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2. Construct a square of 2" side, and through an angle
draw a line cutting off one-third of its area. (8.) *3. Describe a circle touching the given line ab in c, and passing through the given point p.
Solid Geometry. 4. Represent by their traces :a. Two planes at right angles to each other and to the
vertical plane of projection, and one of them inclined
at 40° to the horizontal plane. b. Two parallel planes not at right angles to either plane of projection.
(8.) 5. Draw the trace of a plane parallel to and 21" above the
horizontal plane, and determine the projections of a point in this plane 31" from the ground line.
(10.) *6. Obtain the projections of two points P and Q on the given
line ab, a'b'; such that P is 1.4" from the vertical plane, and Q 2" from the horizontal plane. Determine and
write down the real length of the line PQ. (10.) *7. ab is the plan of one side of an equilateral triangle lying in
the given plane. Complete the plan and draw the elevation of this triangle.
(12.) *8. The plan abcv of a triangular pyramid standing on the hori.
zontal plane is given. The vertex of the pyramid is in the given plane mon. Draw the elevation of the pyramid and also a section on the line xıyı:
(12.) 9. Draw the plan of a hexagon of 13" side in any position, such that its plane is neither horizontal nor vertical.
(12.) *10. The T square, supposed to have no thickness, rests with
the angles a and b on the horizontal plane and its own plane is vertical. Draw an elevation on a plane making 35o with the plane of the T square.
(12.) *11. ab, a'b' are the projections of a given line; cd is the plan,
and p'a point on the elevation of a second line intersecting the first. Determine the traces of the plane containing the two lines.
(12.) *12. The plan and elevation of a simple solid are given. Draw an elevation on a line parallel to nyi:
(14.) *13. Make a sectional elevation of the solid (Question 12) on the line AB.
(16.) Graphic Arithmetic. *14. The given line a represents the product of the lines b and c. Determine and write down the length of the unit.
15. Taking one-third of a (Question 14) as unit, determine a line representing Vo
Second Stage or Advanced Examination.
Read the General Instructions at the head of the Elementary paper.
Only eight questions are to be attempted.
Plane Geometry. 21. Two points a, b are 33 miles apart. Determine the position
of a point p, such that pa is 1% miles, and the angle apb 73o. Scale 1" = 14 miles.
(14.) 22. Two circles of 1.8" and 2.75" diameter have centres 2.6"
apart. Two rods ao, ob, 2-3" and 3.2"' long, jointed at 0, are tangents to the circles respectively touching them at the extremities a, b. Draw the rods in all possible positions.
(16.) *23. Reduce the given figure acdefgb to a trapezium with ab as
base, and its two parallel sides as aa' and bb'. (16.)
Solid Geometry. 24. Two points a, b, on the ground line are 2" apart. A point
P is 2" from a, 27'' from b, and his from the vertical plane. Obtain its projections.
(16.) *25. Determine a plane, bisecting the angle between the two given planes
(18.) *26. Two lines are given by their figured plans. From the
point p on one of them draw a line 23" long terminating on the other.
(20.) *27. The Maltese cross rests with the point b on the horizontal
plane. Its plane is inclined at 40°, and the edge ac at 35o. Draw the plan and also an elevation on a plane parallel to the plan of ac.
(22.) 28. A right cone, height 4", diameter of base 3", stands on the
horizontal plane. A point starting from the base of the cone, moves round its surface at a uniform speed, and rises half the height of the cone in turning round to cut the generatrix from which it started. Draw the plan and an elevation of the curve traced by the point.
*29. The plans of the edges of a four-faced right prism w
horizontal axis are given. The prism is penetrated
(2 *30. The plan of a right cylinder and of a sphere are given,
right cone, diameter of base 23", height 31", stands ou
Draw its plan and show the points of contact.
half plan of which are given. (N.B.-An isometric i
(2€ *32. The plan and elevation of a desk are given. Draw a f elevation on a line parallel to 2291
(28 *33. Make a sectional elevation on AB of the desk (Question
by construction what force acting along cd will have
(18) 35. Three forces of 11, 191 and 26 lbs. act at a point P in si
directions that their resultant is nil. Draw. lines rep senting the forces in direction and magnitude. (18.)
Read the General Instructions at the head of the Elementai
Paper. Only eight questions are to be attempted.
Plane Geometry. *41. abc is a hoop within which revolves a circular disc turnin
about A as centre; dq is a rod rigidly attached to th hoop at d; the point q can only move along the line Aq. Trace the locus of the point p.
(40.) *42. Draw a curve representing the velocity of the point 9
(Question 41) at all positions along its path. (40.) *43. Construct an equilateral triangle which has one angle at
the point b on the given line ob and the remaining angles on oa and oc respectively.