RELATIONS-1

Let R={(10,3), (14,1), (-2,-6), (11,-20)}. Find the domain and range of R.

solution

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

    Domain={10, 14, -2, 11}

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

    Range={3, 1, -6, -20}

Hence Domain={10, 14, -2, 11} and Range = {3, 1, -6, -20}

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

Let R={(8,3), (-11,-8), (-3,-6), (19, 0)}. Find the domain and range of R.

AXIS OF SYMMETRY-1

Find the axis of symmetry for F(x) = 4x² + 50x + 8

Solution

a=4, b=10

Axis of symmetry = -b/2a

                                 =  -(50)

                                      2 x 4

                                 =   -50

                                        8

                                 =   -25

                                        4

Hence the axis of symmetry is ^-25/4

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

Find the axis of symmetry for F(x) = 7x² + 28x + 3.

SIMPLE INTEREST-1

Priya deposited the amount of 90,000/= in a bank which gives an interest rate of 3% for 5 years. Find the simple interest she got.

Solution

I = ?,  P = 90,000/=, T = 5 years, R = 3%

I  = PRT

      100

I  = 90,000 x 3 x 5

            100

I  = 90,000 x 3 x 5

            100

I  = 900 x 3 x 5

          

I  = 13,500/=

Hence the simple interest was Tsh 13,500/=

TRY THIS………………….

Edmund deposited the amount of 50,000/= in a bank which gives an interest rate of 2% for 4 years. Find the simple interest he got?

SETS-1

If n(A)= 173 , n(B)= 160 and n(AnB)=140, find n(AuB).

Solution

n(AuB) = n(A) + n(B) - n(AnB)

             = 173 + 160 – 140

             = 333 – 140

             = 193

Hence n(AuB) = 193 answer

TRY THIS…………………………….

If n(A)= 146 , n(B)= 164 and n(AnB)=130, find n(AuB).

FACTORIZATION-1

Factorize 6x² + 13x - 5

Solution

= 6x² + 13x - 5.  We split the middle term (+13x) to be (-2x + 15x).

= 2x² - 2x + 15x – 5                (-3x) = -14x + 5x.

= (2x² -2x) + (15x - 5)

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

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

Hence 6x² + 13x – 5 = (2x + 8) (x - 1) answer.

TRY THIS…..

Factorize 4x² - 17x – 15.

MID POINT-1

Find the midpoint of a line from (11, 4) to (17, 10)

Solution

x1=11, x2=17, y1=4, y2=10.

Mid point = (x1 + x2, y1 + y2)

                         2            2

Mid point = (11 + 17,  4 + 10)

                        2            2

Mid point = (28, 14)

                     2    2

Hence midpoint = (14, 7)

TRY THIS……………………..

Find the midpoint of a line from (14, 18) to (22, 12)

ALGEBRA-3

Find w in the following equation;

3w - w-3 = w

7       2       5

solution

3w - w-3 = w

7       2       5

The LCM of 5, 7 and 2 is 70. So, we multiply by 70 throughout

70x 3w - 70(w-3) = w x 70

      7              2            5

¹⁰70x 3w - ³⁵70(w-3) = w x 70¹⁴

         ₁7              ₁2         5₁

10 x 3w - 35(w-3) = w x 14

30w - 35w + 105 = 14w

-5w + 105 = 2w

105 = 2w + 5w

105 = 7w

105 = 7w

7       7

15 = w

Hence w = 15

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

Find a in the following equation:

4a  -  a-3 = 3a

5        2       5

WORD PROBLEMS-1

1/9 of the lessons is Allocated to mathematics and 2/5 is allocated to civics. What fraction is left for other subjects?

solution

Amount of lessons allocated = 1  +  2

                                                9      5

Amount of lessons allocated = 5  +  18

                                                     45

Amount of lessons allocated = 23

                                                45

Now, the total number of lessons  = 1 = 45

                                                               45

Fraction for other subjects = total number of lessons  -  amount of lessons allocated.

Fraction for other subjects = 45  -  23

                                             45     45

Fraction for other subjects = 22 

                                            45    

Hence fraction for other subjects is 31/45

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

⁷/10 of the lessons is Allocated to mathematics and ⁵/8 is allocated to Geography. What fraction is left for other subjects?

POLYGONS-2

A regular polygon has 30 sides. Find the total angles of that polygon.

Solution

n = 30

Total angles = (n - 2)180⁰

                   = (30 – 2)180⁰

                   = 28 x 180⁰

                   = 5040⁰

Total angles = 5040⁰

TRY THIS……………………….

A regular polygon has 44 sides. Find the total angles of that polygon.

ARC LENGTH-1

Find radius if the length of an arc of the circle is ^∏/₃₆ cm.

Solution

L= ^∏/₃₆  , r = ?

L = ∏r

      180

^∏/12  = ∏r

           180

180  x ^∏/12  = ∏r  x   180   

                      180

 180 ∏  = ∏r 

     36      

                    

 180 ∏  = ∏r 

    36∏  ∏

5   =  r 

1      

     

r = 5cm

Hence radius is 5cm

TRY THIS………………..

Find radius if the length of an arc of the circle is ^∏/₂₀ cm.