RATIOS 3

Given the ratios U:V = 9: 8 and V:W = 20:7 Find the ratio U:W.

solution

U = U x V

W   V   W

U =   9 x 20⁵

W   ₂ 8    7

U =   9 x 5

W       2 x 7

U =   45

W     14

Hence U:W = 45:14

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

Given the ratios D:E = 5:7 and E:F = 3:15;  Find the ratio D:F.

FACTORIZATION 2

Factorize 2x² - 9x - 35

Solution

= 2x² - 9x – 35.  We split the middle term (-9x) to be (-14x + 5x).

= 2x² - 14x + 5x – 35                (-3x) = -14x + 5x.

= (2x² -14x) + (5x - 35)

= 2x(x - 7) + 5(x - 7)

= (2x + 5) (x -7)

Hence 2x² - 9x – 35 = (2x + 5) (x - 7) answer.

TRY THIS…..

Factorize 7x² - 27x – 4.

VECTORS 2

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

solution

= 2u - 6v

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

= 12i + 4j - 18i - 60j

= (12i + 18i) + (4j - 60j)

= 30i - 56j

Hence 2u - 6v = 30i - 526j

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

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

SETS 1

If n(A)= 140 , n(B)= 160 and n(AnB)=150, find n(AuB).

Solution

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

             = 140 + 160 – 150

             = 300 – 150

             = 150

Hence n(AuB) = 150 answer

TRY THIS…………………………….

  

If n(A)= 140 , n(B)= 160 and n(AnB)=130, find n(AuB).

LOGARITHMS 2

Find x if Log_x16 = 4

solution

Log_x16 = 4

16 = x⁴ .

2⁴ = x⁴ . [since 16 = 2⁴ by prime factorization]

2⁴ = x⁴ . [ powers cancel out]

x = 2

Hence x = 2

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

Find y if Log_y27 = 3

RATIOS 2

Given the ratios M:N = 9: 8 and N:P = 8:7 Find the ratio M:P.

solution

M = M x N

P      N     P

M =   9 x 8¹

P     ₁ 8    7

M =   9 x 1

P       1 x 7

M =   9

P      7

Hence M:P = 9:7

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

Given the ratios A:B = 11:3 and B:C = 3:13 Find the ratio A:C.

DIFFERENCE OF 2 SQUARES

Evaluate 392² – 382²

Solution

392² – 382² = (392 + 382)( 392 – 382)

                   = (674)( 10)

                   = 6740

392² – 382² = 6740

TRY THIS…………….

Evaluate 605² – 505²

SIMPLE INTEREST 1

Dikshi deposited the amount of 9000/= in a bank which gives an interest rate of 3% for 4 years. Find the simple interest she got.

Solution

I = ?,  P = 9,000/=, T = 4 years, R = 3%

I  = PRT

      100

I  = 9000 x 3 x 4

            100

I  = 9000 x 3 x 4

            100

I  = 90 x 3 x 4

          

I  = 1080/=

Hence the simple interest was Tsh 1080/=

TRY THIS………………….

Edmund deposited the amount of 50,000/= in a bank which gives an interest rate of 6% for 4 years. Find the simple interest she got?

VECTORS 1

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

solution

= 2u - 3v

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

= 12i + 4j - 21i - 30j

= (12i + 21i) + (4j - 30j)

= 33i - 26j

Hence 2u - 3v = 33i - 26j

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

If u = 9i + 3j and v = 2i + 4j;  find 2u + 3v.

LOGARITHMS 1

Find x if Log_x256 = 8

solution

Log_x256 = 8

256 = x⁸ .

2⁸ = x⁸ . [since 256 = 2⁸ by prime factorization]

2⁸ = x⁸ .

x = 2

Hence x = 2

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

Find y if Log_y81 = 4

RATIOS 1

Given the ratios M:N = 9: 8 and N:P = 4:7 Find the ratio M:P.

solution

M = M x N

P      N     P

M =   9 x 4¹

P     ₂ 8    7

M =   9 x 1

P       2 x 7

M =   9

P      14

Hence M:P = 9:14

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

Given the ratios A:B = 5:3 and B:C = 6:7 Find the ratio A:C.