Catalonia PAU Technical Drawing (Dibuix Tècnic II) study plan

Construct perpendiculars, parallels, angle bisectors and segment divisions using compass and straightedge only, checking each construction against a stated geometric property.

Draw the three classical tangency problems (line-circle, circle-circle external and internal) and justify each tangency point by locating the centre on the bisector or radical-axis locus.

Produce an inscribed and a circumscribed regular polygon (pentagon, hexagon, octagon) in a given circle, verifying side lengths numerically.

Set up a clean A3 layout with title block, construction lines in 0.3 mm HB and final lines in 0.6 mm 2H, and label every auxiliary line.

Construct ellipses, parabolas and hyperbolas from focus-directrix definitions and from the two-focus sum/difference method, marking foci, axes and directrices.

Draw tangent and normal lines to each conic at a given point and from an external point.

Apply homothety, translation and rotation to a plane figure and state the invariant properties in one sentence per transformation.

Solve an inversion problem (point to point, line to circle through the inversion centre) and check that the product of distances equals the power of inversion.

Project points, lines and planes into the dihedral system across all four quadrants and identify true length, slope and bearing from the projections.

Determine the intersection point of a line with a plane and the intersection line of two planes, using auxiliary projecting planes.

Construct true shape of a plane figure by the change-of-plane method and by rotation about a trace.

Classify line-plane and plane-plane parallelism and perpendicularity conditions and apply them to two short problems.

Compute the intersection of a polyhedron (prism, pyramid) with an oblique plane and draw the true section.

Develop the lateral surface of a right prism and an oblique prism, checking that the developed edge lengths match true lengths from the projections.

Find the intersection curve of a cylinder and a cone with a plane, distinguishing ellipse, parabola and hyperbola sections.

Determine the piercing points of a line through a solid and mark visible versus hidden segments.

Draw the five Platonic solids in dihedral projection with correct hidden-line treatment and one section each.

Construct the development of a truncated cone and a truncated cylinder, computing the ellipse of the cut in true shape.

Solve two surface-intersection problems (cylinder-cylinder, cone-sphere) by the auxiliary-sphere or auxiliary-plane method.

State Euler's relation for each polyhedron drawn and verify vertex, edge and face counts.

Dimension a multi-view drawing to ISO/UNE conventions: no redundant dimensions, correct arrowheads, leaders, radii, diameters and symmetry notes.

Convert a set of views into a full and a half section, applying hatching at 45 degrees and omitting hidden lines in the sectioned view.

Apply scale factors (1:2, 2:1, 1:5) to the same object and recompute all dimension values so the drawing stays dimensionally true.

Audit a drawing for line-weight hierarchy, alignment and lettering, and correct at least five defects against a checklist.

Build isometric, dimetric and trimetric axonometries of the same simple solid and compare axis reduction coefficients.

Construct a cavalier and a cabinet oblique projection of a part with circular features, applying the correct reduction on the receding axis.

Draw a one- and a two-point perspective of a box-like volume using station point, horizon and vanishing points, and place a second volume correctly in depth.

Convert one axonometric view into an orthographic three-view set and check consistency of edges.

Produce a freehand sketch of a mechanical part within 10 minutes and then re-draw it instrumentally, comparing proportion errors.

Build a labelled diagram (flow or exploded view) that communicates an assembly sequence using only graphical conventions.

Complete a timed 3-hour mock paper covering plane geometry, dihedral geometry and normalisation, allocating time per section in advance.

Mark the mock against a rubric of accuracy, layout and line quality, and list the three weakest skills with a revision action for each.