PERCENTAGE PROFIT 2

Dikshi got a profit of 1,794/= after selling an item for 24,794/=. Find the percentage profit.

Solution

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

                        B.P

But; Profit = SP - BP;     [where S. P. represents Selling Price.]

So; B.P = SP – Profit

B.P = 24,794 – 1794

       = 23,000

%’ge profit = 1794   x  100    

                      23000

%’ge profit = 1794 

                      230

%’ge profit = 7⁴/5%   

        

              

Hence Percentage Profit was 7⁴/5%   

TRY THIS………………..

Janhwi got a profit of 220,000/= after selling an item for 266,200/=. Find the percentage profit.      Answer 21%

AXIS OF SYMMETRY 1

Find the axis of symmetry for F(x) = 7x² - 50x + 7

Solution

a=7, b=-4

Axis of symmetry = -b/2a

                              =  -(-50)

                                  2 x 7

                              =    50

                                   14

                              =     25

                                     7

Hence the axis of symmetry is ²⁵/7

TRY THIS…………

Find the axis of symmetry for F(x) = 8x² - 15x + 7 

VECTORS 1

If u = 6i + 2j and v = 7i + 10j find 5u - 3v

solution

= 5u - 3v

= 5(6i + 2j) - 3(7i + 10j)

= 30i + 10j - 21i - 30j

= (30i + 21i) + (10j - 30j)

= 51i - 20j

Hence 5u - 3v = 51i - 20j

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

If u = 7i + 3j and v = 4i + 4j;  find 2u + 6v.

LOGARITHMS 9

Evaluate Log₂(1024 x 8).

Solution

= Log₂(1024 x 8)

= Log₂1024 +  Log₂8          (applying the product rule)

= Log₂2¹⁰ +  Log₂2³             ( 1024= 2¹⁰ and 8=2³ )

= 10Log₂2 +  3Log₂2       ( remember  Log_aa^c = cLog_aa )

= (10 x 1) +  (3 x 1)          ( remember  Log_aa = 1 )

= 10 + 3

= 13

hence Log₂(1024 x 8) = 13 

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

Evaluate Log₂(1024 x 64). 

EXPONENTIALS 6

If k⁵ - 200 = 2925; find k.

Solution

k⁵ - 200 = 2925

k⁵ = 2925 + 200 [taking 200 in the right hand side]

k⁵ = 3125

k = 5 [since the 5^th root of 3125 is 5]

Hence k = 3

TRY THIS…………………………

If w⁵ - 20 = 223; find w.

QUADRATICS 3

What must be added to x²  + 40x to make the expression a perfect square?

Solution

a=1, b=12,c=?

b² = 4ac

(40)² = 4 x 1 x c

1600 = 4c

1600 = 4c

 4         4

400 = c

Hence number to be added is 400

TRY THIS……………………

What must be added to x²  + 28x to make the expression a perfect square?  

LOGARITHMS 8

Simplify Log₂128 – Log₅3125 – Log₆216

Solution

= Log₂128 – Log₅3125 – Log₆216

= Log₂2⁷ – Log₅5⁵ – Log₆6³

= 7Log₂2 – 5Log₅5 – 3Log₆6  because Log_aaⁿ =  nLog_aa

= (7 x 1) – (5 x 1) – (3 x 1)    

= 7 – 5 - 3

= -1

Hence Log₂128 – Log₅3125 – Log₆216 = -1 

TRY THIS…………..

Simplify Log₂2048 – Log₃9 – Log₅3125

PROBABILITY 2

A number is chosen at random from 1 – 10 inclusive. Find the probability that it is a multiple of five or an even number.

Solution

THIS IS A MUTUALLY EXCLUSIVE EVENT.

Let n(S) represent sample space

P(E) = probability of even number

P(M) = probability of a multiple of 5

n(S) = {1, 2, 3, 4, 5, 6, 7, 8, 9,10} = 10

n(E) = {2, 4, 6, 8, 10} = 5

n(M) = {5,10} = 2

P(E) = ⁵/10

P(M) = ²/10

………………………….

P(EuM) = P(E) + P(M)

P(EuM) = ⁵/10 + ²/10

∴ P(EuM) = ⁷/10

TRY THIS………………

A number is chosen at random from 17 – 24 inclusive. Find the probability that it is a prime or an even number.

VARIATION 2

x is directly proportional to y. x=12 while y=4. Find y when x is 600.

Solution

x ⍺ y

x = ky

12 = k x 4

12 = 4k

4      4

k = 3

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

k = 3, y= ? x = 600.

600 = 3 x y

600  = 3y       (dividing by 3 on both sides)

 3        3

Hence y = 200 answer.

TRY THIS…………….

x is directly proportional to y. x=20 while y=4. Find y when x is 70.

FUNCTIONS 4

If F(x) = 21x + 10; Find F^-1(x).

Solution

HINT: F^-1(x) means inverse.

PROCEDURE:

Make x the subject and then interchange x and y variables.

Let y=F(x)

So,  y= 21x + 10

y – 10 = 21x

y – 10  = 21x

   21        21

y – 10   = x

   21

x  =   y – 10     after rearranging

           21

 y^-1 = x – 10     after interchanging x and y variables.

             21

F^-1(x) = x – 10     after interchanging x and y variables.

                21

Hence, F^-1(x) = x – 10     

                             21

TRY THIS……………………………

If F(x) = 17x + 26; Find F^-1(x).