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100+ Free Castilla y León PAU Technical Drawing Applied to Plastic Arts and Design II Practice Questions
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Key Facts: Castilla y León PAU Technical Drawing Applied to Plastic Arts and Design II Exam
90 mins
Exam duration for the official Castilla y León PAU written paper
Junta de Castilla y León / USAL / UVA / UBU / ULE
0–10
Official scoring scale (minimum 4.0 required in Access Phase)
Comisión Organizadora PAU Castilla y León
EUR 91.54
Base registration fee for PAU Access Phase set by Junta de Castilla y León
Junta de Castilla y León PAU Fee Regulations
100 MCQs
English-language study adaptation question count in this bank
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Free 100-question study bank in English for the Castilla y León PAU Technical Drawing Applied to Plastic Arts and Design II exam. Note: local questions are an English-language MCQ study adaptation for the official 90-minute practical drafting examination.
Sample Castilla y León PAU Technical Drawing Applied to Plastic Arts and Design II Practice Questions
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1In plane geometry applied to technical drawing, what is the fundamental relationship between a circle's radius and a tangent line at the exact point of tangency?
A.The radius drawn to the point of tangency is strictly perpendicular (forms a 90-degree angle) to the tangent line.
B.The radius drawn to the point of tangency forms a 45-degree angle with the tangent line.
C.The tangent line intersects the radius at two distinct points separated by half the radius length.
D.The distance from the circle center to the tangent line is strictly greater than the radius length.
Explanation: A tangent line touches a circle at exactly one point. The radius drawn from the center of the circle to this point of contact is strictly perpendicular (at a right angle of 90 degrees) to the tangent line. This fundamental geometric principle is essential for resolving tangency problems and smooth curved connections in artistic design.
2In a planar homothety geometric transformation centered at point O with a scaling ratio of k = -2, how are the original figure and its image related?
A.The image is scaled to twice the linear dimensions of the original, inverted relative to center O, and corresponding sides remain parallel.
B.The image is reduced to half the original linear size and stays on the same side of center O as the original object.
C.The image is rotated 90 degrees around center O without any change in linear dimensions or orientation.
D.The image undergoes an oblique shear distortion into a non-similar parallelogram.
Explanation: A homothety (central similarity) maps points along rays passing through center O. When the scaling factor k is negative (k = -2), the image points lie on rays pointing in the opposite direction from O, producing an inverted figure whose linear dimensions are scaled by |k| = 2. Corresponding line segments remain strictly parallel.
3What is the defining geometric locus definition of an ellipse in plane geometry?
A.The set of all points in a plane where the sum of the distances to two fixed points (foci F1 and F2) is constant and equal to the major axis length 2a.
B.The set of all points in a plane equidistant from a fixed point (focus) and a fixed straight line (directrix).
C.The set of all points in a plane where the absolute difference of the distances to two fixed points is constant.
D.The set of all points in a plane whose product of distances to two perpendicular lines is constant.
Explanation: An ellipse is defined as the locus of points for which the sum of the distances to two fixed focus points (F1 and F2) remains constant. By convention, this constant sum equals the length of the major axis, 2a (where PF1 + PF2 = 2a).
4Which conic section is geometrically defined as the locus of all points in a plane that are equidistant from a fixed point (focus F) and a fixed line (directrix d)?
A.Parabola
B.Ellipse
C.Hyperbola
D.Circle
Explanation: A parabola is the conic section formed by the set of all points in a plane that are equidistant from a single focus point F and a directrix line d. Its eccentricity e is exactly equal to 1.
5In the locus definition of a hyperbola, what is the geometric relationship involving any point P on the curve and its two foci F1 and F2?
A.The absolute difference of the distances |PF1 - PF2| is constant and equal to the real axis length 2a.
B.The sum of the distances PF1 + PF2 is constant and equal to the transverse axis 2a.
C.The ratio of the distance PF1 to PF2 is constantly equal to 0.5.
D.The product of distances PF1 * PF2 is constant and equal to the semi-major axis squared.
Explanation: A hyperbola consists of two open branches defined by the locus of points where the absolute difference between the distances to the two foci, |PF1 - PF2|, remains constant and equals 2a, the distance between the two vertices along the real axis.
6In planar geometric inversion (inversión) centered at point O with power K > 0, if point P maps to point P', what algebraic and directional conditions must P and P' satisfy?
A.Points O, P, and P' are collinear on the same ray from O, and the product of distances satisfies OP * OP' = K.
B.Points P and P' lie on a circle centered at O, with OP + OP' = K.
C.Segment PP' is perpendicular to ray OP, with the distance PP' = sqrt(K).
D.Points P and P' are reflected across a fixed axis line with OP - OP' = K.
Explanation: Inversion in a plane relative to a center O and power K > 0 transforms point P into point P' such that O, P, and P' lie on the same line (collinear) and the product of their distances from O equals the power of inversion: OP * OP' = K. If P lies inside the inversion circle of radius r = sqrt(K), P' lies outside it.
7To construct the two lines passing through an exterior point P that are tangent to a given circle with center O, which auxiliary geometric construction is used to locate the exact points of tangency?
A.Draw an auxiliary Thales circle using segment OP as diameter; its intersections with the given circle mark the tangency points.
B.Draw a concentric circle with twice the radius of the given circle.
C.Erect a perpendicular bisector to segment OP and intersect it with the given circle.
D.Draw an equilateral triangle with base OP to locate the points of tangency.
Explanation: By Thales' theorem, any angle inscribed in a semicircle is a right angle (90°). Drawing a circle whose diameter is segment OP creates right angles at the points where this auxiliary circle intersects the original circle. These intersection points are the precise points of tangency T1 and T2.
8What is the condition for two circles with centers O1 and O2 and radii r1 and r2 to be externally tangent (tangentes exteriores)?
A.The distance between centers O1O2 is equal to the sum of radii, O1O2 = r1 + r2.
B.The distance between centers O1O2 is equal to the absolute difference of radii, O1O2 = |r1 - r2|.
C.The distance between centers O1O2 is strictly greater than r1 + r2.
D.The distance between centers O1O2 is zero.
Explanation: Two circles are externally tangent when they touch at a single point located on the segment connecting their centers. The distance between centers O1O2 exactly equals the sum of their radii (r1 + r2).
9What is the distance between centers O1 and O2 for two circles with radii r1 = 8 cm and r2 = 3 cm to be internally tangent (tangentes interiores)?
A.5 cm
B.11 cm
C.14 cm
D.24 cm
Explanation: For internal tangency, one circle lies inside the other, touching at one point. The center distance O1O2 equals the difference between their radii: O1O2 = |r1 - r2| = 8 cm - 3 cm = 5 cm.
10Which of the following geometric properties is preserved in a planar affinity (afinidad) transformation?
A.Parallelism between corresponding line segments.
B.Exact side lengths and segment distances.
C.Interior angles between non-parallel lines.
D.Circle shapes (all circles remain un-distorted circles).
Explanation: Planar affinity is an affine geometric transformation. It preserves parallelism (parallel lines map to parallel lines) and ratios of distances along parallel lines, but it distorts angles, lengths, and can transform circles into ellipses.
About the Castilla y León PAU Technical Drawing Applied to Plastic Arts and Design II Practice Questions
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