PAU Technical Drawing II (Andalusia) study plan

Construct triangles from mixed data (two sides and an angle, two angles and the altitude to a side, side-sum or side-difference cases) using only compass and straightedge, and justify each step in writing.

Apply Thales' theorem and the altitude/leg theorems to solve right-triangle problems where only two magnitudes are known.

Divide a segment into n equal parts and into parts proportional to given ratios, then use the result to build a similar figure at a stated ratio of similarity.

Convert between graphic scale, numerical scale and real measurements, and compute the scale factor that maps one figure onto a similar one.

Sketch by hand, without instruments, the standard construction of a triangle given its three sides, keeping proportions within about 5% of the stated lengths.

Construct regular polygons with 3 to 12 sides inscribed in a given circle, distinguishing exact methods (square, hexagon, octagon, pentagon/decagon) from approximate ones (heptagon, nonagon, hendecagon).

Construct regular polygons from the side length rather than the circumradius, and state which method you used and why.

Solve quadrilateral constructions: square and rectangle from diagonal plus side, rhombus from diagonal and angle, trapezoid from bases plus height plus one angle.

Locate centres, apothems and the inradius/circumradius relationship for each polygon and use them to compute areas as a cross-check on your drawing.

Apply the general method for a regular polygon of n sides given the side, and verify the result by measuring the central angle.

Define the ellipse by both focus and directrix definitions and derive its elements (foci, major and minor axes, centre) from any two of them.

Construct an ellipse by concentric circles and by the trammel/parallelogram method, and compare the accuracy of the two against the exact locus.

Construct the tangent and normal at a point on an ellipse using the equal-angle property with the focal radii, and construct tangents from an external point.

Construct a parabola given focus and directrix, and draw the tangent at a point and the tangent parallel to a given direction.

Construct a hyperbola given foci and transverse axis, and identify its asymptotes and the tangent at a point on the branch.

Construct the common tangents to two circles (external and internal) and classify how many exist for each relative position of the circles.

Build a tangent link between a line and a circle, and between two circles, using an arc of given radius, and identify the locus of centres that makes the link possible.

Solve an ogee or S-curve link between two parallel lines or two circles with a specified radius, and check tangency by construction rather than by eye.

Find the points of tangency and the exact transition points on a composite curve, and mark them on the drawing.

Explain in writing why the locus of centres of circles of fixed radius tangent to a given circle is itself a circle, and use that locus as a construction tool.

Represent points in all four dihedral quadrants, and state the true position of a point from its two projections including the side-view convention.

Determine the true length and true angle of a line by the right-triangle/difference-of-coordinates method, and classify lines as horizontal, frontal, vertical or parallel to the profile plane.

Find the traces of a line and the intersection of a line with a plane, using the auxiliary-plane method, and check the result in a third view.

Construct a plane perpendicular to a line and a line perpendicular to a plane, applying the theorem of the right angle correctly.

Determine the true shape of a plane figure by change of projection plane or by rotation, and verify by measuring the sides.

Draw the three views of a regular polyhedron (tetrahedron, cube, octahedron) resting on a face and on an edge, keeping hidden edges dashed and consistent.

Section a polyhedron with a projecting plane and construct the true shape of the section by change of plane.

Construct the three views of a cylinder, cone and sphere, and locate the apparent contour in each view.

Section a cone with a plane in each of the five positions and identify which conic each section produces, linking back to domain 2.

Develop the lateral surface of a truncated cone and of a prism, and transfer the section points accurately onto the development.

Construct isometric, dimetric and trimetric axonometries of a simple solid from its three orthographic views, applying the correct coefficient of reduction.

Draw a cavalier and a cabinet perspective of the same solid and state the difference in the depth scale factor.

Construct an isometric ellipse (circle in a coordinate plane) by the four-centre method and by the ordinate method, and compare the error.

Place a section plane in an axonometric view and draw the cut solid without returning to orthographic views.

Choose the axonometric axis set that best shows a given solid and justify the choice in one or two sentences.

Dimension a multi-view drawing to UNE/ISO conventions: choice of datum, no redundant dimensions, correct arrowheads, leaders, radii, diameters and chamfers.

Apply the standard rules for section views (hatching, cutting-plane line, aligned sections) and correct a deliberately faulty drawing.

Produce a freehand sketch of a given solid within proportional tolerance, then reproduce it in CAD using layers, object snaps and a dimension style.

Assemble a timed mock exam: solve two full problems in 90 minutes under exam conditions and self-mark against a rubric of construction accuracy, line quality and notation.

Audit your error log from weeks 1–7 and re-solve the three constructions you got wrong most often.