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Key Facts: La Rioja PAU Technical Drawing Applied to Plastic Arts and Design II Exam

90 min

Exam Duration

UR PAU Regulations

4.0 / 10

Minimum Passing Mark

Spanish University Access Regulations

EUR 55.43

Base Exam Fee

UR Fee Structure

6 Blocks

Curricular Content Areas

LOMLOE La Rioja Curriculum

UR

Examining Body

Universidad de La Rioja

The La Rioja PAU Technical Drawing Applied to Plastic Arts and Design II exam (Dibujo Técnico Aplicado a las Artes Plásticas y al Diseño II) is administered by Universidad de La Rioja (UR) for 2º Bachillerato Arts track students. Held over 90 minutes, it tests theoretical principles and graphic resolution skills across six main blocks: Plane Geometry, Transformations, Dihedral System, Axonometry, Conical Perspective, and Normalization/Design Applications. A minimum mark of 4.0 is required in the Access Phase.

Sample La Rioja PAU Technical Drawing Applied to Plastic Arts and Design II Practice Questions

Try these sample questions to review concepts for the La Rioja PAU Technical Drawing Applied to Plastic Arts and Design II exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1According to Thales Theorem of proportionality, if a set of parallel lines intersects two transversal lines, what relationship exists between the corresponding intercepted segments?
A.The intercepted segments on one transversal are directly proportional to the corresponding segments on the second transversal.
B.The intercepted segments on one transversal are inversely proportional to the segments on the second transversal.
C.The intercepted segments on one transversal are always equal in absolute length to those on the second transversal.
D.The sum of the intercepted segments on the first transversal equals the product of the segments on the second transversal.
Explanation: Thales Theorem states that when two transversal lines are cut by a family of parallel lines, the ratio of any two segments on the first transversal equals the ratio of the corresponding segments on the second transversal (direct proportionality, A/B = A'/B').
2In a triangle, which notable point is defined as the intersection of its three angle bisectors (bisectrices)?
A.The Incenter (Incentro), which is the center of the inscribed circle (circunferencia inscrita).
B.The Circumcenter (Circuncentro), which is the center of the circumscribed circle.
C.The Centroid (Baricentro), which is the center of mass.
D.The Orthocenter (Ortocentro), which is the intersection of altitudes.
Explanation: The angle bisectors of a triangle meet at the Incenter (Incentro). Because the incenter is equidistant from all three sides, it serves as the center of the inscribed circle (circunferencia inscrita), tangent to all three sides internally.
3Which geometric ratio defines the Golden Section (Sección Áurea) when dividing a segment AB of length L into a major part C and a minor part c?
A.The ratio of the whole segment to the major part equals the ratio of the major part to the minor part (L/C = C/c = \Phi pprox 1.618).
B.The ratio of the major part to the minor part equals the ratio of the whole segment to the minor part squared.
C.The sum of the major and minor parts equals twice the difference between the whole segment and the minor part.
D.The major part is exactly two-thirds of the total segment length.
Explanation: The Golden Section (Sección Áurea) is defined by the proportion L/C = C/c, where the ratio of the total length L = C + c to the larger segment C equals the ratio of C to the smaller segment c. Solving (C+c)/C = C/c yields the Golden Ratio \Phi = (1 + \sqrt{5})/2 pprox 1.618.
4What is the Power of a Point P (Potencia de un punto) with respect to a circle of radius R and center O, where d = OP is the distance from P to O?
A.\mathcal{P} = d^2 - R^2
B.\mathcal{P} = d + R
C.\mathcal{P} = d^2 / R^2
D.\mathcal{P} = 2\pi R d
Explanation: The Power of a Point P relative to a circle \mathcal{C}(O, R) is defined algebraically as \mathcal{P} = d^2 - R^2, where d = OP. Geometrically, for any secant line through P intersecting the circle at A and B, \mathcal{P} = PA \cdot PB. For an external point, it equals the square of the tangent segment length PT^2.
5What is the Radical Axis (Eje Radical) of two non-concentric circles?
A.The locus of all points in the plane that have equal power with respect to both circles.
B.The straight line passing through the centers of both circles.
C.The locus of points whose sum of distances to both circle centers is constant.
D.The line perpendicular to the line of centers passing through the center of the smaller circle.
Explanation: The Radical Axis (Eje Radical) of two circles is the locus of points having equal power relative to both circles. It is always a straight line perpendicular to the line joining the two circle centers.
6Fundamental Tangency Principle: When a straight line r is tangent to a circle at point T, what angle does line r form with the radius OT drawn to the point of tangency?
A.Exactly 90^\circ (perpendicular).
B.Exactly 45^\circ.
C.Exactly 60^\circ.
D.It varies depending on the radius of the circle.
Explanation: A fundamental property of tangency states that a tangent line to a circle is strictly perpendicular (90^\circ) to the radius drawn to the point of contact T.
7What is the Radical Center (Centro Radical) of three non-aligned circles whose centers do not lie on a single straight line?
A.The unique point in the plane having equal power with respect to all three circles, formed by the intersection of their pairwise radical axes.
B.The centroid of the triangle formed by connecting the centers of the three circles.
C.The point of mutual tangency when all three circles touch externally.
D.The center of the smallest circle passing through the three circle centers.
Explanation: The Radical Center (Centro Radical) of three circles is the point of intersection of the three pairwise radical axes. Because it has equal power with respect to all three circles, a circle centered at the radical center can be drawn orthogonal to all three given circles.
8In the Apollonius problem case of finding circles tangent to two given parallel lines and passing through a given point P, how many solution circles exist in general if P lies between the parallel lines?
A.Exactly 2 solutions.
B.Exactly 1 solution.
C.Exactly 4 solutions.
D.Infinitely many solutions.
Explanation: When point P lies between two parallel lines, the radius of the solution circles is fixed at half the distance between the parallels. The centers of the solution circles lie on the parallel midline at distance R from P. Finding the intersection of a circle of radius R centered at P with the midline yields exactly 2 points, resulting in 2 solution circles.
9What is the defining focal property of an Ellipse with foci F_1 and F_2 and major axis length 2a?
A.For any point P on the ellipse, the sum of distances to the foci is constant: PF_1 + PF_2 = 2a.
B.For any point P on the ellipse, the difference of distances to the foci is constant: |PF_1 - PF_2| = 2a.
C.For any point P on the ellipse, the product of distances to the foci is constant: PF_1 \cdot PF_2 = a^2.
D.The distance from any point P to F_1 is equal to the distance from P to the minor axis.
Explanation: An Ellipse is the locus of points P in a plane such that the sum of distances from P to two fixed points (foci F_1, F_2) is constant and equal to the major axis length 2a (PF_1 + PF_2 = 2a).
10What is the defining focal property of a Hyperbola with foci F_1 and F_2 and transverse axis length 2a?
A.For any point P on the hyperbola, the absolute difference of distances to the foci is constant: |PF_1 - PF_2| = 2a.
B.For any point P on the hyperbola, the sum of distances to the foci is constant: PF_1 + PF_2 = 2a.
C.The distance from any point P to focus F_1 equals its distance to focus F_2.
D.The ratio of distance PF_1 to PF_2 is always less than 1.
Explanation: A Hyperbola is the locus of points P in a plane such that the absolute difference of distances from P to two fixed foci F_1, F_2 is constant and equal to 2a (|PF_1 - PF_2| = 2a).

About the La Rioja PAU Technical Drawing Applied to Plastic Arts and Design II Exam

The La Rioja PAU Technical Drawing Applied to Plastic Arts and Design II exam evaluates 2º Bachillerato Arts students on plane geometry, tangencies, geometric transformations, dihedral projection system, axonometry, conical perspective, normalization, and practical geometric applications to plastic arts and design.

Exam sponsor: Universidad de La Rioja (UR) / Comisión Organizadora de la PAU de La Rioja. 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 55.43 ordinary registration fee for PAU (fee exemptions apply for large families, disability, or victims of terrorism).

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.

20%

Plane Geometry, Tangencies & Conic Curves

Fundamental geometrical constructions, triangles, polygons, tangencies, radical axis/center, Apollonius problems, and conic section properties (ellipse, hyperbola, parabola).

15%

Geometric Transformations & Inversion

Plane transformations (translation, rotation, symmetry, homothety, similarity, homology, affinity) and spatial/plane inversion theory and applications.

25%

Dihedral Projection System

Descriptive geometry fundamentals, point, line, and plane representations, intersections, parallelism, perpendicularity, distances, rabatments, changes of plane, and rotations.

15%

Axonometric & Oblique Projections

Isometric, dimetric, and trimetric projections, reduction coefficients, Cavalier and Military oblique perspectives, plane sections of solids, and axonometric curves.

15%

Conical / Central Perspective Projection

Central perspective principles, horizon line, station point, vanishing points, measuring points, height scale, and spatial representation in visual arts and design.

10%

Normalization, Dimensioning & Plastic Arts Applications

UNE-EN ISO drawing standards, sheet formats, scales, line types, dimensioning rules, cuts/sections, assemblies, CAD concepts, and design project applications.

Preparing for the La Rioja PAU Technical Drawing Applied to Plastic Arts and Design II 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 55.43 ordinary registration fee for PAU (fee exemptions apply for large families, disability, or victims of terrorism). Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
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La Rioja PAU Technical Drawing Applied to Plastic Arts and Design II: Suggested Study Strategy

1Master fundamental dihedral constructions: finding true distances between points/lines and obtaining true shape via rabatment (abatimiento).
2Memorize isometric and oblique reduction coefficients (zsh.816$ for isometry, /2$ or /3$ for Cavalier 569Xaxis).
3Understand the focal properties of conic sections (PF1 + PF2 = 2a for ellipse, |PF1 - PF2| = 2a for hyperbola, PF = distance to directrix for parabola).
4Practice central perspective setups: locate the Horizon Line, Station Point (V), Principal Point (P), and Distance/Measuring Points (D, M).
5Review UNE-EN ISO dimensioning rules: dimension lines must never intersect, arrows touch extension lines cleanly, and values sit above horizontal dimension lines.

Frequently Asked Questions

What is the structure of the La Rioja PAU Technical Drawing Applied to Plastic Arts and Design II exam?

The exam is a 90-minute written and graphic test administered by Universidad de La Rioja (UR). Candidates solve geometric construction problems, projection drawing exercises (dihedral, axonometric, perspective), and normalization/dimensioning questions.

How does Dibujo Técnico II (Arts track) differ from Dibujo Técnico II (Science & Technology track)?

While both cover plane geometry, dihedral system, axonometry, and normalization, the Arts track exam (Dibujo Técnico Aplicado a las Artes Plásticas y al Diseño II) places greater emphasis on conical/central perspective, geometric applications to design and plastic arts, and graphic composition.

What passing grade is required on the exam for university admission?

A minimum score of 4.0 out of 10 is required on the Access Phase exam to be eligible to average with your Bachillerato GPA (60% GPA + 40% Access Phase score >= 5.0).

What registration fee applies to the PAU in La Rioja?

The base registration fee set by Universidad de La Rioja (UR) is EUR 55.43 for the ordinary exam sitting, with reductions or total exemptions for qualifying categories.