ALGEBRA 2

The sum of five consecutive numbers is 525. Find the 4th number.

Solution

Let the numbers be as shown in the table below

1st number	2nd number	3rd number	4th number	5th number	TOTAL
n	n+1	n+2	n+3	n+4	525

Then, n + (n+1) + (n+2) + (n+3) + (n+4) = 525

5n + 1+2+3+4= 525

5n + 10= 525

5n = 525- 10

5n = 515 

5n = 515

5       5

n = 103

4th number = n + 3

                   = 103 + 3

                   = 106

Hence the 4th number is 106

TRY THIS………………….. 

The sum of five consecutive numbers is 1815. Find the largest number.  

FUNCTIONS 1

FACTORIZE 1

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

TRY THIS…………….

Factorize 1 – 49y²

LOGARITHMS 1

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

= -6 x -20

= 120

TRY THIS………..

If Log_aW= -70, find Log_a(¹/W⁴)

ALGEBRA 1

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

                                               6         2

solution

= m - 3 + m+5

      6          2

= m - 3 + 3(m+5)

            6         

= m - 3 + 3m+15

            6         

= m + 3m + 15- 3

            6         

= 4m +  12

         6         

= 4(m +  3)

         6         

= 2(m +  3)

         3         

= 2m +  6       answer

         3         

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

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

                                                3          2

PERIMETER 1

Area of a rectangle is 84 cm². Find its perimeter if its width is 7cm.

Solution

First we find length

A =  l  x w

84 =  l  x 7

84 = 7l

7       7

12 =  l

Now length is 12cm.

We can find perimeter since we have both length and width.     

Let l = length and w = width;

P = 2(l + w)

   = 2(12 + 7)

   = 2 x 19

   = 38

Hence perimeter is 38 cm. 

TRY THIS………………….. 

Area of a rectangle is 72 cm². Find its perimeter if its width is 4cm.

ALGEBRA 1

If │2x – 7 │= 17; Find  x

Solution

±(2x – 11 )= 17

2x -11= 17    OR   –(2x-11) = 17

2x – 11 = 17    OR   -2x+11=17

2x = 17 + 11    OR   -2x= 17-11

2x = 28     OR   -2x  =   6

2      2                -2        -2

x = 14  OR  x = -3

Hence x = 14 OR x = -3

TRY THIS………………………. 

If │2x – 7 │= 35; Find x

EXPAND 1

Expand -10(y – 5)

Solution

= -10(y – 5)

= (-10 x y) – (-10 x 5)

= 10y – ^-50 answer

= 10y + ⁺50

= 10y + 50 answer

TRY THIS………..

Expand ^-8(W– 9)

SETS 1

If n(A)= 90 , n(B)= 100 and n(AnB)=50, find n(AuB).

Solution

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

             = 90 + 100 – 50

             = 190– 50

             = 140

Hence n(AuB) = 140 answer

TRY THIS………….

If n(A)= 140 , n(B)= 150 and n(AnB)=100, find n(AuB).

SIMPLE INTEREST 1

Angloma deposited the amount of 110,000/= in a bank which gives an interest rate of 5% for 5 years. Find the simple interest she got?

Solution

I = ?,  P = 110,000/=, T = 5 years, R = 5%

I  = PRT

      100

I  = 110,000 x 5 x 5

            100

I  = 110000 x 5 x 5

            100

I  = 1100 x 5 x 5

          

I  = 275,000/=

Hence the simple interest was Tsh 275,000/=

TRY THIS………………..

  

Jelna deposited the amount of 18000/= in a bank which gives an interest rate of 3% for 5years. Find the simple interest she got?