FACTORIZE 1B

Factorize 121x²- 100y²

solution

We use difference of two squares a² – b² = (a - b)(a + b)

121x²- 100y² = 11²x² - 10²y²

                     = (11x)² - (10y)²

                     = (11x - 10y)( 11x + 10y)

Hence 121x²- 100y² = (11x - 10y)(11x + 10y)

TRY THIS…………….

Factorize 49m²- 81n²

RADICALS 1B

RADIAN TO DEGREE 1A

Change ^17∏/2 radians into degrees.

Solution

Ө = 180⁰ x s                but s = ^17∏/2

       ∏

Ө = 180⁰  x  17∏              

       ∏     2

Ө =  ⁹⁰180  x  17∏             

         ₁∏    2₁

Ө = 90⁰ x 17

Ө = 1530⁰

Hence ^17∏/2 radian is equal to 1530⁰.

TRY THIS…………….

  

Change ^3∏/10 radians into degrees.

SIMPLE INTEREST 1A

Aakash deposited the amount of 20,000/= in a bank for 4 years and got a profit of 7200/=. Find the interest rate?

Solution

I = 7200/=, P = 20,000/=, T = 4 years, R = ?

I  = PRT

      100

7200  = 20,000 x R x 4

                      100

7200  = 20,000 x R x 4

                      100

7200  = 200 x R x 4

                     

7200  = 800R

          

⁹7200  = 800R

   800     800

Hence the interest rate was 9%

TRY THIS…………………..

Kinjal deposited the amount of 20,000/= in a bank for 6 years and got a profit of 6000/=. Find the interest rate?

RADICALS 1A

CONGRUENCE 1A

In the figure below, prove that ΔABC and ΔCDA  are congruent. 

Solution

GIVEN: Quadrilateral ABCD,

                AD=BC,

                <BCA=<BCA

REQUIRED TO PROVE: ΔABC ≡ΔCDA.

PROOF:  AD=BC           (given)

                <BCA=<BCA   (given)

                 AC= CA          (common)

Hence, ΔABC ≡ΔCDA  (By SAS)

TRY THIS…………………

In the figure below, prove that ΔNPQ and ΔQNR are congruent.

APPROXIMATIONS 1A

Estimate the value of 2.3  x  0.074

solution

= 2.3  x  0.074

= 2.0 x 0.07    [ 2.3 ≈ 2.0 to ones and 0.074 ≈ 0.07 to hundredths]

= 0.14

TRY THIS...................................

Estimate the value of 6.4  x  0.093

RELATIONS 1A

Let R={(7,23), (0,11), (-2,-5), (14,-20)}. Find the domain and range of R.

solution

For domain we check on the values of x in each point.

Domain={7, 0, -2, 14}

For range we check on the values of y in each point.

Range={23, 11, -5, -20}

Hence Domain={7, 0, -2, 14} and Range = {23, 11, -5, -20}

TRY THIS...............

Let R={(12,3), (-33,8), (-18,-9), (29, -14)}. Find the domain and range of R.

MATRIX 1G

VARIATION 1A

x is directly proportional to y. x=32 while y=4. Find y when x is 720.

Solution

x ⍺ y

x = ky

32 = k x 4

32 = 4k    [dividing by 4 both sides]

4      4

k = 8

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 8, y= ? x = 720.

x = ky

720 = 8 x y

720 = 8y

8       8

y = 90.

TRY THIS…………….

x is directly proportional to y. x=40 while y=4. Find y when x is 470.