2. Find the least common multiple of 21, 5,

and 6.

3. A and B, 44 miles apart, travel towards each other. A travels of the whole distance, while B travels of the remainder. How far are they then apart?

4. In what time will $ 680, at 4 per cent simple interest, amount to $ 727.60 ?

5. How many cubic yards are there in a cistern the dimensions of which are 64 dem., 225 cm., and 3.75 m. ?

6. If 9 men build 247 rods of wall in 28 days, in how many days will 8 men build 51 rods?

7. What is the difference between the square root and the cube root of 1771561 ?

8. A can do a piece of work in 10 days, A and C can do it in 7 days, A and B can do it in 6 days; in how many days can B and C together do it?

2. How many kilometres are there in 2 m. 6 fur. 39 rd. 5 yd.?

3. What common fraction equals the sum of 0.18 and 0.307692 ?

4. A cube contains 79507 cubic inches. square inches does its surface contain?

How many

5. Having purchased an acre of land, I sell from it a rectangular lot, 121 yds. long, and 25 yds. wide, for what the whole acre cost me. What per cent do I gain on the land thus sold?

6. A collector who charges 8 per cent commission on what he collects pays me $534.75 for a bill of $775. What amount of the bill does he collect?

7. A can travel around a certain island in 2 days, B in 3 days, C in 3 days. If they set out at the same time from the same point, and travel in the same direction, in how many days will they all come together at the starting-point, and how many times will each man have gone around the island?

ALGEBRA.

I.

1. MULTIPLY a3 + 2 a2 x + 2 a x2+x3 by a3-2 a2x+ 2 a x2

2. Divide 1 by 1-m2, finding five terms of the series. 3. Divide 62496 by 3 x + 6.

by 2 a (x + y).

5. Find the greatest common divisor of numerator and

denominator, and reduce the fraction

1

to its lowest

8. A farmer sells to one man 5 cows and 7 oxen for $370, and to another, at the same rate, 10 cows and 3 oxen for $355. Required, the price of a cow and that of

an ox.

9. What is the fourth power of - 3 p2 q2 ?

10. What is the third root of 729 a6 b3 c12?

-

11. Find (2 a—b)4 by the Binomial Theorem.

11.

+

1. Multiply a 3 aa b2 — 5 a2 ba by 7 a4—4 a2b2+64. 2. What is the value of (103 a3) (10+ 3 a3)?

3. Divide 12 a1 bo — 14 a5 b¤ + 6 ao b3— a7 by 2 a2 b3 — a3.

7. Find the value of x in terms of a, b, c, from the equa

8. The sum of the distance passed over by two locomotives, the first running 6 hours and the second 4 hours, is 228 miles; but the second goes 24 miles more in 8 hours

than the first goes in 12 hours. goes in an hour?

Find the distance each

10. Find by the Binomial Theorem (a - b)6 and (1

a2

1. From 5 a2b+362c7c3 de take-6 a2b- (4 c3 de

2. Multiply x2+ xy + y2 by x2 - x y + y2.

3. Divide 24-y by x-y.

8. Divide the number 75 into two such parts that three times the greater may exceed seven times the less by 15.

11. Find (b -2c34 by the Binomial Theorem.

IV.

1. Reduce a+b-(2a-3b)-(5 a +76)-(-13 a +26) to its simplest form.

2. Multiply a + b2 — c by a2 - 78.

7. How much money have I when the fourth and fifth part amount together to $2.25.

1. Reduce the following expression to its simplest form: a x + b (x + c) + c2 — [(a — b) x − (b − e) (b + c)].

2. Multiply x+2y-3 z by x-2y+3z.