Monday 5 February 2024

ARITHMETIC PROGRESSION A2

 

Find the sum of the 1st 22 terms of the following arithmetic progression: 5+11+17+…………………

 

Solution

 

d=6, A1 = 5,n=22

 

Sn = n[2A1 + (n-1)d]

       2

 

S22 = 22[2(5) + (22-1)d]

        2

 

S22 = 11[10 + 21d]

 

S22 = 11[10 + 21(6)]       since d=6

 

S22 = 11[10 + 126]  

         

S22 = 110 + 1386

          

S22 = 1496

 

 

Therefore the sum of 1st 22 terms is 1496.

 

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

 

Find the sum of the 1st 15 terms of the following arithmetic progression: 6+10+14+…………………


ALGEBRA C2D

Factorize 121-9m2

 

Solution

 

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

 

121-9m2 = 112 - 32m2       

             = 112 - (3m)2     

             = (11 - 3m)(11 + 3m)

 

Hence 121 - 9m2 = (11 - 3m)(11 + 3m)

 

TRY THIS…………….

 

Factorize 225 - 36c2 



EXPONENTIALS K10

 

If 410 = 32a-5; find a

 

Solution

 

410 = 32a-5 

 

(22)10 = (25)a-5 

 

220 = 25(a-5) 

 

220 = 25a-25

 

220 = 25a-25  [Same bases both sides cancels out]

 

20 = 5a – 25

 

20 + 25 = 5a

 

45 = 5a

 

45 = 5a

5      5

 

9 = a

 

Hence a=9

 

TRY THIS……………………….

 

 

If 43 = 32x-2; find x


PIE CHART A1

 

In a survey of 60 people, 28 people said their favourite sport was football. What angle in a pie chart would this represent?

Solution

We make a fraction of 28 ot of 60, then multiply by 3600.

= 28 x 3600.

   60

 

= 28 x 36006

   601

 

= 28 x 6

 

= 1680.

 

Hence the angle is 168

 

TRY THIS………………………   

 

In a survey of 30 people, 23 people said their favourite sport was football. What angle in a pie chart would this represent?


LOGARITHMS K13

 Simplify Log24096 - Log327

 

Solution

 

= Log24096 - Log327

 

= Log2212 - Log333

 

= 12Log22 - 3Log33

 

= (12 x 1) - (3 x 1)

 

= 12 - 3

 

= 9

 

Hence Log24096 - Log327 = 9

 

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

 

 

Simplify Log2256 – Log525

COORDINATES A2

If m(4,6), B(7,10) and C(a,2) are collinear, find a.

 

Solution

 

x1=4, y=6, x2=7, y2=10, x3=a, y3=2.

 

y2 – y1  =   y3 – y2

x2 – x1     x3 – x2

 

10 – 6  =   2 – 10        

7 – 4        a – 7

 

 

4    =   -8         Now we cross multiply

3       a - 7

 

 

 

4(a-7) = 3 x -8

4a – 28 = -24

4a   = -24 + 28

4a  = 4

a= 4/4 =1

 

Hence a = 1.

 

TRY THIS………………..

 

If m(2,-3), B(4,5) and C(w,29) are collinear, find w. 



Monday 29 January 2024

COORDINATES A1

 

Find n if a line which passes through (-11, -8) and (6,n) has a slope of -1/17

 

Solution

 

x1 = -11,  y1 =-8,  x2 = 6,  y2 = n

 

m =  y2 –y1

          x2 – x1

 

 

-1y2 –y1

 17     x2 – x1

 

-1  =   n –(-8)

17      6 –(-11)

 

-1 =   n + 8

 17    6 + 11

 

-1 =   n + 8          

 17      17

 

17(n+8) = -1 x 17

 

7n + 136 = -17

 

7n = -17 - 136

 

7n = -153

 

7n = -153

7         7

 

n = -9

 

 

TRY THIS……………………… 

 

 

Find t if a line which passes through (6, -2) and (-3,t) has a slope of  1/9

LOGARITHMS K12

 Evaluate Log60 – Log0.003 + Log500.

 

Solution

 

= Log60 – Log0.003 + Log500.

 

= Log(60 x 500)

              0.003

 

= Log(30000)

            0.003

 

= Log(30,000,000)

                 3

 

= Log 10,000,000

             

= Log1010,000,000

 

= Log10107

            

= 7Log1010

 

= 7 x 1

 

= 7

 

Log600 – Log0.003 + Log50 = 7

 

TRY THIS……………………….

 

Evaluate Log60,000 – Log4.8 + Log800,0000

QUADRATICS A1

 What must be added to x+ 14x to make the expression a perfect square?

 

Solution

 

a=1, b=14,c=?

 

b2 = 4ac

 

(14)2 = 4 x 1 x c

 

196 = 4c

 

196 = 4c      [dividing by 4 both sides]

4        4

 

49 = c

 

Hence number to be added is 49

 

TRY THIS……………………

 

What must be added to x+ 20x to make the expression a perfect square?

  

AREAS A1

 The areas of the two circles are in the ratio of 49:4 . Calculate the radius of the smaller circle when the radius of the larger circle is 40 cm. 

 

Solution

 

let R = radius of larger circle

let r = radius of smaller circle

R= 40cm, r = ? Ratio = 49:4.

 

 

For larger circle

A1 = R2 …………(i)

 

For smaller circle

A2 = r2 …………(ii)

 

A1 = R2

A2    r2

 

A1 = R2

A2     r2

 

 

A1 = (R/r)

A2

 

(A1/A2) =  (R/r)

 

(49/4) =  (63/r)

 

7 = 63                 We cross multiply

2     r

 

(2 x 63) = (7 x r)   after cross multiply

 

126 = 7r

 

126 = 7r

7       7

 

r = 18

 

radius of smaller circle is 18cm.

 

TRY THIS………..

 

NECTA 1997 QN 5(c)

The areas of two circles are in the ratio of 16:9 . Calculate the radius of the smaller circle when the radius of larger circle is 24 cm.