FACTORIZATION - 6

Factorize 6x² + 7x - 5

Solution

= 6x² + 7x - 5.  ---- We split the middle term (+7x) to be (-3x + 10x).

= 6x² - 3x + 10x – 5             -----   (-3x) = -14x + 5x.

= (6x² -3x) + (10x - 5)   ---- grouping the factors.       

= 3x(2x - 1) + 5(2x - 1)

= (3x + 5) (2x -1)

Hence 6x² + 7x - 5= (3x + 5) (2x -1)answer.

TRY THIS…..

Factorize 14x² + 3x – 2.

SETS - 3

If n(A)= 60 , n(AuB) = 168 and n(AnB)=10, find n(B)

Solution

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

  168     = 60 + n(B)  – 10

  168     = 60 -10 + n(B) 

  168     = 50 + n(B) 

  168 - 50        = n(B)

  118        = n(B)

Hence n(B) = 118 answer

TRY THIS…………………………….

If n(A)= 62 , n(AuB) = 135 and n(AnB) = 33, find n(B).

GEOMETRY - 1

If x-5⁰ and 4x + 35⁰ are complementary angles, find the value of x.

Solution

Complementary angles add up to 90⁰.

so,  x-5⁰ + 4x + 35⁰ = 90⁰.

so,  x + 4x + 35⁰ - 5⁰ = 90⁰.

so,  5x + 30⁰ = 90⁰.

so,  5x = 90⁰ -  30⁰

so,  5x = 60⁰

so,  5x = 60¹²

       5       5

Hence x = 12⁰

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

If 3x - 12⁰ and 2x + 57⁰ are complementary angles, find the value of x.

ALGEBRA - 5

Multiply 9x - 7y by -6a

Solution

= -6a(9x - 7y)

= (-6a x 9x) + (-6a x -7y)

= -54ax + 42ay     [since -6a x -7y = +42ay ]

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

Multiply 12p - 9q by  -2a

LOGARITHMS-8

If log 3= 0.4771; find the value of log 27,000 without using tables.

solution

=log27,000

=log(1,000 x 27)

=log1,000 + log27

=log10³ – log3³

=3log10 – 3log3

=(3x1) –  3(0.4771)

=3– 1.4313

= 1.5687

Hence log27,000 = 1.5687

TRY THIS……………

If log 3= 0.4771; find the value of log 2,700,000 without using tables.

FRACTIONS-1

1/9 of the lessons is Allocated to mathematics and 1/4 is allocated to civics. What fraction is left for other subjects?

Solution

amount of lessons allocated = 1  +  1

                                                9      4

amount of lessons allocated = 4  +  9

                                                  36

amount of lessons allocated = 13

                                                36

Now, the total number of lessons  = 1 = 36

                                                               36

Fraction for other subjects = total number of lessons  -  amount of lessons allocated.

Fraction for other subjects = 36  -  13

                                              36     36

Fraction for other subjects = 23 

                                              36    

Hence fraction for other subjects is ²³/36

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

5/11 of the lessons is Allocated to mathematics and 1/22 is allocated to Geography. What fraction is left for other subjects?

POLYGONS-1

A regular polygon has 83 sides. Find the total angles of that polygon.

Solution

n = 83

Total angles = (n - 2)180⁰

                   = (83 – 2)180⁰

                   = 81 x 180⁰

                   = 14580⁰

Total angles = 14580⁰

TRY THIS……………………….

A regular polygon has 58 sides. Find the total angles of that polygon.

CIRCLES-1

Find radius if the length of an arc of the circle is ^∏/₁₅ cm.

Solution

L= ^∏/₅  , r = ?

L = ∏r

      180

^∏/5  = ∏r

         180

180  x ^∏/5  = ∏r  x   180   

                    180

180∏  = ∏r 

     5      

                    

180 ∏  = ∏r 

    15∏  ∏

180   =  r 

    15      

r = 36cm

Hence radius is 36 cm

TRY THIS………………..

Find radius if the length of an arc of the circle is ^∏/₂₀ cm.

LOGARITHMS-7

If Log_ax = 23, find Log_a(¹/x)

Solution

= Log_a(¹/x)

= Log_ax^-1

= -1 x Log_ax

= -1 x 23

= -23

TRY THIS………..

If Log_aW= 86, find Log_a(¹/W)

APPROXIMATIONS-3

Estimate the value of 8123  ÷ 22.

solution

= 8123     

     22

= 8000      [ since 8123 ≈ 8000   and   22 ≈ 20 ]

     20

= 400

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

Estimate the value of 91623  ÷ 341