EXPONENTIALS-1

If (x³)(y²) = 500; find x and y.

solution

(x³)(y²) = 500  [500=2x2x5x5x5 by prime factorization].

(x³)(y²) = (5³ )x (2²)     [ since 500=5³ x 2³].

equating equal powers,

(x³) = (5³)   

x   =   5

also,

(y²) = (2²)

 y    =   2

∴ x   =   5 and y    =   2

TRY THIS…………

If (m³)(n⁵) = 4000; find m and n.

MATRIX 1

PROBABILITY 2

Given the interval of 1-12 inclusive, Find the probability of having an even number or a prime number.

Solution

This is a non-mutually exclusive event.

n(S) = number of sample space = 12

Let P(E)= probability of even numbers = ⁶/12

Let P(R)= probability of prime  numbers = ⁵/12

P(EnR) = probability of having both even and prime numbers= ¹/12

∴ P(EuR) = P(E) + P(R)  - P(EnR).

 P(EuR) =  6  +  5 – 1

                12    12   12

P(EuR) =  11  -   1 

                12     12  

P(EuR) =  10 

                12      

Hence probability of an even number or a prime number is ^5/6.

TRY THIS........

Given the interval of 1-15 inclusive, find the probability of having an even number or a prime number.

EXPONENTS 2

Simplify 5

            125^-2/3

Solution

=  5

  125^-2/3

=  5 x 1

         125^-2/3

=  5 x 125^2/3        [Since 1/a^-n = aⁿ]

=  5 x (125^1/3)²        [Since 125^1/3 = cube root of 125 = 5]

=  5 x (5)²        

=  5 x 25

= 125        

         

Hence   5        = 125

            125^-2/3

TRY THIS…………………………

simplify 5

             27^-2/3

DEGREES TO RADIAN

Change 1200⁰ into radians.

Solution     

s = ∏Ө/180

            

s = ∏ x 1200

              180

s =  20∏ radians

        3

Hence 500⁰ = 20∏ radians            .

                           3                               

TRY THIS…………….

Change 1500⁰ into radians

ALGEBRA 4

Expand 2x(6x – 5)

Solution

= 2x(6x – 5)

= (2x x 6x) – (2x x 5)

= 12x² – 10x

Hence 2x(6x – 5) = 12x² – 10x

TRY THIS……………

Expand 11a(7a – 4)

EXPONENTS 1

Simplify (m⁴)⁷

solution

= (m⁴)⁷

=  m^4x7

=  m²⁸

TRY THIS........

Simplify  (h¹⁸)⁵

ARITHMETICS 2

Evaluate  20 + 6 – 5 – 7 – 9 + 10.

Solution

= 20 + 6 – 5 – 7 – 9 + 10

= 20 + 6 + 10 – 5 – 7 – 9

= 20 + 6 + 10 – ( 5 + 7 + 9)

= 36 – 21

= 15

TRY THIS

Evaluate  35 + 6 – 4 – 7 – 11 + 8

ARITHMETICS 1

Evaluate 144 x 545 + 455 x 144

Solution

= 144 x 545 + 455 x 144

= 144 x (545 + 455)

= 144 x 1000

= 144000

Hence 144 x 545 + 455 x 144 = 144000

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

Evaluate 132 x 376 + 624 x 132

FACTORIZATION 7

Factorize 3x² - 8x - 35.

Solution

= 3x² - 8x - 35. We split the middle term (-8x) to be (+7x-15x).

= 3x² + 7x - 15x - 35.

= (3x² + 7x) – (15x – 35).

= x(3x + 7) – 5(3x + 7).

= (x - 5) (3x + 7)

Hence 3x² - 8x – 35 = (x - 5) (3x + 7) answer.

TRY THIS…..

2x² - x + 15.