ALGEBRA J1

 

Expand 8w(w – 3 + w²)

 

solution

 

= 8w(w – 3 + w²)

 

= (8w x w) – (8w x 3) + (8w x w²)

 

= 8w² – 24w +   8w³   answer

 

 

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Expand 10p(p + 7 – p²)

LOGARITHMS J1

 

If Log_ax = 46, find Log_a(¹/x⁵)

 

Solution

 

= Log_a(¹/x⁵)

 

= Log_ax^-5

 

= -5 x Log_ax   [Since  Log_axⁿ = nLog_ax]

 

= -5 x 46

 

= -230

 

 

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If Log_aW= 60, find Log_a(¹/W⁷)

PERFECT SQUARES J1

 

If 16x² – 8x + e is a perfect square, find e.

 

Solution

 

a = 16, b = -8, c = e.

 

b² = 4ac

 

(-8)² = 4 x 16 x e

 

64 = 64e

 

64 = 64e

64     64

           

e = 1

 

Hence e = 1

 

 

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If 49x² – 28x + n is a perfect square, find n

FACTORIZATION J1

Evaluate 173² – 163²

 

Solution

 

We use difference of two squares;

a² – b² = (a – b)(a + b)

 

173² – 163² = (173 + 163)(173 – 163)

 

                     = (336)( 10)

 

                     = 3360

 

173² – 163² = 3360

 

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Evaluate 313² – 303²

SIMPLE INTEREST J1

 

Dikshi deposited the amount of 9000/= in a bank which gives an interest rate of 3% for 7 years. Find the simple interest she got?

 

Solution

 

I = ?,  P = 9,000/=, T = 7 years, R = 5%

 

I  = PRT

      100

 

I  = 9000 x 5 x 7

            100

 

I  = 9000 x 5 x 7

            100

 

I  = 90 x 5 x 7

          

I  = 31500/=

 

Hence the simple interest was Tsh 31500/=

 

 

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Anjali deposited the amount of 18 000/= in a bank which gives an interest rate of 6% for 4 years. Find the simple interest she got?