ASSIGNMENT
Math
Class IX
Chapter-1,2,3
Q-1 Find the following rational numbers as decimals and state that whether they are
terminating or non terminating.
437
(i)
999
327
(ii)500 (iii)
2
13
−2
(iv) 15
Ans:
̅̅̅̅̅̅̅̅̅̅(iv)-0.13̅
̅̅̅̅̅(ii)0.654(iii)0.153846
(i)0.437
Q-2 Express each of the following in the form
𝑝
𝑞
.
̅̅̅̅
̅̅̅̅ (iii) 0.123̅ (iv) 125.3̅ (v) 0.00352
(i) ̅̅̅̅̅̅̅
0.001 (ii) 23.43
1
(ii)
999
2320
99
111
(iii)900(iv)
376
3
Ans(i)
349
(v)99000
Q-3 Find two irrational numbers between 0.1 and 0.12.
Q-4 Examine whether the following numbers are rational or irrational.
(i)
2+√3 (ii) (√2 − 2)2 (iii) √4 (iv) (2+√2)(2-√2)
Q-5 Represent the following on Number Line and write the steps of construction also.
√6, √8, √4.7, √10.5
Q-6 Visualise the following on number line by using Successive Magnification.
2.665 , 4.27̅(up to four decimal Places)
Q-7 Evaluate the Following.
(i)
3 −3
58 ÷ 53 (ii) (4)
√2
8
√2
13
(5) ÷(5)
64 −3/2
(iii) 255 × 224 - 212 ×267 (iv) (25)
3
(v) (25)−1/3 × √16 (vi)
Ans: (i) 3125 (ii)
2 1/3
2(25)
Q-8 If 27x =
9
3𝑥
64
27
(iii) 0 (iv)
125
512
(v)
3125
(vi)
4√2
1
, find x. Ans: 2
Q-9 Find the values of x in following.
(i)
3 𝑥
5 2𝑥
(5) (3) =
125
27
(ii) 2x -7 × 5x- 4 = 1250 (iii) 2x -5 × 5x – 4 = 5 (iv) (22)x = (23)4 Ans: (i) 3
(ii) 8 (iii) 5 (iv) 6
3
3
1 −1/2
3
Q-10 Write the value of (i) √125 × 27 (ii) √7 × √49 (iii) (9)
× (64)-1/3
Ans(i)
3
15 (ii) 7 (iii) 4
Q-11 Rationalise the Following.
(i)
2√7
√11
7+3√5
(ii) 7−3√5 (iii)
√2−1
√5
(iv)
√10+√15
√2
Ans: (i)
2√77
11
(ii)
47+21√5
2
(iii)
√10−√5
5
(iv)
2√5+√30
2
Q-12 In each of the following , find the value of a and b.
(i)
√3−1
√3+1
4+√2
= a-b√3 (ii) 2+√2 = a - √𝑏 (iii)
√11−√7
√11+√7
9
4+3√5
= a- b√77 (iv) 4−3√5 = a + b√5
1
61
24
𝐴𝑛𝑠: (i) a=2, b=1 (ii) a=3, b=2 (iii) a=2, b=2 (iv) a= - 29, b= - 29
Q-13 Evaluate each of the Following (i) 185× 185 − 115 × 115 (ii) (97)2 (iii) 0.54× 0.54 −
0.46 × 0.46 (iv)103× 10 (v) (99)3
Ans(i)21000 (ii)9409 (iii)
0.08 (iv) 10609 (v)970299
𝑥
2
2
𝑥
Q-14Find the Products. (i) (2x + 3y)(2x-3y) (ii) (x-1)(x+1)(x2+1)(x4 +1) (iii)(2 − 5) (5 − 2)
𝑛 3
𝑛
– x2 + 2x (iv) (𝑚 + 7) (𝑚 − 7)
5
(iii) - 4x2 +
12
4
𝑛 2
(v)(2x+y)(2x-y)(4x2 + y2)
𝑛2
x - 5 (iv) (𝑚 + 7 ) (𝑚2 − 49) (v) 16x4-y4
5
Ans: (i) 4x2-9y2 (ii) x8-1
Q-15 Write the following in expanded form.(i) (- x + 2y + z)2 (ii) (ab + bc + ca)2 (iii)
𝑥
𝑦
𝑧 2
(𝑦 + 𝑧 + 𝑥) (iv) (a2b – b2a)2
Ans: (i) x2 + 4y2 +9z2 -4xy +12yz – 6zx (ii) a2b2 + b2c2 +
𝑥2
𝑦2
𝑧2
𝑥
𝑦
𝑧
c2a2 + 2a2bc + 2ab2c + 2abc2 (iii) 𝑦 2 + 𝑧 2 + 𝑥 2 + 2 𝑧 + 2 𝑥 + 2 𝑦
𝑦 3
𝑥
𝑥
(iv) a4b2 - 2a3b3 + b4a2
𝑦 3
Q-16 Simplify (i) (a + b +c)2 – (a – b – c)2 (ii) (2 + 3) − (2 − 3) (iii) (6m – n)(36m2 + 6mn
+ n2) – (3m + 2n)3
(iv)(1 – x)(1+x+x2)
Ans: (i) 2(a2 + b2 + c2 + 2bc) (ii)
2𝑦 3
27
+
𝑥2𝑦
(iii) 189m3 – 9n3 –
2
54m2n – 36mn2 (iv) 1 – x3
Q-17 Find the following products: (i) (3x-4y+5z)(9x2 +16y2 + 25z2 + 12xy – 15zx +20yz) (ii)
(2a – 3b – 2c)(9x2+16y2+25z2 +12xy -15zx + 20yz) (iii)(7a – 5b)(49a2 + 35ab + 25b2) (iv)
5
25
(𝑥 + 5𝑥) (𝑥 2 − 25 + 25𝑥 2 ) Ans(i) 27x3 – 64y3 + 125z3 + 180xyz (ii)8a3 – 27b3 – 8c3 –
36abc (iii) 343a3 – 125b3 (iv)
125
𝑥3
+125x3
1
Q-18 Factorize: (i) 21x2 – 2x + 21 (ii) x2 + 6√2x +10 (iii) x3 + x – 3x2 – 3 (iv) x6 + y6 (v) 1 –
27a3 (vi) 8x3 + y3 + 12x2y +6xy2 (vii)x3 + 8y3 + 64z3 – 24xyz (viii) x3 + 6x2 + 11x +6 (ix) x3
– 6x2 +3x +10 (x) 2y3 -5y2-19y +42
Ans: (i) (√21𝑥 −
1
2
) (ii) (x + 5√2)(x + √2)
√21
(iii) (x-3)(x2 +1) (iv) (x2 +y2)(x4 – x2y2 + y4) (v) (1-3a)(1+3a+9a2) (vi) (2a+b)3
(vii)(x+2y+3z)(x2 + 4y2 + 16z2 -2xy-8yz-4zx) (viii) (x+1)(x+2)(x+3) (ix) (x+1)(x-2)(x-5) (x)
(y-2)(y+3)(2y-7)
Q-19 If x=2 and x=0 are zeroes of polynomial f(x)= 2x3 – 5x2 + ax + b. Find the value of a
and b. Ans :a=2, b=0
Q-20 Using Remainder theorem find the remainder when f(x) is divided by g(x).
(i)
1
F(x)= 4x3 – 12x2 + 14x – 3, g(x) =x - 2
3
Ans(i) 2 (ii) -
(ii) f(x) = x3 – 6x2 + 2x – 4 , g(x)= 1- 3x
107
27
Q-21 If the polynomials ax3 + 4x2 + 3x – 4 and x3 – 4x + a leave the same remainder when
divided by (x-3) , find the value of a.
Ans: a=-1
Q-22 Show that x + 1 and 2x – 3 are factors of 2x3 – 9x2 + x + 12, without actual divison.
Q-23 Find the value of a such that (x – 4) is a factor of 5x3 – 7x2 – ax - 28.Ans: 45
Q-24 Plot all points on graph paper by taking suitable scale on axes.
7
21
15
(24, - 2); (-18,14); (-12, - 2 ); (30, 7); ( 2 , -21)
Q-25Plot the points on Graph paper and also tell that to which quadrant these points belong.
(2,5); (4,-3); (-5,-7); (7,-4); (7,0); (-4,0); (0,0); (0,-4); (0,7).