients, isometric ellipse representation, oblique axonometry (cavalier and cabinet perspective), and central/angular conical perspective.

20%

Technical Standardization & Dimensioning

ISO/UNE technical drawing conventions, standard line types, drawing scales (enlargement/reduction), dimensioning principles and symbols, orthogonal view arrangements (First-Angle European vs Third-Angle American), cuts, and sections.

Preparing for the PAU Technical Drawing II (Aragón) 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 75.00 ordinary registration fee (Access Phase plus two voluntary subjects); EUR 30.93 per additional voluntary subject (UNIZAR 2026) 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 Technical Drawing II (Aragón): Suggested Study Strategy

1Master the fundamental properties of conic sections (foci, directrices, tangent lines, conjugate axes) and tangency theorems (Incenter, Power of a Point, Radical Axis).
2Practice dihedral system auxiliary views (abatements, plane changes, rotations) to efficiently determine true distances and true angles.
3Memorize standard axonometric reduction factors (sqrt(2/3) ~ 0.816 for isometric without scale expansion, 1.0 for isometric expanded drawing).
4Understand UNE/ISO dimensioning conventions, ensuring dimension lines never overlap with contour lines and correct symbols (diameter, radius, S-diameter) are applied.
5Differentiate clearly between European (First-Angle) projection, where the right view is drawn to the left of the front view, and American (Third-Angle) projection.

Frequently Asked Questions

What is the format of the official Aragón PAU Technical Drawing II exam?

The official PAU Technical Drawing II exam in Aragón (UNIZAR) is a paper-based graphic drawing exam where students use drawing instruments (ruler, set squares, compass) to solve geometric and descriptive projection problems within 90 minutes. Note that this online practice bank provides an English-language multiple-choice question (MCQ) study adaptation to help students test their understanding of the underlying geometric principles, rules, and procedures.

What score is needed to pass the Technical Drawing II exam in Aragón?

The exam is graded on a scale of 0 to 10. In the compulsory Access Phase (Fase de Acceso), a minimum score of 4.0 is required so that it can be weighted into the university admission mark (60% Bachillerato average grade + 40% PAU Access Phase grade must equal at least 5.0). In the Voluntary Admission Phase (Fase de Admisión), scores above 5.0 earn up to 2 additional points depending on university degree weighting coefficients (0.1 or 0.2).

What topics are covered in the 2nd Bachillerato Technical Drawing II curriculum in Aragón?

The curriculum is divided into four main blocks: Plane Geometry & Transformations (tangencies, conics, inversion, affinity), Descriptive Geometry (Dihedral System, intersections, true metrics, polyhedra), Axonometric and Conical Perspective Systems (isometric, cavalier, perspective), and Technical Standardization & Dimensioning (ISO/UNE standards, views, cuts, sections, and dimension lines).

How much does it cost to register for the PAU exam in Aragón?

The base registration fee set for the PAU Access Phase in Aragón is EUR 75.00. Fee exemptions or reductions apply for large family status (Familia Numerosa) and recognized disability.

Why are these practice questions presented as multiple-choice questions in English?

While official PAU exams require manual drafting in Spanish, this digital resource serves as an accessible English-language MCQ study adaptation. It allows students, international scholars, and bilingual candidates to systematically review theoretical rules, geometric definitions, transformation properties, and technical standards.