FUNCTIONS D1

Find the maximum value of the quadratic equation:3-6t-8t².

 

Solution

 

a=-8, b=-6, c=3

 

Maximum = 4ac-b²

                        4a

 

Maximum = (4 x -8 x 3) - (-6)²

                          4(-8)

 

Maximum = (-96)- 36

                         32

 

Maximum= -132                         since (-96)- 36=-132

                     32

 

Maximum = -66 =  -33 

                     16       8    

 

Hence maximum value is -33/8

 

TRY THIS………………………………..

 

NECTA  2003 QN. 10c

 

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

REGULAR POLYGONS D1

 

A regular polygon has 82 sides. Find the total degrees of that polygon.

 

Solution

 

n = 82

 

Total degrees = (n - 2)180⁰

 

                       = (82 – 2)180⁰

 

                       = 80 x 180⁰

 

                       = 14400⁰

 

Total degrees = 14400⁰

 

 

TRY THIS……………………….

 

A regular polygon has 57 sides. Find the total angles of that polygon.

 

LOGARITHMS D1

 

Simplify Log₂256 - Log₃729

 

Solution

 

= Log₂256 - Log₃729

 

= Log₂2⁸ - Log₃3⁶   [Since 256=2⁸ and 729=3⁶].

 

= 8Log₂2 - 6Log₃3    [since Log_aa = 1]

 

= (8 x 1) - (6 x 1)

 

= 8 - 6

 

= 2

 

Hence Log₂256 -Log₃729 = 2

 

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

 

Simplify Log₂2048 - Log₅625

 

VARIATIONS D1

 

x is inversely proportional to y. x=22 while y=5. Find y when x is 10.

 

Solution

 

x ⍺ k

      y

 

x = k

      y

 

22 = k

        5

 

k = 22 x 5

 

k = 110

 

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

 

k = 110, y= ?, x = 10.

 

x = k

      y

 

10  = 110

          y

 

y x 10 = 110  x  y   (multiply by y on both sides)

               y

 

 

10y = 110

10      10

 

Hence y = 11.

 

TRY THIS…………….

 

x is inversely proportional to y. x=80 while y=4. Find y when x is 8. 

SEQUENCES AND SERIES D1

 

The 1st term of an arithmetic progression is 33 and the common difference is 40. Find the nth term

 

solution

 

A1=33, d= 40, n=?

 

An =A1 + (n-1) d

 

An=33 + (n-1)40

 

An=33 + 40n -40

 

An=40n + 33-40

 

An=40n – 7   since  33-40= (-7)

 

Hence the nth term is An=40n - 7  

 

TRY THIS………………….. 

 

The 1st term of arithmetic progression is 140 and the common difference is 74. Find the nth term

DISTANCES 1

 

Change 760 nautical miles into kilometers.

 

Solution

 

1 nautical mile= 1.852 km

760 nautical mile= ?

 

 = 1.852 x 760

          1

 

= 1407.52

= 1407.52 to 2 d.p

Hence 760 nautical miles= 1407.52km.

 

TRY THIS…………….

 

Change 80 nautical miles into kilometers