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Exam Review

Key Facts: La Rioja PAU Technical Drawing II Exam

90 Minutes

Exam duration

Universidad de La Rioja PAU Commission

EUR 55.43

Base registration fee

Universidad de La Rioja 2026 Fees

0–10 Scale

Grading scale (minimum 4.0 required)

Spanish Ministry of Education

4 Core Blocks

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

UR Syllabus

100 Questions

Practice bank question count

OpenExamPrep

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

Sample La Rioja PAU Technical Drawing II Practice Questions

Try these sample questions to review concepts for the La Rioja 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 sum is (6 - 2) × 180° = 720°. Dividing 720° by 6 equal angles yields 120° for each 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 is related to its altitude h by r = h / 3. Since h = (s√3) / 2, we have r = (s√3) / 6, which rearranges to s = 6r / √3 = 2r√3.
3Which algebraic expression defines the exact numerical value of the Golden Ratio (Phi, Φ)?
A.Φ = (1 + √3) / 2 ≈ 1.366
B.Φ = (1 + √5) / 2 ≈ 1.618
C.Φ = (1 + √2) / 2 ≈ 1.207
D.Φ = (2 + √5) / 2 ≈ 2.118
Explanation: The Golden Ratio Φ is derived from dividing a segment into extreme and mean ratio (x² - x - 1 = 0), yielding the positive root Φ = (1 + √5) / 2 ≈ 1.6180339...
4A point P is located at a distance d = 10 cm from the center O of a circle with radius R = 6 cm. What is the power of point P with respect to this circle?
A.16 cm²
B.64 cm²
C.36 cm²
D.100 cm²
Explanation: The power of a point P with respect to a circle centered at O with radius R is defined as Power(P) = d² - R², where d is the distance PO. Here, Power(P) = 10² - 6² = 100 - 36 = 64 cm².
5What geometric locus is defined as the set of all points in a plane that have equal power with respect to two non-concentric circles?
A.The radical center
B.The radical axis
C.The polar line
D.The axis of homothety
Explanation: The radical axis (eje radical) is the straight line perpendicular to the line connecting the centers of two non-concentric circles, comprising all points with equal power to both circles.
6Given three circles with non-collinear centers, how is their radical center constructed?
A.As the centroid of the triangle formed by the three circle centers
B.As the point of intersection of the three pairwise radical axes
C.As the circumcenter of the triangle formed by the three circle centers
D.As the center of the circle tangent to all three given circles
Explanation: The radical center (centro radical) of three circles is the unique point where their three pairwise radical axes intersect, possessing equal power with respect to all three circles.
7In Apollonius tangency problems, what does the PPP case represent, and how many solutions exist for three non-collinear points?
A.Circle passing through 3 points; exactly 1 solution (circumcircle)
B.Circle tangent to 3 lines; exactly 4 solutions (incircle and 3 excircles)
C.Circle tangent to 3 circles; up to 8 solutions
D.Circle passing through 3 points; exactly 2 solutions
Explanation: The PPP case requires constructing a circle passing through three given non-collinear points. This is the unique circumcircle of the triangle formed by the three points, giving exactly 1 solution.
8In a plane inversion with center O and positive power K, what is the inverse image of a circle passing through the center of inversion O?
A.A circle passing through the center of inversion O
B.A straight line not passing through the center of inversion O
C.A point at infinity
D.A circle concentric with the inversion circle
Explanation: Under plane inversion centered at O, any circle that passes through O is transformed into a straight line that does not pass through O (and is parallel to the tangent of the circle at O).
9In a plane inversion with center O and positive inversion power K > 0, which geometric figure consists entirely of invariant points (points that invert to themselves)?
A.The center of inversion point O
B.The circle of inversion (círculo de inversión) centered at O with radius R = √K
C.Any line passing through O
D.The radical axis of any two inverse circles
Explanation: The circle of inversion centered at O with radius R = √K has power OP × OP' = R² = K. For any point P on this circle, OP = R, so OP' = R and P' = P, making every point on the circle invariant.
10In a plane homothety centered at O with a negative scale factor k = -0.5, where does the image of a point P lie relative to O?
A.On the ray OP at half the distance from O
B.On the opposite ray from O (180° turned) at half the distance from O
C.Perpendicular to ray OP at distance 0.5 OP
D.At twice the distance from O on the ray OP
Explanation: Homothety vectors satisfy OP' = k · OP. When k is negative (k = -0.5), the image point P' lies on the line OP but on the opposite side of O from P, with distance OP' = |k| · OP = 0.5 OP.

About the La Rioja PAU Technical Drawing II Exam

The La Rioja PAU Technical Drawing II examination (Pruebas de Acceso a la Universidad, UR 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: Universidad de La Rioja (UR) / Comisión Organizadora de la PAU de La Rioja. 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 La Rioja 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 55.43 base registration fee (Comisión Organizadora de la PAU de La Rioja 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 (acotación), fits, tolerances, and CAD principles.

Preparing for the La Rioja 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 La Rioja PAU paper, requiring separate practice for ruler and compass graphical drafting tasks.
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 55.43 base registration fee (Comisión Organizadora de la PAU de La Rioja 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

La Rioja PAU Technical Drawing II: Suggested Study Strategy

1Master Monge dihedral system projections: finding plane traces (α₁, α₂), line-plane intersections, line true lengths via right-angled triangles or auxiliary plane changes, and plane abatment (abatimiento).
2Understand conic section geometry: focus-directrix properties, focal distances (2a, 2b, 2c where a² = b² + c² for ellipse and c² = a² + b² for hyperbola), and principal circle tangent constructions.
3Know axonometric projection principles: isometric reduction factor √2/3 ≈ 0.816, cabinet vs Cavalier reduction factors, and conic perspective horizon/vanishing line relationships.
4Review ISO/UNE dimensioning standards: datum selection, functional vs non-functional dimensioning, standard line weights, section view rules (omitting section lines on ribs and shafts), and fit tolerance symbols.

Frequently Asked Questions

Are these official La Rioja PAU Technical Drawing II questions?

Local practice items are an English-language MCQ study adaptation of the official open/graphical La Rioja PAU paper, designed to test concept mastery and calculation accuracy alongside standard drawing practice.

What is the official format of the La Rioja PAU Technical Drawing II exam?

The official exam administered by Universidad de La Rioja is a 90-minute paper containing graphical geometric construction problems, dihedral projections, perspective drawings, and ISO dimensioning tasks.