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Sample Canary Islands PAU Technical Drawing II Practice Questions

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

1At which notable point of a triangle do the three perpendicular bisectors of its sides converge, and what is its fundamental geometric property?
A.Centroid (barycenter); it represents the center of mass of the triangle.
B.Circumcenter; it is the center of the circle circumscribed about the triangle.
C.Orthocenter; it is the point of intersection of the three altitudes.
D.Incenter; it is the center of the circle inscribed in the triangle.
Explanation: The circumcenter is the point where the three perpendicular bisectors of a triangle intersect. Since the perpendicular bisectors are the loci of points equidistant from the endpoints of each side, the circumcenter is equidistant from the three vertices, making it the center of the circumscribed circle.
2The centroid G of a triangle divides each of its medians into two segments. What is the ratio of the distance between the centroid and the midpoint of the opposite side to the median's total length?
A.It corresponds to 1/4 of the median's total length.
B.It corresponds to 1/2 of the median's total length.
C.It corresponds to 1/3 of the median's total length.
D.It corresponds to 2/3 of the median's total length.
Explanation: The centroid G divides each median in a 2:1 ratio, counted from the vertex. Therefore, the distance from the centroid to the midpoint of the opposite side is exactly 1/3 of the median's total length, while the distance to the vertex is 2/3.
3In a non-equilateral triangle, the Euler line contains three of its notable points. Which set of notable points must necessarily lie on the Euler line?
A.Circumcenter, Centroid, and Orthocenter.
B.Incenter, Circumcenter, and Centroid.
C.Incenter, Centroid, and Orthocenter.
D.Circumcenter, Incenter, and Orthocenter.
Explanation: The Euler line of any non-equilateral triangle passes through the circumcenter (O), the centroid (G), and the orthocenter (H). Furthermore, the vector relation GH = 2 · OG holds. The incenter belongs to this line only in isosceles triangles.
4The nine-point (Feuerbach) circle of a triangle passes through nine of its notable points. Which of the following statements about its radius is correct?
A.Its radius equals twice the radius of the circumscribed circle.
B.Its radius equals the radius of the inscribed circle.
C.Its radius is exactly half the radius of the circumscribed circle.
D.Its radius equals 1/3 of the sum of the triangle's three altitudes.
Explanation: The radius of the nine-point (Feuerbach) circle ($R_N$) equals half the radius of the circle circumscribed about the triangle ($R_N = R/2$). Its center is the midpoint of the segment joining the circumcenter and the orthocenter.
5To construct a triangle knowing side a, the altitude $h_a$, and the opposite angle $∠A$, which locus must be drawn relative to the given segment a?
A.The perpendicular bisector of a and a concentric circle.
B.The bisectors of angle $∠A$ applied at the endpoints of a.
C.A homothety of segment a with ratio $h_a$.
D.The inscribed-angle locus (arc) subtending angle $∠A$ over segment a, together with the lines parallel to a at distance $h_a$.
Explanation: Vertex A must simultaneously belong to the inscribed-angle locus (arc) that subtends angle $∠A$ over segment a (the locus of points from which a is seen at angle $∠A$) and to the line parallel to a located at distance $h_a$. The intersection of both figures determines the position of A.
6Which notable center of a triangle is obtained by drawing the bisectors of its three interior angles?
A.The orthocenter.
B.The circumcenter.
C.The incenter.
D.The main excenter.
Explanation: The incenter is the point where the bisectors of the triangle's three interior angles meet. It is the center of the inscribed circle, which is tangent to the triangle's three sides.
7In the golden section of a segment of length L, the larger segment x satisfies the relation $x^2 = L · (L - x)$. What is the approximate numerical value of the larger golden ratio $Φ = x / (L - x)$?
A.1.414
B.1.618
C.1.732
D.2.618
Explanation: The golden ratio $Φ = (1 + √5) / 2 ≈ 1.618033...$ represents the proportion between the larger and smaller sections of a segment divided in golden section.
8What geometric relationship exists between the length of side $d_{10}$ of a regular decagon inscribed in a circle of radius R and that radius R?
A.Side $d_{10}$ is the golden section of radius R.
B.Side $d_{10}$ equals radius R multiplied by $√(3)$.
C.Side $d_{10}$ is the harmonic mean between R and the side of the hexagon.
D.Side $d_{10}$ is exactly half the radius ($R/2$).
Explanation: In a regular decagon inscribed in a circle of radius R, side $d_{10} = R · (√5 - 1) / 2$, which coincides exactly with the larger golden section of radius R.
9When constructing a regular pentagon inscribed in a circle of radius R using the classical method, the decagon side $d_{10}$ and the hexagon side $l_6 = R$ are obtained first. How is the length of the pentagon side $l_5$ obtained numerically and graphically?
A.It is the geometric mean between radius R and the decagon side $d_{10}$.
B.It is the sum of the sides $l_6 + d_{10}$.
C.It is the difference between the sides $l_6 - d_{10}$.
D.It is the hypotenuse of a right triangle whose legs are $l_6 = R$ and the decagon side $d_{10}$.
Explanation: In the right triangle formed in the classical Richmond/Ptolemy construction, the legs measure $R$ (hexagon side $l_6$) and $d_{10}$ (decagon side). By the Pythagorean theorem, the hypotenuse is $l_5 = √(R^2 + d_{10}^2)$.
10How many distinct regular star polygons with 7 vertices (star heptagons) can be constructed?
A.None, because 7 is a prime number.
B.Three, with steps 2, 3, and 4.
C.Two, with steps 2 and 3.
D.Only one, with step 2.
Explanation: The valid steps p for a star polygon with N vertices must satisfy $1 < p < N/2$ and be coprime with N. For N = 7, $N/2 = 3.5$, so the valid integer steps are $p = 2$ and $p = 3$. Therefore, there are 2 distinct star heptagons.

About the Canary Islands PAU Technical Drawing II Exam

The Canary Islands PAU Technical Drawing II (Dibujo Técnico II 2º Bachillerato COPAU 2026) examination assesses core competencies in technical drafting, descriptive geometry, spatial visualization, and standardization. This practice question bank features 100 rigorous multiple-choice questions covering plane geometry (tangencies, inversion, transformations, conics), dihedral system (intersections, perpendicularity, distances, angles, changes of plane, rebattments, polyhedra), axonometric and conic perspectives, and ISO drafting standards.

Exam sponsor: Canary Islands PAU Organising Commission (COPAU) / ULPGC & ULL. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

90-minute examination covering Plane Geometry (~30%), Descriptive Geometry & Dihedral System (~40%), Axonometric & Perspective Projections (~18%), and Technical Standardization & CAD (~12%).

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 76.12 base registration fee for PAU Access Phase (set by Gobierno de Canarias / COPAU).

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.

30%

Plane Geometry

Polygons, triangle properties and centers, tangency and radical power, inversion in the plane, geometric transformations (translation, rotation, reflection, homology, affinity), and conic sections (ellipse, parabola, hyperbola).

40%

Descriptive Geometry & Dihedral System

Point, line, and plane representations, relative positions, intersections, parallelism, perpendicularity, distances, angles, auxiliary plane changes, rotations, rebattments, and polyhedra and curved surfaces.

18%

Axonometric & Perspective Projections

Isometric, dimetric, and trimetric projections, axonometric scales and reduction coefficients, Cavalier projection (perspectiva caballera), conical perspective (perspectiva cónica), and sectioning of bodies.

12%

Technical Standardization & CAD

ISO/UNE line types, dimensioning standards, scales (ISO 5455), surface finishes, dimensional tolerances, and CAD coordinate systems, layers, and vector entities.

Preparing for the Canary Islands PAU Technical Drawing 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: 90-minute examination covering Plane Geometry (~30%), Descriptive Geometry & Dihedral System (~40%), Axonometric & Perspective Projections (~18%), and Technical Standardization & CAD (~12%).
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 76.12 base registration fee for PAU Access Phase (set by Gobierno de Canarias / COPAU). 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

Frequently Asked Questions

Is this practice bank in the same format as the real Canary Islands PAU exam?

No, and it is important to know the difference. The official Canary Islands PAU paper is a 90-minute examination sat in Spanish and built around graphic construction executed on paper with drawing instruments, plus written justification of the method. Under the 2026 PAU design rules agreed by COPAU and the CRUE, open and semi-constructed responses must account for at least 70% of every paper, so the real exam contains no multiple-choice section. This bank is an English-language multiple-choice study adaptation of the same official 2º Bachillerato syllabus — not an official translation, not a past paper, and not a simulation of the exam format. Use it to drill the underlying knowledge and reasoning quickly, then practise executing accurate geometric and dihedral constructions by hand with drawing instruments separately, because that is what the examiners actually mark.

What is the format of the Canary Islands PAU Technical Drawing II exam?

It is a 90-minute written examination administered at ULPGC and ULL designated centers, featuring geometric construction problems, dihedral-system (descriptive geometry) exercises, axonometric/perspective projections, and normalized technical drafting tasks.

How is the exam scored for university entrance in Spain?

The exam is graded on a 0–10 scale. In the compulsory Access Phase, a minimum mark of 4.0 is required to combine with Bachillerato GPA (60% Bachillerato + 40% PAU Access Phase >= 5.0). In the Admission Phase, it can serve as a weighting subject for technical and design-related degrees.

Who should take this exam?

Students in 2º Bachillerato (Science & Technology or Arts modality) in the Canary Islands who are applying to architecture, engineering, design, or fine arts degree programs that weight Technical Drawing II.

Which universities manage the PAU in the Canary Islands?

The exam is organized jointly by the Canary Islands PAU Organising Commission (COPAU), Universidad de Las Palmas de Gran Canaria (ULPGC), and Universidad de La Laguna (ULL).