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100+ Free PAU Technical Drawing Applied to Plastic Arts (Cantabria) Practice Questions
Cantabria PAU Technical Drawing Applied to Plastic Arts and Design II 2026 (Pruebas de Acceso a la Universidad, Universidad de Cantabria) practice questions are available now; exam metadata is being verified.
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2026 Statistics
Key Facts: PAU Technical Drawing Applied to Plastic Arts (Cantabria) Exam
90 min
Exam time duration for the PAU modality-subject paper
University of Cantabria (UNICAN) PAU Organising Commission
0–10 scale
Scoring system (minimum 4.0 required in Access Phase)
Cantabria PAU Regulations
5 Blocks
Official saberes básicos blocks (RD 243/2022): Geometry, Axonometry/Dihedral, Perspective, Normalization/Scales, CAD
2º Bachillerato Artes Curriculum (LOMLOE)
100
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OpenExamPrep
Master the 2026 Cantabria PAU Technical Drawing Applied to Plastic Arts and Design II exam with 100 practice questions covering plane geometry, modular tessellations, axonometry, dihedral projections, conic perspective, technical normalization, scales, and CAD digital drafting. This multiple-choice study bank drills the core theoretical principles behind the practical written drawing exam.
Sample PAU Technical Drawing Applied to Plastic Arts (Cantabria) Practice Questions
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1In design composition and applied plane geometry, what is the exact mathematical definition of the Golden Ratio (proporción áurea, φ)?
A.The ratio φ = (1 + √5) / 2, approximately equal to 1.61803
B.The ratio φ = (1 + √3) / 2, approximately equal to 1.36602
C.The ratio φ = √2, approximately equal to 1.41421
D.The ratio φ = (3 + √5) / 2, approximately equal to 2.61803
Explanation: The Golden Ratio φ (phi) is defined as (1 + √5) / 2, which equals approximately 1.61803. In applied arts and design, it represents a harmonic division where the ratio of the whole line segment to the longer part equals the ratio of the longer part to the shorter part.
2Which geometric steps construct a Golden Rectangle starting from a square ABCD of side length s?
A.Draw both diagonals AC and BD, find their intersection O, and draw a circle centered at O passing through A
B.Bisect side AB at midpoint M, draw diagonal MC to corner C, and swing an arc of radius MC centered at M to extend side AB
C.Erect a 45° angle at corner A, extend side AB by length s, and connect to vertex C
D.Construct an equilateral triangle on side AB and project its apex vertically upward by distance s
Explanation: To construct a golden rectangle from a square ABCD, bisect side AB at midpoint M. The segment MC has length s·√(1 + 1/4) = s·√5/2. Swinging an arc of radius MC centered at M extends side AB to point E such that AE = s/2 + s·√5/2 = s·φ.
3Which set of regular polygons can form regular (monohedral) tessellations of the Euclidean plane without overlaps or gaps?
A.Equilateral triangles, regular pentagons, and regular octagons
B.Squares, regular pentagons, and regular decagons
C.Equilateral triangles, squares, and regular hexagons
D.Regular hexagons, regular heptagons, and regular octagons
Explanation: Only three regular polygons can form monohedral regular tessellations of the plane: equilateral triangles (interior angle 60°), squares (90°), and regular hexagons (120°). Their interior angles divide 360° evenly (6×60°, 4×90°, 3×120°).
4Why is it impossible to create a regular monohedral tessellation using only regular pentagons?
A.Regular pentagons do not possess line symmetry across their vertices
B.The perimeter of a regular pentagon cannot be divided into an even number of modular units
C.Regular pentagons have an odd number of sides, which prevents mirror symmetry in plane grids
D.The interior angle of a regular pentagon is 108°, and 360° is not divisible by 108°
Explanation: A regular pentagon has an interior angle of 108°. At any shared vertex in a plane tessellation, the sum of surrounding interior angles must equal 360°. Since 3×108° = 324° (leaving a 36° gap) and 4×108° = 432° (an overlap), pentagons cannot cover the plane regularly.
5In applied craft design and ceramic tile layout, what constitutes an orthogonal modular network (red modular ortogonal)?
A.A grid formed by two perpendicular families of parallel lines spaced at equal modular intervals
B.A network of concentric circles intersected by radial lines at 30° increments
C.A lattice formed exclusively by equilateral triangles meeting six per vertex
D.A freeform curvilinear grid composed of overlapping Archimedean spirals
Explanation: An orthogonal modular network is a square or rectangular grid constructed from two sets of parallel lines intersecting at right angles (90°) at uniform intervals. It serves as the structural foundation for tile patterns, brickwork, textiles, and modular furniture systems.
6What is the fundamental geometric condition for a straight line r to be tangent to a circle C with center O at point T?
A.Line r must bisect the angle between radius OT and the horizontal axis
B.Line r must be perpendicular to the radius OT at the point of tangency T
C.The distance from center O to line r must be equal to twice the radius OT
D.Line r must pass through center O and intersect circle C at two opposite points
Explanation: By definition, a line r is tangent to a circle C at point T if and only if line r is perpendicular (at 90°) to the radius OT drawn to the point of contact. This ensures line r touches the circle at exactly one point.
7How is the dynamic √2 rectangle constructed from a unit square, and what is its primary application in technical drawing?
A.Its longer side equals the height of an equilateral triangle on the square; it is used exclusively for golden spiral frames
B.Its short side is doubled while keeping the diagonal constant; it defines the module for 3D isometric cubes
C.Its longer side equals the diagonal of the unit square (1 : √2 ≈ 1 : 1.414); it is the basis for ISO 216 (DIN A) paper formats
D.Its area is exactly double that of the unit square; it defines the aspect ratio of widescreen CAD viewports
Explanation: A √2 dynamic rectangle has a width-to-height ratio of 1 : √2 (approx. 1 : 1.414). Laying the diagonal of a unit square (length √1² + 1² = √2) down as the longer side creates this rectangle. When folded in half parallel to its short side, the ratio remains 1 : √2, which forms the mathematical foundation of standard ISO 216 (DIN A0 to A4) paper sizes.
8A decorative brass motif with an area of 25 cm² undergoes a homothety (homotecia) with a scale factor k = -2. What are the area and orientation of the transformed motif?
A.Area = 50 cm²; the image maintains identical direct orientation
B.Area = 100 cm²; the image is mirrored across an axis of symmetry
C.Area = 25 cm²; the image is scaled linearly by -2 without changing surface area
D.Area = 100 cm²; the image is inverted (rotated 180°) relative to the original center
Explanation: Under a homothety with scale factor k, all linear dimensions are multiplied by |k|, and the surface area is multiplied by k² = (-2)² = 4. Thus, the new area is 25 × 4 = 100 cm². Because k is negative (k = -2), the image is located on the opposite side of the center of homothety and is inverted (equivalent to a 180° rotation).
9In planar affinity (afinidad), what geometric shape is formed when a circle of radius R undergoes an affinity transformation relative to an axis e?
A.An ellipse whose major or minor axis lies along or parallel to the axis of affinity
B.A hyperbola whose asymptotes intersect at the center of affinity
C.A parabola whose vertex lies on the axis of affinity e
D.A smaller circle whose radius is reduced by the affinity ratio k
Explanation: Planar affinity compresses or stretches geometry along a specified direction of affinity relative to an axis. Under affinity, parallel lines remain parallel, but angles and distances change non-uniformly, transforming a circle into an ellipse.
10In textile and surface design, what is a super-module (supermódulo)?
A.The single smallest indivisible geometric shape in a tessellation
B.A higher-order structural unit created by grouping and arranging several basic modules according to a compositional law
C.The outer framing border surrounding a complete decorative panel
D.A digital CAD block containing rendering shaders and lighting information
Explanation: A module (módulo) is the basic elemental unit in design. A super-module (supermódulo) is formed when several modules are grouped together (via rotation, reflection, or translation) to form a larger composite unit, which is then itself repeated across a network to create complex patterns.
About the PAU Technical Drawing Applied to Plastic Arts (Cantabria) Practice Questions
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