PERFECT SQUARES C1

 

What must be added to x²  + 14x to make the expression a perfect square?

 

Solution

 

a=1, b=14,c=?

 

b² = 4ac

 

(14)² = 4 x 1 x c

 

196 = 4c

196 = 4c

 4       4

 

49 = c

 

Hence number to be added is 49

And the expression will be: x²  + 14x +49=0

 

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What must be added to x²  + 10x to make the expression a perfect square?   

VECTORS C1

 

FACTORIZE C1

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Factorize 1-25m²

 

Solution

 

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

 

1-25m² = 1²-5²m²       

 

            = 1² - (5m)²       

 

            = (1 - 5m)(1 + 5m)

 

Hence 1-25m² = (1 - 5m)(1 + 5m)  answer

 

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Factorize 1 – 49y²

ALGEBRA C2

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If 12w² = 588; find w.

Solution

12w² = 588

 

12w² = 588               [Dividing by 12 both sides]

12          12

 

w² = 49

w = 7          Because the square root of 49 is 7.   

 

Hence w = 7 . 

 

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If 14u² = 224; find u.

LOGARITHMS C1

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If Log_ax = -20, find Log_a(¹/x⁶)

 

Solution

 

= Log_a(¹/x⁶)                        

 

= Log_ax^-6                   [since ¹/cⁿ =c^-n]

 

= -6 x Log_ax       [since Log_mxⁿ   = nLog_mx]               

 

= -6 x -20

 

= 120

 

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If Log_aW= -30, find Log_a(¹/W⁵)

ALGEBRA C1

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Express as a single fraction m - 3 + m+5

                                               6         2

Solution

 

= m - 3 + m+5

      6          2

 

= m - 3 + 3(m+5)              [Since LCM of 6 and 2 is 6]          

            6         

 

= m - 3 + 3m+15               [Since 3(m+5)  = 3m+15]               

            6         

 

= m + 3m + 15- 3

            6         

 

= 4m +  12

         6         

 

= 4(m +  3)

         6         

 

= 2(m +  3)

         3         

 

= 2m +  6       answer

         3         

  

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Express as a single fraction 4n - 1 + n+1

                                                3          2

EXPAND C1

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Expand (y – 10) (y – 16)

 

solution

 

= (y – 10) (y – 16)

 

= y (y – 16) – 10 (y – 16)

 

= y² – 16y – 10y + 160 

 

= y² – 26y + 160  since (– 16y – 10y) = – 26y

 

= y² – 26y + 160 answer

 

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Expand (w – 2) (w – 11)

METRIC UNITS C1

 

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Change 51260m into Hm.

  

Solution

 

 

1Hm = 100m

?  =  51260m

 

 

= 1  x  51260

       100

 

=     551260

       100

 

= 512.6Hm

 

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Change 3502m into Hm.

RATES AND VARIATIONS B1