APPENDIX. MISCELLANEOUS PAPERS. NOVEMBER, 1854. 1. Multiply £25. 9s. 74d. by 51, and divide the product by 42. 2. Find in what time a body moving with the velocity of sound (1130 feet per second) would pass from the earth to the sun, a distance of 95 millions of miles. 3. At what price must linen which cost 2s. 103d. per yard be sold to gain 15 per cent.? 4. If a gallon contain 277-274 cubic inches, and a cubic foot of water weigh 1000 ounces; what quantity and weight of water will fill a rectangular cistern 5 feet long, 3 feet wide, and 2 feet 9 inches deep? 5. Multiply together 314 and 3.21, and reduce to its simplest value the expression 435.1 x .0046 6. A merchant invests a sum of money in 100 casks of sugar, each containing 5 cwt. 3 qrs. 15lb., at 17s. 11 d. per cwt., what price must he sell them at after 6 months to realize the same interest as he might have had for his money at 3 per cent.? 7. Extract the square root of 37613689. 8. If 27 men cut down 108 acres of grass in days, working 10 hours a day, how many acres would 16 men cut down in 9 days, working 12 hours a day? 9. Find the area of a floor whose length is 13 ft. 7 in. and its breadth 11 ft. 9 in., and shew by means of a diagram what surface is represented in each term of the answer. 10. Add together ar - by, x+y, and (a−1)x−(b+1)y, and from 2 (a+b)−3 (c–d) take a+b-4(c–d). 11. Multiply 7x-3y+5z by 3y-5x+11z, and find the 5th term in the quotient of 1- -r divided by 2-3x+5x2. 12. If quantities be proportional according to the algebraical definition, they are proportional according to the geometrical definition. 14. A farmer buys a flock of sheep at the rate of £7 for every 5 sheep; he afterwards loses 9, and sells the remainder at the rate of £16 for every 11, and the sum for which he sells the flock is £24 more than that which he gave for it: how many sheep were there? JANUARY, 1855. 1. Shew that the value of a vulgar fraction is not altered by multiplying its numerator and denominator by the same number. Add together the fractions, 1, 1, and, and reduce the result to its lowest terms. 2. Find the period of the decimal fraction equivalent to, and reduce £1. 17s. 6d. to the decimal of £5. 3. Standard gold being worth £3. 17s. 10d. per oz. troy, what will be the price of 2 lbs. 9 oz. 6 dwts. 16 grs.? 4. What sum of money will amount to £735. in two years at 5 per cent. compound interest, and what will it amount to in two more years? 5. A merchant sells 49 quarters of corn at a profit of 7 per cent., and 84 quarters at a profit of 11 per cent. : and if he had sold the whole at a profit of 9 per cent. he would have received £2. 10s. 9d. less than he actually did; what was the price he paid for the corn? 6. The gross receipts of a railway company in a certain year are apportioned as follows: 43 per cent. to pay the working expenses, 52 per cent. to give the shareholders a dividend at the rate of 3 per cent. on their shares, and the remainder £25000, is reserved: find the paid-up capital of the company. 7. Four men working 8 hours a day take 22 days to pave a road 440 yards long and 35 feet broad: how many days will four men, two of whom work 8 hours and two 10 hours a day, take to pave a road 1575 yards long, and 36 feet 6 inches broad? 8. Find the number of inches in the side of a cube whose solid content is 5.359375 cubic feet. 9. Prove the rule of signs in the multiplication of algebraical quantities, and multiply together x3 + 4x2+5x-24, and x2-4x + 11. 10. Reduce to its most simple form the expression 11. Shew that (a+b+c) (ab+be+ac) - abc a+b is equal to (b+c) (a+c). 12. Define proportion, and if a b: cd, shew that ad is equal to bc, and that a+ba-b :: c + d : c-d. 14. A and B play at a game, agreeing that the loser shall always pay to the winner one shilling more than half the money the loser has: they commence with equal quantities of money, but after B has lost the first game and won the second, he has twice as much as A: how much had each at the commencement? JANUARY, 1855. 1. If 100 quarters of wheat are sold for 77s. 8d. per quarter, and 50 quarters for 78s. 3d. per quarter; what is the average price per bushel? 2. Find the value of 3 of £128. 9s. 103d. 3. What is the price of 284-8665 bushels of wheat at 7s. 04d. per bushel? 4. Multiply 7 by 19; and divide 144 by 192. 5. Find the value of (1·05)1o, and the square root of 1.7959, each to four places of decimals. 6. What length must be cut off a board 6 inches wide that the area cut off may be a square foot? 7. A bankrupt's assets are £675, out of which he pays 15s. in the pound on half his debts, and 12s. on the other half; find the amount of his debts. 8. Find the present worth of £132. 3s. due 24 years hence at 4 per cent. simple interest. Explain the reason for the process employed. and shew that 4xy (x2+y2) = (x2 +xy + y2 )2 − ( x2 − xy + y2)3. 11. When does one quantity vary as another? Given that the area of a circle varies as the square upon its radius, and that the area of a circle is 1 foot 10 inches when the radius is 7 inches, find the area of a circle of which the radius is 14 inches. 12. If the increase in the number of male and female criminals be 1.8 per cent., while the decrease in the number of males alone is 4.6 per cent., and the increase in the number of females is 9·8; compare the numbers of male and female criminals respectively. 14. A farmer wishes to enclose a rectangular piece of land to contain 1 acre 32 perches with 176 hurdles, each two yards long; how many hurdles must he place in each side of the rectangle? What is the greatest rectangle that could be enclosed with these hurdles? FEBRUARY, 1855. 1. Shew that the value of a fraction is not altered by multiplying its numerator and denominator by the same quantity. Add together,}, 4}, and §. 2. Reduce to a decimal, and 3s. 7 d. to the decimal of half a crown. 3. If 72 men dig a trench in 63 days, in how many days will 42 men do the same? 4. Find the value of 370 cwt. 3 qrs. at £4. 13s. 7d. per cwt. Prove the truth of your result by long division. 5. Find the compound interest on £750 for 2 years at 4 per cent., and the amount of this sum in two years if the interest be payable half yearly. 6. If the solid content of a cube be 9393931 inches, what is the length of the edge of the cube? Find the square root of '5 to three places of decimals. 7. If 12 cwt. cost £37, what is the price of 1 cwt.? 8. Find the discount on £318. 3s. due 73 days hence, at 5 per cent. Give reasons why the interest is greater than the discount on this sum for the given time. 9. Simplify the expression 11. Define proportion. If a b c d, then a+bb:: c+d: d. On the same supposition, shew that 3a +7bb:: 3c +7d: d. 12. When does one quantity vary inversely as another? If r varies inversely as y, and when x=3, y=2, find the relation between r 14. A man buys a certain number of sheep for £60: if he had bought one-third more for the same money, they would have cost 10s. each less. How many sheep 3. If 312 yds. of stuff be purchased at 2s. 3 d. per yard, and 3rds be disposed of at a profit of 50 per cent., the remainder at a profit of 30 per cent., find the prices charged and the whole gain. 4. Find the value of 312 cwt. 3 qrs. 17 lbs., at 16s. 7ąd. per cwt. 5. The solid contents of a sphere being of of a cube, the side of which is the radius of the sphere, and a cubic foot of iron weighing 450 lbs.; find the diameter (in inches and tenths of an inch) of a 68 lb. cannon ball. 6. Find the interest on £3715. 10s. for 2 yrs. and 131 days, at 4 per cent. simple interest. 8. Prove the rule for the pointing in the multiplication of decimals. Multiply 315 by 037, and divide 0359432 by 7160. 9. Suppose £1 = 10 florins = 100 denars = 1000 (new) farthings, and a person have to receive wages for 217 days, at 1 fl. 2 d. per diem, interest on £65. 432 f. at 1 denar on £1 for the same period, and the profit on an investment of £25. 1A. on which he made 30 per cent.; find the whole amount. |