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100+ Free PAU Technical Drawing II (Aragón) Practice Questions
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2026 Statistics
Key Facts: PAU Technical Drawing II (Aragón) Exam
90 min
Exam Time Limit
UNIZAR / PAU Aragón
0–10
Grading Scale (Min 4.0 for Access Phase)
Gobierno de Aragón
EUR 75.00
Ordinary Registration Fee
UNIZAR PAU inscription page 2026
4 Core Blocks
Plane, Dihedral, Axonometric, ISO Standards
2nd Bachillerato Curriculum
The Technical Drawing II exam for the Aragón PAU (Prueba de Acceso a la Universidad) features a 90-minute university entrance test administered by UNIZAR / PAU Commission of Aragón. Graded on a 0–10 scale, a minimum mark of 4.0 is required in the Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU >= 5.0 to pass). The official exam consists of practical graphic drawing tasks; this dataset provides an English-language MCQ study adaptation designed for core concept practice, rule verification, and theoretical mastery.
Sample PAU Technical Drawing II (Aragón) Practice Questions
Try these sample questions to test your PAU Technical Drawing II (Aragón) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1What is the locus of the centers of all circles that are tangent to two given non-parallel lines?
A.The perpendicular bisector of the segment connecting their intersection point to infinity
B.The angle bisectors of the angles formed by the two lines
C.A circle concentric with the intersection point
D.A parabola whose focus is the intersection point
Explanation: The locus of points equidistant from two intersecting lines consists of the two perpendicular angle bisectors of the angles formed by those lines. Since any circle tangent to both lines must have its center at a point equidistant from both lines, the center must lie on an angle bisector.
2In plane geometry, what is the 'power' of a point P with respect to a circle of radius R and center O, where d is the distance PO?
A.Power = d / R
B.Power = d^2 + R^2
C.Power = d^2 - R^2
D.Power = (d - R)^2
Explanation: The power of a point P with respect to a circle O(R) is defined as K = d^2 - R^2, where d = PO. If P is outside the circle, K > 0 and equals the square of the length of the tangent segment from P to the circle.
3The radical axis of two non-concentric circles is defined as:
A.The line connecting the centers of the two circles
B.The locus of points having equal power with respect to both circles
C.The common tangent line passing through the midpoint between centers
D.The circle passing through the intersection points of both circles
Explanation: The radical axis (eje radical) of two non-concentric circles is the straight line containing all points that have equal power with respect to both circles. It is always perpendicular to the line of centers.
4Where is the radical center of three circles with non-collinear centers located?
A.At the circumcenter of the triangle formed by the three centers
B.Three circles with non-collinear centers do not have a radical center
C.At the centroid of the triangle formed by the three centers
D.At the intersection point of the three radical axes taken in pairs
Explanation: The radical center (centro radical) of three circles whose centers are not collinear is the unique point where the three pairwise radical axes intersect. This point has equal power with respect to all three circles.
5In plane inversion (inversión plana) with center O and positive ratio K (K > 0), what is the inverse of a straight line NOT passing through the center of inversion O?
A.A circle centered at O
B.A parabola with focus at O
C.A straight line parallel to the original line
D.A circle passing through the center of inversion O
Explanation: In plane inversion, a straight line that does not pass through the center of inversion O transforms into a circle that passes through O, with its diameter along the perpendicular line from O to the original line.
6What is the inverse of a circle that passes through the center of inversion O?
A.A circle not passing through O
B.A straight line not passing through O
C.A point at infinity only
D.An ellipse centered at O
Explanation: By the reciprocal property of geometric inversion, since a line not passing through O inverts into a circle through O, any circle passing through O inverts into a straight line not passing through O.
7Which transformation property is fundamental to plane inversion (inversión)?
A.It is conformal (preserves angles between curves)
B.It maps all straight lines to parallel straight lines
C.It preserves the area of all closed figures
D.It preserves distances between all pairs of points (isometry)
Explanation: Plane inversion is a conformal transformation (transformación conforme), meaning it preserves the magnitude of angles between intersecting curves, though it reverses their sense (orientation).
8In a homothety (homotecia) with center O and ratio k = -2, if segment AB has a length of 5 cm, what is the length and orientation of the transformed segment A'B'?
A.Length 2.5 cm, perpendicular to AB
B.Length 5 cm, rotated by 180 degrees
C.Length 10 cm, parallel to AB in the opposite direction
D.Length 10 cm, parallel to AB in the same direction
Explanation: In homothety, any segment AB transforms into a parallel segment A'B' whose length is |k| * |AB| = |-2| * 5 = 10 cm. Since k < 0 (negative ratio), A'B' is oriented in the opposite direction relative to center O.
9Homology (homología) in plane geometry is defined by which minimum set of independent elements?
A.Three non-collinear invariant points
B.Two parallel axes and a scale ratio
C.Center of homology and radius of inversion
D.Center of homology, axis of homology, and a pair of homologous points
Explanation: A central homology (homología plana) is uniquely determined by its center O, its axis e, and one pair of corresponding (homologous) points P and P' (or a vanishing line / dirección de rectas homólogas).
10In an affinity transformation (afinidad) in the plane, which property remains invariant?
A.Lengths of segments in all directions
B.Circle shapes (all circles remain circles)
C.Angles between lines
D.Parallelism between lines
Explanation: Affinity is an affine transformation. Key invariants include: straight lines remain straight lines, parallel lines remain parallel, and ratio of segments along parallel lines is preserved. Angles, lengths, and circle shapes are generally altered.
About the PAU Technical Drawing II (Aragón) Practice Questions
Verified exam format metadata for Aragón PAU Technical Drawing II (Dibujo Técnico II) Exam is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.