Mathematics Homework For Summer Vacation

Summer Home Work Class 10th (2009) QUADRATIC EQUATIONS 1. Solve the following equations by factorization. a. x 2 + 2 x − 35 = 0 b. x 2 + 20 x + 51 = 0 c. 4 x 2 − 13 x − 66 = 0 d. 7 x 2 + 58 x − 45 = 0 e. 25 x 2 − 414 x − 187 = 0 f. 28 x 2 + 51x − 27 = 0 g. 5 x 2 + 4 x + 1 = 3(1 − 3 x ) 2. Solve the following equations. 2 a. ( x + 3) = 25 b. ( 2 − 2 x ) 2 = 14 c. 6 x 2 − 7 x = 3 d.

4 x 2 − 7 = 14 x

e. x 2 − 7 x − 5 = 0 1 2 1 x − 3x = f. 5 4 3. Solve the following inequalities and illustrate each solution by a number line. a. x + 3 ≥ 4 b. x + 8 ≤ 9 c. 15 − x 〈−4 d. 8 − 2 x < 5 − 5 x e. 6( 3 x + 4) > 10( 2 x − 1) 1 f. 12 − 2 x ≥ ( x _ 5) 2

VARIATIONS 4.if x : y = 4 : 5, then find 3 x + 2 y : 2 x + 4 y 5.The ratio of two numbers is 2 : 3 . If 8 is added to both numbers, then the new ratio becomes 4:5. Find the numbers. 6.Find the value of x if, 17 − x : 31 − x :: 25 − x : 47 − x 7.Find the value of x if,

3 2 x +1 x − 2 : :: : x −1 x −1 3 4

8.Find the unknown term in the following proportions; a) ? : a 2 + ab + b 2 :: a 2 − ab + b 2 : a 3 − b 3 b) 6 x 3 y 3 z 3 : 2 xyz 2 :: 3 x 2 yz : ? 1 and x = 8, y = 3 ; then find value of “x” when y = 2 y3

9.If xα

10.Given that y varies directly as x and y=20 when x=200, find a. y when x=10 b. x when y=3 11.Complete the following table where m s

15

30 36

mα s ;

75 72

12.If y varies inversely as y when x=100.

x and y=5 when x=16, find the value of

13.A developer estimates that he needs 96 men to build a house in 14 days. If he asked to complete the building in 12 days, how many more men must he hire, assuming that the men work at the same rate? 14.Given that

c.

AαB and that

A when B =

1 and 3

A =1

2 5 when B = , find 3 6

d. B when A = 7

1 2

16.If a : b = c : d ,(where a,b,c,d ≠ 0 ) then prove that; e.

( a − b) a 2 − ab + b 2 = c 2 − cd + d 2 ( c − d ) 2

f.

a+b = c+d

2

a 2 − ab + b 2 c 2 − cd + d 2

 1 1  1 1  ( a − b )( a − c ) −  −  = abc  a b  d c 

g. 

17.If

a b c = = , ( where a, b, c, d ≠ 0), then prove that p q r h. i. j.

p 2 q 2 r 2 qr rp pq + + = + + a 2 b 2 c 2 bc ca ab a+b+c a+b−c a−b−c = = p+q+r p+q−r p−q−r p 3 q 3 r 3 pqr + − = a 3 b 3 c 3 abc

18-26)Eliminate the indicated variable from the following equations

a) x  2t ,

3 y  5t

(Eliminate t)

b) 2 x  1  3t ,

y  5  2t

(Eliminate t)

c) u  3 p  1,

v  2p 7

(Eliminate p)

d) x  2t  1,

y  t2 1

(Eliminate t)

e) x  y  1,

2x  3y 1  0

(Eliminate x)

4x  y  6

(Eliminate y)

f) 3 x  2 y  3,

g) 2 x  p  1  0, 4 x  2 p  7

(Eliminate p)

h) x  at 2 , y  2at

(Eliminate t)

i)

x  3t ,

y  5t

(Eliminate t)

27-32)Eliminate the indicated variable from the following equations

a) y  4 x  3, 2 x  y  1  0

(Eliminate y)

b) 2 x  3 y  1  0, 2 x  y  3  0

(Eliminate x)

c) y  mx  c, x  2 y  1  0

(Eliminate y)

d) x 2  my,

(Eliminate x)

e) v  u  at ,

y  lx 1 s  ut  at 2 2

(Eliminate a)

33-39)Eliminate x from the following equations a)

x

1 1  t , x 2  2  2t x x

b)

x

1 1  p  1, x 2  2  5 p x x

c)

x

1 1  p, x 2  2  q x x

d)

x

1 1  2t , x   4t x x

e)

x

1 1  p  1, x   2 p  3 x x

f)

x2 

g)

2 x2 

1 1  r , x 2  2  2r  1 2 x x 1 1  p, 2 x 2  2  q  1 2 2x 2x

40-45.Rewrite the following statements by replacing k in place of a) y  t b)

v t

c)

y  x2

d)

r

e)

v  r3

A

46.Find the value of k from the following tables

x y

3 6

6 12

12 24



x y

9 3

27 9

15 5

x y

1 6

2 12

5 30

47.There is direct variation between x and y, and y=5 when x=10, find

a) y when x = 10 b) x when y = 15 48.There is direct variation between

x 2 and y, when x=7, y=49, find

a) Y when x = 9 b) X when y =100

49.There is direct variation between

x and y, and x=25, y=5, find

a) Y when x = 7 b) X when y = 4 50.If

y  x then complete the following tables:

x y

4 2

6

x y

2

4 28

51.if

7 42

A  r 2 then complete the following table:

R A 52.If

15 3,5

1 22/7

y

3 88/7

x then complete the following table:

x y

1 2

4

x y

4 6

9

25/4 6 9/4 15

53.If

r v

v  r 3 then complete the following table: 1 3

2

4 81

54.There is direct variation between n and a+2. when n = 24, a = 2, find a) n when a =6 b) a when n =54 55.A hedge is made of wooden planks. The thickness of the hedge varies directly as the number of planks. 4 planks make 12 cm thick edge. Find: a) Thickness of the hedge when number of planks is 6. b) Number of planks when thickness of the hedge is 9cm. 56.In a fountain, pressure ‘p’ of water at any internal point varies directly as depth ‘d’ the from surface. Pressure is 51 Newton/cm2 when depth is 3 cm. Find pressure when depth is 7cm. 57.A body is thrown down resting position. Distance covered ‘d’ varies directly as time ‘t2’. Body covers a distance of 45m in 3 seconds. Find: a) Distance covered in 6 seconds. b) The time when the body falls up to 20m. 58.Pressure of gas in a container varies directly as the temperature. When pressure is 50 N/m2, temperature is 750. Find pressure when temperature is 1500. 59.If y varies inversely with the square root of x and y=5 when x=16, find the value of y when x=100.

60.Given that y is inversely proportional to value of y when r=8.

r 2 , and y=32 when r=1, find the

61.Two quantities s and t vary such that

s  at  bt 2 . If s=82 when t=2 and

s=171 when t=3, find the value of s when t=4.

62.Given that

p

1 , copy and complete the table below: q

Q

2

p

6

63.If y varies directly as

3

1

x 2 and if the difference in the values of y when x=1

and x=3 is 32, find the value of y when x=-2.

64.

Solve by using Componendo-dividendo property: (x + 7)² + (x – 5)² -- 5 (x + 7)² - (x – 5)² 4

65.

If m 

4ab , then find the value of: ab m + 2a _ m + 2b by using Componendo-dividendo property. m - 2a m - 2b

x  5  14  x 1  2 x  7     6 4 12  2 67. Find the mean, median and mode.

66.

Find the solution set of

Max. Load (Kg) No. of Ropes 93 – 97 2 98 – 102 5 103 – 107 8 108 – 112 12 113 – 117 6 118 – 122 2 The ratio among the sides of a triangle is 3, 4 and 5. Its perimeter is 156m. Find the length of each side.

68.

69.

Find the solution set of | x – 2 | ≤ 4, where x ε R. Also represent it on the number line. .

3

12

70.

Find the relation independent of “t” for: 1 v  u  at ; s  ut  at 2 (t) 2