Unit 1 Number Systems

There are two types of Real numbers

Rational 

Irrrational

Rational numbers are of form p/q and terminating. Eg 5/7

Irrational numbers are repeated eg √2+5

Zeros of polynomial 

2x²+3x+5 = 0 find x=-1 is zero of polynomial or not 

We put value of x in above equation

2(-1)²+3(-1)+5

2-3+5

4 which is not equal to zero so it is not zero of polynomial 

If after calculation its value becomes zero then that was zero of polynomial

Distance formula

✓(x1~x2)²+(y1~y2)²

Find distance between points A(2,1) and B (3,6)

✓(3-2)²+(6-1)²

✓(1)²+(5)²

✓1+25=√26

Perimeter of circle = 2πr 

Area of circle =πr²

Find perimeter and area of circle for radius 7cm 

Perimeter = 2π×7 = 14π cm 

Area = πr²= π7×7= 49 π cm²

Determination of roots

ax²+bx+c = 0 

discriminant =✓b²-4ac 

If discriminant is greater than 0 then roots are real and unequal

If discriminant is equal to zero roots are equal

If discriminant is less than zero roots are imaginary 

Nth term of AP 

a+(n-1) d

Where a. is first term d is common difference and n is number of terms 

Que find 5th term for series

2,4,6,8.......

a= 2.    d=4-2=2.   n = 5

T(5) = 2+(5-1)2

         = 2+4×2

         = 2+8=10

Sum of series 

S= n/2{2a+(n-1)d}

Find sum of series for 

3,6,9,12....... Up to 20 terms 

first term 3

common difference 6-3=3

number of terms n=20 

S = 20/2 {2×3+(20-1)×3}

    = 10 {6+19×3}

   = 10 × {6+57}

    = 630