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114. If a=l, b=2, c=3, d=4, find the value of
a2 +60 + ca

1
b4 + +de+(a+b)(6+c)

+3(aq +60 + cc)

+

+
115. I rode one-third of a journey at 10 miles an hour, one-third

more at 9, and the rest at 8 miles an hour; if I had
ridden half the journey at 10, and the other half at
8 miles per hour, I should have been half a minute longer

on the way: what distance did I ride?
116. The product of two factors is (3.x+2y)3 – (2x + 3y), and

one of the factors is x - Y; find the other factor.
117. If a+b=1, prove that (a? — 62)2=a3 + b3 ab.
118. Resolve into factors :

(1) 203 + y2 + 3xy (x+y). (2) m3 – n3 - m (m2 -- na)+n(m, n)?
119. Solve (1) 23-y=281 (2) 22 -6.xy+lly=91
x2 + xy + y2=7 ):

x-3y=1)
120. Find the square root of

(a - b)* - 2 (a + b)(a - b)2+2 (a* +84).
121. Simplify the fractions

1
(1)

1+

1
a3 – 1

(2)
1
at

a+1
122. Find the H.C.F. of

a2b+boc abc ab2 and ax2 + ab-q2-bx2.
123. A village had two-thirds of its voters Republicans: in an

election 25 refused to vote, and 60 went over to the
Democrats; the voters were now equal. How many
voters were there altogether ?
.x2

2ax
124. Solve (1) +(a - b)

a+b
3
2

1
(2) + 6

= 2.
y Y

2x
y2 + 22 – 22

12 +42 – 22
125. Simplify

+

(1
2yz

2avy
(2+1)3-(3-1)3
(2)

(2+1)-(3-14
126. Divide
24+(a - 1) 23 – (20+1).x2 + (a? +4a - 5) x+3a +6

2 – 3x +a+2.

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a+b:

(1) (1

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by

127. Resolve into factors:

(1) 12+5xy-24y2+x-3y.

(2) --

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128. Find the square root of pe – 39 to three terms,

-5 6 2-1 x - 2
129. Solve (1)

6 7 X - 2

(2) ax +1-by+1=ay + bx.
130. Find the H.C.F. of 3x2 +(4a - 26) x – 2ab+a? and

202 +(2a - b)2 (2ab-a2)x-a2b.
131. Simplify

(24)3 (20)
(1)

+

1

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[ocr errors]
[ocr errors]

(2)

Х
xcta

Х

132. At a cricket match the contractor provided dinner for 27

persons, and fixed the price so as to gain 127 per cent.
upon his outlay. Six of the cricketers being absent,
the remaining 21 paid the fixed price for their dinner,
and the contractor lost $3: what was the charge for
the dinner ?

a

and y

Y+1

22
+

2013

133. Prove that x(y+2)+-+

Y is equal to a, if
y
y

2

2
134. Find the cube root of

108 48 8
203 - 12.02 +54x – 112+

X
135. Find the H.C.F. and L, C, M. of

23 + 2ax+ ax+ 223 and 23 - 2ax2 + ax - 223.
136. Simplify

3y 3x 4y (3x – 2y 2x 3y 1
(1) 42

- 56
6

7 85
4b+a

a-46 22 - 362
(2)

+

+

36 a2-962
137. Resolve 4ao (43+18ab2) - (32a5 +962,2-3) into four factors,
138. Solve (1) 5/3.0 -1=775.0 – 29.
XY

YZ
(2)

=84, =140,
++y 2+%

y+%

3b+a

a-

[ocr errors]

=70,

[ocr errors]
[ocr errors]

a

с

+

+

[ocr errors]

X-a

X-C

X-a

3

3

3

3

3

3

27n

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139. Show that the difference between

b
+

and
6

- 0
is the same whatever value x may have.
140. Multiply x2 + 2y2 + 322 by 22 – 2yż – 3z7.
141. Walking 41 miles an hour, I start 1} hours after a friend

whose pace is 3 miles an hour: how long shall I be in

overtaking him?
142. Express in the simplest form

1

gr. 3ox
) )

(2)

3-1

331 x 9
143. Find the square root of

+3-2

2
y
144. Simplify

1 2.3-1 (2-1)(x+1)+ x2
(1)
X - 1

20+1 x4 + x2 + 1

aé +ay fab – aʻy2 a4 – 2axy +a’ya)
a2 +ya

a3+y3

al ay + y2
145. Find the value of
(1) 18+V50 - V18+V48. (2) 735 +14 76.
-0

2 (a-6)
146. Solve (1)

x-63-(a+b)
(2) 2x+3y=1}

4.22 +9xy +9y2=11 )
147. Show that
(a+0)3-03 (6+c)3 - a3, (c+a)3 – 63

+
(a+b)-c +

cta-6
is equal to 2(a+b+c)2+a? +12 +0.
148. Divide

a-x+ 4a7v- 4a2zł
by

a2+2 xĀ - 27
149. Find the square root of

(a-1)4+2 (a++1) - 2 (a2+1) (a - 1).

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[ocr errors][merged small][merged small][merged small][merged small]

4,

23

150. How much are pears a gross when 12 more for a dollar

lowers the price five cents a dozen ?
151. Show that if a number of two digits is six times the sum

of its digits, the number formed by interchanging the

digits is five times their sum.
152. Find the value of
1
1

1
(a-6) (6-c) (6-c) (

ac) (c-a) (6-a)'
153. Multiply
12+41x +36x?

26x - 82– 14
3+5x –

by 5 – 2x+
4+73

3-43
1

1

1
154. If x

22

3.30 23
155. Solve (1) +

11 x +4 3
(2) 2x2 – 3y2=231

2xy-3y2 = 3
156. Simplify

dx 143
(1

5

y
157. Find the H.C. F. of (p2 – 1) x2+(3p – 1) x P(P-1) and

p(p+1)x2 - (p2 – 2p - 1)x-(p-1).
158. Reduce to its simplest form

1
axt-

(xy - 1)
y?
y

5
7
bx2 -

(x4y4 – 1)
y

y?
159. Find the square root of

(1) 1–22n +1 +42n. (2) gn – 2.6% +4".
160. A clock gains 4 minutes a day, What time should it

indicate at 6 o'clock in the morning, in order that it
may be right at 7.15 P.M. on the same day?

4
161. If x=2+1/2, find the value of x2+

26

a

x2 +

Х

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162. Solve

Natasara Ni+&+V1-30
(1)

3.
(2)
Nx-b Jx

V1+x-W1 - x
163. Simplify
a?
72

ca
+

+
(b-a)(c-a) * (c-6)(a-6) * (a-c)(6-c)

164. Find the product of zv5, v2, , 75, and divido

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}]

1+1

P

(a

P

8-425 35-7

by

75+1 5+27 165. Resolve 9x9y2 576y2 – 4.28 + 256x2 into six factors. 166. Simplify

a? 1

(x+a)
(1)

x (x+2a)
(c+a) (c-a) (x2 - a) (x+a)2
6.x'ya

[3(m - n)x. 14 (r - 8) p2 - 32
mtn 7 (r+8)

121xy 4(ina – )

a2p 167. Simplify (1) (

ap)p+9

(a-1)(2) 714-1132. 168. Find the H.C.F. and L.C. M. of

20x4 + x2 – 1, 2524 + 5.43 – X – 1, 25x4 – 10.x2 +1. 169. Solve (1) a+x+ 2ax + x2=6.

1
(2) X+95 + 8.

11

8 170. The price of photographs is raised $3 per dozen, and

customers consequently receive ten less than before
for $5: what were the prices charged ?
1\2

1 171. If

=3, prove that a3 +

+ 7

(a+2) =

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172. Find the value of
x + 2a X – 2a 4ab

+
26+3

x2 - 462

ab when x=

+

2b - x

a+b

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