EXPONENTIALS 4

Simplify 11

              64^-2/3

Solution

=  11

  64^-2/3

=  11 x 1

          64^-2/3

=  11 x 64^2/3        [Since 1/a^-n = aⁿ]

=  11 x (64^1/3)²        [Since 64^1/3 = cube root of 64 = 4]

=  11 x (4)²        

=  11 x 16

= 176        

         

Hence   11        = 176

             64^-2/3

TRY THIS…………………………

simplify 7

             27^-2/3

EXPAND 1

Expand 8w(5w + 3 - w)

Solution

= 8w(5w + 3 - w)

= (8w x 5w) + (8w x 3) - (8w x w)

= 40w² + 24w - 8w²

= [40w² - 8w²] + 24w collecting like terms

= 32w² + 24w answer

TRY THIS………..

Expand 4a(7a+ 12 - a)

TRANSPOSITION 1

SIMPLIFY 2

Simplify: 2 + 6(6n ÷ ⁿ/2) - 30

Solution

=2 + 6(6n ÷ ⁿ/2) - 30

=2 + 6(6n x ²/n) – 30

=2 + 6(6n¹ x ²/n₁) – 30  cancelling n

=2 + 6(6 x  2) – 30  

=2 + 6(12) – 30  

=2 + 72 – 30  

=74 – 30  

=44  

=44 answer

TRY THIS……..

Simplify 20 + 4(10n ÷ ⁿ/2) - 70

LOGARITHMS 4

Evaluate Log₂(2048 x 16).

Solution

= Log₂(2048 x 16)

= Log₂2048 +  Log₂16          (applying the product rule)

= Log₂2¹¹ +  Log₂2⁴             ( 2048= 2¹¹ and 16=2⁴ )

= 11Log₂2 +  4Log₂2       ( remember  Log_aa^c = cLog_aa )

= (11 x 1) +  (4 x 1)          ( remember  Log_aa = 1 )

= 11 + 4

= 15

hence Log₂(2048 x 16) = 15

TRY THIS…………………

Evaluate Log₂(8 x 512)

SIMPLIFY 1

Simplify 11x-3(x-y)+5

Solution

=11x-3(x-y)+5

=11x-3x+3y+5

=8x+3y+5 answer

TRY THIS……..

Simplify 14x-9(x-y)+12

POLYGONS 3

An interior angle of a regular polygon is 78⁰ greater than an exterior angle. Find the interior angle.

Solution

Let i = interior angle, e = exterior angle.

Now i  + e=180⁰…………………(1)

But i = e+78⁰ …………………(2)

Substitute (2) in (1) above.

e+78⁰   + e=180⁰

e+ e+78⁰   =180⁰

2e+ 78⁰   =180⁰

2e=180⁰ - 78⁰   

2e=102⁰

2e=102⁰          dividing by 2 both sides.

2      2

e = 51⁰

But i  + e=180⁰…………………(1)

i  + 51⁰=180⁰.

i  =180⁰ - 51⁰

i = 129⁰

Hence i = 129⁰ 

TRY THIS………………………   

An interior angle of a regular polygon is 82⁰ greater than an exterior angle. Find the interior angle.

ALGEBRA 5

If a² – 20 = 61; find a.

SOLUTION

a² – 20 = 61

a² = 61+ 20

a² = 81

√a² = √81    keep root sign on both sides

a = √81   

 a = 9     since the square root of 81 is 9.

Hence a = 9

TRY THIS………..

If m² – 23 = 98; find m.

INTERCEPT 1

If 2x + 5y -11 = 0; find x-intercept.

Solution

x-intercept is when y=0.

2x + 5y -11 = 0

2x + 5(0) - 11 = 0

2x - 11 = 0

2x = 0+ 11

2x = 11

2      2

x= ¹¹/2

Hence x= ¹¹/2

TRY THIS………..

If 8x - 3y - 17 = 0; find x-intercept.

MIDPOINT 1

Find a if the midpoint of a line from (a, 6) to (8, 10) is (10, 7)

Solution

x1=a, x2=8, y1=6, y2=10.

(10, 7)= (x1 + x2, y1 + y2)

                2             2

(10, 7)= (a + 8,  6 + 10)

                2          2

(10, 7)= (a + 8, 16)

                 2      2

Equating values of x;

10= a + 8

         2      

2 x 10= (a + 8)  x 2 ¹

               2 ₁     

20 = a + 8

20-8 = a

a = 12.

Hence a=12

TRY THIS……………………..

Find m if the midpoint of a line from (m, 19) to (13, 10) is (9, 11)