THE HONGKONG GOVERNMENT GAZETTE, 15та FEBRUARY, 1896. · 127
Classes I. B. & I. Ca.
1. Define ratio, proportion, surd.
2. Write down the product of -9 by x2-16; and state why or why not each term in the product
is a perfect square.
3. What are the factors of (i) a3+b2; (ii) 27a3-8b3; (iii) 16a-1; (iv) x2-10x+16;
(v) 9x-32x-16; (vi) ab+be+cd + da.
4. Divide 62-2*y—10x1y3 +31x3y3 — 14x*y* —9xy3 + 12yo by 3x2 + 4x3y—5x2y2 + 3y*.
-
5. Find the H. C. F. of 2x3 — 5x2 + 5x-3, 2x3-x2−5x+3, 2x3-3x2 + 6x-9, and the L. C. M. of 3(a2-b3), 6(a3—b3), 9(a3-2ab+2ab2-b3), and 12(a3 — 3a2b+3ab2 −63), expressing it in factors. 6. Solve the equations:-
9 10
+ a y
(i)
21
25
X
У
(ii)
x2 - 5xy+4y2
54 18 (y-x).
7x 4
-
7x + 4
(iii)
3x 4
1 +
3x + 4
7. Prove that a° - = 1, and simplify
x
(a) 2
x* 3x-1÷
of
22
3/
1
a2 + b2 + c2
1
1
8. Simplify
α
b
b
-
C
C
―
α
(b-a) (c-b) (a–c)
9. A man walked 60 miles at a certain pace: when he had gone twice as many miles as the number of minutes in which he went one mile, he found he would be 6 hrs. 40 min. more on his journey. Find the pace at which he walked.
Classes I. Cb. & II. A.B.
1. What is a quadratic equation? And what do you mean by "cyclic order"? Give examples. 2. Add together a (b+c) - b (c-a), b (c+a) - c (a-b), and c (a+b) – a (b−c).
3. Subtract a (b−c) — b (c-a) from c (a-b)
b (c-a) from c (a−b) — a (b+c).
4. Find the square root of—
5. What are the factors of—(i) a3
6. Find the H. C. F. of 3æ* x2 + 3x
wwwwwwww
6x1 + 4x2 + 9x2 12x + 4.
b3; (ii) a1 1; (iii) x2 + xy — 30y3; (iv) 6a2b + 3abc
-
9bc.
1 and 3x2- x2 3x + 1.
-
7. Solve the equations—
-
3x 4 2x + 3
(i)
6x
4x + 9
(ii)
J21x + 17y =
173
18.x 5ly
114
(iii)
3x2-7x 6
www.
0
8. Simplify
(c
a + b (e-a) (bc)
b + c
+
(a - b) (c-a)
e + a
(b−c) (a - b)
9. Two different numbers are represented by the same two digits: the larger number is 21 times as great as its units figure: the difference between the two numbers is 12 less than the smaller number.
What are they?
Classes II. Ca. & III. A.B.
1. What is a negative quantity? And what are simultaneous equations?
2. Add together 3x-2y-5z, 4y-2x-8z, 4x+3y-10x, x-y-6z, 5y+8z+9x, 32-9y-6x.
3. From a-7ab-56+2 subtract -5a+6ab-3b+4.
4. Multiply 2a-3b+4c by 2a-36-4c.
5. Divide 3x-4x3+4x2+8x−3 by x2-2x+3.
6. Simplify-
4 {3(b - 2a) - 2(c - 3b)} − 4 [a − 4 {2c - 3(b − 2a)}].
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