LOGARITHMS 1

Evaluate Log60 – Log0.3 + Log500.

Solution

= Log60 – Log0.3 + Log500.

= Log(60 x 500)

               0.3

= Log(30000)

             0.3

= Log(300,000)

              3

= Log 100,000

             

= Log₁₀100,000

= Log₁₀10⁵

            

= 5Log₁₀10

= 5 x 1

= 5

∴ Log600 – Log0.3 + Log50 = 4

TRY THIS……………………….

Evaluate Log600 – Log4.8 + Log80,000

MATRIX 2

POLYGONS 1

The total interior angles of the regular polygon is 14580⁰. Find the number of sides.

Solution

Total angles = (n - 2)180⁰

14580⁰ = (n - 2)180⁰

⁸¹14580⁰ = (n - 2)180⁰   dividing by 180⁰ both sides.

    180⁰             180⁰

81 = n - 2

81 + 2 = n

n = 83

Hence number of sides is 83

TRY THIS……………………….

The total interior angles of the regular polygon is 11160⁰. Find the number of sides.

MAKING SUBJECT 1

SIMILARITY 2

Prove that the 2 triangles below are similar.  

Solution

<XWY = <YZW = 26⁰ ------- Given

<WYX = <ZYW = 90⁰ ------- Given

<WXY= <ZWY = 64⁰ ------- (3^rd angles of a triangle)

Hence ΔWYX = ΔZYW --- (By AA – Similarity theorem)

TRY THIS……………………..

Prove that the 2 triangles below are similar.

EXPONENTIALS 1

If 5^(6m-7) x 3^(2n+22) = (3⁴⁴) x (5⁵³); Find m and n.

Solution

Equating equal bases;

5^(6m-7) =  5⁵³

5^(6m-7) =  5⁵³

6m - 7 = 53

6m  = 53 + 7

6m  = 60

¹6m  = 60¹⁰

₁6         6₁

m = 10

again for n we equate equal bases.

3^(2n+22) = 3⁴⁴

3^(2n+22) = 3⁴⁴

2n + 22 = 44

2n = 44 - 22

2n = 22

2       2

n = 11

Hence m = 10 and n = 11

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

If 8^(2x-19) x 13^(2y+40) = (13⁶⁶) x (8⁴³); Find x and y.

SIMILARITY 1

Prove that the 2 triangles below are similar.  

Solution

<FEG = <EHG = 37⁰ ------- Given

<EGF = <HGE = 90⁰ ------- Given

<EFG = <HEG = 53⁰ ------- (3^rd angles of a triangle)

Hence êEGF = êHGE --- (By AA – Similarity theorem)

TRY THIS……………………..

Prove that the 2 triangles below are similar.

PROBABILITY 2

A bag contains 12 red balls and 8 blue balls. Two balls are taken from the bag. What is the probability that they are both blue?

Solution

(This is a problem with replacement)

n(R) = 12, n(B) = 8, n(S) =20

P(B) = n(B)

            n(S)

1st pick = 8/20

2nd pick = 8/20 as well.

P(B) =  8      x    8

           20          20

P(B) =   64    =      4 

            400          25  

Therefore Probability of drawing a blue ball is 4/25     

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

A bag contains 10 purple stones and 12 blue stones. Two stones are taken from the bag. What is the probability that they are both blue?

ARITH. PROGR. 1

The first term of an AP is 13 and the last term is 157.If the arithmetic progression consists of 20 terms, calculate the sum of all the terms. 

Solution

A₁ = 13, n=20, A_n = 157

S_n = n(A₁ + A_n)

       2

S₂₀ = 20(13 + 157)

         2

S₂₀ = 10 x 170

S₂₀ = 1700

Hence the sum of all 20 terms is 1700.

TRY THIS………….

The first term of an AP is 11 and the last term is 107.If the arithmetic progression consists of 30 terms, calculate the sum of all the terms. 

ALGEBRA 2

Find a if 50 + 24 =56

                        a

Solution

50 + 24 =52

        a

   24  = 52 - 50

   a

   24  =  2

    a

¹ a  x  24  =  2 x a

        ₁ a

24 = 2a

24  = 2a

2       2

12 = a

Hence a=12.

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

If 30 + 24 = 38; find c

           c