Andalusia PAU Technical Drawing Applied to Plastic Arts and Design II common mistakes
Andalusia PAU Technical Drawing Applied to Plastic Arts and Design II · Understand the traps and how to avoid them.
When a problem asks for a segment proportional to three given segments (fourth proportional) or to two given segments (third proportional), the candidate sets the compass opening on the wrong leg of the similarity construction, so the resulting segment is the reciprocal of the required one - e.g. giving a·b/c instead of a·c/b.
The similarity construction is memorized as a picture (two rays from a vertex, marks transferred by parallels) without tracking which given segment sits on which ray. Because the figure looks symmetric, the student cannot tell which ray must carry the product terms and which carries the divisor, and there is no habit of checking the answer numerically against a chosen example.
What to do instead
Before drawing, write the required relation as a proportion with named letters (e.g. a/b = x/c, so x = a·c/b) and note which segment is the 'unit' term on the auxiliary ray. After constructing, verify with two convenient numeric values (say 2, 3, 4 cm) that the measured result matches the formula; if it is inverted, swap the divisor segment to the other ray. Practise both fourth and third proportional in the same session so the difference in the proportion, not the picture, drives the construction.
In a homothety or similarity-transformation problem, the candidate places the centre correctly but uses the ratio inverted (scale factor k instead of 1/k), or applies the ratio to the wrong side of the centre, producing a figure on the wrong side or of the wrong size.
Students copy the ratio as written in the statement without deciding whether it describes image/original or original/image, and they do not distinguish positive ratio (same side of centre) from negative ratio (opposite side). The construction procedure is followed mechanically, so the error only surfaces at the end when the figure does not fit the paper.
What to do instead
At the start, write 'k = image/original' explicitly and mark on the sketch which vertex is original and which is image. Decide the sign from the statement ('on the same side' = positive, 'opposite side' = negative) and check one vertex by measuring distances from the centre: the ratio of the two distances must equal |k|. Verify at the end that all corresponding sides are parallel and in the ratio k.
When drawing a tangent line or circle to a given circle from an external point, or a common tangent to two circles, the candidate draws the radical-axis/auxiliary-circle construction but marks the tangent points on the auxiliary circle instead of transferring them back to the given circle, so the tangency is approximate and visibly off.
The auxiliary circle (diameter = distance from point to centre, or the circle with diameter equal to the difference/sum of radii for internal/external tangents) is a means, not the answer, but students lose track of the role of each circle in a multi-step construction and stop one step early. Without a final perpendicularity check, the small angular error is invisible at a glance.
What to do instead
Label each circle in the construction (given, auxiliary, auxiliary-of-sum/difference) and write the sequence of steps before drawing. After locating the tangent point on the auxiliary circle, always transfer it by drawing the radius of the given circle through that point - the tangent point lies where that radius meets the given circle. Finish by checking that the radius to the tangent point is perpendicular to the tangent line, using a set square.
In an external tangency problem (circle tangent to a line and to a given circle, or tangent to two lines and a circle), the candidate forgets to offset the given circle's radius, so the constructed centre lies on the wrong locus and the resulting circle is not tangent - it either overlaps or misses the given circle.
The method of loci is understood as 'intersection of two loci', but the student does not appreciate that tangency to a circle is equivalent to the centre lying on a circle concentric with the given one whose radius is r ± R. The +R/−R choice for external versus internal tangency is the step most often omitted.
What to do instead
For every tangency problem, first list the locus for each condition in words: distance from a line = r (a parallel line), distance from a point = r (a circle), distance from a given circle externally = r + R, internally = |r − R|. Draw all loci with their offsets marked, then intersect. After drawing the solution, measure the centre-to-centre distance and confirm it equals r + R or |r − R| exactly.
When constructing an ellipse, parabola or hyperbola from its focus-directrix definition or from conjugate diameters, the candidate uses the major axis length where the focal distance is required (or vice versa), producing a curve that is too flat or too pointed; in the parabola the directrix is placed at the wrong distance from the focus.
The definitions are recalled as formulas (PF + PF' = 2a, PF = distance to directrix) but the student does not connect each symbol to the actual segment in the drawing. Because several lengths (a, b, c, focal distance, directrix distance) appear in the statement, the mapping from symbol to segment is done hastily and never re-checked.
What to do instead
Before drawing, write the definition with the actual numbers substituted and annotate the drawing: mark a, b, c on the axes and verify c² = a² − b² (ellipse) or c² = a² + b² (hyperbola). For the parabola, fix the focus–directrix distance first and mark the vertex at its midpoint. After completing the curve, test one constructed point by measuring both distances (to focus and to directrix, or to both foci) and confirm they agree.
In the dihedral system, the candidate determines the visibility of a line or plane correctly in plan but not in elevation (or vice versa), or reports the true intersection point of a line and a plane at the point where the projections cross rather than where the line actually pierces the plane.
The apparent crossing of two projections is visually compelling, and students treat the drawing as a picture rather than as two related projections. Visibility rules (the projection with greater height/depth wins) are known in principle but not applied systematically, so the answer is decided by eye.
What to do instead
For intersection, always use an auxiliary plane containing the line, find its intersection line with the given plane, and intersect that line with the given line; then transfer the point to the other projection with a vertical reference line. For visibility, apply a fixed rule each time (e.g. compare the depth of the two elements at the apparent crossing in plan to decide the elevation) and state the rule in writing next to the drawing before marking solid/dashed lines.
When asked for the true magnitude of a segment or the true shape of a plane figure, the candidate measures the projection directly, or performs the change of plane but keeps the reference line at the wrong distance, so the true length or true shape is not obtained.
True magnitude requires a change of plane parallel to the element (or a rotation), and the student confuses 'parallel to the new reference line' with 'parallel to the projection'. The invariance of the distance to the reference line is a subtle rule that is dropped under time pressure, and there is no final check because the student trusts the measurement.
What to do instead
Use a fixed routine: (1) draw the new reference line parallel to the projection that already shows the element's direction; (2) transfer each point's distance from the old reference line to the new one, measured perpendicular to the new line; (3) the resulting projection is the true length. For true shape of a plane, change plane until the plane projects as a line, then change again parallel to that line. Verify by checking that the true length is always greater than or equal to any projection.
In polyhedra and solids of revolution, the candidate draws the outline of the solid but omits or misplaces the hidden edges and the tangent generatrices, so a cone or cylinder is drawn with a sharp corner at the silhouette, or a polyhedron's hidden edges are drawn solid.
The silhouette of a curved surface is the locus of tangency points of the generatrices with the outline, which is a concept, not a memorized shape; students draw the base ellipse and join it with straight lines to the apex, which is only correct for a cone seen in a special position. Hidden-line conventions are treated as decoration.
What to do instead
For each solid, identify the contour generatrices explicitly: for a cone, the two generatrices whose projections are tangent to the base ellipse in the view; for a cylinder, the same; for a sphere, the great circle perpendicular to the viewing direction. Draw those tangencies first, then the base. Apply a consistent hidden-line rule (dashed only for edges not visible in that view) and audit each edge against it before finishing.
In axonometric and cavalier perspective, the candidate applies the reduction coefficients incorrectly - using the same scale on all three axonometric axes, or measuring the cavalier depth at full scale along a 45° axis without applying the conventional 1/2 reduction - and does not relate the axonometric axes to the coordinate axes of the object.
The coefficients are memorized as numbers without the underlying idea that axonometric projection is an orthogonal projection onto an inclined plane, so lengths along the axes are foreshortened by different amounts. In cavalier perspective, the 'half scale on the depth axis' is a convention that is easily forgotten because the drawing still looks plausible without it.
What to do instead
Write the axis trihedron first, with the angles between axes fixed by the chosen axonometric system, and mark the coefficient on each axis before drawing any edge. For isometric, use equal coefficients; for dimetric/trimetric, use the stated values. For cavalier, always halve measurements along the receding axis and keep the frontal face true. Check the result by confirming that parallel edges remain parallel and that the three axis directions are consistent throughout.
On a dimensioned drawing or a scale problem, the candidate measures the drawing with a ruler and reports the measured length as the real dimension, or converts a scale incorrectly (e.g. treating 1:50 as 'multiply by 50' when the drawing is already at a different scale, or mixing units between mm and cm).
The habit of measuring from the sheet is carried over from geometry exercises, but in standardized drawing the dimension figures are authoritative and the drawing may not be to scale. Scale conversion errors come from treating the ratio as an operation to be guessed rather than as drawing/real = 1/n, and from unit slips between millimetres and centimetres.
What to do instead
Adopt the rule: never scale off a drawing; read the dimension figures, and use the stated scale only when the problem explicitly gives a drawn length without a dimension. Write the ratio as drawing/real = 1/n and solve for the unknown algebraically, converting all lengths to millimetres first. When dimensioning, follow the norm: dimension lines outside the figure where possible, no repeated dimensions, and arrowheads and figures of uniform size.