ALGEBRA - 4

Expand 13w(w – 7)

solution

= 13w(w – 7)

= (13w x w) – (13w x 7)

= 13w² – 91w answer

TRY THIS………..

Expand 3a(a+ 5)

SIMPLE INTEREST-2

Krina deposited the amount of 16000/= in a bank which gives an interest rate of 3% for 4 years. Find the simple interest she got.

Solution

I = ?,  P = 16,000/=, T = 4 years, R = 3%

I  = PRT

      100

I  = 16000 x 3 x 4

            100

I  = 16,000 x 3 x 4

            100

I  = 160 x 3 x 4

          

I  = 1920/=

Hence the simple interest was Tsh 1920/=

TRY THIS………………….

Edmund deposited the amount of 50,000/= in a bank which gives an interest rate of 8% for 4 years. Find the simple interest she got.

SETS-2

If n(A)= 170 , n(B)= 160 and n(AnB)=150, find n(AuB).

Solution

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

             = 170 + 160 – 150

             = 330 – 150

             = 180

Hence n(AuB) = 180 answer

TRY THIS…………………………….

If n(A)= 150 , n(B)= 165 and n(AnB)=140, find n(AuB).

MID POINT - 1

Find the midpoint of a line from (11, 4) to (13, 10)

Solution

x1=11, x2=13, y1=4, y2=10.

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

                         2             2

Mid point = (11 + 13,  4 + 10)

                        2           2

Mid point = (24, 14)

                    2    2

Hence midpoint = (12, 7)

TRY THIS……………………..

Find the midpoint of a line from (12, 9) to (2, 17)

RATIOS - 1

Given the ratios U:V = 9: 8 and V:W = 24:7 Find the ratio U:W.

solution

U = U x V

W   V   W

U =   9 x 24³

W   ₁ 8    7

U =   9 x 3

W     2 x 7

U =   27

W     14

Hence U:W = 27:14

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

Given the ratios D:E = 5:7 and E:F = 28:15;  Find the ratio D:F.

DIFFERENCE OF 2 SQUARES 1

Evaluate 397² – 387²

Solution

397² – 387² = (397 + 387)( 397 – 387)

                   = (784)( 10)

                   = 7840

397² – 387² = 7840

TRY THIS…………….

Evaluate 708² – 608²

SIMPLE INTEREST - 1

Dikshi deposited the amount of 16000/= in a bank which gives an interest rate of 3% for 4 years. Find the simple interest she got.

Solution

I = ?,  P = 16,000/=, T = 4 years, R = 3%

I  = PRT

      100

I  = 16000 x 3 x 4

            100

I  = 16,000 x 3 x 4

            100

I  = 160 x 3 x 4

          

I  = 1920/=

Hence the simple interest was Tsh 1920/=

TRY THIS………………….

Edmund deposited the amount of 50,000/= in a bank which gives an interest rate of 8% for 4 years. Find the simple interest she got?

APPROXIMATIONS-2

Estimate the value of 2.3  x  0.034.

solution

= 2.3  x  0.034

= 2.0 x 0.03      [ 2.3 ≈ 2.0 to ones and 0.034 ≈ 0.03 to hundredths]

= 0.06

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

Estimate the value of 6.2  x  0.083

LOGARITHMS - 5

Evaluate Log₂(512 ÷ 8).

Solution

= Log₂(512 ÷ 8)

= Log₂512 -  Log₂8          (applying the quotient rule)

= Log₂2⁹ -  Log₂2³             ( 256= 2⁸ and 8=2³ )

= 9Log₂2 -  3Log₂2       ( remember  Log_aa^c = cLog_aa )

= (9 x 1) - (3 x 1)          ( remember  Log_aa = 1 )

= 9 - 3

= 6

hence Log₂(128 ÷ 64) = 6

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

Evaluate Log₂(1024 ÷ 32). 

RELATIONS - 1

Let R={(5,3), (6,1), (-2,-6), (14,-20)}. Find the domain and range of R.

solution

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

Domain={5, 6, -2, 14}

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

Range={3, 1, -6, -20}

Hence Domain={5, 5, -2, 14} and Range = {3, 1, -6, -20}

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

Let R={(7,1), (-13,5), (-1,-2), (14, -9)}. Find the domain and range of R.