Certificate of Secondary Education (CSE) Technical Drawing Syllabus

Define acute, obtuse, and reflex angles by their size ranges.

An acute angle is less than $90^{\circ}$; an obtuse angle is between $90^{\circ}$ and $180^{\circ}$; a reflex angle is between $180^{\circ}$ and $360^{\circ}$.

What are complementary and supplementary angles?

Complementary angles add up to $90^{\circ}$; supplementary angles add up to $180^{\circ}$.

Classify triangles by their sides.

Equilateral (all three sides equal, all angles $60^{\circ}$), isosceles (two sides equal, two equal base angles), and scalene (all three sides and angles different).

State the angle sum of a triangle and use it to find the third angle of a triangle with angles $50^{\circ}$ and $70^{\circ}$.

The interior angles of a triangle sum to $180^{\circ}$, so the third angle is $180^{\circ} - 50^{\circ} - 70^{\circ} = 60^{\circ}$.

How do you construct a perpendicular bisector of a line segment with compasses?

Set the compasses to more than half the line length, draw arcs above and below the line from each endpoint, and join the two points where the arcs intersect; this line bisects the segment at $90^{\circ}$.

How is an angle bisected using compasses?

With the compass point at the vertex, draw an arc cutting both arms. From each of those two intersection points draw equal arcs that cross, then draw a line from the vertex through the crossing point to bisect the angle.

What is a regular polygon?

A regular polygon is a closed plane figure with all sides equal in length and all interior angles equal.

Give the names of polygons with 5, 6, 7, and 8 sides.

5 sides = pentagon, 6 sides = hexagon, 7 sides = heptagon, 8 sides = octagon.

State the formula for the sum of the interior angles of a polygon with $n$ sides, and the value of one interior angle of a regular hexagon.

Sum of interior angles $= (n-2) \times 180^{\circ}$. For a regular hexagon: $\frac{(6-2)\times 180^{\circ}}{6} = 120^{\circ}$.

What is the exterior angle of a regular polygon with $n$ sides?

$$\text{exterior angle} = \frac{360^{\circ}}{n}$$

Define the radius, diameter, and circumference of a circle, and give the relationship between radius and diameter.

The radius is the distance from the centre to the edge; the diameter is the distance across through the centre; the circumference is the distance around the circle. The diameter $d = 2r$.

State the formula for the circumference and the area of a circle of radius $r$.

Circumference $= 2\pi r$ (or $\pi d$) and area $= \pi r^{2}$.

Distinguish between a chord, a tangent, and an arc of a circle.

A chord is a straight line joining two points on the circle; a tangent is a straight line that touches the circle at exactly one point; an arc is part of the circumference between two points.

What is the relationship between a tangent to a circle and the radius drawn to the point of contact?

The tangent is always perpendicular ($90^{\circ}$) to the radius drawn to the point of contact.

Define a locus in technical drawing.

A locus is the path traced out by a point that moves according to a fixed rule or condition.

What is the locus of a point that moves so that it is always a fixed distance from a single fixed point?

A circle, whose centre is the fixed point and whose radius equals the fixed distance.

What is the locus of a point that is always equidistant from two fixed points?

The perpendicular bisector of the line segment joining the two fixed points.

Define an ellipse as a locus.

An ellipse is the locus of a point that moves so that the sum of its distances from two fixed points (the foci) is constant.

What curve is traced by a point on the circumference of a circle that rolls along a straight line without slipping?

A cycloid.

What is an involute curve?

An involute is the curve traced by the end of a taut string as it is unwound from around a circle (or polygon), or the path of a point on a line that rolls around the circle.

What is the key difference between first angle and third angle orthographic projection?

In first angle projection the object is placed between the observer and the plane, so each view is projected to the far side (view drawn beyond the object). In third angle the plane is between observer and object, so each view is drawn on the near side (the side it is seen from).

In first angle projection, where is the plan (top view) placed relative to the front view, and why?

The plan is placed below the front view, because the object is projected through onto a plane behind it, so the top view falls beneath the elevation.

In third angle projection, where is the plan (top view) placed relative to the front view?

The plan is placed above the front view, because each view is drawn on the side from which it is observed.

What is the standard symbol used to indicate which projection (first or third angle) a drawing uses?

A truncated cone (frustum) symbol: the two views of the cone are arranged differently for first angle versus third angle, placed in the title block to declare the projection system used.

Name the three principal views (elevations/plan) shown in an orthographic drawing of an object.

The front view (front elevation), the side view (end elevation), and the top view (plan).

What is an orthographic projection?

Orthographic projection is a method of representing a 3-D object using two or more separate 2-D views (front, side, plan) drawn at right angles to one another, with projectors perpendicular to each plane.

What is a sectional view and why is it used?

A sectional view shows the object as if it were cut through by an imaginary cutting plane, exposing internal features. It is used to show hidden interior detail more clearly than hidden (dotted) lines would.

How is the cut surface of a sectioned component shown, and how is the cutting plane indicated?

The cut surface is shown with thin, evenly spaced hatching (section lines) usually at $45^{\circ}$. The cutting plane is indicated by a chain line with arrows showing the direction of viewing and labelled (e.g. A–A).

State two common conventions for parts that are NOT sectioned (hatched) even when a cutting plane passes through them.

Items such as shafts, bolts, nuts, rivets, keys, webs/ribs, and spokes are conventionally left un-hatched (shown in full) even when the cutting plane passes through them lengthwise.

What angles are used to draw an isometric projection, and what happens to the vertical edges?

Receding edges are drawn at $30^{\circ}$ to the horizontal on each side, while vertical edges remain vertical. The two $30^{\circ}$ axes and the vertical form three axes $120^{\circ}$ apart.

In true isometric projection, how do drawn lengths compare with the real lengths?

True isometric lengths are foreshortened to about $0.816$ (approximately $\frac{82}{100}$) of the real length. In common practice 'isometric drawing' uses full true lengths for convenience.

What is the main characteristic of oblique projection?

In oblique projection the front face of the object is drawn true to shape and size (as a flat front view), and the receding edges are drawn going back at an angle, commonly $45^{\circ}$.

What is the difference between cavalier and cabinet oblique projection?

In cavalier oblique the receding edges are drawn at full (true) length; in cabinet oblique the receding edges are drawn at half their true length to give a more realistic appearance.

What is the key advantage of oblique projection over isometric for certain objects?

Because the front face is drawn true to shape, circles and curves on the front face appear as true circles (easy to draw with compasses), making it convenient for objects with circular front features.

What is perspective drawing and how does it differ from isometric/oblique projection?

Perspective drawing represents an object as the eye actually sees it, with parallel edges converging to vanishing points so distant parts appear smaller. In isometric and oblique, parallel edges stay parallel and do not converge.

Define the horizon line and vanishing point in perspective drawing.

The horizon line represents the observer's eye level. A vanishing point is a point on (or related to) the horizon line at which receding parallel lines appear to meet.

What is the difference between one-point and two-point perspective?

One-point perspective uses a single vanishing point (the front face is parallel to the picture plane); two-point perspective uses two vanishing points on the horizon (the object is viewed at an angle so two sets of horizontal edges recede to separate points).

Why are construction lines drawn lightly and not erased prematurely in geometric constructions?

Construction lines are drawn lightly so they do not dominate the final outline and can be left to show the method/working; keeping them allows accuracy to be checked and the construction to be understood.

When dimensioning, why should dimensions generally be placed outside the outline of the view?

Placing dimensions outside the outline keeps the view clear and uncluttered, avoids crossing object lines, and makes the figures easier to read without confusing them with the drawing detail.