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Free Practice Questions for Canary Islands PAU Technical Drawing Applied to Plastic Arts & Design II

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Sample Canary Islands PAU Technical Drawing Applied to Plastic Arts & Design II Practice Questions

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

1In applied plane geometry, what is the fundamental condition for a circle to be tangent to a straight line at a specific point T?
A.The chord passing through T must be equal to half the circumference length.
B.The center of the circle must lie on a line parallel to the tangent line at distance equal to the diameter.
C.The center of the circle must lie on the perpendicular line to the tangent line erected at point T.
D.The radius drawn to point T must form an angle of 45° with the tangent line.
Explanation: By definition of tangency in plane geometry, the radius connecting the circle's center to the point of tangency T is strictly perpendicular to the tangent line at T. Therefore, the center of any tangent circle must lie along the normal (perpendicular) line drawn at T.
2In a geometric plane inversion defined by center O and positive power K, what is the inverse of a circle that passes through the center of inversion O?
A.A straight line not passing through the center of inversion O, perpendicular to the diameter connecting O to the circle's center.
B.Another circle of identical radius passing through the center of inversion O.
C.A straight line passing directly through the center of inversion O.
D.A parabola whose vertex is located at the center of inversion O.
Explanation: In plane inversion, any circle that passes through the inversion center O transforms into a straight line that does not pass through O. The resulting line is perpendicular to the line connecting O to the center of the original circle.
3When applying homothety with ratio k = -0.5 to scale a design module centered at O, how does the transformed module relate to the original?
A.It is translated by 0.5 units along the x-axis without changing size.
B.It is reduced to half its linear size and kept in the exact same orientation relative to O.
C.It is enlarged by a factor of 2 and kept in the same orientation relative to O.
D.It is inverted (rotated 180° relative to O) and reduced to half its original linear dimensions.
Explanation: A negative homothety ratio k = -0.5 scales all vectors from O by a factor of 0.5 in the opposite direction. This produces a 180° inverted figure reduced to 50% of its original linear dimensions.
4To construct a circular arc of given radius R tangent to two non-parallel intersecting lines, where must the center of the arc be located?
A.At the midpoint of the segment connecting the vertices of the two lines.
B.At the intersection of the angle bisector with the original lines.
C.On the perpendicular bisector of the line segment joining the two line endpoints.
D.At the intersection of two lines drawn parallel to the original lines at a distance R, lying on the bisector of the angle between them.
Explanation: The locus of points equidistant by radius R from a straight line consists of two parallel lines at distance R. Intersecting the parallel lines corresponding to both original lines places the center on the angle bisector at exact distance R from both lines.
5An ellipse used in industrial product design has a major axis 2a = 100 mm and a minor axis 2b = 60 mm. What is the focal distance 2c between its two foci F1 and F2?
A.80 mm
B.40 mm
C.70 mm
D.90 mm
Explanation: In an ellipse, the semi-axes a, b, and semi-focal distance c satisfy the Pythagorean relation a² = b² + c². Here a = 50 mm and b = 30 mm. Thus c = √(50² - 30²) = √(2500 - 900) = √1600 = 40 mm. The total focal distance 2c = 2 × 40 = 80 mm.
6What is the defining geometric locus property of a parabola applied in parabolic solar reflector design?
A.Every point on the parabola is equidistant from a fixed point (focus F) and a fixed line (directrix d).
B.The sum of the distances from any point on the curve to two fixed foci is constant.
C.The difference of the distances from any point on the curve to two fixed foci is constant.
D.The product of the distances from any point to two perpendicular axes is constant.
Explanation: By definition, a parabola is the locus of points in a plane whose distance to a fixed point (the focus F) equals its perpendicular distance to a fixed line (the directrix d). This property directs parallel incident rays to converge at the focus.
7In the design of a hyperbolic cooling structure, the hyperbola has semi-transverse axis a = 30 mm and semi-conjugate axis b = 40 mm. What are the equations of its asymptotes relative to the principal center axes?
A.y = ± (4/3) x
B.y = ± (3/4) x
C.y = ± (5/3) x
D.y = ± (3/5) x
Explanation: The asymptotes of a hyperbola with horizontal transverse axis 2a and vertical conjugate axis 2b centered at the origin are given by y = ± (b/a) x. Given a = 30 mm and b = 40 mm, the slope is b/a = 40/30 = 4/3, giving y = ± (4/3) x.
8In a plane inversion with center O and positive power K, a circle C does NOT pass through O. What is the nature and position of its inverted figure C'?
A.C' is a straight line parallel to the tangent line at O.
B.C' is another circle not passing through O, homothetic to C with respect to O, but its inverted center O' does not coincide with the inverse of C's center.
C.C' is an ellipse centered at O with major axis proportional to K.
D.C' is a parabolic arc tangent to the radical axis of inversion.
Explanation: An inversion transforms a circle not passing through the center of inversion O into another circle C' not passing through O. Under inversion, the center of C does not map to the center of C' (geometric center is not invariant under inversion).
9In an axial affinity transformation applied to alter a graphic logo, which property remains invariant for all corresponding points and line segments?
A.Circles always transform into identical congruent circles.
B.Distances between all arbitrary pairs of points are strictly preserved (isometric).
C.Angles between intersecting lines are preserved without distortion.
D.Parallelism between lines is preserved, and points on the affinity axis remain invariant (fixed).
Explanation: Axial affinity is an affine transformation that leaves all points on the affinity axis fixed and preserves parallelism between lines. However, it alters angles and distances, transforming circles into ellipses.
10In plane homology (central collinearity), what defines the vanishing line (línea límite) L of the original plane?
A.It is the locus of points whose homologous points lie at infinity; it is parallel to the homology axis.
B.It is the line connecting the homology center O to the origin of coordinates.
C.It is the line where homologous lines intersect at 90°.
D.It is the perpendicular bisector of the segment between O and the axis.
Explanation: In central homology, the vanishing line (línea límite L) is the line parallel to the homology axis containing all points whose homologous images are located at infinity. Conversely, L' in the homologous plane receives images of points at infinity.

About the Canary Islands PAU Technical Drawing Applied to Plastic Arts & Design II Exam

The Canary Islands PAU Technical Drawing Applied to Plastic Arts and Design II (Dibujo Técnico Aplicado a las Artes Plásticas y al Diseño II 2º Bachillerato COPAU 2026) examination tests geometric mastery, spatial visual skills, modular composition, perspective rendering, shadow projection, and technical design drafting standards. This question bank contains 100 high-quality practice questions designed to prepare students in the Arts (Plastic Arts, Image, and Design) modality for the university entrance exams in the Canary Islands.

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 Applied Geometry & Transformations (~20%), Modular Networks & Tessellations (~20%), Perspective Systems Applied to Design (~25%), Shade & Shadow Projection (~15%), Graphic Presentation & Rendering (~10%), and Design Standards & Normative (~10%).

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.

20%

Applied Geometry & Transformations

Tangency, regular and irregular polygon construction, conic sections applied to design objects, homothety, similarity, inversion, affinity, and geometric transformations.

20%

Modular Networks & Tessellations

Flat regular and semi-regular grids, structural module development, supermodules, pattern movements (rotations, translations, glides, dilations), wallpaper groups, and surface pattern design.

25%

Perspective Systems Applied to Design

Dihedral system applied to 3D design volumes, axonometric projection (isometric, dimetric, Cavalier) for industrial and interior design, and conical perspective (central and oblique) for architectural and spatial visualization.

15%

Shade & Shadow Projection

Shadow determination in dihedral, axonometric, and conic perspectives, directional sun lighting, point-source illumination, self-shadows, cast shadows, and tonal gradation.

10%

Graphic Presentation & Rendering Techniques

Design sketching, dimensioned croquis, line code conventions, manual rendering techniques (markers, ink, pencils), texture representation, and graphic presentation standards for design projects.

10%

Design Representation Standards & Normative

ISO/UNE line conventions, standardized dimensioning for product and spatial design, scale applications (ISO 5455), sectional views, cuts, and technical symbolization.

Preparing for the Canary Islands PAU Technical Drawing Applied to Plastic Arts & 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: 90-minute examination covering Applied Geometry & Transformations (~20%), Modular Networks & Tessellations (~20%), Perspective Systems Applied to Design (~25%), Shade & Shadow Projection (~15%), Graphic Presentation & Rendering (~10%), and Design Standards & Normative (~10%).
  • 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, applied to plastic arts and design briefs. 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 applied graphic 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 Applied to Plastic Arts and Design II exam?

It is a 90-minute written examination administered at ULPGC and ULL designated centers, featuring applied geometric construction, modular network design, perspective and shadow-projection problems, and normalized graphic presentation 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 Arts-track degrees.

Who should take this exam?

Students in the Arts (Plastic Arts, Image and Design) modality of 2º Bachillerato in the Canary Islands who are applying to design, fine arts, architecture, or related degree programs.

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).