'Value.
15.
LEAVING CERTIFICATE EXAMINATION.
997
7. A triangle ABC being given, inscribe a square in it, so that one
side of the square may lie on BC, and a vertex on each of the
sides AB and CA.
If x be the length of the side of this square, a the length of
BC, and the perpendicular on BC from A, prove that
15 8. A, B, C, D are any four points in space, prove that the straight
line which joins the mid point oi AB to the mid point of CD
intersects the straight line which joins the mid point oi AC to
the mid point of BD, and that both lines are bisected at their
point of intersection.
Show that the straight line joining the mid points of BC and
AD is also bisected at that point.
15' 9. Prove that the volume of a tetrahedron is ^ the volume of a prism
on the same base and with the same height.
MATHEMATICS.
Higher Grade—II.
Wednesday, 21st June.—2 p.m. to 4 P.M.
10 Candidates should answer only six questions, namely, Nos. 1, 2, 3,
4. and any two of the remaining five questions. Marks are
given for neatness and good style.
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.
Square-ruled paper and four place logarithmic tables are provided.
15. 1. The straight lines A and B give the length and breadth of a
rectangle ; measure these lines correct to the nearest millimetre
and find the area of the rectangle in square centimetres.
If your measurements do not differ from the true measurement by
more than half a millimetre, show that the error in your result
is less than one square centimetre.
A
B —
15. 2. Simplify
(!)&+/ (62 + c2- a2) +C-±^ (c2 + a2 - &2)+ ^ («2 + V~ *)
.g. (l - 10.x -t- 5a;2)2 + a:(5 - IQs + x2)a
' ' (1 + 2a; +
1 -I- a;15
(3)
(1 + a;) (1 - a; +. ^ (1 - a: +