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?

MATRICES G1

 

PERCENTS D1

 

In a box of 500 books, 160 are red in colour, 110 are yellow in colour while the rest are bluish in color. Give out the percentage of blue books.

 

solution

 

1st we have to get the number of blue books.

 

 blue books = 500 – 160 - 110 = 230

 

then,=  230 x 100

            500

 

then,=  230

             5

 

   = 46%

 

Hence percentage of blue books is 46%

 

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In a box of 800 books, 300 are yellow in colour, 260 are red, while the rest are greenish in color. Give out the percentage of green books.

QUADRATICS A3

Show that  4w² – 20w + 25=0  is a perfect square.

Solution  

a=4, b=-20, c=25. 

We use the formula: b² = 4ac.

b² = 4ac.

(-20)² = 4 x 4 x 25

(-20 x -20) = 4 x 4 x 25

+400 = 16 x 25

+400 = +400

LHS = RHS. Hence shown!   

 

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Show that  9w² – 30w + 25=0  is a perfect square. 

LOGARITHMS J6

 

If log₈(3x + 19)=2; find x

 

   Solution

 

Log₈(3x + 19)=2

 

 (3x + 19)=8²   [changing logarithmic form into exponential form]

                      

 3x + 19=64

 

 

3x = 64 – 19

 

3x =  45

 

 

3x =  45         [dividing by 3 both sides]

3        3

 

x = 15

 

Hence x = 15

 

 

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If log₃(3u - 39) = 5; find u.

SETS C2

 

If n(A)= 173 , n(B)= 170 and n(AnB)=200, find n(AuB).

 

Solution

 

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

 

             = 173 + 170 – 200

 

             = 333 – 200

 

             = 133

 

Hence n(AuB) = 133 answer

  

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If n(A)= 187 , n(B)= 169 and n(AnB)=125, find n(AuB).  

QUADRATICS A2

 

What must be added to x²  + 48x to make the expression a perfect square?

 

Solution

 

a=1, b=48,c=?

 

b² = 4ac

 

(48)² = 4 x 1 x c

 

2304 = 4c

 

2304 = 4c

 4         4

 

576 = c

 

Hence number to be added is 576

 

 

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What must be added to x²  + 32x to make the expression a perfect square?  

FUNCTIONS 3E

 

Find the axis of symmetry for F(x) = 7x² - 54x + 7

 

Solution

 

a=7, b=-54

 

Axis of symmetry = -b/2a

 

                              =  -(-54)

                                  2 x 7

 

                              =    54

                                   14

 

                              =     27

                                     7

 

 

Hence the axis of symmetry is ²⁷/7

 

 

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Find the axis of symmetry for F(x) = 4x² - 48x + 7