SLOPE OR GRADIENT 1E

 

Find the slope of a line which passes through (-15, -2) and (6,-9)

 

Solution

 

x₁ = -15,  y₁ =-2,  x₂ = 6,  y₂ = -9

 

m = y2 –y1

       x2 – x1

 

m =   -9 –(-2)

           6 –(-15)

 

m =   -9 + 2

           6 + 15

 

m =    - 7

           21

 

 

Hence the slope is -7/21

 

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 Find the slope of a line which passes through (-15, -6) and (1,-9)

RADICALS 1E

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INEQUALITIES 1E

 

Solve for x if 2x – 1 ≤ x + 50 ≤ 6x.

 

solution

 

2x – 1 ≤ x + 50 and  x + 50 ≤ 6x

 

2x – x ≤ 1+ 50 and  50 ≤ 6x - x

 

x ≤ 51 and  50 ≤ 5x (having divided by 5 both sides)

 

x ≤ 6 and  10 ≤ x

 

 

x ≤ 6 and  x ≥ 10 

 

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Solve for x if 2x – 8 ≤ x + 40 ≤ 11x

ARITHMETIC PROGRESSION 1E

 

The first term of an AP is 5 and the last term is 67.If the arithmetic progression consists of 20 terms, calculate the sum of all the terms. 

 

Solution

 

A₁ = 5, n=20, A_n = 67

 

S_n = n(A₁ + A_n)

       2

 

S₂₀ = 20(5 + 67)

         2

 

S₂₀ = 10 x 72

 

 

S₂₀ = 720

 

 

 

Hence the sum of all 20 terms is 720.

 

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The first term of an AP is 7 and the last term is 75. If the arithmetic progression consists of 24 terms, calculate the sum of all the terms

SIMPLE INTEREST 1F

 

Dikshi deposited the amount of 90,000/= in a bank which gives an interest rate of 3% for 2 years. Find the simple interest she got.

 

Solution

 

I = ?,  P = 90,000/=, T = 2 years, R = 3%

 

I  = PRT

      100

 

I  = 90000 x 3 x 2

            100

 

I  = 90000 x 3 x 2

            100

 

I  = 900 x 3 x 2

          

I  = 5400/=

 

Hence the simple interest was Tsh 5400/=

 

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Edmund deposited the amount of 40,000/= in a bank which gives an interest rate of 6% for 5 years. What was her simple interest?

FORM ONE MATHS

 

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SETS H20

 

 If n(A)= 85 , n(B)= 96 and n(AuB)= 119, find n(AnB).

 

Solution

 

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

 

119 = 85 + 96 - n(AnB)

 

119 = 181 - n(AnB)

 

119 - 181 = - n(AnB)

 

-62 = -n(AnB)

 

n(AnB) = 62 [after dividing by -1 both sides]

 

Hence n(AnB) = 62 answer

 

 

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If n(A)= 91 , n(B)= 95 and n(AuB)= 127, find n(AnB).

SIMPLIFY D2A

 

Simplify the expression c² - t²/ (c + t)

 

Solution

 

from difference of two squares p² - q² = (p - q)(p + q)

 

= c² - t²/ (c + t)

 

= (c + t)(c - t)

      c + t

 

= (c + t)(c - t)

      c + t

 

=  c - t    answer

      

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Simplify the expression 

 

u² - y²/ (u + y)

SIMPLE INTEREST 1E

 

Rayan deposited the amount of 8,000/= in a bank for 5 years and got a profit of 2800/=. Find the interest rate?

 

Solution

 

I = 2800/=, P = 8,000/=, T = 5 years, R = ?

 

I  = PRT

      100

 

Where P=Principal amount

            I = simple Interest

           T= Time

           R=Rate

 

2800  = 8,000 x R x 5

                      100

 

 

2800  = 8,000 x R x 5

                      100

 

2800  = 80 x R x 5

                      

2800  = 400R

          

⁷2800  = 400R

  400       400

 

Hence the interest rate was Tsh 7%

 

 

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Kibonde deposited the amount of 15,000/= in a bank for 4 years and got a profit of 3000/=. Find the interest rate?

 

EXPAND 3C

Expand 8w(5w + 7 – w²)

 

Solution

 

= 8w(5w + 7 – w²)

 

= (8w x 5w) + (8w x 7) - (8w x w²)

 

= 40w² + 56w - 8w³ answer