PERCENTAGES-1

What percentage of 1 hour is 3 minutes?

solution

1 hour = 60minutes

To get %'ge we take the fraction of 3min in 1 hour(60min) and multiply by 100.

= 3      x 100

  60

= 3 ¹     x 100

 60₂₀

= 1      x 100

 20

= 5%

Hence percentage of 1 hour is 3 minutes is 5 %

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

NECTA FORM II - 2013 QN. 7

What percentage of 1 hour is 15 minutes?

LOGARITHMS - 3

If log 2= 0.3010; find the value of log 5,000,000 without using tables.

solution

log 5,000,000 = log(10,000,000÷ 2)

=log10,000,000- log2

=log10⁷ – log2

=7log10 –log2

=(7x1) – (0.3010)

=7– (0.3010)

= 6.699

Hence log5,000,000 = 6.699

TRY THIS……………

If log 2= 0.3010; find the value of log 500,000,000 without using tables.

SETS - 1

If n(A)= 60 , n(AuB) = 130 and n(AnB)=10, find n(B)

Solution

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

  130     = 60 + n(B)  – 10

  130     = 60 -10 + n(B) 

  130     = 50 + n(B) 

  130 - 50        = n(B)

  80        = n(B)

Hence n(B) = 80 answer

TRY THIS…………………………….

If n(A)= 67 , n(AuB) = 140 and n(AnB) = 33, find n(B).

PERCENTAGE PROFIT 1

A man got a profit of 130/= after selling an item for 2600/=. Find the percentage profit.

Solution

%’ge profit = Profit   X  100    [where B. P. represents Buying Price.]

                      B.P.

%’ge profit = 130   X  100   

                    2600

%’ge profit = 5%   

                       

Hence Percentage Profit is 5%

TRY THIS……………………………

A man got a profit of 1000/= after selling an item for 60,000/=. Find the percentage profit.

FACTORIZATION 3

Factorize 1-d²

Solution

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

1-d² = 1²-d²       

        = (1 - d)(1 + d)

Hence 1-d² = (1 - d)(1 + d)

TRY THIS…………….

Factorize 36 - y²

LOGARITHMS 2

Evaluate Log₂(256 x ¹/₃₂).

Solution

= Log₂(256  x ¹/₃₂).

= Log₂256 +  Log₂(¹/₃₂)          (applying the product rule)

= Log₂256 +  Log₂32^-1         ( since  ¹/₃₂ = 32^-1 )

= Log₂2⁸ +  Log₂(2⁵) ^-1                      ( since 256= 2⁸ and 32=2⁵ )

= Log₂2⁸ +  Log₂2^-5   

= 8Log₂2 +  -5Log₂2       ( remember  Log_aa^c = cLog_aa )

= (8 x 1) +  (-5 x 1)          ( remember  Log_aa = 1 )

= 8 + (-5)

= 3

Hence Log₂(256 x ¹/₃₂) = 3

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

Evaluate Log₂(512 x ¹/₁₂₈).

AXIS OF SYMMETRY 1

Find the axis of symmetry for F(x) = 11x² + 40x + 8

Solution

a=11, b=40

Axis of symmetry = -b/2a

                                 =  -(40)

                                   2 x 11

                                =    -40

                                       22

                                =   -20

                                     11

Hence the axis of symmetry is ^-20/11

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

Find the axis of symmetry for F(x) = 5x² + 70x + 1

LOGARITHMS 1

If log₆(3x + 210)=3; find x.

   Solution

Log₆(3x + 210)=3

 (3x + 210)=6³   

                      

 3x + 210= 216

3x = 210 – 216

3x =  6

3x =  6   

3        3

X = 2

Hence x = 2

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

If log₂(2x - 26)=4; find x

ALGEBRA 1

Divide 48ax + 22ay - 10az by 2a

solution

= 48ax + 22ay - 10az

               2a

= ²⁴48ax  +  ¹¹22ay  -  ⁵10az       [cancelling by 2a throughout]

       2a            2a          2a

= 24x + 11y - 5z

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

Divide 80am - 32an + 76ap by 4a

ARITHMETIC PROGRESSION 1

The 1st term of an A.P. is 70 and the common difference is 16. Find the 10th term.

Solution

A₁= 70, d = 20

A_n = A₁ + (n-1)d

A₁₀ = A₁ + (10-1)d

A₁₀ = A₁ + 9d

A₁₀ = 70 + (9x16) [ after substituting A₁= 70, d = 16 as given above]

∴ A₁₀ = 70 + 144

A₁₀ = 214

Hence the 10th term is 214.

TRY THIS……………

The 1st term of an A.P. is 30 and the common difference is 43. Find the 9th term.