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X 7

prove that

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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
a3 + 73
57. Simplify

a+b isa
64 - 64 ? - 62 2 la? +62 a-6
2.0 +
1

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
every day's absence from work he should forfeit $1.50;
at the end of the time he received $51 : how many days
did he work?
375 43.x2

77.203 33x x2
61. Divide
+27

by
4
4
8 4 2

+3–X.
62. Find the value of
4y

3x 4y

1

5

(78 4y) 5 10

1 when x=

+

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and y=2.

10.x - 11 10.8 – 1 22 – 2x+5 63. Simplify

+
3(2:2 – 1) 3(x2+x+1)^(-x:3 — 1)(x+1)

a3c3 3a-c 3ab 64. Find the cube root of

73

26 63

-2005 +

с

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+

4X – 17 10x - 13 8x – 30 5x – 4 65. Solve

+
-4 2x - 3 2.x - 7

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
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

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X 7

1 2X – 15 77. Solve

+
x+7*2(x+7) 2x - 6

24 – x2 – 2x + 2 78. Reduce

to its lowest terms.

2x3 – X – 1
79. Add together the fractions :

I
1

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
the number is diminished by 180; if the left-hand digit
be halved, and the middle and right-hand digit be inter-
changed, the number is diminished by 336: find the
number.
152 106 28

14 81. Divide 1-50 +

23 X4

- 205 by 1 15 225 9

15
1

find the value of
(p2+q?) – (P-9) p2+2pq+q?.

2p+q-p-(-p)
3x3

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

+
x+1 4x +4 3x+1

5.x3 – 14x2 +16 86. Reduce

to its lowest terms.
3x3 – 2x2 + 16x - 43
87. Find the square root of

1
404 +9 (alt +12a(ax+1)+18.

82. If p=1, 9=2

– 5x2 + +9 by se

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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
3

2
2x 3y + 4z — 5=0

2y 98. Simplify

(u? - 5 - 6 -3 -2
-
2y

y2-6y +5y+2)
72

(2)

32

y-1

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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
(2)

+
x2 – 5x + 6 - 2 3

X

-X

atx

a-X

2.23

102. Simplify (1) a2 + ax + x2 + a2 – ax+x2 * a4+a’x2 +24°

+

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+6=

+

.

a+'

also the cube root of the result.
104. Divide 1 - 2x by 1+3x to 4 terms.
105. I bought a horse and carriage for $450; I sold the horse

at a gain of 5 per cent., and the carriage at a gain of 20
per cent., making on the whole a gain of 10 per cent.

Find the original cost of the horse.
106. Find the divisor when (4a2 +7ab+56) is the dividend,

8 (a+26)2 the quotient, and 12 (9a+116)2 the remainder.
107. Solve (1) 5x (x – 3)=2 (x 7).

1

3 2
(2)
(x - 1)(x - 2)

2

1
(a - )2

a+b ab
108. If x=a+b+.

and

+

y=-
4(a+b)'

4
prove that (x-a)2-(y-7)=62.
109. Find the square root of

1051x2 14.73

6x
49.24 +

+9.
25 5
atx

3a
110. Solve

+
a2 + ax + x2 a’ – ax+22x (at +a%22+x4)
X+3

3+4
111. Subtract

from
2+x-12

22 – X – 12'
and divide the difference by 1+;

2 (x2 – 12)

x2 + 7x + 12
112. Find the H.C.F. and L, C. M, of

2x2 +(6a – 100) x - 30ab and 3x2 – (9a + 156) X+45ab.
113. Solve (1) 2cx2 abx + 2abd=4cdx.

22

8x - 1
(2)

2(x+3) 22 - 9 4 (x-3)

a-

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