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XXVII.

27 1. Divide 0.75 by X 0.081.

15 2. Find the least common multiple of 15, II, 23, 5,

and 61:

3. A and B, 44 miles apart, travel towards each other. A travels i 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 dcm., 225 cm., and 3.75 m. ?

6. If 9 men build 2471 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?

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XXVIII.

is how many

0.5

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1. The sum of

8 X 0.83} 23 X

and

33 times the difference?

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

3. What common fraction equals the sum of 0.i8 and 0.307692 ?

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

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 21 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.

202

1. MULTIPLY C: + 2 ax + 2 a 2 + 200 by Q8 — 2 a 2 + 2 a 22 - 23. x 2. Divide 1 by 1 — m2, finding five terms of the series. 3. Divide - 6x4 + 96 by — 3x + 6.

4 ( - y2) (a+) 4. Divide

by 2 a (x + y).

2

3 m2 5. Find the greatest common divisor of numerator and

X2 1 denominator, and reduce the fraction

to its lowest

a + a terms.

ab

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ac-CX

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6. Divide

by a + P

atp

a aca 7. Reduce 1

to the form of a fraction.

az + c2 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

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an ox.

9. What is the fourth power of — 3 paga?

qe 10. What is the third root of — 729 a6 13 (12?

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

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II.

1. Multiply ab + 3 a4 32 — 5 a? 64 by 7 at — 4 a2 72 + 64.

a4 2. What is the value of — (10 — 3 a3) (10 + 3 a) ? 3. Divide 12 af 79—1405 76 + 6 a® 73— a? by 2 a2 13 — 03.

a

a

5 a?

2 x

a

cx

XC4
-

ya 4. Reduce

to its lowest terms. (22 + y2) (x2 2 x y + y2)

35 62 + ab - a? 5. Reduce [ +

to its simplest cd

b c d form as a single fraction.

10 a 22 6. Divide

by

and reduce the answer to 9 m® ya 27 m ya its lowest terms. 7. Find the value of x in terms of a, b, C,

from the equab c tion

What does this value become 6 when a =

. 1, and c = 3 ? 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. Find the distance each goes in an hour ?

64 a 191 9. (— 7 22 y)2 = what? 7

= what?

ch 10. Find by the Binomial Theorem (a - 6)6 and (1) 3 28)

a

2, 6

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III.

e

1. From 5 a2 b +362 c— 703 d e take — 6 a 6 -- (4 de

-472c). 2. Multiply x2 + xy + ya by 22 - xy + ya.

+ y2 3. Divide 24 — 2 by x y.

YA

y
(72 - y2) (x - y)

ac 4. Reduce

to its lowest terms. (x + y) (x2 – 2 xy + y)

22 5. Add together 3 x +

5

9 x + 2

2 + 3 6. Multiply

by 22

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82

and a

a

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X

x (a +6) a? 72 7. Divide

by -1

2 x + 1 8. Divide the number 75 into two such parts that three times the greater may exceed seven times the less by 15. 9. What is the fourth power of ?

27 79 10. What is the third root of 2000? ? 11. Find (b — 2 c3)4 by the Binomial Theorem.

a x2

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IV. 1. Reduce a +6—(2 a —36)—(5a +76)-(-13 a + 2b) to its simplest form.

2. Multiply a3 + 72 — c by a? 68.
3. Divide -1 + a na by 1+ an.

2 4. Reduce to one fraction +

28

a

a+2

a

ax

a X

a -X

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by

5. Multiply a + by

at x a+ 2 ab +62

72 6. Divide

X4 y* x2 32 7. How much money have I when the fourth and fifth part amount together to $ 2.25. 8. Find the fifth

power

of 2 a?

a: 7,20 C4 9. Find the fourth root of

16 012 2160 10. Find (5 a — 4x )4 by the Binomial Theorem.

5

V.

1. Reduce the following expression to its simplest form: a a + b (x + c) +62 — [(a - b) x — (6 —c)(b + c)].

[ ) 2. Multiply x + 2y— 3 z by x – 2y + 3 z.

- .

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