POLYGONS H1

 

A regular polygon has 42 sides. Find the total degrees of that polygon.

 

Solution

 

n = 42

 

Total degrees = (n - 2)180⁰

 

                       = (42 – 2)180⁰

 

                       = 40 x 180⁰

 

                       = 7200⁰

 

Total degrees = 7200⁰

 

 

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A regular polygon has 33 sides. Find the total angles of that polygon.

 

MIDPOINT G1

 

Find the midpoint of a line from (33, 12) to (5, 20)

 

Solution

 

x1=33, x2=5, y1=12,y2=20.

 

Mid point = (x1 + x2, y1 + y2)

                          2            2

 

Mid point = (33 + 5,  12 + 20)

                         2          2

 

Mid point = (38, 32)

                     2     2

 

Hence midpoint = (19, 16)

 

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Find the midpoint of a line from (-9, 24) to (9, -4)

FUNCTIONS G2

 

SEQUENCE & SERIES G1

 

The 1st term of an arithmetic progression is 60 and the common difference is 40. Find the nth term

 

solution

 

A1=60, d= 40, n=?

 

An =A1 + (n-1) d

 

An=60 + (n-1)40

 

An=60 + 40n -40

 

An=40n + 60-40

 

An=40n + 20

 

Hence the nth term is An=40n + 20  

 

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The 1st term of arithmetic progression is 148 and the common difference is 170. Find the nth term

FUNCTIONS G1

 

Find the maximum value of the quadratic equation:7-6t-8t².

 

Solution

 

a=-8, b=-6, c=7

 

Maximum = 4ac-b²

                        4a

 

Maximum = (4 x -8 x 7) - (-6)²

                          4(-8)

 

Maximum = (-224)- 36

                         32

 

Maximum= -260                         since (-224)- 36= -260

                       32

 

Maximum = -130 =   -65

                       16          8

 

Hence maximum value is -65/8

 

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NECTA  2003 QN. 10c

 

Find the maximum value of the quadratic equation:3+30t-5t².

 

SIMPLIFY G1

 Simplify (6a)² - 30a². 

 

Solution

 

= (6a)² - 30a²    

 

= 6².a² - 30a²               Since (mn)² =m² . n²

 

= 36a² - 30a²   {since the square number of 6 is 36}

 

= 6a²

 

TRY THIS………………

 

Simplify (8m)² – 80m².

PROBABILITY F1

 

A bag contains 4 red balls and 8 blue balls. Two balls are taken from the bag. What is the probability that they are both red?

 

Solution

 

(This is a problem with replacement)

 

n(R) = 4, n(B) = 8, n(S) = 12

 

P(R) = n(R)

            n(S)

 

P(R) = 4

          12

 

1st pick = ⁴/12

2nd pick = ⁴/12 as well.

 

 

P(RR) =  4      x    4

             12            12

 

P(RR) =   ¹⁶ /144 = ¹/9       

 

Therefore Probability of drawing a red ball is 1/9     

 

 

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A bag contains 7 purple stones and 11 yellow stones. Two stones are taken from the bag. What is the probability that they are both purple?

ALGEBRA 3F

 The sum of four consecutive even numbers is 316. Find the 3rd number.

 

Solution

 

Let the numbers be as shown in the table below

 

1st number	2nd number	3rd number	4th number	TOTAL
n	n+2	n+4	n+6	316

 

Then, n + (n+2) + (n+4) + (n+6) = 316

 

4n + 2+4+6= 316

 

4n + 12 = 316

 

4n = 316 – 12

 

4n = 304 

 

4n = 304

 4        4

 

n = 76

 

3rd number = n +4

 

                   = 76 + 4

 

                   = 80

 

Hence the 3rd number is 80

 

TRY THIS………………….. 

 

The sum of four consecutive even numbers is 372. Find the largest number.

ALGEBRA F3

 The sum of four consecutive even numbers is 316. Find the 3rd number.

 

Solution

 

Let the numbers be as shown in the table below

 

1st number	2nd number	3rd number	4th number	TOTAL
n	n+2	n+4	n+6	316

 

Then, n + (n+2) + (n+4) + (n+6) = 316

 

4n + 2+4+6= 316

 

4n + 12 = 316

 

4n = 316 – 12

 

4n = 304 

 

4n = 304

 4        4

 

n = 76

 

3rd number = n +4

 

                   = 76 + 4

 

                   = 80

 

Hence the 3rd number is 80

 

TRY THIS………………….. 

 

The sum of four consecutive even numbers is 372. Find the largest number.

LOGARITHMS F9

 Evaluate Log1,000,000,000 -  log 0.01 + log₃243

 

Solution

 

= Log1,000,000,000 -  log 0.001 + log₃243

 

= Log10⁹ -  log 10^-3 + log₃3^-5

 

= 9Log10 -  (-3log 10) + (-5log₃3)

 

= (9x1) - (-3x1) + (-5x1)

 

= 9 - (-3) + (-5)

 

= 7

 

Hence Log1,000,000,000 +  log 0.001 + log₃243 = 7

 

TRY THIS……………..

 

 

Evaluate Log1,000,000,000  -   log 0.0001 + log₃81