4. Divide 2 by 31.

5. Add together 12.07043, 7131, 754-5, 6-3, and '07385.

6. Subtract 82.6874 from 701.212.

7. Multiply 0263 by 2.36.

8. Divide 4336218 by 7362.

9. Reduce 16.08 pennyweights to the decimal of a pound troy.

10. Add together 1, 1, and 5%.

11. Subtract 3 from 83.

12. Multiply together 24 of 1, 23 of 4, and 3 of 1. 13. Divide 4 by 12.

14. Add together 5·2 of a day and '0265 of an hour, and give the answer in minutes and the decimal fraction of a minute.

15. Subtract 6·42 of a furlong from 3.64 of a mile, and give the answer in yards and the decimal fraction of a yard. 16. Multiply 382 by ·148.

17. Divide 81.27 by 481 to 3 places of decimals.

18. Reduce 0325 of £5 to the decimal of £3 6s. 8d.

19. Reduce 1 mile 3 furlongs 10 poles 2 feet to feet. 20. If 1 ton 5 cwt. of iron cost £1 11s. 3d., what will 1 cwt. 2 qrs. cost?

21. Find (by Practice) the dividend on £8976 5s. at 138. 3d. in the pound.

22. Find the simple interest on £1760 for 9 years at 33 per cent. per annum.

XXXV.

1. Add together 43, 3, 15, and 38.

2. Subtract from 6.

3. Multiply 131⁄2 by 15.

4. Divide 7 by 13.

5. Add together 006, 1.27, 39.567, and 140.806.

6. Subtract 159.643 from 240-321.

7. Multiply 537.6 by 40.56.

8. Divide 16-0134 by 39.

9. Express 6.545 of 12s. 6d. in pence and the decimal of a penny.

10. Reduce 2 qrs. 3 bus. 2 pks. to pints.

11. If 37 articles cost £8 11s. 1d.; how many can be bought for £35 3s. ?

12. Find the simple interest on £480 for 5 years at 3 per cent. per annum.

13. Add together 32, 4, 1, and 1.

14. Subtract 217 from 5.

15. Multiply together 54 of 23, §, and 15. 16. Divide 4 by 12%.

17. Add together 12.36 of a ton and 03475 of a cwt., and give the answer in pounds, ounces and decimal of an

ounce.

18. Subtract 18-52 of a shilling from 21.43 of a crown. 19. Multiply 4.0576 by ⚫0068.

20. Multiply together 01, 17, and 1'06.

21. Divide 01461201 by 357.

22. Divide 75973 by ⚫00205.

23. Reduce 13 yds. 27 ins. to the decimal of 5 miles. 24. If 6 yards of silk cost £1 7s. 9d., what will 177 yards cost?

25. At what rate per cent, will £2630 amount to £3090 5s. in 3 years?

26. If the price of 3 per cent. Consols is 96, what interest does it afford to an investor?

XXXVI.

1. Add together 3, 1, §, and §.

2. Subtract 3 from 101.

3. Multiply by 1g.

4. Divide 33 by 1

5. Add together 8.376, 06703, 37.04, and 28-064015.

6. Subtract 28.4532 from 320.6.

7. Multiply 4.2635 by 068.

8. Divide 8-4605 by 248 to three places of decimals. 9. Find the value of 3.75 of £2 14s. 8d.

10. In 1250784 seconds how many weeks, days, &c., are there?

11. If 3 tons of iron cost £16 10s., what will be the value of 3 cwt. 2 qrs. 14 lbs.?

12. Find the simple interest on £732 for 8 years at 3 per cent. per annum.

13. Add together 1, 3, and 25.

14. Subtract 5 from 101.

15. Multiply together 13, 2, 81%, and 2.

16. Divide 213 by 41.

17. Add together 2·16 of a yard and '05 of a mile. 18. Subtract 4.42 of an hour from 3.64 of a day.

19. Multiply 506 by '632.

20. Divide 13.915 by 575.

21. Express 13s. 4d. as the decimal of £4.

22. In 8156704 cubic inches how many cubic yards and cubic feet are there ?

23. When the income tax was reduced from 6d. to 4d. in the pound, a person found that he had £42 3s. 9d. less income tax to pay. What was his income?

24. In what time will £230 15s. amount to £305 14s. 10d. at 2 per cent. simple interest?

25. Find the dividend on £2560 5s. at 12s. 8d. in the £. 26. If 7 men received £17 10s. wages for 15 days, what will be the wages of 30 men for 6 days?

XXXVII.

1. State and prove the rule for pointing in the divisior of decimal fractions.

Divide 4.8 by 12 and by ⚫12.

2. Find the value of

(x+y)√x2+y3—(x—y)√4(x2—y2)

when x=4 and y=3.

3. Divide x3

(a + b + c)x2 + (ab + bc + ca)x — abc b. To the product of what three factors is the first dividend equal?

by x c, and divide the quotient by x

4. Simplify

(x − y)3+(x+y)3+3(x+y)2 (x−y)+3(x+y)2(x-y).

5. Show that if 2s=a+b+c

(s-a)2+(s—b)2+(s—c)2+s2=a2+b2+c2.

6. Find the greatest common measure of—

x1 — ax3 — a2x2 — a3x--2a1 and 3x3-7ax2+3a2x-2a3.

7. State and prove the rule for the extraction of the square root, and find the square root of—

{

24

22

bx+cy+az=cx+ay+bz=ab+be+ca.

9. A, B and C travel from the same place at the rates of 4, 5, and 6 miles an hour respectively; and B starts two hours after A. How long after B must C start in order that they may overtake A at the same instant?

10. The following is an extract from a logarithm book :—

N. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Dif. 1905 2798950 9178 9406 9634 9862 0090 0317 0545 0773 T001 228

What is the logarithm of 190 and of 190595·7? Divide the product of these two quantities by 19057.5, using logarithms to obtain the result to two places of decimals. 11. What are the characteristics of the logarithms of 10 and to the bases 3, 3, 3, and respectively?

1

12. What is the cube root of

19.053

to six places of

decimals, having given log. 3.74408-5733455, and the logarithms in Question 10?

13. An officer proceeding to India in a troop ship is allowed 60 cubic feet of baggage. A lieutenant had two cases and a basket, one case being 4 feet 2 inches long, 2 feet 3 inches wide, and 2 feet 4 inches deep, and the other being half those dimensions in length, width, and depth, and the cylindrical basket being 3 feet high by 2 feet in diameter. By how much did he exceed or fall short of his allowance, actual contents being taken for the cylinder, and fractions of a cubic foot being omitted in the result?

14. The chord of an arc is 8 feet and the height of the arc is 2 feet, what is the radius of the circle ?

15. The great pyramid of Egypt was 481 feet high, when complete, and its base was 764 feet in length; find the volume to the nearest number of cubic yards.

XXXVIII.

1. Write down the quotient of 22, and show that the

X- y

quotient of xm-y is always finite, if m is any positive integer.

x-y

2. Prove the rules for the multiplication and division of decimals. When a fraction is converted into a decimal, in what cases will a terminating decimal be obtained? If a recurring decimal is obtained, what limit is there to the number of figures in the recurring period?

3. Divide a +46 by a3—2a*b*+261.

4. Reduce to its simplest form

\x+y x+y>

x (1

x2+xy