4. What is the cost of papering a room 17 ft. 4 in. long, 12 ft. 8 in. broad, and 12 ft. high, with paper 2 ft. wide, at 74d. the yard?

5. Add together 'i of a guinea, 'IĠ of a shilling, and reduce the result to the decimal of a sovereign.

6. Find the square root of 42849, 119'0281.

7. A cistern 5 ft. deep, 16 ft. long, and 4 ft. 6 in. broad, is filled by one pipe in 45 minutes; in what time will a cistern 6 ft. deep, 20 ft. long, and 5 ft. broad be filled by three similar pipes?

8. What is the compound interest and amount of 2000/. for 3 years at 5 per cent.?

9. I have 13000l. in the Three and a Half per Cents., and sell out when they are at 98: how much money do I realise ? and how much must I add to secure an equal income in the Three per Cents., buying in at 87?

10. The total rent of a farm is 1000l.; the following charges have to be made :-Land tax at I per cent.; poor rates at 7d. per £; other local rates at 11d. in the £; tithe charge, 967. 10s.; and insurance at 3s. per cent. What are the net receipts?

2. Find the value of 33 of 67. 13s. 3 d., and the difference between of 5 furlongs and of mile.

3. Multiply 416 by '025, divide the product by 3.25, and reduce the result to a vulgar fraction.

4. What decimal of 5 cwt. is equal to 1590 of a ton?

5. A room being 19 ft. 6 in. long, 15 ft. 3 in. wide, and 12 ft. 9 in. high, find the area of the floor, the volume of the room, and the cost of the carpet, which is yd. wide, at 5s. 6d. per yard.

6. If the simple interest on 216. 15s. amounts to 371. 18s. 74d. in 3 years, what is the interest on 1197. 10s. for 51 years at the same rate?

7. One field is three times as large as another, and a third is half as large again as the other two together. If the three fields together contain 52 acres 3 roods 30 poles, what is the size of each?

8. A person invests 3276. in Three per Cent. Stock at 91; at the end of six months he receives the halfyear's dividend, which he invests in the same stock, then at 90. What is his second half-year's dividend?

9. A and B having money in the proportion of 5:7, B pays of his money to A and receives back of what A then has, thus leaving B with 6s. more than A. How much had each at first?

10. A clothier gains 25 per cent. by selling cloth at 20s. 10d. per yard; but a bale of 80 yds. being damaged, he has to reduce the price by 10 per cent. What is now his profit on the bale, and his gain per cent.?

11. Three men and five women, working together, earn between them 41. 10s. in a week; but if one man and one woman were absent for half the week, the joint earnings would be only 37. 18s. What are the wages of each man and woman?

12. If I lb. of gold, 22 carats fine, be worth 461. 14s. 6d., in what proportion ought copper (regarded as worthless) to be mixed with pure gold to make a compound worth 27. 11s. IId. per oz.?

65

QUESTIONS AND EXERCISES.

=

ALGEBRAICAL

I. EVALUATION.

1. If a 1, b = 3, c = 5, d = 0, find the values of (1) a2+2b2+3c2 + 4d2.

2. When a = 1, b = 2, c = 3, d = 4, shew that

{d−(c—b+a)} {(d+c)−(b+a)}
=d2 — (c2+b2)+a2+2(bc―ad).

3. Find the value of

5. If a=25, b=9, c=4, d=1, find the value of

3√a+2√4b−√9c+ √16d.

F

20

6. When a=0, b=2, c=4, d=6, find the value of

33/2b2—a+23/b2 + c2 + 7 − 3⁄4/2 (b+c)2 — (b+d)3°

7. If a=1, b=1, c=0, d=2, find the value of
(ac-bd) (ad-bc) (ab—cd).

8. Evaluate (1-ab) (1—ac) (1—bc), when a=1, b=0,

C=-I.

9. If a=0, b=2, c=-3, d=4, find the value of
4 (ad-bc)-(a—b)—(c–d)}2.

10. Evaluate a— {bd—(b—4c)} — _1326(ab—

if a=2, b=-3, c=0, d=1.

4ab(ab→bc+ad)2

11. Find the value of 2a2b2c-3{a-(b-c)3}2, when a=-3, b=−2, c=— I.

15. Find the value of

p0+mq-1—r, when m=6, q=3, r=4.

16. If a=3, b=4, c=9, find the value of
2ab√c−8+3√2(c−1).

3 ac+(a2b−1)a-b

II. ADDITION AND SUBTRACTION.

1. Add together

(1) 4x3-3x2y+7xy2 — 10y3

and 2x3- 5x2y—xy2+2y3.

(2) x3 +x2y—4xyz, y3 — 3y2z+3xy3,

2≈3 + 3xz2−3yz2, and 3x2%-2xyz — 23.

(3) bx2+(a2 — ab) x+a3

and (a—b)x2 + (a2 + ab)x — (a3 —b3).

(4) (b−c)x+(c−a)y+(a−b)z

and (2a-b)x+(3b−c)y+(4c—a)s.

(5) ax3+ (a+b)x2-(2a-b)x+b

and bî3 — (a—c)x2 + (b+c)x−(a+b+c). (6) a + b −3 c+d and fa-3b+c-id. (7) 3 (+8) + (8+x), 2(x+x)+3(x+y), 1(x + y) + 1 1 (y + z).

2. Subtract

(1) 4x3-3x2-x+2 from 7x-6x2+2x-1.

(2) 111-3x-21 from §11+x2+3x − 13.
(3) (b−c)x2+(c—a)xy+ (a−b)y3
from ax2+bay+cy2.

(4) 2−(a+3)x+a2x—5a2x2

from 3a2x-2a2+x+1.

(5) a(x-y)+by−z)+c(z−x)

from a(x+y)+b(y + z) +c(z+x).

(6) bxTM+(a+b)xm—n — axm−2n

from am++(a+b)x+2bxm-n

(7) (a−b) √x2+ y2+c(a+x)3

from (a+b)√x2 + y2 + (a+c)(a + x)3.