III. TRINITY TERM, 1902. 1. Find the value of

(1) 2[1-{1-(1-1-p)+p}]?;

(2) a + ab + abc + abcd + b + bc + bcd +c+cd when a= 1, b = -2, c = 3, d = 0.

2. Multiply 322 — 4xy + 5 yo by 5x2 + 4 xy + 3y? ; and divide 45 (as +28) — 24 a2b2 (at_-64) + 54 a464

by 15a4 + 12 a2b2 +964. 3. Resolve into factors :

(1) 21x2 + 5x – 44 ; (2) 8p3 – 27q8 ; and show that

(p+2+3)(9–2+3)=p+2

02

4. Find the G. C. M. and L. C. M. of

2x2 – 5% — 3, 382 – 11x +6, 6x3 – 19x? +x+6. 5. Simplify 2 2

1 ä-a+1 - (a + 1)2 + (a + 1)3 * 6. Find the square root of:

(1) 9.24 + 36 c®y + 48 22y2 + 24 xy3 + 4 y* ;

7. Solve the equations :

ab
3x-2y = 91L.
20C + 3y = 214)

3 . y 8. A number is divided into two parts such that their difference is half their sum, and the smaller part is 25; find the number.

+ 818 013

+

9. A and B each go into business, A starting with thrice B's capital. Each makes £50, and then A has 2 times B's capital. With what capital did each start?

10. The price of a wine being raised 10 shillings a dozen, 4 dozen now cost the same as 5 dozen cost before the change of price. Find the price of the wine.

IV. SEPTEMBER, 1902. 1. Find the value of p-9-1-(9-P)]} wben

p=1, q=-3, p= -4. 2. Simplify (p+q+r)2-(p-9-r)?, and divide 60p+ 193p8q + 382p* q2 + 456 pøq+ 386 poq*

+191 pa + 6096 by 4p2 + 3 pg + 592. 3. Find the coefficient of ain the product of

a® (b-c)+ b3 (c-a)+c(a-b) by a+b+c. 4. Obtain the factors of

(p-1)2 – 36, 1+125p3, 8p2 – 6 pq- 99%. 5. Find the G.C. M. of

24 +pRq+2p?q% + 3pq' +, and pt +poq + 2 p q + 3 pqo + pqp2 +* + qopa. 6. Find the L. C. M. of

6(P+q)?, 3p2 – 3q", 15 (p3 +93). 7. Simplify: (1) Vp#+2 p* (q + r) +p(* + y2 + 4qr) +2 pgr (q+r") + q* pt;

2+9_2 ? + 9 + 2
q'
pq Pi (3)

af + 3a? – 10
p-9 P+9

af - 3 a2 + 2 8. Solve the equations :

X-P__ (2xếp)

X-9 (2x-9)2'
(2) + 3y = 7, 443? = 3 y– 4.

9. Divide 810 into two parts such that one part may be two-thirds of the other.

10. A bill of £6. 38. was paid in half-crowns and florins, and the whole number of coins was 56: how many coins were there of each kind ?

11. A bicycle is travelling at the rate of a feet in b seconds. Express this speed in miles per hour.

V. MICHAELMAS TERM, 1902.

1. Simplify: 5-[4-(3-(2-1 -2)}].

What value of x will make the expression equal to zero ?

2. Multiply 3p+59 +77 by 7p+59 +3r, and divide

a3 + b3 - 3ab + 1 by {[(a−b)2 + (1 - 1)2 + (a−1)2]. 3. Resolve into factors

pu-pq2, 2p2 + pq-37, 3p2- P9 -29%. 4. Find the G. C. M. of

382 +2.cy + 702 — 542 — 7 42,

7 0:2 - 2xy + 3xz — 54°– 3yz. 5. Find the L. C. M. of 4 (x + y), 6 (22- ay + y2), 8 (22 - y2),

12 (23 — 2 y + 2 xy2 – yi). 6. Simplify: 1+1

632 + 13x + 6 (1) P--! ; (2)

122c2 + 17% + 6 1 1 2x + 2ac2

1 -a 1 + 1 + x - x2 – xc3 * 7. Find the square root of

and

and

1+1

8. Solve the equations :

(1) (3x – 4)-(2 - 5x) = 0;
(2) 3 - ay = b,

X +by = a.) 9. Divide 54 apples among A, B, and C, so that A gets 1 more than B, and B 1 more than C.

10. I borrow equal sums from A, B, and C. A asks no interest, B asks 5 per cent., C asks 3 per cent. per annum. At the year's end I have to pay £77 in all. What did I borrow of each?

11. A cistern is filled by 3 pipes A, B, and C. A alone fills it in x minutes, B in y minutes, C in 60 minutes; B and C together in 36 minutes; A, B, and C all together in 24 minutes. Find x and y.

VI. HILARY TERM, 1903.

1. (1) Find the value of

{4-(1-a)} {1+2a-(1-a)} when a = -1.

(2) Write down an expression for the number consisting of three digits, of which the first is a, the second zero, and the third b. 2. Multiply

p2-2pq+q2 + gu2 by p2+2pq+q2–72. 3. Prove that, if p2 (2+1) + q* (r +p)+g2 (p+q) + 3pqr is divided by qr+rp+ pq, the quotient is p+q+r. 4. Find the G. C. M. of

(p+9)3 + 3 (p +9)*+ 3 (p+9) 72 +993 and p? (q + r) + q* (r+p) + m2(P+q) + 3 pqr. 5. Resolve into factors :

(1) - po (a + b)2 + 2 pq (a–)- q* (a−b)2;
(2) (4 p+39) - (3p+ 4q).

6. Simplify:

(1) p8 + que , p3-03
" pe-pq+q2 * p + pq +923

- 7p 39

? 7p-39' 39-7p 7. Solve the equations :

(1) (x-p) (3-9) = (2-p-9);

8. Divide 100 into two parts, so that one half of their difference may be 15.

9. If 2 lb. of tea and 18 lb. of sugar cost 98. 6d., and 3 lb. of tea and 44 lb. of sugar cost 188. 6d., find the price of 4 lb. of sugar.

10. Seven years ago A was three times as old as B then was, and seven years hence A will be twice as old as B will be: find their present ages.

VII. TRINITY TERM, 1903. 1. Simplify

a-[a-{a-la-u-1)-1}-1)-1; and find the value of 1

1 at

when a = 4, b = 3, c= 2, d= 1.
2. Express in as many factors as possible:

(1) 28 -1; (2) 23 – 2x2y + 2 xy2 --ys.