126
squares
described
THE HONGKONG GOVERNMENT GAZETTE, 15TH FEBRUARY, 1896.
8. If the square described on one of the sides of a triangle be equal to the sum of the
on the other two sides, the angle contained by these two sides is a right angle. 9. Two circles intersect: prove that, by joining the centres with one another, and with the points of
intersection, two equal triangles are thus formed.
10. Prove that if the bisectors of the angles at the base of an isosceles triangle meet within the triangle
they are equal to one another.
Class III. A.
1. Define a straight line, a scalene triangle, a circle, a square.
2. From a given point to draw a straight line equal to a given straight line.
3. Enunciate Proposition 4 of Book I.
4. If two angles of a triangle be equal, the sides also which are opposite to the equal angles shall be
equal to one another.
5. If two triangles have the three sides of the one equal to the three sides of the other each to each
they shall be equal in all respects. (Proposition 8.)
6. To draw a straight line perpendicular to a given straight line of unlimited length from a given
point without it.
7. Any two sides of a triangle are together greater than the third side.
8. Two circles intersect: prove that if their centres be joined with one another and with the points of
intersection two equal triangles are thus formed.
Classes II. Ca. & III. B.
1. Define-a straight line, a scalene triangle, a circle.
2. From a given point to draw a straight line equal to a given straight line.
3. Enunciate Proposition 4 of Book I.
4. If two angles of a triangle be equal, the sides also which are opposite to the equal angles shall be
equal to one another.
5. To bisect a given rectilineal angle.
6. From the centres A and B describe two circles at a distance equal to half AB.
How would you show that the two circles are equal?
ALGEBRA. Class I. A.
1. Define-a progression, duplicate ratio, inverse variation.
2. Write down the factors of—(i) aa—b*; (ii) aa—b2; (iii) ao + b3 ; (iv) 4a′ + 1; (v) 20x2 — 43x — 12 ;
(vi) x'x'y2+y".
3. Find the continued product of-
(i) (a−b) (a+b) (a−b) (a2+b2) (a*+b1). (ii) (a+b+c) (a+b−c) (a−b+c) (a−b−c).
4. Divide a3 + b3 + c3 – 3abc by a+b+c. 5. Solve the equations :—
(i)
2+ 3
2x 9
3x + 1
xX -
-3
- 6
3
(ii)
+
X 2
X -7
X
x-4
ᏍᏆ ---
-5
•
35-0.
(iii) 2x2+9x
(iv)
{ x2 + xy + y2=39 1(xy)3-27
6. Simplify (first arranging in cyclic order):-
2α-b-c
c+a-26
(a-b) (a-e) (b-c) (b-a)
2c-a-b (a–c) (c-b)'
7. Write down the Arithmetical, Geometrical and Harmonic means between
they are in geometric progression.
8. Find the sum of-
(i) (ii)
(iii)
to 15 terms.
...to 4 terms.
...to 4 terms.
р and 9. and show that
9. Solve the quadratic ax2 + bx + c = (); and if a and B are the roots show that a3 + ß3—”
3abc-b3
a
10. A spends half as much again as B who saves one third of his income. B spends £200 less than
A, who saves three times as much as B. Find their incomes.
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