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Key Facts: PAU Technical Drawing II (Castilla y León) Exam

90 min

Exam Duration

COPAU Castilla y León

0–10

Grading Scale (Min 4.0 for Access Phase)

Junta de Castilla y León

EUR 76.82

Base Registration Fee

Castilla y León PAU Fee Structure 2026

5 Core Blocks

Plane, Transformations, Dihedral, Axonometric, ISO Standards

2nd Bachillerato LOMLOE Curriculum

The Technical Drawing II exam for the Castilla y León PAU (Prueba de Acceso a la Universidad) features a 90-minute university entrance test administered by COPAU and the public universities of Castilla y León (USAL, UVA, UBU, ULE). 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 (Castilla y León) Practice Questions

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

1In plane geometry, what is the geometric relationship between a tangent line and the radius of a circle at the point of tangency?

A.They are parallel to each other.

B.They intersect at an angle of 45 degrees.

C.They are perpendicular to each other.

D.They intersect at an angle of 60 degrees.

Explanation: According to the fundamental properties of circle tangency, a line tangent to a circle is always perpendicular to the radius drawn to the point of tangency. This 90-degree angle relationship is essential for constructing tangents from external points or between circles.

2In any triangle, the center of the inscribed circle (incircle) is located at the intersection of which set of lines?

A.The three perpendicular bisectors of the sides

B.The three internal angle bisectors

C.The three altitudes from the vertices

D.The three medians connecting vertices to midpoints

Explanation: The incenter (incentro) of a triangle is the common point of intersection of its three internal angle bisectors. Because every point on an angle bisector is equidistant from the two adjacent sides, the incenter is equidistant from all three sides, making it the center of the inscribed circle.

3Which triangle center is formed by the intersection of the perpendicular bisectors (mediatrices) of its three sides?

A.Orthocenter

B.Incenter

C.Circumcenter

D.Centroid

Explanation: The circumcenter (circuncentro) is the point where the three perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle, serving as the center of the circumscribed circle.

4What is the name of the triangle center obtained by finding the intersection point of its three altitudes (alturas)?

A.Incenter

B.Orthocenter

C.Circumcenter

D.Excenter

Explanation: The orthocenter (ortocentro) is defined as the common point where the three altitudes (perpendicular lines dropped from each vertex to the opposite side or its extension) meet.

5The centroid (baricentro) divides each median of a triangle into two segments. What is the ratio of the distance from the vertex to the centroid compared to the distance from the centroid to the opposite side midpoint?

A.1 : 1

B.3 : 1

C.2 : 1

D.1 : 2

Explanation: The centroid divides each median in a 2:1 ratio. The segment from the vertex to the centroid is twice as long as the segment from the centroid to the midpoint of the opposite side.

6The golden ratio (sección áurea) divides a line segment AB at point C such that the ratio of the whole segment AB to the larger part AC equals what ratio?

A.The ratio of AC to the smaller part CB

B.The ratio of CB to the larger part AC

C.The ratio of AC to the sum AB + CB

D.The square of the ratio of AC to CB

Explanation: By definition, the golden section divides a segment AB at point C so that AB / AC = AC / CB = phi ≈ 1.618. The whole is to the greater part as the greater part is to the lesser part.

7For a point P located at distance d from the center of a circle O with radius R, what is the formula for the geometric power of point P (potencia de un punto) with respect to circle O?

A.K = d / R

B.K = d^2 + R^2

C.K = d^2 - R^2

D.K = (d - R)^2

Explanation: The power K of a point P relative to a circle with radius R and center O is defined as K = d^2 - R^2, where d = PO. When P is outside the circle, K is positive and equals the square of the length of the tangent segment drawn from P to the circle.

8What is the radical axis (eje radical) of two non-concentric circles?

A.The line segment connecting the centers of both circles

B.The locus of points having equal power with respect to both circles

C.The circle passing through the centers and intersection points of both circles

D.The perpendicular bisector of the line connecting their centers

Explanation: The radical axis of two circles is the locus of all points in the plane that have equal power with respect to both circles. It is always a straight line perpendicular to the line of centers.

9How is the radical center (centro radical) of three circles with non-collinear centers constructed geometrically?

A.As the midpoint of the triangle formed by the three centers

B.As the intersection of the three radical axes taken in pairs

C.As the center of the circumscribed circle passing through all three circle centers

D.As the average position of the three circle centers

Explanation: The radical center is the unique point in the plane having equal power with respect to three given circles. It is found by determining the radical axes of two pairs of circles; their intersection point is the radical center.

10For two mutually intersecting circles, where does their radical axis lie?

A.It is tangent to both circles at their highest points

B.It is the line passing through their two points of intersection

C.It is parallel to the line connecting their centers

D.It passes halfway between their centers regardless of radii

Explanation: When two circles intersect at two points, those intersection points have zero power with respect to both circles. Since zero power is equal power, the line passing through the two intersection points is the radical axis.

About the PAU Technical Drawing II (Castilla y León) Exam

The Castilla y León PAU Technical Drawing II (Dibujo Técnico II) exam evaluates secondary students across Castilla y León high schools and university admission candidates on plane geometry, geometric transformations, 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 COPAU curriculum.

Exam sponsor: Comisión Organizadora de la Prueba de Acceso a la Universidad (COPAU) / Junta de Castilla y León. 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 76.82 base registration fee for PAU Access Phase (plus EUR 10.33 per voluntary subject) set by Junta de Castilla y León.

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%

Plane Geometry & Geometrical Constructions

Fundamental plane geometry, regular polygons, tangencies, power of a point, radical axis and radical center, Apollonius problems, cycloidal curves, and technical curves.

20%

Geometric Transformations & Conic Sections

Plane transformations (homothety, similarity, homology, affinity, plane inversion) and metric construction and properties of conics (ellipse, parabola, hyperbola).

25%

Descriptive Geometry & Dihedral Projection System

Dihedral (orthographic) representation of points, lines, and planes; traces; intersections; true distances and angles; auxiliary operations (abatements, plane changes, rotations); polyhedra and sections.

25%

Axonometric Systems & Conical Perspective

Orthographic axonometry (isometric, dimetric, trimetric), reduction factors, isometric circles, oblique axonometry (cavalier and cabinet perspective), and central/angular conical perspective.

10%

Technical Standardization, Dimensioning & Industrial Views

ISO/UNE technical drawing standards, standard line types, drawing scales, dimensioning rules and symbols, orthogonal view arrangements (First-Angle vs Third-Angle), cuts, and sections.

Preparing for the PAU Technical Drawing II (Castilla y León) 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 76.82 base registration fee for PAU Access Phase (plus EUR 10.33 per voluntary subject) set by Junta de Castilla y León. Official sources

Using Our Practice Resources

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PAU Technical Drawing II (Castilla y León): Suggested Study Strategy

1Master fundamental tangency properties, such as the relationship between circle centers, tangency points, and the radical axis of intersecting or tangent circles.

2Understand the metric properties of conic sections, including the relationship between focal distance, major axis, minor axis ($a^2 = b^2 + c^2$ for ellipse), directrices, and focal circles.

3Practice dihedral system auxiliary methods (abatements/abatimientos, plane changes, rotations) to quickly solve true metric problems like true distances and dihedral angles.

4Memorize orthographic axonometric reduction factors (\sqrt{2/3} \approx 0.816 for unscaled isometric) and oblique axonometric reduction factors (k = 1/2 for cabinet perspective).

5Review UNE/ISO dimensioning standards thoroughly, ensuring proper placement of dimension lines, origin symbols, and projection views (European First-Angle vs. American Third-Angle).

Frequently Asked Questions

What is the format of the official Castilla y León PAU Technical Drawing II exam?

The official PAU Technical Drawing II exam in Castilla y León is a paper-based graphic drawing examination where students use drawing instruments (ruler, set squares, compass) to complete technical drawing and descriptive geometry exercises within 90 minutes. Note that this digital practice bank provides an English-language multiple-choice question (MCQ) study adaptation to help students master theoretical rules, definitions, and construction procedures.

What score is needed to pass the Technical Drawing II exam in Castilla y León?

The exam is graded on a 0 to 10 scale. In the compulsory Access Phase (Fase de Acceso), a minimum score of 4.0 is required to calculate the final university access mark (60% Bachillerato average grade + 40% PAU Access Phase mark >= 5.0). In the Voluntary Admission Phase, scores of 5.0 or higher earn up to 2 weighted bonus points depending on degree affinity coefficients.

What topics are covered in the 2nd Bachillerato Technical Drawing II curriculum in Castilla y León?

The curriculum encompasses five main blocks: Plane Geometry & Constructions (tangencies, power of a point, radical axis), Geometric Transformations & Conic Sections (homology, affinity, inversion, conics), Descriptive Geometry & Dihedral System (projections, true metrics, polyhedra), Axonometric Systems & Conical Perspective (isometric, cavalier, perspective), and Technical Standardization & Dimensioning (ISO/UNE standards, views, cuts, sections).

How much does registration for the PAU exam cost in Castilla y León?

The ordinary registration fee set by Junta de Castilla y León for the PAU Access Phase is approximately EUR 76.82, with an additional EUR 10.33 per subject taken in the voluntary admission phase. Fee reductions or waivers apply for large families (Familia Numerosa), students with recognized disabilities (>= 33%), and other protected categories.

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.

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