Value.
1000
EXAMINATION PAPERS.
15. 6. Show that in every triangle ABC
b
where R is the radius of the circumscribing circle ;
(2) ma A = y + ^<
Hence prove that
a3 (6a -f c2 - a2) _
6* (<? -
• V) = c3 (a3 + V -c. *)
15. 7. If in the triangle ABC
c = 74, 5 = 56, £ = 35° 15',
find both values of A and the smaller value of a with the help
of the tables.
15- 8. The side of a regular 12-sided polygon inscribed in a circle is one
inch in length; employ any method you choose to find the
radius of the circle to two decimal places.
15. 9. Find (1) the cosine of the angle between the side and the diagonal
of a cube, (2) the cosine of the angle between two faces of a
regular tetrahedron.
ALGEBRA.
Honours Grade.
Wednesday, 21st June.—11 A.M. to 12.30 p.m.
10.
15.
All the work must be shown, and such explanation added as is required
to indicate the methods adopted.
Before attempting to answer any question, candidates should read
the whole of it very carefully, since time is often lost through
misapprehension as to what is really required.
Additional marks will be given for neatness, arrangement, and style.
Candidates may answer six questions only, namely, Nos. 1, 2, 3, and
one of the alternatives in each of Nos. 4, 5, 6.
.
1. If 7i be a whole number, such that both Sti + 1 and 7ti + 1 are
square numbers, prove that n must be a multiple of 5.
2.5 2. Explain the meaning of mathematical induction.
Prove by induction, or otherwise, that
n(n + 1) n(7i + H (w + 2) . , to(ti + 1) ... (ti +7-- 1>
!+«+ l-2~+ 1.2,3 +•••+ 1.2...7-
(71 + 1) (71 + 2) . . . (71 + 7-)
1 . 2 . . . r