Canary Islands PAU Technical Drawing II study plan

Construct any triangle from three given data (SSS, SAS, ASA, two sides and an angle opposite) using compass and straightedge, and justify each step in writing.

Locate the circumcentre, incentre, orthocentre and centroid of a scalene triangle in one drawing and state which lines (perpendicular bisectors, angle bisectors, altitudes, medians) produce each.

Draw the nine-point circle and Euler line for the same triangle, verifying that the orthocentre, centroid and circumcentre are collinear.

Construct regular polygons with 5, 6, 8 and 10 sides by exact methods (general method of inscribed polygon plus the specific constructions for pentagon and hexagon).

Build quadrilaterals (square, rectangle, rhombus, trapezium) from given diagonals, sides and angles, and state the property that guarantees the construction is unique.

Construct the tangent lines to a circle from an external point and the common tangents (external and internal) to two circles of unequal radius.

Solve the three classic tangency problems (point-line-circle, line-line-circle, circle-circle-circle) using the auxiliary-circle or dilatation method, and name the method used in each case.

Apply the radical axis and homothety centre to locate tangent points quickly, and check results by measuring the tangent length with the Pythagoras relation.

Draw an ellipse by the concentric-circle method and by the trammel method given the major and minor axes, and mark both foci.

Construct the tangent at a point on an ellipse and the tangents from an external point using the focal property (equal angles with the focal radii).

Construct a parabola given its axis, vertex and a point, and draw the tangent at a point and the tangent parallel to a given direction using the directrix-focus definition.

Construct a hyperbola given its asymptotes and one point, and draw tangents at a point and from an external point.

Produce the tangent to a conic from a point on it by the focus-directrix or Dandelin reasoning, and explain in writing why the construction is valid.

Apply homothety to scale a given polygon about a centre with a stated ratio, including negative ratio, and verify that parallel lines stay parallel.

Perform a rotation and a translation on a composite figure and determine the isometry (or glide reflection) that maps one figure onto the other.

Determine the true length of a segment and its angles to the two projection planes using the difference-of-departure and difference-of-elevation construction.

Find the traces of a plane defined by three points or two intersecting lines, and decide whether a given point lies in that plane.

Construct the intersection point of a line with a plane, and the intersection line of two planes, in both cases using a projecting auxiliary plane.

Draw a perpendicular from a point to a plane and measure the true distance, using the right-angle-in-projection rule for lines parallel to a plane.

Test parallelism and perpendicularity between lines and planes by projection criteria and record the rule applied for each case.

Draw the complete dihedral representation of a regular hexagonal prism and a regular square pyramid given their base and height, including hidden edges.

Cut each solid with an oblique plane and construct the true shape of the section by change of plane or rabatment.

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

Construct the intersection curve of a cylinder with a plane and of a cone with a plane, identifying which conic each section produces.

Determine the true shape of a planar face of a polyhedron by rotation about a line of maximum slope.

Produce first-angle and third-angle multiview drawings of the same simple machined part and label the six principal views correctly in each system.

Place and label a cutting plane and produce a full section and a half section, applying the correct hatching conventions and omitting hidden lines in sectioned views.

Create an auxiliary view to show the true shape of an inclined face, choosing the correct auxiliary direction and projecting the feature's true size.

Dimension a part completely using ISO conventions: no redundant dimensions, correct arrowheads, leaders, radii, diameters, chamfers and tolerances, and no dimension crossing a dimension line.

Select the correct line type and thickness for visible, hidden, centre, symmetry, cutting-plane and dimension lines, and lay out a drawing sheet with title block, scale and format according to ISO A-series rules.

Build an isometric axonometric of a given part from its three orthographic views, using the isometric scale and the 30-degree axes correctly.

Construct a dimetric and a trimetric axes set from a stated set of angles or reduction coefficients, and explain why the isometric coefficients are equal.

Draw a cabinet and a cavalier oblique projection of the same object, applying the correct foreshortening (one half for cabinet) on the receding axis.

Place circles on the three isometric planes as ellipses using the four-centre approximate method and check the major-axis orientation on each face.

Add dimensions to an axonometric drawing using the aligned dimensioning method appropriate to axonometric views.

Complete three full past-paper-style mock exams under timing (one per session) covering plane geometry, tangencies, dihedral and axonometric content.

Score each mock against the official weighting per domain and list the three weakest sub-topics with the exact error made.

Re-drill the two weakest sub-topics with targeted constructions until each is completed without reference material.

Audit every drawing for standards compliance: line hierarchy, construction arcs, labels, scale and title block.

Assemble a one-page personal checklist of construction steps for the highest-frequency exam problems and rehearse it once under time pressure.