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Class IX
ACTIVITIES:1.Draw square root spiral
2. Verify Geometrically Algebraic Identity (a + b) 2 = a2 + 2ab + b2.
3. To represent the square root of 34 on a number line using graph paper.
PROJECT WORK
(1) Mathematics without zero.
(2) Contribution of Indian Mathematicians for the development of Mathematics
Assignment:1.Ex. 1.1:-
2, 3
2. Ex. 1.2:- Q. 3
3. Ex. 1.3 :-
4.Ex. 1.4 :-
1
5.Ex. 1.5 :- 1, 2, 4, 5
6. Ex.:- 1.6
7. Ex. 2.2
2,3,4
8. Ex. 2.4
9.Ex. 2.5
3, 8, 9
HOTS
CLASS:- IX
Number System
𝑝
𝑞
1. Express 0.8 + 0. 7 + 0.43 in the= form , where p and q are integers and 𝑞 ≠ 0
2. Locate 3 +
3.If x =
4. If a =
5. If x =
7
5
2 on the number line.
5
𝑥
and = 𝑝 7, find p.
3+ 2
,𝑏
3− 2
=
3− 2
,
3+ 2
find a2 + b2
5 +2 6
, show that x2(x
5−2 6
– 10)2 = 1
2−1
.
2+1
6. If 2 = 1.4142, then find the value of
7. If x =
8. If x =
9. If
3+ 5
,
2
3
,
2
then find the value of x2 +
then show that
9𝑛 ×32 ×(3−𝑛 2 − 27 𝑛
33𝑚 ×23
=
1+ 𝑥
1+ 1+𝑥
1
,
27
+
1
𝑥2
1−𝑥
1− 1−𝑥
=1
show that m = 1 + n
1
𝑥
10.If 2x = 3y = 6-z find the value of +
1
𝑦
+
1
𝑧
4
11. Find the value of
216
−
2
3
1
+
−
256
3
4
2
+
243
−
1
5
Polynomials
12. If (x – a) is a factor of x3- mx2 – 2nax + na2, then prove that a = m + n and 𝑎 ≠ 0.
1
2
13.If both (x – 2) and (x − ) are factor of px2 + 5x + r, show that p = r
14.If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3 , find the value of
a.
15. The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves remainder 19. Also find the remainder
when p(x) is divided by x + 2.
16. If
𝑥
𝑦
+
𝑦
𝑥
= −1, find the value of x3 – y3
17. Factorise:- (a) 25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz
(c)27p3 -
1
216
9
2
1
4
(b)8p3 +
12
5
6
𝑝2 +
25
𝑝+
1
125
(d) (p – q)3 + (q – r)3 + (r – p)3
− 𝑝2 + 𝑝
18. The remainder of the polynomial 5 + bx -2x2 + ax3, when divided by (x – 2) is twice the remainder when it is divided
by (x + 1). Show that 10a + 4b = 9
19.If x – y = 5 and xy = 84, then find the value of x3 – y3
20. Without actual division, prove that (2x4 – 6x3 + 3x2 + 3x – 2 ) is exactly divisible by (x2 – 3x + 2).
21. If a, b and c are all non-zero and a + b + c = 0, then prove that
𝑎2
𝑏𝑐
+
𝑏2
𝑐𝑎
+
𝑐2
𝑎𝑏
=3
SELF ASSESSMENT (SET-1)
CLASS:- IX
SUB:- MATHEMATICS
TYPE A:-
1X5=5
1. Select the rational numbers among 15,
2. Find the value of
2
4
2× 2 ×
3. Which one is polynomial.𝑥 +
12
3
𝑥
23,
225 , 0.2050050005…………..
32.
2
𝑥
+ 3,3 𝑥 +
+ 5, 2𝑥 2 − 3𝑥 + 6,
𝑥 10 + 𝑦 3 + 8
4. Find the remainder when x31 + 31 is divided by x + 1.
5. Find the zero of P(x) = 2x + 3
TYPE B:-
2 x 5 = 10
6.Find two irrational number between 1/7 and 3/7.
7. Simplify:- ( 5 +
3) ( 5 − 3)
8. Find the value of 32
2
5
+ 125
1
5
9. Show that x – 3 is a factor of f(x)= x3 + x2 – 17x + 15
10. Evaluate:- (101)3
TYPE C:11. Arrange in ascending order:-
3 x 5 =15
3
6,
6
4
24 , 8
12. Evaluate:13. If
4+ 5
4− 5
81 −3 4
16
×
25 −3 2
9
÷
5 −3
2
= 𝑎 + 𝑏 5, find the value of a and b.
14. Find the value of (30)3 – (18)3 – (12)3
15. Factorise:- x3 – 2x2 – x + 2
TYPE D:-
4 x 5 = 20
16. Visualise 4. 26 on number line, up to 4 decimal places.
17. Locate 8.7 on number line.
18. If a =
2− 5
2+ 5
and b =
2+ 5
,
2− 5
then find the value of a2 – b2.
19. Find the value of a and b so that the polynomial (x 3 – 10x2 + ax + b) is exactly divisible by (x – 1)as well as (x – 2 ).
20. Using factor Theorem and factorise: 6x2 + 5x – 6
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