PAU Technical Drawing II (Castilla y León) study plan

Construct triangles from mixed data (two sides and included angle, two angles and a side, two sides and the altitude to the third) using ruler-and-compass steps written out in order.

Apply the standard constructions for regular polygons of 3 to 12 sides inscribed in a given circle, and state which ones are exact and which are approximations.

Resolve at least four tangency problems between circles, lines and points by locating the centre as the intersection of two loci, and justify each locus in one sentence.

Draw the conic as a locus of points (constant sum of distances for the ellipse, constant difference for the hyperbola, equidistance from focus and directrix for the parabola) with at least 12 plotted points per curve.

Derive the elements of an ellipse (foci, major and minor axes, vertices) from the focal definition and construct the curve by the concentric-circles and the string/pins method.

Construct a parabola from focus and directrix and from a tangent at the vertex plus a point, and locate its axis, focus and directrix in both cases.

Construct a hyperbola from its foci and a vertex, and draw the asymptotes from the rectangle of the transverse and conjugate axes.

Draw the tangent and normal at a point on each of the three conics, and draw tangents from an external point to an ellipse.

Determine the true length and true angle of a segment from its dihedral projections by the difference-of-heights (right-triangle) method.

Find the trace points of a line and the traces of a plane given by two intersecting lines, and classify the plane (horizontal, frontal, profile, oblique) from its traces.

Solve intersection problems: line with plane, plane with plane, using auxiliary projecting planes, and identify visibility of the resulting segment.

Construct a perpendicular from a point to a plane and a plane perpendicular to a given plane through a given line, using the theorem of the right angle.

Project a prism, a pyramid, a cylinder and a cone in first-angle dihedral projection, given the position of the axis relative to the horizontal and vertical planes.

Obtain the section of each solid by an oblique plane using change of plane (auxiliary view) and draw the true shape of the section.

Determine which edges are hidden in each view and apply the correct line convention to them.

Develop the lateral surface of a truncated prism and a truncated cylinder by the triangulation and the normal-section methods.

Develop the lateral surface of an oblique cone and of a truncated pyramid by triangulation, marking the true lengths of all generators.

Build an isometric projection of a solid with circular features by drawing the isometric ellipses for the three coordinate planes and reducing the isometric scale correctly.

Produce a cavalier and a cabinet oblique projection of the same object, applying the correct coefficient on the receding axis in each case.

Construct a one-point and a two-point conical perspective of a simple box form with a given station point, horizon and picture plane, and locate the measuring points.

Dimension a multi-view drawing to UNE/ISO conventions: place dimensions outside the outline, avoid duplication, use diameter, radius, square and spherical symbols, and apply the correct arrowheads and gaps.

Compute and apply a stated scale (enlargement and reduction) including the graphical scale of a drawing, and convert measured lengths back to real dimensions.

Produce a full section and a half (broken-out) section of a part with a rib and a hole, applying the correct hatching angle, spacing and the rule for ribs and webs in longitudinal cut.

Annotate a threaded shaft and its mating nut: metric thread designation, major and minor diameters, thread run-out, and the simplified representation of the internal thread.

Apply geometric tolerancing frames (straightness, flatness, concentricity, position) with datum references and add surface-finish symbols with roughness values and machining notes.

Sketch freehand, in proportion, a standard hexagonal-head bolt, nut and washer assembly and a keyed shaft-and-hub joint, then check the proportions against the standard tables.

Interpret a supplied assembly drawing and list the parts, their standard designations and the fits shown (clearance, transition, interference) in a parts table.

Read a drawing cold: extract every dimension, tolerance and finish callout into a checklist and flag any missing or conflicting information.

Reproduce a given multi-view drawing in a CAD environment using layers for outlines, hidden lines, centre lines and dimensions, and export it to scale.

Solve one full past-paper-style problem from each of the four heaviest domains under exam timing (dihedral intersection, solid section with true shape, conic with tangents, polygon/tangency construction).

Self-mark each attempt against a written rubric covering construction accuracy, line conventions, dimensioning and completeness, and log every recurring error.

Redo, from scratch, the three constructions that produced the lowest rubric scores until each is completed without reference material.

Assemble a one-page formula and construction recall sheet (loci, conic relations, true-length method, section-by-auxiliary-view steps) for final review.