PERIMETER 1

Area of a rectangle is 84 cm². Find its perimeter if its width is 7cm.

Solution

First we find length

A =  l  x w

84 =  l  x 7

84 = 7l

7       7

12 =  l

Now length is 12cm.

We can find perimeter since we have both length and width.     

Let l = length and w = width;

P = 2(l + w)

   = 2(12 + 7)

   = 2 x 19

   = 38

Hence perimeter is 38 cm. 

TRY THIS………………….. 

Area of a rectangle is 72 cm². Find its perimeter if its width is 4cm.

ALGEBRA 1

If │2x – 7 │= 17; Find  x

Solution

±(2x – 11 )= 17

2x -11= 17    OR   –(2x-11) = 17

2x – 11 = 17    OR   -2x+11=17

2x = 17 + 11    OR   -2x= 17-11

2x = 28     OR   -2x  =   6

2      2                -2        -2

x = 14  OR  x = -3

Hence x = 14 OR x = -3

TRY THIS………………………. 

If │2x – 7 │= 35; Find x

EXPAND 1

Expand -10(y – 5)

Solution

= -10(y – 5)

= (-10 x y) – (-10 x 5)

= 10y – ^-50 answer

= 10y + ⁺50

= 10y + 50 answer

TRY THIS………..

Expand ^-8(W– 9)

SETS 1

If n(A)= 90 , n(B)= 100 and n(AnB)=50, find n(AuB).

Solution

n(AuB) = n(A) + n(B) - n(AnB)

             = 90 + 100 – 50

             = 190– 50

             = 140

Hence n(AuB) = 140 answer

TRY THIS………….

If n(A)= 140 , n(B)= 150 and n(AnB)=100, find n(AuB).

SIMPLE INTEREST 1

Angloma deposited the amount of 110,000/= in a bank which gives an interest rate of 5% for 5 years. Find the simple interest she got?

Solution

I = ?,  P = 110,000/=, T = 5 years, R = 5%

I  = PRT

      100

I  = 110,000 x 5 x 5

            100

I  = 110000 x 5 x 5

            100

I  = 1100 x 5 x 5

          

I  = 275,000/=

Hence the simple interest was Tsh 275,000/=

TRY THIS………………..

  

Jelna deposited the amount of 18000/= in a bank which gives an interest rate of 3% for 5years. Find the simple interest she got?

LOGARITHMS 1

Simplify Log₂1024 - Log₃27

Solution

= Log₂1024 - Log₃27

= Log₂2¹⁰ - Log₃3³

= 10Log₂2 - 3Log₃3

= (10 x 1) - (3 x 1)

= 10 - 3

= 7

Hence Log₂1024 - Log₃27 = 7

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

Simplify Log₂256 – Log₅125

EXPONENTIALS 1

If 5^2w (40^w) = 0.000001 ; Find w.

Solution

5^2w (40^w) = 0.000001

(5²)^w (40^w) = 10^-6

(25)^w (40^w) = 10^-6

(25 x 40)^w = 10^-6

(1000)^w = 10^-6

(10³)^w = 10^-6

10^3w = 10^-6   (Bases are alike, so they cancel out)

3w = -6

3w = -6²

3       3

w = -2

TRY THIS…………………………   

If 4^2a (2^a) = 128 ; Find a.

FUNCTIONS 1

If f(x) = x⁴ + kx² + 6x + 7 has a remainder of 10 when divided by x+2; find k.

Solution

f(x) = x⁴ + kx² + 6x + 7

x + 2 = 0

x = -2

f(x) = (-2)⁴ + k(-2)² + 6(-2) + 7 = 10

16 + 4k + (-12) + 7 = 10

16 + 4k - 12 + 7 = 10

16 + 4k - 5 = 10

4k + 16 - 5 = 10

4k + 11= 10

4k = 10 - 11

4k = -1

4k = -1

4      4

k = ^-1/4

hence k= ^-1/4

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

  

If f(x) = x⁴ - kx² + 2x - 1 has a remainder of 18 when divided by x-3; find k.

VARIATION 1

x is directly proportional to y. x=32 while y=4. Find y when x is 184.

Solution

x ⍺ y

x = ky

32 = k x 4

32 = 4k    [dividing by 4 both sides]

4      4

k = 8

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

k = 8, y= ? x = 184.

x = ky

184 = 8 x y

184 = 8y

8        8

y = 23.

TRY THIS…………….

x is directly proportional to y. x=40 while y=4. Find y when x is 170.

SLOPE/GRADIENT 1

Find the slope of a line which passes through (-11, -8) and (6,-9)

Solution

x₁ = -11,  y₁ =-8,  x₂ = 6,  y₂ = -9

m = y2 –y1

       x2 – x1

m =   -9 –(-8)

          6 –(-11)

m =   -9 + 8

          6 + 11

m =    - 1

            17

Hence the slope is -1/17

TRY THIS……………………… 

Find the slope of a line which passes through (-11, -2) and (9,-14)