PERCENTS J4

 

In a box of 500 books, 60 are red in colour, 140 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 – 60 - 140 = 300

 

then,=  300 x 100

            500

 

then,=  300

             5

 

   = 60%

 

Hence percentage of blue books is 60%

 

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

  

In a box of 800 books, 300 are yellow in colour, 200 are red, while the rest are greyishish in color. Give out the percentage of grey books.

SQUARES J2

 

Evaluate 20396² – 20386²

 

Solution

We use difference of two squares;

a² – b² = (a – b)(a + b)

 

20396² – 20386² = (20396 + 20386)(20396 – 20386)

 

                     = (40782)(10)

 

                     = 407820

 

20396² – 20386² = 407820

 

TRY THIS…………….

 

 

Evaluate 457308² – 457208²

FUNCTIONS J2

 

Find the axis of symmetry for F(x) = 4x² + 20x + 8

 

Solution

 

a=4, b=10

 

Axis of symmetry = -b/2a

 

                               =  -(20)

                                    2 x 4

 

                               =    -20

                                      8

 

 

Hence the axis of symmetry is -2.5

 

TRY THIS…………………

 

 

Find the axis of symmetry for F(x) = 6x² + 40x + 3

ALGEBRA J3

 

Solve the following equations by substitution method.

x + y = 3

x + 3y = -3

 

Solution

 

x + y = 3 ----------- (i)

x + 3y = -3 ---------- (ii)

 

from equation (i)

 

x + y = 3

x = 3 - y ----------(iii)

 

substitute equation (iii) in (ii) above,

 

x + 3y = -3

 

(3 - y) + 3y = -3

3 - y + 3y = -3  

3 + 2y = -3  

2y = -3 - 3 

 

2y = -6           [since –y+3y=2y]

 

 

 

2y = -6

2      2

 

y = -3

 

 

From equation (iii)

x = 3 - y

x = 3 – (-3) ----------(iii)

x = 3+3

x=6

Hence x=6 and y=-3.

 

 

TRY THIS………………………..

 

 

5x - 2y = 14

x  -  y = 4

EXPAND J2

 

Expand 7w(w – 60 - w²)

 

solution

 

= 8w(w – 60 - w²)

 

= (8w x w) – (8w x 60) + (8w x w²)

 

= 8w² – 480w +   8w³   answer

 

 

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Expand 4e(e + 70 – e²)

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

 

 

TRY THIS………..

 

 

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/=

 

 

TRY THIS……………………

 

 

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?