1. The identity (a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca is valid for negative values of a, b, and c. 2. For c = 0, the identity becomes (a+b)2 = a2 + b2 + 2ab. 3. When c is negative in (a+b+c)2, the terms 2bc and 2ca become negative.

1. VIVA VOCE
Verbal Questions
l . What is a square root spiral?
Ans. A square root spiral is a spiral composed of right triangles, placed edge-to-edge.
2. What is an irrational number?
Ans. A number which can not be expressed in the form P where p, q are integers, q :;c Oand p, q are co-prime is
known as an irrational number. q
3. Can ✓
4 be marked on number line without any construction as required for ✓
2?
Ans. Yes, because ✓
4 = 2 that can be marked straight away on number line.
4. State Pythagoras theorem.
Ans. Pythagoras theorem states that in a right angled triangle the square of hypotenuse is equal to the sum oi
squares ofother two sides.
5. How many irrational numbers lie between any two real numbers?
Ans. Infinite number ofirrational numbers lie between any two real numbers.
.1ultiple Choice Questions fMCQsJ
1. Which ofthe following is an irrational number?
- -
(a) 1.41 (b) 1.123 (d) .Jsi.
2. Which ofthe following is a rational number?
(ef2.3111 l... (b) ✓
S (c) 3.10100... (d) ✓
11
3. Which ofthe following is not a Pythagorean triplet?
M"(1, 2, 3) (b) (3, 4, 5) (c) (5, 12, 13) (d) (7, 24, 25)
4. In which triangle, Pythagoras theorem is applicable? ,. ..✓-
(a) Acute angled triangle llt1') Right angled triangle
(c) Obtuse angled triangle (d) None ofthese
5. How many irrational numbers lie between 2 and 5?
(a) 4 (b) 2 ~ infinite (d) 100
_--, _ . -
-· - ~- s,·_-.,, "%· MCQ Answers -. , .. · .;.__ ·
l. (c) 2. (a) 3. (a) 4. (b) 5. (c)
I I I
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2. VNA VocE
'erbal Questions
1. Where do we fix the perpendicular strip in order to represent ✓
7.
lns. We fix the perpendicular strip at ✓
6 in order to represent ,fi.
2. Is every irrational number, a real number?
.ns. Yes, as real numbers consist ofboth rational and irrational numbers.
3. "Product oftwo irrational numbers is an irrational number': Is this statement true?
.ns. No, product oftwo irrational numbers may be rational or irrational.
4. How would you find a perpendicular in a right angled triangle, ifhypotenuse and base are given?
ns. Perpendicular= J(Hypotenuse)
2
- (Base)
2
5. Give examples to show that sum oftwo irrational numbers may be rational or irrational.
ns. (-.fi)+✓
3 = 0 is rational. f
2-Js+3-Js= 5-Js is irrational.
:
ultiple Choice Questions [MCQs]
1. Which ofthe following is an irrational number?
1
(a) - (b) 2.512
3
2. Which ofthe following has an irrational square root?
(c) 7
{4(Js (b) ✓
BI (c) ✓
l44
3. 2✓
3• 3✓
2 =
(a) 54 (c)02
(efs.81234...
(d) ✓
4
(d) 18
t Ifhypotenuse is equal to 25 cm and base is equal to 24 cm, then perpendicular is35JUal to
(a) 49 cm (b) 25 cm (c) 24 cm (-dJ 7 cm
;, Relation between hypotenuse (h), base (b) and perpendicular (p) is /
(a) h2 = b2 - p2 (b) h2 = p2 - b2 (~ b2 = h2 +p2 (d(h2= b2+p2
(d) 2. (a) 3. (b) 4. (d) 5. (d)

3. - · · r-'"''-<1llu11 or any algebraic expression.
VIVA VOCE
Verbal Questions
1. Simplify: (x + y)2+ (u + v)2- 2xy - 2uv
Ans. (x + y)
2
+ (u + v)2- 2xy - 2uv = x2+ y2 + u2 + v2
2. Factorize : 4x2+ y2+ 4xy
Ans. (4x2+ y2 + 4xy) = (2x + y)2
3. What are the dimensions of two rectangles ifthe dimensions of two squares are 3 x 3 cm,
1.5 cm x 1.5 cm in this activity?
Ans. 3 cm x 1.5 cm.
4. ,Vrite the coefficient ofx in (Sx + 2)2•
Ans. 20
5. Is (a+ b)2, a binomial or trinomial algebraic expression?
Ans. (a+ b)2 is a trinomial algebraic expression as (a+ b)2= a2 + b2 + 2ab.
llultiple Choice Questions [MCQs)
1. How will you find the value of (102)2
by using identity (a + b)2?
(a) 1002
+ 22
(b) (100 - 2)2
tefooo+ 2)2
2. Simplify: (3x + 2y)2
(a) 3x2
+ 2y2
3. Find factors ofx2
+ 9y2
+ 6y.
(b) 9x2
+ 4y2
+ 6xy
(a) (x - 3y) (x - 3y) (b) (x - 3y) (x + 3y)
(t)9x2
+ 4y2 + 12xy
0{x+3y) (x+3y)
4. W9at will be the area ofa square of side (2x + 1) cm?
(/) (2x + 1)2
(b) 4x2
+ 1 (c) 2x2
+ 1
5.
1
If ~a+ b)2 = 25, a2
= 4, 2ab = 12, then what will be the value ofa and b?
(' ) a= 2, b = 3 (b) a= 2, b = - 3 (c) a= - 2, b = 3
1. (c) 2. (c) 3. (c) 4. (a)
(d) None of these
(d) 3x + 2y + 12xy
(d) (x + 3y) (x - 3y)1
(d) Sx
(d)a=4,b=3
5. (a)

4. 2. The identity can also be used for simplifying / factorisation ofsome algebraic expressions.
VerbalQuestions
l. Factorise: x2
+3- 2✓
3 x
Ans. (x- ✓
3 )2
2. Write the coefficient ofa2
in (2a - 3b)2.
Ans. 4
3. Expand (x - 2)2.
Ans. (x- 2)2
= x2
- 4x +4
VIVA VOCE
4. Find the value of992
by using algebraic identity.
Ans. 992
= (100 - 1)2=1002
+ l2- 2 (100) (1) =10000 +1- 200 = 9801
5. What are the dimensions oftwo rectangles in this activity ifthe dimensions oftwo squares are 5cm x5err
and 3cm x 3 cm?
Ans. Dimensions oftwo rectangles are 3cm x 2cm.
Multiple Choice Questions [MCQs]
l. How will you find the value of~ by using identity (a - b)2?
(a) 902
- 82
(~ (100 - 2)2
(c) 1002 - 22
(d) 1002
- 2
2. Simpjify: (Sx - 3y)2.
(~25x2
+9y2
- 30xy (b) 9x2
+25y2
- 30xy (c) 2Sx2 - 9y2
(d) None ofthese
3. Find the factors of49x2
- 14x +1.
(a) (49x - 14) (x - 2) (bj"(?x - 1) (7x - 1) (c) (7 - x) (7 - x) (d) 7x (x-1)
4. ~ will be the area ofasquare ofside (l lx +12)?
(a'J (llx +12)
2
• (b) (llx + 12) (12x + ll)
(c) (11 + 12)2
(d) 12lx2 +144
5. If(y'b)2
= 16, a2
= 25 and 2ab = 10, then what will be the values ofa and b?
(;1fa= 5,b = l (b)a=5,b=2 (c)a=7,b=2 (d)a=3,b=4
•· ·· ..,,MCQ Answers
2. (a) 3. (b) 4. (a) 5. (a)

5. VNA VOCE
Verbal Questions
1. Is a2
- b2
, a binomial?
Ans. Yes
2. Write coefficient ofx2
in (3x - y) (3x + y).
Ans. (3x - y) (3x + y) = 9x2
- y2. So, coefficient ofx2 is 9.
3 F t · 2 l
. ac onse: 4x __
4x2
2 1 1 1
Ans. 4x - -= 2x- - 2x+-
4x2 2x 2x
4. Simplify: (5 - x) (5 + x)
Ans. (5 - x) (5 + x) = 25 - x2
5. Find the value of98 x 102.
Ans. 98 X 102 =(100 - 2) (100 + 2) =10000 - 4 =9996
Multiple Choice Questions fMCQsJ
1. (2x - 9y) (2x + 9y) is a /
(a) monomial ., (ff)binomial (c) trinomial
2. The ~fficient ofx2y2
in (xy- 2) (xy + 2) is
(~ (b) 2 (c) 3
3. WrJ,tnhe dimensions ofa rectangle whose area is (25x2
- 4).
(c!J (5x - 2) (5x + 2) (b) (5x - 2) (5x - 2) (c) (5x + 2) (Sx + 2)
4. Write the zeroes of100x2
- 1.
/ 1 -1
(') --,-
10 10 10 10
5. IsS,,,- 3) a factor of64x2
- 25?
~) No (b) Yes
- l - 1
(c) w
'io
(c) Can't say
(d) none ofthese
(d) 4
(d) (25x - 2) (25x +2)
1 1
(d) 100 '100
(d) None ofthese

6. L - - -- - - - -
_ ~,.uu vJ.. uu.c:c '--VllVt:lllt:Il( nUmOerS.
V: ,;
Verbal Questions
1. Is the identity, (a+b+c)2
= a2
+ b2
+c2
+2ab + 2bc + 2ca, valid for negative values ofa, band c?
Ans. Yes
2. For c = 0, the identity (a+b+c)2 = a2
+ b2
+c2
+2ab + 2bc + 2ca, changes to a new identity. What is it?
Ans. (a+b)2
= a2
+ b2
+2ab
3. How many terms become negative in the expansion of (a+b+c)2
ifc becomes negative?
Ans. Two terms 2bc and 2ca become negative in the expansion of(a+b+c)2
when c is negative i.e.,
(a+ b - c)2 = a2
+ b2
+ (- c)2 +2ab + 2(b) (- c) + 2 (- c) (a)= a2
+ b2
+ c2
+ 2ab - 2bc - 2ca
4. Find the expansion of(x + 2y + 7z)2
•
Ans. (x + 2y + 7z)2
= (x)2
+ (2y)2
+(7z)2
+2(x)(2y) + 2(2y)(7z) + 2(7z)(x) = x2
+ 4y2
+ 49z2
+4xy + 28yz +I4zx
5. Calculate 1112
using the identity: (a+b+c)2
= a2
+ b2
+c2
+2ab + 2bc + 2ca.
Ans. (111)2
=(100 +10 + 1)2
=(100)2
+ (10)2
+(1)2
+2(100)(10) + 2(10)(1) + 2(1)(100)
= 10000 + 100 + l + 2000 + 20 + 200 = 12321
Multiple Choice Questions [MCQsJ
1. What is the coefficient ofyz in the expansion of(x + 2y ~..i.)2?
(a) 1 (b)2 (tj"4 (d)B
2. Factorise: 9x2
+ y2
+z2
+6xy + 2yz + 6xz /
(a) (3x + y + z) (3y + x + z) (b) (3x + 3y + z)2
(G{(3x + y + z)2
(d) (x + y + z)2
3. Which ofthe following is not required for this activity? /.,
(a) Scissors (b) Geometry box (91 Graph (d) Adhesive
4. The sum ofthe coefficients ofxy~d yz in the expansion of(2x + 3y + 5z)2
is
(a) 21 (~2 (c) 25 (d) 50
5. Coefficients ofy2
and z2
in the expansion of(x + Sy + 3z)2
are
(a) 25,36 (b)9,25 (c)l0,6
3. (c)
5.

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