X – 7 prove that a 3 2 48. Simplify X-4 X-5 (0-2)(x-3) 49. Find the L. C. M. of 8x3 + 38x2 +593 +30 and 6x3 – 1322 – 13x+30. 50. A boy spent half of his money in one shop, one-third of the remainder in a second, and one-fifth of what he had left in a third. He had 20 cents at last; how much had he at first? 51. Find the remainder when 7 – 10.26 +82,5 – 7.003 + 3x – 11 is divided by x2 – 5x +4. 3 40 52. Simplify 4 6 (2a-6)+2 3 25 3 53. If a= b=l, c= 16' 4' 3c4 (a - b) (Na+b) Ja-b=va 54. Find the L.C.M. of 22 – 7x+12, 3x2 - 6x – 9, and 2.22 — Cx – 8. 55. Find the sum of the squares of ax+by, bx – ay, ay+bx, by — ax; and express the result in factors. Y 3.x - 52 56. Solve 7y 6 + =1. 4 5 4 16 a+b isa 5 58. Solve 2 – 3x (2x+67) + 1+ 10 6 59. Add together the following fractions : 2 - 4.2 22 x2 x2 + xy + y2' 23 – 33' y(x - y)2' xøy – 34 60. A man agreed to work for 30 days, on condition that for every day's work he should receive $2.50, and that for 77.203 33x x2 by +3–X. 3x – 4y 1 5 (78 – 4y) 5 10 1 when x= + and y=2. 10.x - 11 10.8 – 1 22 – 2x+5 63. Simplify + a3c3 3a-c 3ab 64. Find the cube root of 73 26 63 -2005 + с + 4X – 17 10x - 13 8x – 30 5x – 4 65. Solve + 1 66. Find the factors of (1) 202 + 5x2+x+5. (2) x2 – 2xy – 323y. 67. Solve (x+y)+23-21 Зr - w (y+z)=65 1 x+3 (x+4 – 2)=38 68. Simplify x + 2y 3.x2 +63ry +70,2 2x* + 3xy - 357 7 x - y 69. Find the square root of – (36 – 2c-2a)3 (2(a+c) – 36}. 70. The united ages of a man and his wife are six times the united ages of their children. Two years ago their united ages were ten times the united ages of their children, and six years hence their united ages will be three times the united ages of the children. How many children have they? 71. Find the sum of 42-3xy - , 2,2 – 32+zo, xy - y2 +yo, and 2xy y 72. From {(a + b)(a-x) -(a-6) (6- x) subtract (a+b)2 -26%. 73. If a=5, b=4, c=3, find the value of Cabc+(6+c)3+(c+a)3 + (a+0)3-(a+b+c)3. 74. Find the factors of (1) 3x3 +6x2 – 189x. (2) a2 + 2ab +62+a+b. 75. Solve px=qy) (P+q) x-(2-P)y=r y2 x+ 2 76. Simplify 43 2.c + xy + 2 22 2 X – 7 1 2X – 15 77. Solve + 24 – x2 – 2x + 2 78. Reduce to its lowest terms. 2x3 – X – 1 I 1 and 2x2 - 4x +2' 23x2 + 4x +2' 1- x2 80. A number consists of three digits, the right-hand one being zero. If the left-hand and middle digits be interchanged 14 81. Divide 1-50 + 23 X4 - 205 by 1 15 225 9 15 find the value of 2p+q-p-(-p) 22 83. Multiply - X+3. 2 2 84. Find the L. C. M. of (ab - 2ab2), 2a2 - 3ab - 20%, and 2 (2a®+ab) 2x+3 4.0+5 3x + 3 85. Solve + 5.x3 – 14x2 +16 86. Reduce to its lowest terms. 1 82. If p=1, 9=2 – 5x2 + +9 by se 90. A bag contained ten dollars in dimes and quarters; after 17 dimes and 6 quarters were taken out, three times as many quarters as dimes were left: find the number of each coin. 91. Find the value of 5(a - b) – 2 {3a-(a+b)} +7{(a – 20) – (5a – 20)}, 1 when a= b. 9 92. Divide 3x4 – 523 +702 – 11x – 13 by 3x – 2. 93. Find the L. C. M. of 15(p3+q), 5(po-P1+), 4(p2 + pq+q?) and (p2-4*). 94. Resolve into factors : (1) a3 – 8615. (2) – x2+2x – 1 + 24. x+a x+3a 95. Solve X + b +a+6° 96. Simplify 35a262c2 - 4963c3 (1) y4 – 743 +8y2 – 124 63a5bc-91836-c2. 2/*-2 - 60 97. Solve 7x — 9y+4z=16 x+y x+y+z1 2 2y 98. Simplify (u? - 5 - 6 -3 -2 y2-6y +5y+2) (2) 32 – y-1 99. Find the square root of 4a2 12ab 6bc + 4ac +962 + cm 4a2 +9c2- 12ac 100. The express leaves New York at 3p.m. and reaches Albany at 6; the ordinary train leaves Albany at 1.30 p.m. and arrives at New York at 6. If both trains travel uniformly, find the time when they will meet. 101. Solve (1) •6x+.752 - 16=x-.583x+5. 37 4 7 + X -X atx a-X 2.23 102. Simplify (1) a2 + ax + x2 + a2 – ax+x2 * a4+a’x2 +24° + +6= + . a+' also the cube root of the result. at a gain of 5 per cent., and the carriage at a gain of 20 Find the original cost of the horse. 8 (a+26)2 the quotient, and 12 (9a+116)2 the remainder. 1 3 2 2 1 a+b ab and + y=- 4 1051x2 14.73 6x +9. 3a + 3+4 from 22 – X – 12' 2 (x2 – 12) x2 + 7x + 12 2x2 +(6a – 100) x - 30ab and 3x2 – (9a + 156) X+45ab. 22 8x - 1 2(x+3) 22 - 9 4 (x-3) a- |