ARITHMETIC PROGRESSION H6

 

The 1st term of an A.P. is 200 and the common difference is 80. Find the 10th term.

 

Solution

 

A₁= 200, d = 80

 

A_n = A₁ + (n-1)d

 

A₁₀ = A₁ + (10-1)d

 

A₁₀ = A₁ + 9d

 

A₁₀ = 200 + (9x80) [after substituting A₁= 72, d = 80 as given above]

 

∴ A₁₀ = 200 + 720

 

A₁₀ = 920

 

Hence the 10th term is 920.

 

  

TRY THIS……………

 

 

 

The 1st term of an A.P. is 600 and the common difference is 130. Find the 5th term.

VARIATION H3

 

x is directly proportional to y. x=32 while y=8. Find y when x is 184.

 

Solution

 

x ⍺ y

x = ky

 

32 = k x 8

 

32 = 8k    [dividing by 8 both sides]

8      8

 

k = 4

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

 

k = 4, y= ? x = 204.

 

x = ky

 

204 = 4 x y

 

204 = 4y

4        4

 

y = 51.

 

TRY THIS…………….

 

 

x is directly proportional to y. x=40 while y=4. Find y when x is 190.

ALGEBRA H4

If │2x – 7 │= 37; Find  x

 

Solution

 

±(2x – 11 )= 37

 

2x -11= 37    OR   –(2x-11) = 37

 

2x – 11 = 37    OR   -2x+11=37

 

2x = 37 + 11    OR   -2x= 37-11

 

2x = 48     OR   -2x  =   26

2      2               -2        -2

 

x = 24  OR  x = -13

 

 

Hence x = 14 OR x = -3

 

TRY THIS………………………. 

 

 

If │2x – 15 │= 63; Find x 

SIMPLIFY G8

 

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

                                              8         2

solution

 

= m - 3 + m+5

    8          2

 

= m - 3 + 4(m+5)                [Since the LCM of 8 and 2 is 8]

            8         

 

= m - 3 + 4m+20

            8         

 

= m + 4m + 20 - 3

            8         

 

= 5m +  17

        6                       

 

= 5m +  17       answer

        6         

 

 

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

 

Express as a single fraction 7e - 1 + e+1

                                              3          6

FACTORIZE G9

 

Factorize 121-25m²

 

Solution

 

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

 

121-25m² = 11²-5²m²       

 

            = 11² - (5m)²       

 

            = (11 - 5m)(11 + 5m)

 

Hence 121-25m² = (11 - 5m)(11 + 5m)  answer

 

 

TRY THIS…………….

 

 

 

Factorize 64 – 49y²

MID-POINT E1

Find a and b if the midpoint of a line from (a, 6) to (8, b) is

(60, 70)

 

Solution

 

x1=a, x2=8, y1=6, y2=b.

 

(60, 70)= (x1 + x2, y1 + y2)

                   2             2

 

(60, 70)= (a + 8,  6 + b)

                  2          2

 

Equating equal values of x;

 

60= a + 8

         2      

 

2 x 60= (a + 8)  x 2 ¹

                2 ₁     

 

120 = a + 8

 

120-8 = a

 

a = 112.

 

Equating equal values of y;

 

70 = 6 + b

        2

 

2 x 70= (6 + b)  x 2 ¹  multiplying by 2 both sides.

                2 ₁     

 

140 = 6 + b

 

140 – 6 = b

 

b = 134

 

Hence a = 112 and b=134

 

TRY THIS……………………..

 

Find e and f if the midpoint of a line from (e, 19) to (13, f) is (10, 20)

 

 

GEOMETRICAL PROGRESSION A3

 

Find the sum of the 1st eight terms of the geometrical progression 4+16+64+…….

 

Solution

 

G₁ = 4, r=4, n=8

 

S_n = G₁(rⁿ-1)/ r-1

             

 

S₈ = 4(4⁸-1)/4-1

             

 

S₈ = 4(4⁸-1)/3 

             

 

S₈ = 4(262144-1)

             3

 

S₈ = 4(262,143)

             3

 

 

S₈ = 349,524

            

 

 

Hence the sum of the 1st eight terms is 349,524.

 

TRY THIS……………..

 

 

Find the sum of the 1st eight terms of the geometrical progression 3+12+48+…….

LOGARITHMS H6

 

Evaluate Log10,000,000,000 -  log 0.0001 + log₃243

 

Solution

 

= Log10,000,000,000 -  log 0.0001 + log₃243

 

= Log₁₀10¹⁰ -  log₁₀ 10^-4 + log₃3^-5

 

= 10Log10 -  (-4log 10) + (-5log₃3)

 

= (10x1) - (-4x1) + (-5x1)

 

= 10 - (-4) + (-5)

 

= 9

 

Hence Log10,000,000,000 +  log 0.0001 + log₃243 = 9

 

TRY THIS……………..

 

 

Evaluate Log1,000,000,000  -   log 0.000001 + log₃9