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Key Facts: Balearic PAU Technical Drawing II Exam

90 Minutes

Exam time duration

UIB PAU Commission

EUR 69.21

Ordinary registration fee for Access Phase

UIB 2026 Fees

0–10 Scale

Grading scale for Bachillerato and PAU exams

Spanish Ministry of Education

4 Core Blocks

Plane Geometry, Dihedral System, Axonometry/Perspective, and Technical Standardization

UIB Syllabus

100 Questions

Practice bank size in OpenExamPrep

OpenExamPrep

Balearic Islands PAU Technical Drawing II (UIB 2026) is a 90-minute university entrance exam assessing 2º Bachillerato Technical Drawing II across plane geometry, dihedral system, axonometry, and ISO standardization.

Sample Balearic PAU Technical Drawing II Practice Questions

Try these sample questions to review concepts for the Balearic 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.

1What is the measure of each interior angle in a regular convex hexagon?
A.108°
B.120°
C.135°
D.140°
Explanation: The sum of interior angles of an n-sided convex polygon is given by (n - 2) × 180°. For a hexagon (n = 6), the total sum is (6 - 2) × 180° = 720°. Dividing by 6 equal interior angles yields 720° / 6 = 120° per interior angle.
2In an equilateral triangle circumscribed about a circle of radius r, what is the side length s of the triangle in terms of r?
A.s = r√3
B.s = 2r√3
C.s = 3r
D.s = 2r
Explanation: The inradius r of an equilateral triangle with side s is related to its altitude h by r = h/3, where h = (s√3)/2. Substituting h gives r = (s√3)/6, which rearranges to s = 6r/√3 = 2r√3.
3How many non-isomorphic star octagons (represented by Schläfli symbols {8/k}) can be constructed from eight equally spaced points on a circle?
A.1
B.2
C.3
D.4
Explanation: A star polygon {n/k} requires k to be coprime to n and 1 < k < n/2. For n = 8, the integers strictly between 1 and 4 are 2 and 3. The integer 2 shares a common factor with 8 (gcd(8,2)=2, forming two overlapping squares), while 3 is coprime to 8 (gcd(8,3)=1). Thus, only k = 3 forms a single regular star octagon {8/3}.
4Which of the following regular n-sided polygons CANNOT be constructed using only a straightedge and compass according to the Gauss-Wantzel theorem?
A.15-gon (Pentadecagon)
B.17-gon (Heptadecagon)
C.9-gon (Enneagon / Nonagon)
D.20-gon (Icosagon)
Explanation: According to the Gauss-Wantzel theorem, a regular n-gon is constructible with straightedge and compass if and only if the odd prime factors of n are distinct Fermat primes (3, 5, 17, 257, 65537). For n = 9, the prime factorization is 3², which contains a repeated odd prime factor (3²), making the regular 9-gon non-constructible.
5What is the exact algebraic value of the golden ratio φ (phi)?
A.(1 + √3) / 2
B.(1 + √5) / 2
C.(1 + √5) / 3
D.(1 + √2) / 2
Explanation: The golden ratio φ is defined by the proportion (a+b)/a = a/b = φ, which yields the quadratic equation φ² - φ - 1 = 0. Solving this equation via the quadratic formula gives the positive root φ = (1 + √5) / 2 ≈ 1.618033...
6What are the interior angle measures of a golden isosceles triangle (an isosceles triangle whose sides are in the golden ratio φ : 1 : φ)?
A.36°, 72°, 72°
B.45°, 45°, 90°
C.30°, 75°, 75°
D.54°, 54°, 72°
Explanation: A golden triangle is an isosceles triangle where the ratio of a leg to the base is φ. Bisecting a base angle creates a smaller similar golden triangle, implying the base angles are double the vertex angle (2θ + 2θ + θ = 180° => 5θ = 180° => θ = 36°). Thus, the angle measures are 36°, 72°, and 72°.
7Given a segment AB of length L, which geometric construction correctly locates the golden section point C on AB such that AC / CB = φ?
A.Erect a perpendicular BD of length L/2 at B, draw hypotenuse AD, draw an arc from D with radius DB intersecting AD at E, then draw an arc from A with radius AE to cut AB at C.
B.Erect a perpendicular BD of length L at B, bisect hypotenuse AD at M, then draw an arc from A with radius AM to cut AB at C.
C.Construct an equilateral triangle ABD on AB, bisect side BD at M, then drop a perpendicular from M to cut AB at C.
D.Draw a semicircle on diameter AB, erect a perpendicular at mid-point O of length L/2 to intersect the arc at P, then drop P onto AB.
Explanation: In right triangle ABD with legs AB = L and BD = L/2, hypotenuse AD = √(L² + (L/2)²) = (L√5)/2. Subtracting DE = BD = L/2 gives AE = (L√5)/2 - L/2 = L(√5 - 1)/2. Transferring AE onto AB yields AC = L(√5 - 1)/2, which divides AB in the golden ratio because AC / CB = φ.
8What is the angle between a circle's radius and a line tangent to the circle at the point of contact?
A.45°
B.60°
C.90°
D.180°
Explanation: By fundamental circle geometry, a line is tangent to a circle if and only if it is perpendicular (90°) to the radius drawn to the point of tangency.
9Two circles with radii R1 = 9 cm and R2 = 4 cm are externally tangent to each other. What is the length of their common external tangent segment between the points of contact?
A.12 cm
B.13 cm
C.10 cm
D.6 cm
Explanation: The length t of the common external tangent segment between two externally tangent circles with radii R1 and R2 is given by t = 2√(R1 × R2). Substituting R1 = 9 and R2 = 4 yields t = 2√(9 × 4) = 2√(36) = 2 × 6 = 12 cm.
10In the classical Apollonius problem of finding circles tangent to three given geometric entities, how many solutions generally exist for the Case PPP (three non-collinear points)?
A.1 solution
B.2 solutions
C.4 solutions
D.8 solutions
Explanation: A circle passing through three non-collinear points (PPP) is uniquely defined as the circumcircle of the triangle formed by those three points. Its center is the unique circumcenter (intersection of the perpendicular bisectors), giving exactly 1 solution.

About the Balearic PAU Technical Drawing II Exam

The Balearic Islands PAU Technical Drawing II examination (Proves d'Accés a la Universitat, UIB 2026) evaluates 2º Bachillerato students on plane geometry (tangencies, conics), Monge dihedral system (intersections, true lengths, abatments, polyhedra), isometric/conic perspective, and ISO technical dimensioning standards. This practice bank provides 100 high-quality questions with detailed explanations for all options.

Exam sponsor: PAU Organising Commission of the Balearic Islands / UIB. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written and graphic 90-minute standardized exam evaluating Plane Geometry, Descriptive Dihedral Geometry, Axonometry, and Technical Standardization. Local practice items are an English-language MCQ study adaptation of the official open/graphical Balearic Islands PAU paper, requiring separate practice for ruler and compass graphical drafting tasks.

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 69.21 ordinary registration fee (Access Phase); EUR 13.85 per additional Admission Phase subject paper (UIB 2026)

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.

25%

Plane Geometry & Technical Curves

Polygons, golden ratio, tangency theorems, Apollonius problems, homothety, homology, affinity, and conic sections (ellipse, parabola, hyperbola).

30%

Descriptive Dihedral Geometry

Monge dihedral system, projections of points/lines/planes, intersections, true length/shape, abatment, plane changes, distance calculations, and polyhedra.

25%

Axonometric & Perspective Projections

Isometric axonometry (scale factor 0.816 vs 1:1), Cavalier oblique perspective, and conic perspective (vanishing points, horizon line, measuring points).

20%

Technical Standardization & CAD

ISO/UNE drawing standards, line types, first-angle vs third-angle projection, sections/cuts, dimensioning rules (acotació), fits, tolerances, and CAD principles.

Preparing for the Balearic 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: Written and graphic 90-minute standardized exam evaluating Plane Geometry, Descriptive Dihedral Geometry, Axonometry, and Technical Standardization. Local practice items are an English-language MCQ study adaptation of the official open/graphical Balearic Islands PAU paper, requiring separate practice for ruler and compass graphical drafting tasks.
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 69.21 ordinary registration fee (Access Phase); EUR 13.85 per additional Admission Phase subject paper (UIB 2026) 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

Balearic PAU Technical Drawing II: Suggested Study Strategy

1Master dihedral system projections: trace lines, plane traces (alpha1, alpha2), line-plane intersections, and finding true length using auxiliary plane changes or abatment (abatiment).
2Understand conic sections: focal definitions of ellipse (PF1 + PF2 = 2a), parabola (PF = PD), hyperbola (|PF1 - PF2| = 2a), and tangent construction techniques.
3Know isometric projection scale rules: isometric reduction factor is sqrt(2/3) ~ 0.816, used when drawing real scale vs 1:1 isometric drawings.
4Review ISO dimensioning standards: datum lines, continuous vs chain dimensioning, sectioning rules (hatching at 45 degrees, omitting rib/shaft sectioning).

Frequently Asked Questions

Are these official Balearic Islands PAU Technical Drawing II questions?

Local practice items are an English-language MCQ study adaptation of the official open/graphical Balearic Islands PAU paper, not an official translation or format simulation. Graphical drawing tasks require hands-on practice.

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

The official PAU Technical Drawing II exam administered by UIB is a 90-minute paper featuring graphical geometric constructions, dihedral system problem solving, and technical standardization exercises.