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LEAVING CERTIFICATE EXAMINATION.
MATHEMATICS
Higher Grade.—III.
Thursday, 22nd 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. All the figures should be accurately
drawn.
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. Draw the graph of sin 6 + cos 0, from 0 ■■= 0 to 0 = 180°.
Find from your figure the approximate values of 0 in which sin 0 +
cos 0 = 1'2.
15. 2. If A and B are each less than 45°, prove geometrically that
cos ^4 -f cos B = 2 cos J (A + £) cos | (A — B).
Prove that
cos A + cos (A + 120°) + cos (A + 240°)= 0.
15. 3. Write down the expression for cos A in terms of the sides of the
triangle ABC, and deduce the expression for sin —.
If a = 8, 6 = 9, c = 10,
find all the angles of the triangle to the nearest minute with
the help of the table of logarithms.
15 4. From a point A in a straight road AB two objects, P and Q, in a
plane through AB are observed, such that
A PAB = 45° 30', QAB = 27° 10'.
The observer now walks along the road in the direction of B,
until he reaches a point C, whence P and Q appear in the same
straight line. If A £7 be 125 yards, and
PC A = 52° 45',
find the length of PQ to the nearest yard by the help of the
tables.
Answer TWO questions out of the following five.
5. Find three values of cos A which satisfy the equation
3 sin A sin 2A + cos 2A = 1
Having given that A is an acute angle, use the corresponding value
of cos A to construct the angle, and measure the angle to the
nearest degree.
Verify your result by means of the table.