Observation

The candidates were required to draw a cycloid and then construct a tangent and a normal to the locus on a certain point on it.

Candidates were expected to do the following:

CYCLOID
A.        DRAWING THE CYCLOID
(i)         draw a straight line;

(ii)       draw the circle Ø 60 tangential to the straight line and dividing it into 12 equal parts;

(iii)      project lines from the divisional points on the circumference of the circle parallel to the straight lines;

(iv)       transfer the divisional points on the circumference of the circle to locate the perimeter on the straight line;

(v)       draw vertical lines on the divisional points on the perimeter;

(vi)       locate the points for the cycloid;

(vii)      join the points to obtain a smooth cycloid.

B.        DRAWING THE TANGENT AND NORMAL

(i)         locate the point of tangency T on the curve 50 from the right end of the curve;

(ii)        use point T as centre to draw a circle Ø60 to intercept the centre line at point C;

(iii)       draw a perpendicular from point C to the straight line to locate point M;

(iv)      join point M to point T and extend for the normal;

(v)       construct a perpendicular at T on line MT extended for the tangent.

The solution is shown below: