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? XXVIII. is how many 0.5 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 ac-CX 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 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. 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 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 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 82 and a a 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 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. 2 4. Reduce to one fraction + 28 a a+2 a ax a X a -X 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. - . |