Number System
What is a decimal expansion of an irrational number?
Non-terminating and Non-recurring
Expand (a+b+c)2
a2 + b2 + c2 + 2ab +2bc +2ac
Is y=7 a linear equation in two Variables?
Yes, because we can write it as
0x + y = 7
What is the relationship between two corresponding Angles formed on parallel line?
Their values will be same.
What do you mean by congruent?
When two figures are exactly same in shape and size then they are called congruent.
What will be p/q form of 0.6666666..........?
2/3
Is x=2 a zero of Polynomial
P(x) = x2 + 2x - 8
Yes
Because
P(2)= 22 + 2(2) -8 = 4 + 4 - 8 = 0
How many solutions does a linear equation in two variable has?
Infinite Solutions
What is the total of all the angles formed on a straight line?
180°
Expand CPCT
Corresponding parts of Congruent triangles
Is it rational or irrational?
√225 + 7/ √289
Rational
As √225 = 15.
√289 =17
15 + 7/17 = 262/7 which is in p/q form and q≠0
Factorise:
x3 – 23x2 + 142x – 120
How many factors will it have? Tell all the factors of this cubic polynomial.
It will have 3 factors because it is a cubic polynomial.
(x-1)(x-10)(x-12)
Steps to factorise cubic polynomial-
1. Do hit and trial to find one zero of the polynomial.
2. Then do long division using the factor we recieved using hit and trial method.
Give two solutions of linear equation in two variable:
-x +5y =3
There are infinite solutions possible.
Put x=0 then y=3/5
(0, 3/5) is one solution.
What is the value of Complete angle?
360°
Name all 5 criterias of Congruency of triangles.
SSS
ASA
SAS
AAS
RHS
What kind of decimal expansion does 7/18 has?
Non-terminating but Recurring
7/18 = 0.3888888888........
Find the value of k, if x – 1 is a factor of
f(x) = 4x3+ 3x2 – 4x + k.
k = -3
As x-1 is a factor of f(x) , so x= 1 is a zero of f(x). So,
f(1)=0
4(1)3 + 3(1)2 - 4(1) + k =0
4 + 3 - 4 + k =0
3+k =0
K= -3
What does a linear equation in two variables looks like on a graph?
A straight line
What is a relationship between alternate interior angles formed on a pair of parallel lines?
Their values are same.
Is SSA and AAA criteria of Congruency of triangles?
No
Can all irrational numbers be represented on number line?
Yes
For eg- √2 can be represented on a number line.
What is a difference between a zero of a polynomial and factor of a polynomial?
If x=7 is a zero of a polynomial then what is it's factor.
Zero of a polynomial is a number whose value of we put in the polynomial it will make the value of polynomial 0.
Factor of a polynomial is a polynomial which gives remainder zero when we divide the given polynomial with it's factor.
If x=7 is a zero of Polynomial then it's factor is x-7
If (-2,3) is a solution of the linear equation in two variable
ay -8= x
Then find 'a'.
a = 2
a(3) - 8 = -2
3a = -2 +8
3a = 6
a = 6/3
a =2
What is the relationship between Co-Interior Angles formed by parallel lines and a transversal?
Sum of Co-Interior Angles is 180°
Tell isosceles triangle property and it's converse.
Isosceles triangle property-
Angles opposite to equal sides are equal.
Converse-
Sides opposite to equal angles are equal.