50
THE HONGKONG GOVERNMENT GAZETTE, 23RD JANUARY, 1886.
FIRST CLASS. EUCLID. Friday, 9-12.
1. Upon the same base and on the same side of it there cannot be two triangles having their sides
terminated in one extremity of the base equal &c., &c., &c.
2. If from the ends of a side of a triangle there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle but shall contain a greater angle.
3. (a.) Prove that the angles made by the sides of a regular hexagon with each other are each equal
to 120°.
3. (b.). Prove that the angles made at the intersection of the diagonals of a regular hexagon are each
equal to 60°.
4. (a.) To a given straight line apply a parallelogram which shall be equal to a given triangle and
have one of its angles equal to a given rectilineal angle.
4. (b.) The greater side of every triangle is opposite to the greater angle.
5. (a.) Parallelograms upon equal bases and between the same parallels are equal to one another.
5. (b.) If a straight line falling on two other straight lines make the alternate angles equal to each
other these two straight lines shall be parallel."
'
6. (a.) If in the triangle A B C; B C be bisected in D, A D joined and bisected in E, B E joined and bisected in F; and C F joined and bisected in G then the triangle E F G will be equal to one eighth of the triangle A. B. C.
6. (b.) Write out the Enunciations of XI, XIII, XX, XXVI.
FIRST CLASS.
ALGEBRA.
1. Find the value of
a2-bc (a-b) (a-c)
Thursday, 9-12.
b2 + ca (b+c) (b-a
c2 + ab (c-a) (c+b)
2. Find that number the third part of which added to its seventh part makes 20.
3. Find the value of
X-a b
x-b
a
when X-
a2 a-b
4. Find the G. C. M. of 4x2 + 9 x3 + 2x2 —2x-4 and 3x2 + 5x2-x + 2.
5. (a.) The sheet of a newspaper contains a certain number of letters, columns, lines in each column, and letters in each line. If there were, one column less there would be 12 more letters in a line. If there were 11 less lines there would be 4 more letters in each line. If there were 22 lines less there would be one more column. Find the whole number of letters.
5. (b.) Express in factors a2-3ab-10b2; .x2-ac + ax—cx.
6. (a.) Solve (3x-5) (2x-5)=(x+3) (x-1).
6. (b.) Multiply
x2 + xy x2 + xy + y2
by
-y" xy (x+y)
FIRST CLASS.
MENSURATION.
1. What is the diameter of a circle equal in area to a triangle the length of whose sides are 24 yards
0 ft. 9 in; 25 yds. 2 ft. and 20 yds. 2 ft. 3 in.?
2. A floor measures 20 ft. by 18 ft, what would be the dimensions of a similar floor the area of which
was 562 sq. ft. ?
3. What is the volume of the largest cone that can be cut out of a pyramid 2 ft. high with a square
base the side of which is 30 in. long?
4. An iron pipe is 3 in. in bore, half an inch thick and 20 ft. long. Find its weight if a cubic inch
of iron weighs 4.526 ozs.
5. What is the length of the side of an equilateral triangle in which can be inscribed a circle whose
diameter is 10 ft.?
6. A room is 18 ft. by 25 ft., and 10 ft. high. Find the area of a partition from floor to cieling, placed
parallel to the diagonal of the room and at 4 ft. from it.