Value.
LEAVING CERTIFICATE EXAMINATION.
993'
6. ABCD is a quadrilateral in which the diagonals AC, BD are at
right angles to each other, prove that AB~ + CD2 =BC2 +DA2.
If AB, BC, CD be 6, 7, 8 cm respectively, use the above
relation to find the length of DA to two decimal places.
Draw a quadrilateral with these measurements, having also
AC= 10 cm •, measure BD.
15* 7. A and B are fixed points, 2 inches apart; P is a variable point
which moves so that the angle ABB is 30°. Construct the
complete locus of P, and prove that your construction is correct.
15. 8. ABC is a triangle, whose sides BC, CA, AB are bisected in D,E,F ;
prove that AD, BE, CF meet in a point.
15. 9. If AB, CD be two chords of a circle which intersect in an internal
point E, prove that the rectangles AE.EB, CE.ED, are equal in
area.
PQ is a straight line 6 inches in length, and (9 is a point in
PQ such that PO = 2,56 inches. If from 0 a straight line OB,
be drawn in any direction 3-01 inches in length, calculate to
two decimal places how many inches R0 must be produced to
S, in order that the four points P, Q, R, S may lie on a circle.
:
MATHEMATICS.
Lower 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 other 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 mis¬
apprehension as to what is really required.
Square-ruled paper is provided for the graphical work.
1. Multiply
x* + Ux + i
and divide the product by
by x* - \\x + 30,
Write down the equation connecting your answer with the three
expressions given in the question, and verify this equation when a: = 2.
2. Simplify ^ ^
(a + tif - {a - b)3 a2 4- b'1 + 2b2
' ^ (a + by + — by
(2)
i + b2 2a2
x2 - b2
x2 - ax + bx - c
‘ x:2+ ax + bx+ ab-